Music Theory ~ Review Video (AP and Undergraduate)

hey everyone i decided to put together this comprehensive music theory review video that covers a very wide range of topics this can be a very useful resource for those of you who are taking ap music theory undergraduate music theory courses and for those of you who simply want to learn some new things about music theory because this is a review video i'm going to be going fairly quickly through all the different topics this video isn't really designed to teach you these things for the first time but rather to help you review the most important things you should have taken away from every topic i'd appreciate it if you share this video with anyone who might find it beneficial and useful that being said let's get started first things first is a general introduction to harmony so harmony is the aspect of western art music that really distinguishes it from other types of music around the world harmony is the vertical aspect to music it's the result of hearing two or more different pitches at the same time now the music that we talk about uses tonal harmony so tonal harmony is music that has a tonal center and this was really the harmonic focus of composers from the common practice period otherwise thought of as the year 1650 to about 1900. once the 20th century arrived composers began to focus more on post-tonal music and methods now some characteristics of total harmony include the use of a tonal center major and minor scales chords more specifically tertian chords which means built of thirds take this example we have a c major chord c to e is a third e to g is the third so this whole chord is built of thirds and the chords that we use in tonal harmony are mostly tertian finally we have functional harmony which is the idea that chords tend to have functions in standard roles within a key and if you're watching this video as a review you should already be familiar with this example the five chord has dominant function and the five chord wants more than anything to go to the one chord which is the tonic so that's related to the idea of functional harmony now we are going to start talking about the fundamentals of music the students who tend to struggle in mostly music theory are the ones who don't have a solid understanding of the fundamentals so you're going to want to make sure you're familiar with these things before moving on pitch and music that refers to the highness or lowness of a sound and we name pitches using the first seven letters of the alphabet a through g if you're studying music theory you're going to want to be familiar with the piano keyboard and how it's outlined this will help you to count half steps whole steps and solve just about any music theory problem that you come across so the piano has the white keys which use the letters of our alphabet and then it has black keys that come in groups of two and three now the c in the middle of a full 88 key piano is known as middle c also known as c4 because it's the fourth c on the piano that's going to be an important note as we talk about shortly now what is an octave an octave is the distance from one note to the next highest or lowest note of the same letter in accidental for example this c and that c are an octave apart same note just apart by an octave an octave register is a collection of pitches from one c up to but not including the next c so from this c every single note through this note b here they're all part of the same octave register and we number the notes of an octave register using regular numbers so if this is c4 that would be d4 e4 f4 g4 a4 b4 and then the number changes so then it would be c5 now when we notate music for others to read we do this on a staff the staff is the five lines and four spaces where we notice music now you can use ledger lines to extend a staff indefinitely for example you see this note right here that's a c you have a ledger line it's basically just another staff line that allows you to extend the staff below or above now to indicate very specific pitches we have to use a clef such as these four that you see here the clef indicates very specific notes that you want to hear this one right here that's known as the treble clef also known as a g clef why well it kind of looks like the letter g in a way and also you see how this loop here around this second line that note is a g specifically g4 which is the g above middle c this clef that's your bass clef used for the lower pitches it's also known as f clef these two dots around this line that note is an f it's the f below middle c so it would be f three so this note right in the middle of the treble and bass clef that is c4 or middle c so basically the bass clef flows directly into the treble clef and all the notes are connected together and you could join the treble clef and the bass clef together with a brace and that forms what we know as a grand staff grand staff is when you connect two clutch together through the use of a brace if you're reading piano music you're going to see that a lot and if you're studying music theory that's also something you're going to see frequently finally is the idea of our c-clefs why they called c-clefs we're going to talk about that in a second first one is our alto clef so how do we read this you see how there's the two curves that come together at this line that note is middle c or c4 this clef you see how it's the same clef but shifted up c clefts are movable you can move them up or down and the thing is that whenever you have these two curves that come together whatever that line is where they come together that note is always c4 or middle c this clef is your tenor clef so these clefs are used to indicate where middle c is specifically the treble clef middle c is just below the staff and in the bass clef middle c is just above the staff and we use these clefts the majority of the time to indicate the notes that we desire the major scale is an essential part of music theory and tonal harmony now the major scale is simply a specific pattern of half steps and whole steps that encompass one octave so what are whole steps and half steps well a half step is when you go from one note to the very next note above or below that note on a keyboard while a whole step is when you go up two half steps or you could just think of it as skipping a key and going to the next one now the major scales formula is this we do a whole step whole step then a half step then a whole step whole step whole step and finally a half step so c major scale that's everyone's favorite because it's the easiest one it's using only the white keys on a keyboard so here we go so we start with c go up a whole step that's d whole step e half step f whole step g whole step a whole step b half step c so that is your c major scale and the important thing about a scale is you always need one of every single note letter you can't leave anyone out now scale degrees are represented using numbers and carrots above the number those represent where you are on the scale so if you have a c major scale the note c is scale degree one while the note g would be scale degree five and so on the c major scale or any scale could also be thought of as being broken up into two tetrachords which are simply groups of four note patterns that are similar for example this tetrachord c d e f that's a whole step whole step half step this tetrachord that's a whole step whole step half step so they're both similar patterns but they're just separated by a whole step here in the middle so that's what the idea of the basic scale is for a major scale now for other scales we're going to wind up using accidentals those are going to help us to spell our scales so it's important to be familiar with these so a double sharp raises note a whole step a sharp raises note a half step a natural cancels any previously seen accidentals it also represents the unaltered version of a note a flat lowers a note by a half step and then a double flat lowers the note by a whole step so now let's practice it with these two scales so i want to do a g major scale and an f major scale so the first thing is to make sure you give yourself one of every single note letter g a b c d e f g we need one of every letter and now use your formula what's a whole step above g a whole step above a b half step above b c now we need a whole step above c which is d whole step above d which is e now we need a whole step above e what's a whole step above e we land on this note that would be an f sharp so when you write an accidental next to a letter it goes after the letter like this when you write it next to a note it goes before the note finally after f sharp we need a half step f sharp to g that is a half step so this is our g major scale now let's do our f major scale so again first thing you want to make sure you give yourself one of every single letter that's always the first thing you need to do and now apply your formula whole set that works whole step this works we need a half step above a a half step above a lands you on b flat so we need a b flat here now a whole step above b flat is c whole step d whole step e finally a half step f so that's your f major scale if you know how to apply this formula you are able to spell any major scale that you want to if you are a serious musician it's a good idea to know all of your major key signatures by heart so the term key is used in music to identify the first degree of a scale for example the key of c major the first scale degree is the note c now a key signature is a pattern of sharps or flats that appears at the beginning of a staff and it indicates that certain notes are to be consistently raised or lower these are your major key signatures that have sharps and these are your major key signatures that have flats and it's a good idea to memorize these it's a lot easier to memorize them than to always count the whole step whole step half step formula for every single key now in music we have something known as enharmonic equivalence this refers to notes that have the exact same pitch but they're spelt differently for example the note b and the note c flat they sound the exact same they're at the same spot on the keyboard but they're spelled two different ways you can have n harmonic keys too for example the key of b major and the key of c flat major will have the same notes but they're just spelled two different ways those are known as enharmonic equivalents this also applies to f-sharp and g-flat as well as c-sharp and d-flat if you have two major keys that are not inharmonic they're considered transpositions of each other to transpose means to write or play music in some other key other than the original for example the key of d major has the same pattern of whole steps and half steps as c major g major f major or any other major scale they're all transpositions of each other now if you want to memorize your key signatures it's a good idea to memorize the circle of fifths the circle of fifths is used for a lot of things in music it helps you to memorize your key signatures and to know the order of sharps and flats so if you look at the top the key with zero sharps and zero flats is c major the key with one sharp that's g major as you see here the key with one flat is f major as you see here and the distance from one key to the next on the circle of fifths is the distance of a fifth for example if i start with c major we always count the starting key as one so c is one d is two e is three f is four g is five so from c to g is a fifth if i went the other way c b a g f c to f that's also a fifth so that's why it's known as your circle of fifths and you can use this to memorize all of your different key signatures these are your key signatures for major keys that involve sharps and these are your key signatures that involve flats at the bottom of the circle of fifths you'll notice that some of the keys are in harmonic for example b major has five sharps it also lands at the spot for seven flats which is c flat major six flats is g flat and six sharps is f sharp and harmonic keys sound the same spelled differently d flat major has five flats it lands at the same spot as c sharp major which has seven sharps now last thing to talk about here is the order of sharps and flats so if you look at the sharps they keep adding on to each other for example we start with f sharp the next one is f sharp c sharp the next one is f sharp c sharp g sharp so every key keeps taking the accidentals that you see in the previous key so the order that sharps appear is f c g d a e b and the order that the flats appear is just the reverse b e a d g c f if you have trouble remembering that you could also refer to your circle of fifths for that look for all of your keys that don't have any accidentals so the first one here is f if you go in the direction of sharps that's your order of sharps f c g d a e b and go the reverse way or in the direction of flats if you want to get the order of flats b e a d g c f so if i said what does the key of b flat major have you would say okay b flat major that has two flats what are the flats it's going to be b flat and d flat if i said the key e major you'd say okay e major has four sharps the sharps are f sharp c sharp g sharp d sharp so the circle of fifths is a really useful resource in music theory to help you get more accurate results and to solve some other problems similar to major scales minor scales are commonly used by songwriters and composers of tonal music there are three types of minor skills you want to be familiar with the natural minor scale harmonic minor scale and melodic minor scale to form a natural minor scale you're going to take a regular major scale and you're going to lower scale degrees 3 6 and 7. so let's say we wanted to form a c natural minor scale start with your c major scale and then take scale degrees 3 6 and 7 and lower them by a half step that gives you the natural minor scale the harmonic minor scale is the same exact thing only difference is scale degree 7 is going to be raised so instead of b flat we're going to have a b natural and this is the most commonly used of the minor scales because b natural is a leading tone to c it's a half step away from your tonic c is the most important note you could say in the key of c minor b natural is a half step below it has such a strong gravitational pull to get to that note c in the natural minor scale b flat is a whole step away from c it's not as powerful so the harmonic minor scale is the most commonly used of the minor scales because of this leading tone the melodic minor scale is a little bit trickier because it's different on the way up and down on the way up you're going to have a natural minor scale but you're going to have a raised leading tone and a raised six scale degree so it would be c d e flat f g a natural b natural and c the reason for the scale a flat to b natural is an awkward interval to sing for some a to b is a whole step that's easier to sing and to look at so it makes singing a melody line going upwards a lot easier to sing on the way down it's a regular natural minor scale so we have lowered scale degree 7 6 and 3. so on the way down it would be the same as a natural minor scale now if you wrote a key signature for a minor scale you're going to always do it based on the natural minor scale so if i wanted to write any key of c minor i would use the key signature for c natural minor which is 3 flats now relative keys are keys that share the same key signature so c minor three flats that's the same key signature as e flat major so those are relative keys c major and a minor those are other relative keys they both have no sharps and no flats parallel keys are keys that share the same starting note like c major and c minor now you could use your circle of fifths to help you figure out all of your natural minor scales and notice how at the bottom of the circle of fifths you have n harmonic keys again similar to with the major keys now sometimes you might have to try to identify what key you're in and you might be wondering how do i distinguish if i'm in major or minor if the key signature is the same here's an easy way to tell the difference let's say this was your key signature your possibilities would be e flat major or c minor right because those are the keys that have three flats now in a major key you're not going to have any accidentals generally but remember what i said about minor scales we tend to use the harmonic minor scale the most if we use scale degree 7 we need to have a b natural because the key signature has a b flat if we want to raise it we have to put a natural sign so if you're in a minor key you're going to be seeing a lot of accidentals because those are going to be your raised leading tones they're going to be taking you back to scale degree 1. if you're an e flat major you're not going to be seeing b naturals but if you're in c minor you're going to be seeing b naturals because that's the leading tone another example let's say you're an a minor you would have the leading tone of g sharp because g sharp is a half step below a so if you saw a piece that had no sharps or flats you would say okay it's either c major or a minor if you see g sharps in the music that's the leading tone to a that tells you that you're in a minor key so use that to help you distinguish between major keys and minor keys when you're trying to figure out what key a piece is in so let's say you're given a piece of music and you're asked to figure out what key it's in the major keys are easy to determine from the key signature as long as you know your major key signature is based on the circle of fifths the minor keys might be harder to remember but you can use relative keys to help you figure this out let's see how to do this if you want to go from a major key to the relative minor key you're going to go down three half steps if you want to go from a minor key to a relative major key go up three half steps so let's take this example let's say we have a piece of music with no sharps and no flats you should automatically know that one possibility is c major so c major is the possible major scale what about the minor scale let's figure out the relative of c major to go from a major to a relative minor you go down three half steps so if you go three half steps below c you get a so the relative minor of c major is a minor both keys have the same exact key signature let's take this one let's say we're in b flat minor and we want to figure out the relative major you're going to go up three half steps now if you're using your piano as a visual aid start with b flat and go up three half steps if you do this you're going to land on a black key and you might say okay it's c sharp but that's not true because the distance of b to c of any kind is a second b c and relative keys need to be a third apart to have the same key signature so instead of c sharp it would be d flat d flat major has five flats b flat minor has five flats if you thought of it as c sharp major c sharp major has seven sharps b flat minor has five flats those aren't the same key signature so the letters of relative keys are always going to be a third apart c b a b c d so make sure it's always a third apart but three half steps gets you to the note you need at least so let's say you're given this key signature right here we see two flats so you know that your possibility is b flat major and then you have to figure out your relative minor go down three half steps from b flat and you land on the note g so it would be g minor and is that a third apart b a g yes it is what about this one you see three sharps three sharps you should know is a major what's the relative of a major go three half steps down you land on f sharp is this a third a g f yes it is and again how would you know which one you're in if you're in g minor remember you're going to use raised leading tones the leading tone to g is a half step below g which is f sharp so if you see f sharps you're going to be in g minor if you see f naturals you're most likely going to be in b flat major what about this one a major you're going to see no sharps no flats in the middle of the music if you're an f sharp minor what's the leading tone to f sharp well what's a half step below f sharp on your keyboard you might say f but we can't have f natural and f sharp it has to be a different spell it needs to be an e of some kind because e is the seventh scale degree in any f key so we would call this an e sharp e sharp is the same thing as an f natural they sound the exact same but they're spelt differently e sharp is the leading tone to f sharp they're a half step away so if you see this key signature and in the middle of the music you see a ton of e sharps you're probably an f sharp minor if you don't see e sharps you're probably in a major so that's how you go about figuring out your relative keys and this is a really important skill you need to have when you try to figure out what key a piece of music is in in music theory we have various names for the different scale degrees it makes it easier to have conversations about them and to refer to them so here's how they're named scale degree 1 is your tonic it's your home base if i'm in the key of c major the first note is going to be c that's my tonic scale degree 2 is the super tonic super means above so scale degree 2 is above your tonic super tonic scale degree 3 is your median scale degree 4 is a subdominant i'll come back to this one in a second scale degree 5 an important one this is your dominant now dominant means 5 sub means below so what's a 5th below scale degree 1 well we always count that as our first number so c b a g f f is scale degree four so if you go five below your tonic you get your subdominant note that's why it's called subdominant scale degree six that's your sub median median means three sub means below so what's a third below c c b a that gets you scale degree six sub median if you're in the natural minor key you're going to wind up having a lowered seventh scale degree like b flat that's your sub tonic sub means below and remember tonic is one so what's below your tonic scale degree seven now if you have a regular seventh scale degree that's a half step from your tonic note that's your leading tone that's found in your major scales and in your harmonic minor scale and the melodic minor scale on the way up if you have a seventh scale degree that's a half step from scale degree one that's a leading tone so subtonic is a whole step from your tonic leading tone is a half step from the tonic another important fundamental in music theory is the concept of intervals an interval is the measurement of the distance and pitch between two notes and there are two types harmonic intervals result when you hear two notes performed simultaneously while melodic intervals are when you hear two notes played successively we also have what are known as simple intervals and compound intervals if you have an interval that is less than an octave that's a simple interval if you have an interval greater than an octave or including the octave that's a compound interval over here we have the various intervals you need to become familiar with so the first important thing to know is that with an interval the number part of the interval is always based on the distance in letters between two notes so from c to c that's just one c to d c d that's two c to e c d e that's a third so the number part is always based on the letter distance of the notes the modifier such as the letters p lowercase m uppercase m those are all based on the actual distance of the notes and half steps so let's look at these if you have a note and the exact same note heard at the same time that is known as a unison because it's the exact same note there's no difference zero half steps the other way to abbreviate it is perfect unison or p1 now c to d flat well c to d of any kind is a second if you have one half step that's a minor second c to d natural again c to d is a second a whole step or two half steps that is a major second now c to e no matter what type it is that's a third c d e three half steps minor third four half steps major third now c to f of any kind is a fourth c to f natural is five half steps that's a perfect fourth now we have this one which is six half steps and there's another one here that's six half steps so let's say we have c to f sharp well c to any type of f is a fourth if you have an interval greater than a perfect interval it becomes an augmented interval so this is an augmented fourth and a symbol for augmented is a little plus symbol what about this one c to g flat well c d e f g is a fifth c to g flat is six half steps that's known as a diminished fifth and a symbol for diminished is the little degree symbol here c to f sharp and c to g flat are n harmonic they both sound the same they're both six half steps this interval the augmented fourth and the diminished fifth is known as the tritone you're going to want to become familiar with that name it's a harsh sounding interval that really wants to resolve now here c to g is a fifth and if you have seven half steps that's a perfect fifth c to a of any kind c d e f g a it's a sixth eight half steps is a minor sixth nine half steps major six c to b so c d e f g a b is a seventh and then ten half steps is a minor seventh eleven half steps is a major seventh finally c to c well c d e f g a b c that's an eight or an octave and it's considered a perfect octave remember what an octave is it's an interval when you go from one note to the same note letter above or below so c to c is an octave or 12 half steps you're going to want to remember these intervals because they're going to help you when stacking chords or solving basically any type of music theory problem you come across you at least want to memorize these at least up to the perfect fifth come up with some way to help yourself remember the number of half steps you should know your thirds especially because those are going to help you with your chords you should be familiar with your perfect fifth and perfect fourth those are going to come up a lot seconds are important the unison is important and also the tritone is important it's going to come up in different times such as when we learn seventh chords now one last idea with intervals is the idea of consonant intervals and dissonant intervals constant intervals are considered pleasing to hear and these consist of thirds six the perfect fifth and perfect octave dissonant intervals are harsher to hear this includes seconds sevenths augmented intervals diminished intervals and the perfect fourth when it involves the bass and in music our goal is basically to resolve dissonances to consonances it creates a pleasing effect it creates forward motion and music some momentum we want to have distances that resolve to constances that gives the music interest some motion and it keeps the listener engaged so those are the basics that you need to know with intervals the final thing to talk about on the subject of intervals is inverting intervals an interval inversion is when you take an integral and flip it the other way around so take this example d to a the inversion of this interval would be a to d to invert something in music basically just means to rearrange it in some other way this could be extremely useful when you're trying to figure out a larger interval take this one for example we have c to b so that's a harder one in counting half steps it's going to take you a long time and you might not be as accurate if you're not careful you can use an interval inversion to help you out so if we invert c to b it becomes b to c b to c is a second b c b to c on the keyboard is a half step away you should know a half step is a minor second so how do we use this to figure out this interval here's how it works you're going to take the number 9 you're going to subtract your inverted interval number from 9 and that gives us 7. is c to be a 7th yes it is what about the modifier here's what you do major flips to minor and vice versa perfect stays perfect augmented flips to diminished and vice versa so we have a minor interval that flips to a major interval so minor second is the same as a major seventh when you invert it let's do some other quick practice ones so we have a major second nine minus two is seven major flips to minor we have an augmented fourth nine minus four is five augmented flips to diminished a perfect fifth nine minus five is four and perfect stays perfect so these become easier once you understand the concept let's say we have this example we have the note g and we wanna figure out a minor sixth above g well what is a sixth above g first of all g a b c d e so it's going to be some type of an e but let's say you're not sure which one it is here's what you're gonna do invert the interval so it's going to be e g minor 6 what does that become 9 minus 6 is 3 minor flips to major so the note g has to stay the same because we can't change this note so what is a major third a major third is four half steps go four half steps below g what note do you get you get an e flat so a minor sixth above g would be an e flat finally let's take this example let's say you have a major sixth below this note so we're in bass clef we have an f sharp and we want to go a major six below intervals we usually like to count upwards that's easier so here's what we're going to do we're going to invert this interval major sixth becomes minor third right so we have f sharp a third above f sharp is an a of some kind a minor third is three half steps go three half steps above f sharp what do you get you get a natural so the final step to do is to bring this a down the octave by transposing it and now we have a major sixth below f sharp major six below f sharp is the same thing as a minor third above f chart we're just taking the interval and inverting it so interval inversions can help you to solve larger interval problems and also to make sure you get accurate answers when you're trying to figure out what interval you're dealing with and that's it on the concept of intervals the next fundamental that we are going to talk about is rhythm rhythm is a general term that's used to refer to the time aspect of music these are the various durational symbols you're going to want to be familiar with the main ones include the brev or double whole whole half quarter eighth and sixteenth and this continues we have thirty seconds sixty-fourths and so on you're also going to want to know how the note durations and the restorations are determined for example a whole note is equal to two half notes a half note is equal to two quarter notes and so on the same thing applies to the rests if you have any durations that are other than the ones in this table that needs to be indicated through the use of ties dots or other musical symbols so the dot a dot following a symbol always adds to the duration one half the value of the note rest or dot that precedes it for example if we have a dotted quarter note that's going to be equal to a quarter note plus half the quarter note which is an eighth note the beat is the basic pulse of a musical passage and the rate at which beats occur is called your tempo now beats tend to be grouped into patterns that are consistent throughout a passage the pattern of beats is called your meter and groups of beats are called measures a measure can also be thought of as one unit of meter that consists of a certain amount of accented and unaccented beats the end of a measure is always indicated by a vertical line that goes to the staff and this is known as your bar line and an important thing to note is that bar lines cancel any accidentals that appeared in the measure in music we use the words duple triple and quadruple to refer to the number of beats in a measure for instance a two beat measure is duple meter a three beat measure is triple meter and a four beat measure is quadruple meter meters often have a pattern of stresses which are known as metric accents for instance duple meter is strong followed by weak triple meter is strong followed by weak weak quadruple meter is strong weak less strong weak those are the types of metric accidents that you're going to find in these meters hypermeter refers to a regular grouping of measures and it's analogous to meter for instance if you have a song that's in triple meter and it might have measures that form groups of four this creates a quadruple hypermeter another important thing to know is that beats can be divided this is known as divisions of the b when you listen to a musical passage you're going to often hear the durations that are shorter than the actual beat itself when a beat divides into two equal parts that's a simple beat and when the beat divides into three equal parts that's a compound beat now let's turn our attention to time signatures a time signature is a symbol that tells the performer how many beats will occur in each measure what note value will represent the beat and whether the beat is simple or compound let's look into this simple time signatures they're going to have the number 2 3 or 4 as the top number the top number will indicate the number of beats per measure and the bottom number will indicate the beat note value let's look at some examples 2 2 that's also known as cut time or all abrev there are two beats per measure that's based on the top number the beat note is a half note we found that out because of the bottom number two represents half note and the division of the beat simple time signature is divided into two divisions so a half note divides into two coordinates four four that's also known as common time beats per measure it'll be four because of the top number beat note it's the quarter note we have four on the bottom four represents quarter the division of the beat a quarter note divides into two eighth notes finally three eight there'll be three beats per measure the beat note is the eighth note and the division of the beat an eighth note divides into two sixteenth notes compound time signatures they'll have the number six nine or twelve as the top number if a beat divides into three equal parts such as in a compound beat the note value representing the beat will have to be a dotted value so in a compound time signature the top number will indicate the number of beats in the measure just like simple but the bottom number is going to indicate the beat division value so let's look at some examples of this so let's say we have 6 4 there's gonna be two beats per measure six will always have two beats for measure you're going to take the top number and divide it by three to get the number of beats per measure now the beat note we're going to figure that out based on the division so again 6 4 the bottom number is going to tell you the division of the b so we see 4 which is quarter so we're going to have three quarter notes and three quarter notes form the beat which is a dotted half note nine eight nine divided by three is three so there's three beats per measure eight is our division value so we're going to have three eighth notes and three eighth notes form a dotted quarter note finally 12 8 12 divided by three gives you four so there's four beats per measure eight is our division so we have three eighth notes and again three eighth notes form the dotted quarter how would these sound well let's say for example we're in four four and let's say this is our beat this would be the division one and two and three and four and let's keep the same beat here and let's do nine eight it would be this one and a two and a three and so you have to understand the difference on how to hear the two now if you look at a time signature the bottom number can apply to a simple time signature or a compound time signature so let's say we have x over four if we're in simple time signature again that bottom number tells you what note is getting the beat so it would be a quarter note x over eight it would be an eighth note for a compound beat duration to figure this out you'd have to go to the next longest note value and then add a dot so for example what's the next longest value after a quarter note a half note and you're going to make a dotted a dotted half note is equal to three quarter notes an eighth note the next highest longest value will be a quarter note and you're going to add a dot to it dotted quarter note is equal to three eighth notes so that helps you to figure out the simple beat durations and the compound beat durations let's take a look at a few more ideas related to rhythm when you're notating rhythms you want to make sure that the metric accents and the individual beats are clear look at this example in three four the coordinate gets the b and each quarter note divides into two eighth notes by showing the eighth notes in groups of two we're able to see each of the individual beats on their own it's very clear we wouldn't group three eighth notes together here and three eighth notes together here because then we wouldn't be seeing each beat on its own so you want to make sure you're clear with your rhythmic notation so that it's easier for the musician to read syncopations are rhythmic figures that stress normally weak beats or divisions look at this example these first two notes they land on the beat beats one and two the eighth note here lands on beat three but then this quarter note lands on the end of b3 and this eighth note lands on the end of b4 so that's the idea of syncopation when you're stressing normally weak beats or divisions when you have upbeats and beats and that's when you're hearing notes that's the idea of syncopation a tuplet is a generic term that describes a grouping of notes that would not normally occur within a b let's say we're in a simple meter and we have a quarter note a quarter note divides evenly into two eighth notes or four sixteenth notes but let's say we wanted to hear three notes in the length of a quarter note and we wanted them to be equal length to do that we would go to the next note value that's shorter than the quarter note so that would be the eighth note we write three eighth notes together and we put a three on top of it showing that we want to hear three notes of equal length within the length of a quarter note let's say we have a dotted quarter note and we're in a compound meter we know that the dotted quarter is equal to three eighth notes let's say you wanted to hear two notes within the span of the dotted coordinate note you would write two quarter notes and put a bracket with a two above it showing that we want to hear two notes of equal length within the length of the dotted coordinate when it comes to stems when you have a single stem note notated on a staff the stem should go up if the note is below the middle line such as these and the stem should go down if the note is above the middle line like these if your note is on the middle line it can go either way but the majority of the time people tend to notate it with the downward step so just keep that in mind finally beams are used to connect durations that are shorter than a quarter note when the durations occur within the same beat so these are notes that are beamed together and when it comes to the stem direction of beam notes the preference is usually to decide the direction of the stems based on a note that is farthest from the middle line so this note is further from the middle line this note would have a downward stem so we're going to use downward stems in this example that notes further from the middle line it would have an upward stem so we're giving upward stems to all these finally in this example this notes furthest from the middle line and this one would use an upward stem so we're going to use an upward stem for this one too and those are the concepts that you need to know related to rhythm one final thing about rhythm as said earlier the tempo describes the relative speed of music's beat pulse terms are often used to indicate this relative speed try to become familiar with all the following terms which are commonly seen to express various tempos in music other times a specific tempo will be provided usually in beats per minute example the quarter note equals 60 which is 60 beats per minute next we're going to talk about chords so tonal harmony makes use of tertian chords which means they're built to thirds and the fundamental tertiary is the triad which is a three-note chord built of two-thirds you're going to want to be familiar with the intervals of a major third and a minor third because these are how we build our various triads so a major third is four half steps or two whole steps and the minor third is three half steps these are the four main types of triads diminished minor major and augmented you're going to want to know how to spell these these are the formulas for how you build them each of these chords has a root a third above the root and a fifth above the root when we get to seventh chords we have a seventh above the root that's why it's called a seventh chord a seventh chord is basically just extending your triad by adding one more third on the top these are the five main types of seventh chords you wanna know and these are the formulas for how you build these we have the major seventh chord major minor seventh chord or a dominant seventh chord minor seventh chord half diminished seventh chord and a fully diminished seventh chord some quick things to note here if we have the interval of a major seventh the seventh is going to be a half step below your root so in this one we have a b natural that's a half step from c which is our root that's a major seventh in this one we have a b flat that's a whole set from the root of c if it's a whole step away that's going to make it a minor 7th also with this example we see a b double flat you might be thinking wouldn't it be easier to just write it as the note a natural it might look easier but c to a is the interval of the sixth and we want the interval of a seventh to make it a seventh chord so you're going to want to accurately spell these chords finally you're going to want to be familiar with your lychee symbols which are the symbols we use to notate chords in popular music so these are some of the leaching symbols you would use for triads and the ones you would use for seventh chords sometimes there's more than one way to write a leachy symbol the one main thing you're going to want to know is that you always write the root letter as a capital or uppercase letter when you're doing a leaching symbol so all of these chords have the root of c so you're going to use an uppercase c at the start of every single one of these lychee symbols and make sure you memorize and become familiar with how we notate lead sheet symbols so that you at least have some idea of how you would notate it if you had to label a chord using a lead sheet symbol the cool thing about chords is that the root of the chord is not always going to be the lowest tone in a musical context you could have any part of a chord appear as the lowest tone so bass position is an arrangement of the notes of a triad and it's identified by the chord member that is in the lowest sounding voice look at all these examples here we have f major triads we have the notes f a and c in all three examples they all have the same ingredients we're making the same product an f major chord we perceive it as the same chord only differences in this one the a is the lowest sounding note and in this one c is the lowest sounding note but it's the same notes that make up an f major chord so these are inversions of an f major chord so this is root position it's what i call snowman form it's when your chord is stacked in thirds and the root is the lowest note you hear first inversion is where the third is the lowest note you hear of the chord and second inversion is where the fifth is the lowest note of the chord that you hear now seventh chords have inversions two so we have the root position snowman form here where the root is the lowest sounding note first inversion again where the third is the lowest ending note second inversion where the fifth is the lowest ending note and then seventh chords have third inversion where the seventh is the lowest ending note when we do lead sheet notation for chords that are inverted we use slash notation so this chord here would simply be written as f it's an f major triad this is an f major triad to tell you the identity of the chord we would write uppercase f that tells you the chord slash we would put slash a because a is the lowest sounding note we hear this is an f major chord and c is the low sounding note so it would be f slash c whatever you see to the right of the slash is always the lowest sounding note that you hear when we have seventh chords this is how you do this this is a c major seventh chord so that would be c major seven this is c major seven with e in the bass so it would be c major seven slash e and the same thing would apply to this one where g would be in the base and this one word b would be in the base if you're ever trying to figure out the root of a chord try to get it into snowman form if you're in snowman form like this one and this one the lowest note is your root another trick is if you have seventh chords like these if you're stacked like this where the notes are all close together wherever you see the indent like this one this one and that one the higher note of the indent is always your root so here b and c are indented the c is higher that's a root b and c is indented c is higher b and c are indented c is higher so you can use that to try to figure out the root of a seventh chord as well when we analyze music we often use numbers to indicate the base position of chords and the numbers that are used are derived from the baroque system known as figure bass or thorough bass which was a method of abbreviated notation that consisted of a bass line and symbols that would indicate the chord to be played above each bass note so you're going to want to become familiar with how this whole thing works so let's look at this example we have a g major triad and root position first inversion and second inversion so the figure based numbers are determined based on the intervals you have above the base note so here g is the bass note b is a third above g d is a fifth above g so the figured bass is five three here b is the lowest note d is a third above b and g is a sixth above g so the figure base is 6 3. finally we have the note d in the bass g is a fourth above d and then b is a sixth above d so the figure base is six four so it's always based on the intervals based on the bass note the lowest note you hear and the same thing applies to seventh chords we have seven five three six five three six four three and six four two those are simply the intervals you have above the lowest note that you hear and these are the abbreviated symbols that we most often use so if you don't see any figured bass we're dealing with a root position triad if you see six that refers to a first inversion triad six four is second inversion triad seven is a root position seventh chord six five is first inversion seventh chord four three is second inversion seventh chord and four two is third in version seventh chord some people use this phone number to try to memorize it it's just a clever way to try to remember the numbers in the order so now with figured bass you're also going to want to know how to take a base note and apply figured bass so when you see seven that means you're going to have a root position seventh chord so start by making a root position seven chord like such and then when you see an accidental next to an arabic numeral on the figured bass that's used to raise or lower a note so this is next to the number seven that means it's the lower the seventh above the bass so the seventh above c is b they want you to lower it to a b flat and this one when you see an accidental by itself it always refers to the third above the base and it's used to alter that note so we don't see figured bass numbers so that means root position triad so first make a root position triad and it says you want to raise the third the third is the g you're going to make it a g sharp finally if you see a slash through a number or a plus sign next to a number that means to raise the note they both mean raise so here six four three we're going to go above six four and three so three above a that's c a fourth above a is d and a six above a f sharp remember we always count a as one the lowest note we always count as one so one two three one two three four one two three four five six and now it's saying we want to raise the fourth above a which is the d make it a d sharp and we want to raise the sixth above a which is the f so make that an f sharp so that's how figured bass symbols work another symbol you might see is a horizontal line and that means to keep the same note accord for instance if you see 5 3 and then you see 6 with a dash under it that means to use the same base note for root position triad followed by one and first inversion finally the idea of realization was used in performance during the baroque period and that term simply means to practice improvising chords based on the given figure based part as a music student and a musician you're going to want to be able to analyze a chord by simply looking at the different notes you're given so let's do some practice with this let's say you see this chord you have four notes that are heard at the same time and are scattered throughout the grand staff so how do we name this chord first make an inventory of all the different pitch classes that you have so we have the note e we have the note g c and c so make a list for your notes on the side we have an e a g and a c if you have a note that's doubled you don't have to write it twice now what you want to do is figure out how can you get these three notes in root position or snowman form how can you get them so they're stacked in thirds if you have trouble doing this you can use this chart of thirds to figure it out look for the three notes c e g and wherever you see the lowest note that's your root so this would be c e g c to e is a third e to g is a third now you want to know your chords so c e and g forms a c major chord so the lead sheet would be uppercase c and we have an e in the bass so it would be slash e let's do another practice example so we have this one we have the notes g f d and b flat always look at your key signatures and make sure you're careful with that so if you write your notes on the side g f d and b flat so we have four different notes that indicates that we're probably dealing with a seventh chord how can we get this in snowman form or a position again look for the four note letters we have a g f d and it doesn't matter if there's a flat or a sharp or anything like that and we're just caring about the letter right now so it's a b flat so we have b this would be root position if g is our base note so g b flat d f g b flat d is a g minor triad and then g to f is a minor seventh because f is a whole step away from g so this is a g minor seventh chord g is our lowest note so it's in root position so that would be how you analyze this chord now that you have an understanding of chords we can start talking about diatonic chords so most chords in tonal music are made up only of notes from the scale or key on which a musical passage is based these are diatonic chords chords that are part of your key on the other hand altered chords or chromatic chords are chords that use notes that are not found in the scale or key on which your musical passage is based so if you're reading a piece of music and you come across a chord with an accidental that's an altered or a chromatic chord there are various ways to analyze these types of chords and we're going to be covering a lot of them later on in the video for now we're going to be sticking with the diatonic chords roman numerals are used in music theory to analyze chords in a piece of music and these are quite useful because they tell us the scale degree on which a chord is built they tell us the quality of the chord and they also allow us to analyze how chords are functioning in a piece of music to do a roman numeral analysis first you have to write down what key you're in if you're in a major key you use an uppercase letter and if you're in a minor key a lowercase letter and let's say we're in c major start by writing your c major scale and then build a triad on each scale degree these are the possible diatonic triads for a song or a piece in the key of c major we have c major d minor e minor f major g major a minor b diminished no matter what matrix you're in the order of the tri-equalities is always the same you're going to want to recite this and commit it to memory the order of the try equalities and major keys is major minor minor major major minor diminished the roman numerals are going to be the same for all major keys as well if you have a major chord use an uppercase roman numeral a minor chord you use a lowercase roman numeral diminished chords use a lowercase roman numeral because they're smaller chords like minor but you're also going to be adding the diminished symbol to tell you it's a diminished chord augmented chords are not naturally found in major scales or minor scales so you're not going to be encountering these however if you do happen to analyze an augmented chord in the future you would use an uppercase roman numeral because it's a larger chord and you would add the plus symbol to tell you it's an augmented chord but again augmented chords are not naturally found in a major scale or the minor scale now when we get to the minor scale it becomes a little bit more confusing because there are some differences you have to note so if we're in the natural minor scale the five chord would naturally be a lowercase five it would be a minor five chord and the seven chord would be a major seven chord however if you remember earlier in this video we talked about the harmonic minor scale and how that's the most commonly used because we want to have a leading tone that takes us back to the tonic so in minor keys you're often going to be seeing leading tones and that creates a major 5 chord just like in a major key and a 7 diminished chord just like in major keys so the 5 chord and a 7 diminished chord always like to take us back to the one chord so we like to see these in both the major key and the minor key so yes in a minor key can you have a minor five chord and a major seven chord yes the majority of the time though you're going to be seeing the major five chord and a seven diminished chord and whenever you see these chords you're going to be seeing an accidental because you have to raise the seventh scale degree to make it a leading tone the three chord you don't raise the leading tone we don't make it an augmented try we just keep it as a major triad don't do anything to this chord we keep it major so that we have more things that we could do with it so the order of the diatonic tri-qualities and minor keys that you're going to want to remember is minor diminished major minor major major diminished so make sure you could spell these roman numerals accurately and make sure you can remember the diatonic tri-qualities one last thing i want to make sure you don't mix up four and six that's a common beginner mistake roman numeral five is a v so i think of this as one after five that would be six look here we have a one before the five symbol so that would be one before five which is four one before five is four one after five is six so you wanna make sure you don't mix the two up that's a common beginner's mistake so that's how you analyze the diatonic triads in major and minor keys let's say you wanted to determine the diatonic seventh chords that were possible you would start off with all of your diatonic triads and then you would add sevenths to all these chords and this would give you the possible diatonic seventh chords in major and minor keys now the roman numerals themselves are not going to change because the triad qualities are not going to change however we need some sort of indication that tells us we're dealing with seventh chords now for a major seventh chord the uppercase roman numeral tells you have a major triad and then uppercase m seven that tells you major seventh for a minor seventh chord lowercase roman numeral tells you minor triad seven by itself tells you minor seventh for a dominant or major minor seventh chord uppercase roman numeral tells you major triad seven by itself tells you minor seventh half diminished seventh chord diminished symbol tells you have a diminished triad half diminished seven that tells you you have a minor seventh finally fully diminished seven diminished symbol tells you that you have a diminished triad and then diminished seven that tells you you have the interval of a diminished seventh now roman numerals are used together with figure base to indicate the chord and the inversion so for example let's say we were in the key of c major and you saw these notes in this order from lowest to highest pitch e g c you'd look at that and you'd say okay well that's a c major chord c major in the key of c is one if e is the lowest sounding note that's first inversion and the first inversion figured bass for a triad is six the lead sheet would be this let's do another example let's say we were in the key of g major and you saw the following notes in this order a c d f sharp so if you look at this you have to figure out what the root of the chord is in this case it's d d in the key of g is your v chord we have d f sharp ac so that's a five seven chord if a is the lowest sounding note that would be second inversion seventh chord and the figured bass you would have to know is four three and the lead sheet symbol for this chord would be d7 slash a so lead sheet symbols and roman numerals with figure bass are very similar they're telling you what chord you have and what inversion it's in we're going to be using roman numerals and figure bass a lot in music theory to help us analyze the chords that we have in any given key now that we've talked about the fundamentals of music it's time to get into the actual art and craft and music theory we're going to start by talking about the principles of voice leading and the melodic line so voice leading and part writing that can be defined as the ways in which chords are produced by the motions of individual musical lines this relates to the term counterpoint counterpoint is the relationship between voices that are harmonically interdependent yet independent in rhythm and contour in other words counterpoint involves having individual melody lines that are heard together to form harmonies now we're going to talk about how to write a basic melody line you're going to want to stick with simplicity you're not going to want to do anything complex right now so with a basic melody line you want the rhythm to be as simple and straightforward as possible most of the note durations are going to be equal to or longer than the duration of the beat and the final note should always occur on a strong beat when it comes to harmony every note in the melody should belong to the chord that is to harmonize it contour deals with the movement and motion of a melody the melody should be moving mostly in conjunct or stepwise motion this is contrary to disjunct motion which is moving by skips and leaps so you're going to want to stick with stepwise motion or conjunct motion for the majority of the time you also want to have one focal point in your melody which is the highest note in the melody you don't want to have two focal points or more because that takes away from the effect of the focal point when it comes to leaps leaps are best left in the opposite direction so if you leap up to a note it's best left by step in the opposite direction you're going to want to avoid leaps that involve the intervals that are augmented sevenths and intervals that are greater than an octave if you use a diminished interval you can do this as long as you change direction by step immediately after that leap finally is the concept of tendency terms certain scale degrees want to resolve to certain scale degrees scale degree 7 is the leading tone it wants to resolve to scale degree 1. scale degree 4 is a half step above scale degree 3. it likes to resolve down to scale degree 3. if scale degree seven doesn't resolve to one it's usually part of a melody line that's moving downwards by step in other words we have this example scale degree one seven six five so instead of resolving up to one the melody is moving down here's an example of a good basic melody line we're in the key of b flat major here and this is the roman numeral analysis so all these notes are simple rhythms we have quarter notes and a half note every note belongs to the harmony under the roman numerals i wrote the possible notes that you could use based on the chords that you're given each one of these notes belongs to the chord contour the melody is mostly moving by step we do have a leap here but then the leap does resolve down by step we have one focal point here that e flat is your focal point the highest note in the melody line and it's not repeated and then we have tendency tones we don't have scale degree seven in this melody but we do have scale degree 4 and scale degree 4 like we said likes to resolve to scale degree 3 which it did so this is an example of a good basic melody line and you're going to want to be able to compose something very similar to this if you're asked to do so let's talk about notating and voicing chords a musical score shows all the parts of an ensemble arranged one above the other this enables a reader to hear in their mind what the composition will sound like in a full score you're going to see all or most of the parts notated each on their own individual staff while on a reduced score you're going to be seeing the parts notated at concert pitch on as few states as possible the main type of reduced score you're going to be encountering in music theory courses is the satb reduced score which stands for soprano alto tenor bass basically we have a grand staff the soprano and alto voices share the treble clef the tenor and bass voices share the bass clef when you have two parts on a single staff you want to make sure the stems of the top part are pointing upwards and the stems of the bottom part are pointing downwards after you decide on what combination of instruments and voices you want to write for you have to consider how you're going to be voicing your chords how are you going to be distributing and spacing the notes and there are many many different ways you could be doing this there are two types of structure that we talk about in music theory closed structure is when you have less than an octave between the soprano and a tenor so here we have the soprano singing in g here we have the tenor singing a b that distance is less than an octave this is closed structure open structure is when you have an octave or greater between the soprano and tenor parts so here the 10 are singing a g note how we don't have two different g's here we have the g note head and we have the bass stem and the tenor stem sharing that one no head this indicates that we have two parts singing the exact same note so we have the tenor signing of g the sopranos thinking of b that's greater than octave so this is open structure so you can have the same exact chord and it can be voiced many different ways sometimes close structure sometimes open structure when you're voicing chords you want to avoid cross voices you don't want an alto part singing a note above the soprano part and you don't want a tenor part singing a note below the bass part this makes it harder for us to keep track of which part is singing which note when it comes to spacing you want to keep the sat adjacent parts within an octave of each other so for example here we have a g major chord between a soprano and alto that's less than an octave between the alto and the tenor that's less than an octave that's good between the bass and the tenor we have more than an octave that's okay between the bass and the other parts you could have a little bit more than an octave but between the upper three parts you want to make sure they're all within an octave of each other so soprano to outsole should be within an octave outside the tenor should be within an octave finally make sure you're familiar with the various ranges for the soprano alto tenor and bass voices most of the notes are going to be landing on the staff but some might extend a little bit above or below the staff so just make sure you keep the ranges in mind let's quickly talk about motion when music progresses from one chord to the next there are five possible relationships between any two parts static motion is when neither part moves oblique motion is when only one part moves contrary motion is when both voices move but in opposite directions similar motion is when both voices move in the same direction but by different intervals parallel motion is when both voices move in the same direction by the same interval let's look at an example of each this is static motion because knight apart is moving this is oblique motion because only one part is moving this is contrary motion because both parts are moving but in opposite directions this is similar motion because both parts are moving in the same direction but by different intervals this part is falling a fourth this part is falling a second finally this is parallel motion because both parts are moving in the same direction and by the same interval this part is following a second and this part is also following a second in total music and counterpoint we want to make sure that individual parts and voices all have their own independence because of this goal voices that move together in parallel motion must be given special attention composers of tonal music would usually avoid parallel fifths and octaves these are the most stable intervals so when you move two voices by these intervals in parallel motion they're objectionable because listeners find it harder to perceive two independent voices each doing their own thing likewise composers would also try to avoid contrary fits and octaves this occurs when you have two voices that form a perfect fifth or octave and they move in contrary motion into another fifth or octave respectively unequal fifths occur when you have a perfect fifth followed by a diminished fifth or vice versa in the same two voices these are only considered unacceptable when they occur between the base and another voice finally we have direct or hidden fifths and octaves these occur when the outer parts the soprano and bass move in the same direction into a perfect fit or octave with a leap in the soprano part it's acceptable for the outer parts to move in the same direction into a perfect fit or octave as long as the soprano voice moves by step here are some examples of the various types of motion we just talked about so let's say we're in the key of c major and we're going to write an satb arrangement we have the roman numerals those are the chords that we have and these are the voicings that we decided on now let's look at what's going on here in the first example we have c in the bass g and a tenor that's a perfect fifth then we have f in the bass c and a tenor so we moved from a perfect fifth between these two voices into another perfect fifth in these two voices that's parallel fifths also we have a c in the bass and a c in the soprano that's an octave and then we have an f in the bass and f in the soprano another octave so the bass and soprano are moving in parallel octaves you want to avoid those look at what's going on here we have g in the base d in the tenor so g to d in its most simplified form is a perfect fifth so it doesn't matter if it's more than one octave apart g to d in its most reduced form is a perfect fifth so we have a perfect fifth here in the basin tenor and then we have c to g which is another perfect fifth but this time we're moving by contrary motion so these are contrary fifths finally here we have c in the bass e and the soprano so that's the third and then we have g in the bass and g in the soprano which is an octave so the bass and the soprano are moving into an octave by similar motion so that should raise a red flag about direct or hidden octaves and because the soprano note is leaping it is considered a direct or hidden octave so you want to try to avoid those two remember director hidden octaves and fifths occur between the bass and the soprano the outer voices now composers would sometimes use parallels when they desire the oral effect that they would create however for basic practices of counterpoint you're going to want to stick with trying to avoid these types of parallel motion so that you have clear independence between all of your voices when you're doing your voice leading and part writing now we can discuss root position part writing if you follow the conventions that are presented you will not need to worry about voice leading problems such as parallels when you read an satb arrangement you will almost always have all the members of the triad present the root will usually be the note that's doubled sometimes it'll even be tripled you really want to emphasize this note be sure to avoid doubling tendency tones such as the leading them we're not going to be covering three part textures in this video but when you wear the three-part arrangement always make sure that you at least include the root of the chord and the third of the chord you're dealing with the root gives the chord this identity and the third gives it its color let's say you're writing a four part arrangement when you repeat a root position triad you can either keep all the notes at the same spot which would be static motion or the upper voices may be arpeggiated freely this creates a little bit more interest let's say you have triads whose roots are a fourth or a fifth apart they're going to have one note in common when you connect triads whose roots are a fourth or fifth apart you should retain the common tone and move the remaining voices to the nearest place to ensure correct doubling and spacing sometimes you won't be able to retain the common tone it depends on what your melody line is doing if this is the case you'll still need to move the voices to the nearest place to ensure correct doubling and spacing and often this involves moving the upper three parts in contrary motion to the base let's look at an example let's say we're in c major and we have a five chord moving to a one chord well the root of five is g and the root of one is c in this case g up to c is a fourth if we had g go down to c that would be a fifth so we're dealing with fourth or fifth apart whenever i do satb arrangements i always make a checklist of what notes i need so that i can stay organized and keep track of what i have and what i need so the baseline is always taken care of we're dealing with root position so it's going to be g to c the common tone between these two chords is g so we're going to keep that the same these two voices move to the nearest spot so b is a leading tone move it up to c and then the note d can move up by step to e that's how you would resolve this five chord to the one chord you can always have a leading tone that doesn't resolve to scale degree one as long as it occurs in an inner voice the alto or the tenor but if you have the leading tone in an outer voice like you do here you need to resolve it because it really stands out we really want to hear that resolution let's say you have triads whose roots are a third or a sixth apart they're going to have two common notes so when you're connecting triads whose roots are third or sixth apart you should retain the two common tones and move the remaining voice by step to the remaining chord tone that you need let's look at this example a three chord to a one chord in c major that would be e minor going to c the two common tones would be e and g so we know the bass line has to move from e to c because those are the roots of our chords and we're dealing with root position e and g are the two common tones so we're going to keep those the same the final note we have is the b and the b can resolve up to c because it's a leading time so that's how you resolve this finally let's say you have triads whose roots are a second or seventh apart they're not going to have any notes in common when connecting triads whose roots are a second or seventh apart the upper voices should all move in contrary motion to the bass to the nearest chord tone so if the base moves up the upper three voices should move down to the nearest chord tone if the bass moves down the upper part should move up now one exception is the deceptive resolution which is a five chord going to a six chord in this case the leading tone which is present in a v chord will often move parallel with the bass and resolve up to scale degree one and this results in a six chord with a doubled third which is okay let's look at this example we have 5 going to 6. well the base note is going to be g and it's going to resolve to a because those are the roots g is going to resolve down contrary motion to the base to the nearest chord tone which would be an e d resolves to c and b you would resolve to a normally however in this case b is a leading tone we want to resolve that leading tone to c so that's okay we have g to b which is the third we have parallel thirds that's fine so in this chord we have a c c and e so we have a double third but that's okay because we wanted to resolve that leading tone so that's how you do root position part writing transposition is often a confusing topic when musicians first learn about it but musicians need to understand transpositions in order to successfully compose arrange conduct and read instrumental music certain instruments do not read music at concert pitch this means that the notes that they read in their parts produce pitches that are higher or lower than the notes that have the same names on the piano now the overarching idea for most transposing instruments is that the note that is written is higher than the note that is sounded there are a few exceptions to this like the piccolo and the e-flat clarinet but the majority of transposing instruments follow the written above sounding principle so keep this in mind a transposing instrument sees the note c but sounds its key in other words if you have a b flat instrument when you play a c you hear a b flat if you have an f instrument when you play a c you hear an f if you have an e flat instrument when you play your c you hear an e flat let's do some practice exercises let's say you want to hear a concert pitch middle c if you're playing a b flat instrument like the clarinet if you play a c you hear the note a major second below c which is a b flat so in order to hear the note c you would have to write the note a major second above c that would give you the note d so when you play a d on a b flat instrument you hear a c written above sounding and the key transpose is two so let's say you're in c major a major second above c is d so you would change the key signature to d major let's say you have an f instrument like the horn when you play middle c you hear the f below middle c that's a perfect fifth below c so if you want to hear c you have to go a perfect fifth above c that gives you the note g so when an f instrument plays this note g you hear this note c written above sounding and if you're in the key of c major a perfect fifth above c is g so you write the key signature as g major finally let's say you have an e flat instrument like the alto saxophone if you play middle c you hear the e flat below middle c which is a major six below middle c so if you want to hear middle c you have to go a major sixth above that note which gives you the note a so for an e flat instrument when you play this note a you hear this note c written above sounding and again a major six above c would be a so you would write the key signature as a major and those are some practice exercises with transposition you want to make sure you could go from concert pitch to the transposition and from the transposition to what you would be hearing next we are going to look at sequences a sequence is a pattern that is repeated immediately in the same voice but that begins on a different pitch class there are three types to keep in mind a tonal sequence will keep the pattern in a single key this means that interval modifiers might slightly change a real sequence transposes the pattern to a new key this means that the interval will stay the exact same a modified sequence is a sequence wherein the repetitions of the pattern are neither tonal nor real let's look at an example let's say we're in the key of c major and we have this pattern and we want to develop a sequence from it so we're going up a second up a second down a third a tonal sequence will stay in the key of c major so let's start this pattern on the note d go up a second up a second down a third now look the number part of the interval will always stay the same for a sequence the modifier might change here we have major second major second major third here we have major second minor second minor third this is because we want to stay in the key we were starting in so that's what happens when you have a tonal sequence a real sequence you'll have the exact same intervals the number and the modifier so here we have major second major second down to major third we're starting the pattern on the node d we're going up a major second up a major second down a major third so we have the exact same intervals and look we wind up having an accidental it looks like we're in d major now so that's a real sequence it's when you transpose the pattern to a new key related to the concept of the sequence is the idea of imitation imitation is the repetition of a pattern that occurs between two or more voices and real imitation is very similar to a real sequence but with the transposed repetition of the pattern occurring in a different voice than the voice in which the pattern was initially introduced most of the chord progressions that are used in tonal music whether it's classical or popular music come from the circle of fifth progression this is a harmonic sequential pattern where the roots of the chords progress a fifth down or a fourth up let's say we're in the key of c major and these are the roots of the chords we have f going up to b so you're going up a fourth b going down to e you're going down a fifth up a fourth down a fifth up a fourth down a fifth so that's the example of your circle of fifth progression and this is the basis for a lot of chord progressions in tonal music so you're going to want to become familiar with this and how it works in music some chord successions seem to progress and move forward towards a goal whereas others tend to wander and leave our expectations unfulfilled a majority of the chord progressions that are used in tonal music derive from the circle of fifth progression here we have two charts they show the common harmonic progressions of major and minor keys let's talk about how they're derived the ultimate harmonic goal in tonal music is to get to the tonic triad the one chord and the tonic chord can go to any chord that it wants to the tonic triad is most often preceded by the v chord which has dominant function five going to one is considered one of if not the strongest chord progressions in tonal music now you can expand the domain of a chord through the use of subsidiary chords in a process known as prolongation so just keep that in mind also note that the five chord can move to the sixth chord in what's known as a deceptive progression now chords in total music they love to have their roots fall by fifths notice how we have five falling to one if you go a fifth above the root of the five chord you get the root of the two chord that makes it a circle of fifths progression the two chord has predominant function and it likes to progress to the five chord if you continue to go backwards a fifth above the root of the two chord gives you the root of the six chord so the sixth chord likes to progress to the two chord a very common chord progression in popular music is one six two five and back to one the sixth chord can be used as a substitute for one both chords have two common tones they're very similar five likes to go to one sometimes five will go to six so six can sometimes substitute for one to keep the music going longer if you continue to go backwards from six a fifth above the root of the sixth chord gives you the root of the three chord now note that most of the time when you see scale degree three in the bass line the chord is going to be a tonic chord in first inversion this is because the one chord is able to go anywhere the three chord is more limited now the three chord is usually followed by either the sixth chord or it moves up to the four chord the four chord has a root a half step away from the root of the three chord so we still have to talk about seven diminished and four so seven diminished is very similar to the v chord they both have dominant function and seven diminished usually acts as a substitute for the five chord remember they both have the leading tone in there so they both want to resolve to one now seven diminished is often used to prolong a tonic triad by appearing in first inversion between two positions of the tonic triad such as in this progression one seven diminished six one six that's a very common chord progression that uses the seven diminished chord if you use both chords back to back usually seven diminished will move to five since five is the stronger chord and you want to save that for the end now this chord progression i just talked about usually involves a voice exchange this is when two voices that occupy different members of a chord each prolong that chord by moving to the chord member that the other voice had previously occupied so the last chord to talk about is the iv chord the iv chord does a few different things the iv chord has predominant function just like the two chord and it often moves to five or seven diminished four can also prolong the predominant area by moving first to the two chord also the four chord can often proceed straight to the one chord in what's known as a plagal progression so the iv chord has several different functions in music now in the minor mode we can continue to go backwards from three if you go perfect fifth above the root of the three chord you get the root of the seven chord but not the seventh diminished chord the regular subtonic seven chord this chord sounds like the v chord of the relative major which is the three chord so subtonic 7 likes to go to major 3 in a minor key now in the minor mode a chord like the v chord can appear two different ways v chord can appear as the dominant function chord but you could also have a minor v chord the minor v chord doesn't have dominant function instead it's used as a passing chord in progressions like this one 1 5 6 four six to five that's a chord progression that allows the bass line to move down the scale remember minor five chords do not have dominant function now when it comes to harmonic sequences keep in mind that there are other possibilities out there and you're not limited to these also remember that chord inversions do not affect a harmonic sequence finally most seventh chords will function the exact same way as the triads so you could turn these into seventh chords the main idea to keep in mind is that you like to have predominant chords move to dominant chords and then they resolve tectonic chords and that creates the sense of progression in music let's say you wrote a melody line that you're happy with and you decide you want to put chords to it so how do we harmonize a simple melody we're going to practice that with this example in e flat major so you want to start and end with the one chord if possible the one chord establishes what kirin and it's your ultimate harmonic goal so for an e-flat major and the first note of the melody is a g is there a g in the one chord in e flat major yes there is so this works the last note of the melody we have an e flat is there an e flat in the one chord in e flat major yes it's the root of the chord so that works the penultimate chord should be five if possible because remember five to one is our strongest chord progression in tonal music so if you can end a phrase or a melody line with that that's the strongest way to do it so the second last note we have in the melody is an f is there an f in the v chord in e flat major well the v chord is a b flat major triad which is b flat d f so this works now you want to write all the other chord options under the other melody notes and you're going to treat every note as the root third and fifth of a triad let me show you what i mean we have the note f here if f was the root of the chord it would be an f minor triad in e flat major which is your two chord if f was the third of the chord d would be the root and then d in the key of e flat is your seventh diminished chord and then if f is the fifth of the chord b flat would be your root and b flat in the key of e flat major will give you your v chord so you're going to do this for every note of the melody now comes the fun part it's kind of like a puzzle you're going to decide what chords you want to use you have to check your harmonic progressions as you go make sure you follow the harmonic progression chart and you want to try to change the chord for every melody you know if possible so let's practice this i usually avoid using seven diminished chords when i do these because using them in root position is generally not what you do they're usually seen in first inversion so for the purposes of this exercise i'm going to avoid using them let's say for this chord i decided to use the five chord well can five go to five we wanna try to change the chord for every note if possible so five can't go to five five doesn't like to go to seven usually if anything seven would go to five so that wouldn't work and five doesn't go to two so that wouldn't work so we can't use a five chord here we already said we're not going to use seven diminished so here i'm going to use a two chord now two chord where can the two chord go you're not going to go to another two chord you want to change it two is not going to go to seven diminished we already said we're not going to use those can two go to five yes it can so this works so where can five go can five go to four no can five go to one yes can five go to six yes so now you gotta play around with your options let's say you chose six if you had a six chord here can six go to seven diminished no can six go to five no can six go to three no so in this case we can't use the six chord here so we would use our one chord here instead so basically you just have to do this and keep checking all of your harmonic progressions as you go and come up with the chord progression you like there are multiple right answers when you do these types of problems here's an example of what an acceptable answer for this might be we have one two five one i'm going to decide to go with a five chord here because one and five are the safest chords to play with let's see five i'll do one six two two goes to five and then five goes to one so that would be an example of an acceptable harmonic progression that goes along with this melody so that's how you go about harmonizing a simple melody line in most phrases of music you'll see at least one inverted chord chord inversions allow us to keep our music interesting now first inversion chords will have the third in the bass for example a c major chord with an e in the bass here are some reasons to use tries in first inversion one is to improve your bass line contour if you only used root position chords your bass line would be rigid they're also used to provide a greater variety of pitches in the bass line finally they can lessen the weight of chords a first inversion 5 or a first inversion one chord are not as strong as a root position five or a root position one chord so if you use a five or a one chord in the middle of a phrase you might want to lessen their weight since they're not the ultimate harmonic goal yet now the seventh diminished chord is almost always going to be seen in first inversion this allows you to avoid having a tritone between the bass and another voice you'll often see this chord as part of a voice exchange let's look at an example here we're in c major we have a one chord moving to a one chord in first inversion the seventh diminished chord is in between the two now look here we have the bass line moving up c d e in the soprano we have the soprano line moving down e d c so they're mirror reflections of each other they're singing the same notes just in the opposite order that's a voice exchange and here the seven diminished six chord is used right in between to connect the two chords together you'll often see triads in first inversion as part of a bass arpeggiation as well especially in keyboard music another common feature of these chords is the use of parallel six chords this is when you have a series of first inversion triads back to back to connect two chords together these are considered passing chords here's an example of one let's say we have a one chord and we have a one chord at the end here we have several first inversion triads back to back now this doesn't follow our harmonic progression but this is okay because this is simply used as a series of chords to help you to connect one triad to another now when it comes to part writing and voice leading for triads and first inversion the typical thing to do is to double the soprano note usually you're going to try to double one of the stable notes of the chord if possible especially if you have scale degrees one four or five in your chord so here we have a c major chord in first inversion so e is in the bass we have a c in the tenor we have a c in the soprano so the soprano notes doubled and then we have a g if you don't double the soprano note the next best thing to do is to double the bass note now the one note you never want to double is going to be your leading tone so if you have a leading tone in the soprano don't double the leading tone because leading tones want to resolve and you want to avoid the use of parallel octaves so always be careful with your part writing when it comes to triads in first inversion triads in second inversion are commonly encountered in music too second inversion chords occur when you have the fifth of the chord in the bass for example a c major chord with the g in the bass second inversion triads will have a perfect fourth between the bass and another voice and this is considered a dissonant interval when it occurs between the bass and another voice as a result second inversion triads are unstable they're not used as substitute chords rather they have their own specific uses you'll encounter them in different instances such as through bass arpeggiations when you're part writing for these chords you want to double the fifth of the chord which is also your bass note in root position we like to double the bass note here we also like to double the bass note the difference is here the bass note is the fifth of the chord we refer to second inversion triads as 6 4 chords because 6 4 is the figured bass notation for triads and second inversion these are the four types of six four chords you wanna be familiar with arpeggiated six four chords occur when you have the same chord happening multiple times but in different inversions here we have the one chord in root position first inversion and second inversion that's an arpeggiated 6 4 chord the passing six iv chord occurs between two other chords and it involves the bass line moving upwards or downwards by set notice how this bass note allows you to pass from this bass note to this bass note smoothly so that's a passing six four chord the pedal six four chord also occurs between two chords but here the bass note stays static pedal basically means to hold here we're holding this bass note so that's a pedal 6-4 chord the cadential 6-4 chord is commonly used to end pieces of music the chord progression is 1 6 4 5 1. we put a bracket with a 5 underneath the 1 6 4 and the 5 to show that the two chords together share dominant function this one chord is not functioning as a tonic chord it's working together with the v chord and together they share dominant function some music theorists notate this as 564-53 this notation basically says that the five chord starts here with non-chord tones that resolve to the root position v chord here either notation is considered acceptable so figure out the one that you prefer to use or that your professor prefers that you use and that's a little bit about triads and second inversion cadences play a crucial role in tonal music they are kind of like commas and periods in a sentence cadences are chord progressions that either leave you wanting to hear more music or feeling complete and resolved they are interior harmonic goals within a piece and they often occur every four measures there are two main branches of cadences conclusive cadences which conclude with the tonic harmony and progressive cadences which do not conclude with the tonic harmony examples of conclusive cadences are the authentic and plagal cadences and examples of progressive cadences are the deceptive and half cadences let's look more specifically into the different types of cadences we have the perfect authentic cadence that's the most final sounding of your cadences and it's often used to end pieces of music this cadence occurs when you have the v chord resolving to the one chord both in root position with scale degree one in the melody over the one chord now we have three types of imperfect authentic cadences the root position imperfect authentic cadence is the same thing as a perfect authentic cadence but instead of having scale degree one in the melody over the one chord you have scale degree three or five in the melody over the one chord the inverted imperfect authentic cadence is when you have the five chord resolving to the one chord where at least one of the two chords is inverted the leading tone in perfect authentic cadence occurs when you have the seventh diminished chord resolving to the one chord remember seven's a minute shares dominant function with five but seven diminished to one is not as strong as five to one now the plagal cadence is also known as the amen cadence and this cadence involves having a iv chord resolved to a one chord the half cadence occurs when you end a phrase with a v chord this is an unstable cadence that leaves you feeling off balance and wanting to hear more music in order to feel resolved now the phrygian half cadence is a specific type of half cadence that occurs in the minor mode and this cadence occurs when you have a first inversion iv chord resolving to the v chord in this case you're going to have the bass note moving down a half step finally the deceptive cadence is a cadence that results when the ear expects to hear five resolving to one but the music actually hears the v chord resolve to something else most of the time the deceptive cadence has the v chord resolved to the sixth chord which is a substitute chord for one be sure that you are familiar with the following abbreviations that are commonly used to analyze cadences in a piece of music one last thing to note about cadences if the rate at which chords are changing in the music is faster than one chord per measure the last chord of a cadence will generally fall on a stronger beat than the chord that precedes it make sure you're familiar with all of your cadences as they are an essential part of tonal music cadences allow us to analyze phrases of music and this further allows us to analyze the overall form of a piece of music in music a motive is a small identifiable musical idea this can be a pitch pattern a rhythmic pattern or both motives are often developed throughout a piece of music a phrase is a relatively independent musical idea that ends with a cadence sub phrases are distinct portions of a phrase we use lowercase letters to label phrases and music as you see here if the last note of one phrase also searches the first note of the next phrase this is known as an illusion there are certain patterns for organizing phrases and groups of phrases that are constantly found in music let's look at some of them if you have two identical phrases this is simply known as a repeated phrase the period is a multi-phrase unit that usually contains two phrases in an antecedent consequent relationship you can also think of antecedent consequent as a question answer relationship the second phrase will usually have a stronger cadence than the first parallel periods occur in the antecedent and the consequent both begin with similar or identical material as a result we give the two phrases the same letter to analyze them but we refer to the second one as prime since it concludes differently than the first and we notate prime with an apostrophe next to the letter contrasting periods occur when the antecedent and the consequent each begin with different material a repeated period occurs when you simply repeat the entire period that you originally had a three phrase period occurs when you have three different phrases and these phrases will either consist of two antecedents in the consequent or one antecedent and two consequence and the cadences will determine this aspect the double period is similar to a period except that each half of the structure consists of two phrases rather than just one this is different from a repeated period because here we have contrasting cadences at the end of phrases 2 and 4. double periods are labeled as parallel or contrasting based on if the melodic material that begins the two halves is similar or not a phrase group is a multi-phrase unit that consists of several phrases that seem to belong together structurally even though they do not form a period or a double period this usually occurs when the final cadence is not the strongest one the sentence is typically a single phrase in length it is a structural unit that involves the immediate repetition or variation of a musical idea and this is followed by motion towards a cadence when you're analyzing phrases there are some tips that you can follow look for any sort of repetition of a musical idea this can indicate a potential parallel period or sentence when you're searching for a consequent phrase look to see if there's any repetition of the initial measures of your antecedent phrase be sure to look for your cadences including how many you have and the order that they occur this can guide you toward coming up with a good analysis of the building blocks of a pieces form which are the phrase period and sentence and be sure you're familiar with the following phrase diagrams that are used to analyze phrases periods and sentences in music and that is a basic summary of forum on the micro level let's quickly talk about texture and music texture describes how layers of sound within a piece of music interact there are four main types of textures that you should be familiar with monophony is music consisting of a single line or melody without an accompaniment homophony is music concentrated on one voice or part with a secondary accompaniment and or voice polyphony is music employing multiple parts each keeping its own distinctiveness and heterophony is music that has multiple parts or voices performing different versions of the same melody here we have a three note musical idea that is shown in four different textures this is monophony because it's a single line unaccompanied this is homophony because we have a melody line accompanied by chords this is polyphony because we have four different voices each doing their own thing yet they come together to form harmonies and this is heterophany because we have two different versions of the same melody counterpoint is an important idea in music theory and it was a revolutionary idea during the baroque period of music counterpoint is the combining of relatively independent musical lines counterpoint is the relationship between voices that are harmonically interdependent yet independent in rhythm and contour it focuses on the horizontal relationships and music johann joseph fuchs was a composer and a music theorist that wrote a treatise in 1725 titled graduates ad partisan this is considered the most influential counterpoint manual of all time and it taught counterpoint in the context of five different species one to one or first species counterpoint involves the contrapuntal voice or soprano line moving at the same speed as the conscious firmness or the bass line this counterpoint focuses on the sole use of consonances here we have an example of first species counterpoint here we have the intervals between the bass and the soprano listen and as you can see they're all consonant intervals there are some important types of counterpoint that you should be familiar with a canon is a contrapuntal procedure where the instruments or voices perform identical rhythms and contours yet the later sounding parts are offset by one or more beats a round is a type of canon that is perpetual in other words there is no notated ending for the ensemble imitative counterpoint is when similar melodic material is passed from one part into the next part the fugue is a compositional procedure where each voice states a short theme which is known as the subject and then it is fragmented developed and tossed about among the voices in the piece an important concept in total music is that the outer voices the soprano and the bass lines are essential to a piece of music and the inner voice or voices can be considered filler that fills in the gaps in our minds remember composers were focused on the combining of independent musical lines and the concepts of chords and harmonic progression came later on as a result nowadays it is important to be able to compose a good counterpoint while also keeping tonal progressions in mind let's go over how to write a basic unembellished bass line from a given chord progression first notate the bass line in root position based on the progression that you are provided with when it comes to range stay in the range of an e2 up to a c4 or middle c and try to avoid leaps larger than a fifth in the bass line if possible next you have to determine the chords that must remain in root position this includes the first and last chords of each phrase 5 in a 5 1 cadence and 6 in a 5 6 deceptive progression next you have to determine which chords must be used in first inversion this includes any diminished triads and either the 5 or 1 chord in an internal 5 1 chord progression finally you want to try to improve the base contour as much as possible and there are several ways to do this for starters avoid repeating bass notes especially across the bar line try to include one focal point which is the single highest or lowest point in the line also you can use first inversions to convert large leaps into smaller leaps or to try to achieve conjunct and stepwise motion in the baseline you are going to want to have tonal variety which means that you want to avoid over using any particular note if you have a large leap in the baseline change the direction of the baseline right after the leap and also before the leap if possible now you want to avoid the use of augmented intervals sevenths and compound intervals larger than an octave and the only diminished intervals that are generally going to be encountered are the diminished fourth and the diminished fifth in minor keys you're going to occasionally use the melodic minor in order to avoid having an augmented second in a rising stepwise baseline finally consider including cadential six four chords before the cadential dominant when you write your own chord progressions here's an example of a baseline and root position and an improved version of the same baseline now let's look at how to write a counterpoint to your simple baseline you want to make sure your melody has a good contour it should be more conjunct than disjunct make sure you have tonal variety and don't reuse certain pitches too many times do not use the same pitch more than twice in a row and do not repeat the same pitch across a bar line avoid having the melody pull too much in one direction you should have a clear simple and interesting melody line with a single focal point try to move toward and away from the focal point gradually be sure that the range of the contrapuntal voice is no less than a fifth and no more than the tenth always be sure to resolve the leading tone up to the tonic unless the melody line is descending in a stepwise manner when you are writing an ascending melody line in the minor mode use the melodic minor to avoid having an interval of an augmented second when moving from scale degree 6 to the leading tone avoid the use of augmented or diminished intervals sevenths or leaps that are larger than an octave however the descending intervals of a diminished fourth and a diminished fifth when they move to the leading tone are acceptable when you have a leap try to proceed and follow it with motion in the opposite direction however fourths can be preceded by motion in the same direction do not use more than two consecutive leaps in the same direction when you use two consecutive leaps in the same direction they should together span a fifth sixth or an octave when you do connect two consecutive leaps you should proceed and follow the pair of leaps by motion in the opposite direction when you are writing chord progressions with a bass line and a melody always take into account the beginning and the ending if you start with a tonic chord you can begin the melody on any note of the one chord if you start with a v chord you can begin the melody in any other v chord except for the leading tone always end each phrase with some sort of cadence and when you write a period always give the second phrase a stronger cadence than the first for now try to have the final chord land on beat one when you are practicing first species counterpoint always use chord tones consonant intervals especially thirds and six which are also known as imperfect consonances and try to avoid unisons unless they are needed at the beginning and or the end of the counterpoint here's a good example of first species counterpoint that you can look at to reference you always want to maintain relative independence between a contrapuntal voice and a baseline make sure you avoid using parallel and contrary perfect consonances you also want to avoid direct fifths and direct octaves remember if there are similar motion between voices into a perfect fifth or a perfect octave the upper voice needs to move by step for it to be acceptable be sure to use a variety of motion types try to use contouring motion the majority of the time parallel motion of imperfect consonances and similar motion are both good too use oblique motion if one voice repeats a pitch to avoid having complete static motion when you use parallel imperfect consonances which are parallel thirds and parallel sixths avoid using too many of them in a row do not allow voices to cross voice crossing occurs when the contrapuntal voice moves below the baseline here's an example of voice crossing because the contrapuntal voice here is singing a note that is lower than the bass lines note avoid overlapping this occurs when the base rises up above where the upper voice was in the previous chord or when the upper voice dips below where the bass was in the previous chord here are two examples of overlapping here the bass line is singing a note that is higher than the contrapuntal voices previous note here the contrapuntal voice is singing a note that is lower than the bass line's previous note so those are examples of overlapping finally avoid having both parts simultaneously leap in the same direction especially when they are leaps of a fourth or larger here's an example of simultaneous leaps when you are analyzing the two-part counterpoint that you wrote analyze the harmonic intervals that you have as you see here when you have a compound interval reduce it to its simple equivalent for example if you have a tenth analyze it as a third keep it simple counterpoint writing is a skill that needs time and practice to develop so be sure to practice writing bass lines and contrapuntal voices if you are looking to improve your counterpoint writing abilities non-chord tones are an excellent way for composers and songwriters to decorate their music a non-chord tone which is abbreviated nct is a tone that is not a member of the chord this tone can be diatonic or chromatic you need to analyze the chords in a piece of music before you can label the ncts when you do analyze noncore tones use parentheses and abbreviations to label them like you see here every non-chord tone is approached and left in a certain way with that in mind let's go over the various non-chord tones the passing tone is approached by a step and left by a step in the same direction you're passing through the neighboring tone is also approach by step but it's left by a step in the opposite direction think of it like visiting your neighbor and then going back home the suspension is when you have the same tone and then you step down and the retardation is when you have the same tone and then you step up we label suspensions retardations and their resolutions with the harmonic interval that they form with the base note to more specifically analyze them use simple interval numbers to label these ncts unless you have a suspension or retardation that actually involves an octave above the base in something like a 9 8 suspension or a 7 8 retardation look at this example we have a c major chord and we have an f in the melody c in the bass up to f and the melody in its most reduced form is a fourth this fourth results to a third so this is a 4 3 suspension here we also have a c major chord and we have a b in the melody c in the bass up to b in the melody in its most reduced form is a seventh and the seventh resolves up to the octave so this is a seven eight retardation the appoggiatura is approached by a leap and left by a step usually in the opposite direction the escape tone is approached by a step and then left by a leap in the opposite direction think of it like the landing on the moon one small step and one giant leap that's an escape tone the neighbor group is also known as a combiata or changing tones it involves two non-chord tones back to back it's approached by step then it's left by a leap in the opposite direction and then you step back the anticipation is approached by a step or a leap and then it's left by the same tone or sometimes a leap the most common version of the anticipation is a step and then the same tone you're anticipating this note you're getting there early the pedal point is a stationary pitch that begins as a chord tone then becomes a non-chord tone as the harmonies around a change and finally it ends up as a chord tone again when the harmony is once more in agreement with it pedal points usually occur in the bass part look at this example we have a c major chord then a g major chord with a c in the bass so that's a non-chord tone and then we have another c major chord the bass has the note c throughout the whole thing so that non-chord tone is a pedal point an inverted pedal point occurs in a part or parts other than the bass a double pedal point is a pedal point that contains two pitch classes we can also use other terms to more specifically describe non-chord tones for instance ncts can be accented or unaccented diatonic or chromatic ascending or descending and upper or lower there are a few important things to talk about with suspensions suspensions and retardations have three parts the preparation which is the tone that precedes the suspension the actual suspended note and then the resolution a bass suspension occurs when the bass voice is suspended and creates a second or ninth with an upper voice which results in a 2 3 suspension a suspension with change of bass is when an upper voice is suspended while the bass moves on to another chord tone at the same time that the suspension resolves again label suspensions and the resolutions based on the harmonic interval that they form at the base at any specific moment a suspension figure occurs when a chord tone is treated as though it were a suspension often this occurs in conjunction with how the seventh of a five seven chord is approached a chain of suspensions occurs when the resolution of one suspension serves as the preparation for another will often be indicated in the figure base for instance if you saw an example like this with a c in the base and the 4 3 figure based notation underneath it that is the same thing as 5 4 resolving to 5 3 root position triad so here we're going to have to note c f and g you go up a fourth and a fifth above your bass note and then the fourth will resolve down to the third making this a c major root position triad and that is a brief overview of non-chord tones now that we've covered the topics related to diatonic triads we will start looking at diatonic seventh chords starting with the five seven chord the major minor 7th is the most frequently encountered 7th chord and most of the time it is built on scale degree 5 which is why it is known as the dominant 7th remember in the minor mode we like to raise the 7th scale degree which creates a leading tone this results in a major 5 chord instead of a minor 5 chord so the dominant 7th chord occurs in minor modes 2. the 5 7 chord contains a tritone between the 3rd of the chord and the 7th of the chord because of the unstable tritone the five seven chord likes to resolve in a very specific way here are the principles to follow the seventh of the chord almost always resolves down by step the third of the chord which is the leading tone in the 5 7 chord almost always resolves up by step here's a trick that you can use look for the tritone in your chord and determine if it's an augmented fourth or a diminished fifth the augmented fourth will resolve outwards to a sixth the diminished fifth will resolve inwards to a third if you are resolving a root position five seven chord to a root position one chord you need to resolve the third and the seventh of the five seven chord properly if you follow the principles of having the seventh resolve down by step and having the third resolve up by step you will end up having an incomplete tonic triad with a triple root and a third there will be no fifth in this one chord this is perfectly fine as it allows you to avoid having parallel fifths let's look at examples here we're in the key of c major and we have five seven going to one in both scenarios so the chord progression is g seven to c this first example we have g d f b b is the third of the chord it resolves up a step to c f is the seventh of the chord it resolves down a step to e f to b is an augmented fourth the augmented fourth resolves outwards to a sixth and notice here in the one chord we have a triple root c c c and then we have the third of the chord which is an e let's look at the next example we have the five seven chord voiced differently we have g d b f b is the third of the chord it resolves up a step to c after the seventh of the chord it resolves down a step to e b to f is a diminished fifth the diminished fifth resolves inwards to a third and again we have a triple root c c c and the third of the chord which is the note e if you do want to resolve a root position 5 7 chord to a complete tonic triad and root position there are two methods that you can use one method is to use a complete 5 7 chord but put the third of the chord which is the leading tone in an inner part and frustrate its natural resolution the frustrated leading tone will resolve down to the fifth of the tonic triad the other method is to use an incomplete 5 7 chord with an omitted fifth and a doubled root also remember the v chord often moves deceptively to the sixth chord if you have a five seven chord that resolves to the sixth chord the voice leading will be very similar to that of resolving a regular v chord to the sixth chord you will end up having a double third or a frustrated leading tone inverted five seven chords are easier to resolve than root position five seven chords again just remember the principles of having the seventh resolve down by step and having the third resolve up by set in this case the five seven chords are able to resolve to complete tonic triads and finally make sure you remember the figured bass abbreviations that are used for seventh chords seven six five four three and four two you can add a seventh to any diatonic chord certain diatonic seventh chords will occur more frequently than others you'll want to keep the following principles in mind the seventh of the chord almost always resolves down by step the seventh of the chord may be approached in various ways any incomplete seventh chords must contain at least the root and the seventh and you should not double tones like the leading tone nor the seventh of a seventh chord supertonic sevens built on scale degree two are commonly encountered in tonal music this chord usually progresses to the v chord this chord is also most frequently seen in first inversion sometimes this chord is used as a substitute for the iv chord in a playful cadence a personal favorite quarter mind in the minor mode is the two half diminished seventh chord in first inversion which can also be thought of as a four added six chord this chord is often used as part of mode mixture and it has a really distinctive and beautiful sound to it as you'll learn about later on in the major mode the leading tone seventh is a half diminished seventh chord in the minor mode the leading tone seventh is a fully diminished seventh chord both chords usually resolve directly to the tonic or sometimes they change to a 5 7 by taking the seventh of the original chord down one step in the major mode you need to handle resolutions of this chord carefully to avoid parallel fifths this often means doubling the third of the one chord or revoicing the seventh chord so that you would end up having parallel fourths instead of parallel fifths in the minor mode this chord contains two tritones that want to resolve if you resolve the augmented force outward and the diminished fifths inward you will end up having a tonic triad that has a double third which is perfectly fine the subdominant seventh chord usually moves to a five chord or a seven diminished first inversion triad and it often passes through some form of the two chord on the way be careful when you're resolving this chord directly to a five chord because parallel fifths might result if the seventh of the chord is placed above the third of the chord you can correct this problem either with a cadential six four chord or with a v chord that has a doubled fifth sub median seventh chords will usually resolve to the subdominant or supertonic chord in the minor mode you might end up having a sharp six half diminished seventh chord that allows you to pass from a 5 chord to a 7 diminished triad if you add a 7th to the tonic triad this tonic triad will lose its stability the 1 7 chord usually moves to a four chord or sometimes a two chord or maybe even a six chord this chord can be very effective when it's handled well it has a very nice colorful sound to it the diatonic median seventh chord is most often encountered in sequences of seventh chords and it usually progresses to a six or a four chord if there is a circle of fifth sequence in music that involves seventh chords there are certain voice-leading conventions to follow when the seventh chords are in root position complete chords will alternate with incomplete chords as you see here in the following example if the seventh chords are inverted six five chords will alternate with four two chords and four three chords will alternate with root position chords this results in every voice either staying the same or moving down by a step and that is a basic overview of your diatonic seventh chords it's time to start talking about chromaticism in music chromatic notes are pitches that are foreign to the key of a musical passage chromaticism allows composers and songwriters to enhance their music and to add colors to it non-essential chromaticism refers to the use of notes from outside the key as non-chord tones essential chromaticism refers to the use of notes from outside the key as members of quartz which results in altered chords altered quarter chromatic chords are chords that use notes that are not found on the scale on which a musical passage is based we are going to look into some secondary functions a secondary function is a chord whose function belongs more closely to a key other than the main key of the passage secondary functions are used to tonicize different tones in your key tonicization is when there is a short shift of the tonal center and the shift is so short that we don't lose track of the original tonic or feel as though we've modulated consider the following question why is 5 or 5 7 to 1 such a strong chord progression there are several reasons behind this but one of the most important ones is that the third of a five or five seven chord is a leading tone that has gravitational pull to the root of the one chord which is a half step away now consider the two or two seven chord resolving to a five chord this chord progression also falls by a fifth why is it not as strong one reason is that the third of the two or two seven chord is a whole step away from the root of the v chord rather than a half step now think about this what if we raised the third of the two or two seven chord so that this note becomes a half step away from the root of the v chord and acts like a leading tone that brings us to the concept of secondary dominant chords a secondary dominant is an altered chord that has a dominant relationship to a chord in the key other than the tonic for example if we were in the key of c major and had a chord progression that went d7 to g the d7 is an altered chord that tonicizes g the d7 is a secondary dominant the roman numeral notation for secondary dominance is five or five seven slash and then another roman numeral goes in the blank here the slash represents the word of so you read this as 5 of or 5 7 of the roman numeral that goes in the blank is almost always the chord that follows the secondary dominant for example a 5 7 a 6 chord will typically resolve to 6 a 5 7 and 2 chord will usually resolve to 2. going back to this example we're in the key of c major we have a d7 chord that resolves to g well g is the five chord in the key of c so this chord would be a five seven of five five seven to five resolves to five basically this chord progression sounds like a five one progression in the key of g major but the actual passage is in the key of c major all the diatonic chords except for the tonic and any diminished chords may be tonicized by secondary 5 or 5 7 chords here are examples of secondary dominance and major and minor keys that you can look at to reference there are a few things that you should keep in mind about secondary dominance in major keys the five of four sounds and looks the exact same as a one chord because of this five seven of four is often used instead to make the secondary function clear five seven to four will have a chromatic note that allows the chord to tonicize the four chord in minor keys five of three or five seven to three sounds and looks the same as a subtonic 7 or 7 7 chord and also in minor keys 5 of 6 sounds and looks the same as the 3 chord and minor keys you're going to have to look at how the chord is functioning to determine if you're going to classify it as a diatonic chord or as a secondary dominant chord five seven of five is the most frequently encountered secondary dominant sometimes the five chord will be delayed by resolving first to a cadential six four in this example we have five seven of five and first it moves to one six four before moving to five but remember one six four and five together stands for five so this is perfectly acceptable and that's actually a common chord progression now sometimes when you have a secondary dominant it'll resolve to another secondary dominant for example if we're in the key of c major and we have a7 to d7 this would be analyzed as 5702 resolving to 5 7 of 5. now one more thing to keep in mind deceptive progressions occur when the v chord resolves to anything other than the tonic it's not just when 5 resolves to 6. if we had a chord progression where we had a five chord move to a five seven a four and then a four chord that's also considered a deceptive progression secondary dominants are widely used in classical jazz and popular music and these chords allow you to decorate your music and make your music a lot more exciting interesting and colorful you need to be able to spell and recognize secondary dominance in other words go from the roman numeral to the actual chord and go from the chord to the roman numeral if you have a roman numeral for a secondary dominant find the root of the chord that is to be tonicized then go up a perfect fifth and then spell a major triad or a major minor seventh chord depending on what's asked for finally make any inversion adjustments if necessary let's do an example let's say we're an e flat major and we're given five six five of six what are we tonitizing we're ton of sizing six six in the key of e flat major is c specifically c minor so that's what we're ton of sizing go perfect fifth above that note a perfect fifth above c gives you the note g now we have to build our chord six five in the figure bass tells us that we have a seventh chord so we have to build a major minor seventh chord on the note g that would give you the notes g b natural d and f which is a g7 chord finally we have to make inversion adjustments six five is a first inversion seventh chord that means that the third of the chord which is the b natural will be your lowest note so the final answer to this question is b natural d f and g which is g7 slash b that's how you answer a question like that one if you encounter an altered chord in the passage it could be a secondary dominant first check to see if the altered court is a major triad or a major minor seventh chord if it is it's probably a secondary dominant if you think you do have a secondary dominant check to see how this chord is functioning if it functions like a secondary dominant this chord will be followed by the chord that it's tonicizing if you have a secondary dominant first write five or five seven and a slash to start off your roman numeral indicate the correct inversion too then you're going to go a perfect fifth below the root of the altered chord figure out what scale degree that note would be in the key that you are in and what its try equality will be that will give you the missing part of your roman numeral let's do a practice example let's say we're in b minor and we have this altered chord first figure out the name of this chord we have a b d sharp f sharp that's a b7 chord in third inversion so it's a major minor seventh chord so that indicates it's probably a secondary dominant let's see if it's functioning like one if this chord is a secondary dominant we would expect this root b to follow perfect fifth a perfect fifth below b is e what chord do we have here we have g b e that's an e minor trident first inversion so the root b did fall perfect fifth to e so because it's functioning like a secondary dominant that's what it is so start off your roman numeral with five we're in third inversion so that's five four two and a slash now go perfect fifth below b that gives you e what is e in the key of b minor e in the key of b minor is four specifically minor four so this roman numeral would be five four two slash four and then finally what chord do we have here g b e is an e minor chord that's four in the key of b minor and we're in first inversion 54204 did resolve to four that's what we expected it to do so that's how we'd answer a problem like that one recall that the five and seven diminished chords have similar functions in tonal music thus any chord that can be tonicized by a v chord can also be tonicized by a seven diminished chord and this is why we have secondary leading tone chords a secondary leading tone chord or a secondary diminished seventh is a secondary chord that is the leading tone triad or seventh chord of the tonicized chord these are the roman numerals that we use for secondary leading tone chords if you have a secondary leading tone chord that is a seventh chord this can either be fully diminished or half diminished if you are tonicizing a major triad you can use either option if you are tonicizing a minor triad use the fully diminished seventh only here we have some examples of possible secondary leading tone chords here i only used fully diminished seventh chords again you're able to use half diminished seventh chords if you're tonicizing a major chord there are some things that you should note about these chords one is that the seventh diminished of three and the seven half diminished seventh of three and minor are similar to the diatonic 2 diminished chord and the diatomic 2 half diminished 7th chord respectively the context of these chords in the music will allow you to determine how they are functioning and how to best label them also we do not have a 7 half diminished 7 to 5 in the minor mode even though the 5 chord is major this exception results because the key of the dominant is minor even though the dominant triad is major a secondary leading tone chord will resolve the same way that a primary leading tone chord does the leading tone resolves up and the seventh resolves down you need to be careful with your voice leading in order to avoid doubling the leading tone when you resolve a seven diminished seven to five or a seven half diminished seven of five sometimes the secondary leading tone chord will resolve to a cadential six four finally you can embellish the five or five seven to six deceptive progression by adding a seven diminished seven of six in between the two chords to enhance your chord progression just like with secondary dominance you need to be able to spell and recognize secondary leading tone chords to spell a secondary leading tone chord first find the root the chord that is to be tonicized then go down a minor second or half step and then you want to use that note as the root of the diminished triad or diminished seventh chord that the roman numeral instructs you to build make any inversion adjustments if necessary let's do an example we're in g minor and we're given seven half diminished four three of six so we're taunting sizing six which in the key of g minor is e flat specifically an e flat major triad go a minor second below that note a minor second below e flat gives you d natural now we have to build our chord the roman numeral is telling us that they want a half diminished seven chord so we have to build d half diminished seven d half diminished seven contains the notes d f a flat and c natural remember half diminished seven chords contain a minor seventh finally make any inversement adjustments fourth three in the figured bass tells us that we have a second inversion seventh chord where the fifth of the chord will be the lowest sounding note so your final answer in this case will be a flat c d and f and your lychee symbol might look something like this that's how you would answer a problem like that one if you find an altered chord in the passage and it is not a secondary dominant it could possibly be a secondary leading tone chord first check to see if the altered chord is some type of a diminished triad or a diminished seven chord if it is it is quite possibly a secondary leading tone chord if you think you do have a secondary leading tone chord check to see if this chord acts like and functions like a secondary leading tone chord would remember most secondary leading tone chords are followed by the chord that they are tonicizing if you have a secondary leading tone chord first write seven diminished of seven fully diminished seven of or seven half diminished seven enough to start off your roman numeral depending on what you have be sure you indicate the correct inversion then go a minor second above the root of the altered chord find out what scale degree that note would be in the key that you are in and what its triad quality would be that will give you the missing part of your roman numeral let's do an example let's say we're in g major and we see this chord d sharp f sharp a c natural that is a d sharp fully diminished seven chord in root position because we have an altered chord and it's also a fully diminished seven chord this indicates that it's probably a secondary leading tone chord let's see if it functions like one if it is a secondary leading tone chord we would expect the root of d sharp to resolve up a half step to e what chord do we have here we have an e minor triad so indeed this is a secondary leading tone chord so start off your roman numeral with seven this is a fully diminished seven chord in root position so it's diminished seven of what do we have here e minor in the key of g major is your sixth chord and six in a major key is a minor triad so we're tonicizing six so that's the missing part of your roman numeral this chord is a seven fully diminished seven of six and that's how you solve problems involving secondary leading tone chords let's go over a few more advanced concepts regarding secondary functions you can use a long bracket as an abbreviation for longer thomasizations for example if you have several chords back to back that are all ton of sizing five you can put a bracket underneath all the chords and write of 5. sequential patterns in music often use secondary functions the circle of fifth sequence is a common sequential pattern and now you can substitute secondary functions for diatonic chords for example if you're in the key of c major and you have a d minor seven to g chord progression that's two seven to five now you can substitute a d7 which is a five seven a five or an f sharp diminished seven which is seven diminished seven of 5 and place it a d minor 7 chord these are both secondary chords that tonicize the next chord which is 5 or g major you can have deceptive resolutions of secondary functions for instance the 5 or five seven chord might resolve up to the sixth of the chord that was being tonicized let's look at an example let's say we're in the key of c major and we see an e major chord resolving to an f major chord the e major chord you would label as a five of six the f major chord at first glance you might just say is a diatonic iv chord but here that's not how it's functioning here it's functioning as a six of six we have a five six deceptive resolution that tonicizes six so that's the better way to analyze this you might come across other secondary functions that are less common for example we have secondary subdominance which are four of chords there are even secondary medians and secondary subtonics you might encounter secondary supertonics which are two of chords let's look at a chord progression that has this example let's say we're in key of f major and we have this chord progression the f major chord we would label as one the d minor chord we would label as six the a major chord we would label as a five of six so what about this chord we have an e diminished triad at first glance you might say that's seven diminished but seven diminish wouldn't resolve to five of six or six the best way to analyze this is two diminished of six you have a two five one chord progression that time of size is six so that's an example of a chord progression that uses a secondary supertonic and that is an overview of secondary functions let's start talking about modulation most tonal compositions and songs begin and end in the same key however it is common for there to be a key change either in the middle of the music or between movements of a composition change of key refers to a shift of the tonal center that takes place between movements of a composition modulation is a shift of the tonal sensor that takes place within an individual movement it is a change from one tonality to another sometimes it is a challenge to distinguish between tonicization and modulation time is the most important factor in convincing a listener of a modulation elements like a cadential 6-4 and the new key also play a role in making a modulation clear before going into more detail about modulation let's go over key relationships since this is an important concept related to modulation and harmonically equivalent keys are keys that sound the same but are spelt differently for example c sharp major and d flat major there is no modulation between these types of keys because the keynote is unchanged parallel keys are keys that share the same starting note for example c major and c minor parallel keys share the same tonic so we do not use the term modulation when a key moves to its parallel instead we refer to this as a change of mode related to this is mode mixture which is the use of tones from one mode in the passage that is predominantly in the other mode relative keys are keys that share the same key signature for example c major and a minor you can use the term modulation here because there is a shift from one tonic to another closely related keys are keys to have a difference in no more than one sharper flat between their key signatures the majority of modulations in tonal music are between closely related keys if we start with c major these are your closely related keys to c major c major has no sharps and no flats a minor has the same key signature g major and e minor both have one sharp f major and d minor both have one flat so there's a difference of one sharp or one flat between the key signatures there are tricks that you can use to determine closely related keys one way to do this is by taking the keys represented by the tonic subdominant and dominant triads and their relatives for example if c majors are tonic a minor is the relative of c major g major is the dominant and e minor is its relative and f major is the subdominant and d minor is its relative another way to do this is to take the keys represented by the diatonic major and minor triads of the home key so build all of your diatonic triads in the key of c major and ignore the diminished chord this gives you a closely related key to c major we have c major d minor e minor f major g major and a minor so figure out a trick that works for you so that you can figure out your closely related keys foreign relationships refers to key relationships that are not enharmonic parallel relative or closely related distantly related keys are keys to have a difference of more than one sharper flat between their key signatures for example c major and e flat major there are many different ways that you can go about describing modulations between distantly related keys for example a modulation from c major to e flat major can be described as a modulation to the relative major of the parallel minor a modulation from c major to d major can be described as a modulation to the dominant of the dominant so there are different ways that you can describe modulations common core modulation allows a composer to smoothly blend from one key into the next this type of modulation involves the use of one or more chords that are diatonic in both keys as a pivot that links the two tonalities together common core modulation is easier to do when it's between closely related keys for foreign keys an altered chord might need to be used as a common chord let's say you wanted to modulate from c major to g major using common core modulation here are the possible diatonic triads in c major and the possible diatonic triads in g major any of the chords that are boxed in are the possible diatonic chords that can be used as the pivot chord it's usually best to avoid using 5 or 7 diminished as a common chord since modulations that involve these chords sound quite abrupt however you can use things like a deceptive progression and or a cadential 6-4 to delay the 5-1 progression in a new key make sure you are familiar with how common core modulations are notated in a roman numeral analysis when you have the common chord we use this symbol and we indicate what the chord is in the original key and what the chord is in the new key when you're looking for a common chord first you want to find the point of modulation this is the first chord that seems to be functioning more naturally in the second key than in the first one this chord usually contains an accidental that is not found in the first key or it is a tonic six four chord in the second key you're going to back up one chord from the point of modulation and this should be where you encounter a diatonic common chord let's look at this example this chord progression modulates from c major to g major using common core modulation and we're going to do a roman numeral analysis first you want to find the point of modulation what chord seems to be functioning more naturally in g major than in c major that would be this chord the d7 chord in second inversion now you're going to back up one chord from this one that gives you the a minor chord that means that this a minor chord is going to be our diatonic common chord a minor belongs both in the key of c major and in the key of g major so because this is where we have our common chord that's where we're going to put our symbol that indicates we have a modulation and we're modulating to g major so we've got to write our new key here now let's do the roman numeral analysis so we're starting in c major we have one g major is five c is one d minor with f in the bass is two six a first inversion triad g is five a minor that's our diatonic common chord in c major a minor is your six chord in g major a minor is your two chord you have to notate what the chord is in both the original key and the new key d7 slash a so d7 in the key of g now we're in the key of g d seven is five seven and we are in second inversion so this is five four three g in the key of g is one d seven in the key of g is five seven and then g in the key of g is one and that's how you would do a roman numeral analysis of something like this the final thing to note is that it's fairly common for the key signature of the main tonality to be maintained throughout a piece no matter how many modulations occur let's go over some other modulatory techniques it isn't uncommon for altered chords to be used as common chords these include secondary dominance and secondary leading tone chords let's look at this example we're starting in g major and we're modulating to d major the a7 chord is the point of modulation it's the chord that belongs more naturally in the second key however the chord before it which is a minor is not a diatonic common chord in both g major and d major so we're going to take the a7 chord and make that our common chord this is a five seven of five in the key of g major which is an altered chord and a five seven in the key of d major modulations sometimes come about through the use of a sequence this usually involves the composer stating a musical idea at one pitch level and then stating it again immediately at another pitch level let's look at this example we're starting in c major and we have this chord progression of one five four two of five to five then we see the exact same chord progression of one five four two five five in the key of b flat major this is sequential modulation because we're taking a musical idea and we hear it immediately at another pitch level the circle of fifths progression can be used to get from one key to another with a sequential progression such as in this example sometimes the hinge between two keys will be a common tone when this type of modulation occurs the comma tone is often isolated let's look at this example we're in c major and we're modulating to e flat major there's no diatonic common chord that both keys share however both keys have the note g natural here the note g natural is isolated this is scale degree 5 in the key of c major and scale degree 3 in the key of e flat major this note lets us blend from c major to e flat major smoothly and that's an example of modulation by common tone two chords that are linked by a common tone in a common tone modulation usually have what's known as a chromatic medium relationship a chromatic mediant relationship is the relationship between two major triads or two minor triads with roots a minor third or a major third apart both triads are either going to be major or minor here we have examples of chromatic medians to c major c major and e flat major c major and e major c major in a major and c major and a flat major sometimes a modulation will be carried out by a single vocal or instrumental line in what's known as monophonic modulation harmonies are usually implied and the listener will hear tones introduced that emphasize the second key more than the first finally direct modulation is a type of modulation that does not use common chords common tones or sequences these modulations usually occur between phrases and this results in a phrase modulation a possible indicator of a phrase modulation is when you have a fermata that ends a phrase and you find yourself immediately in a new key before labeling a modulation as a direct modulation try to eliminate all the other possibilities and that concludes our discussion about modulation it's time to go over larger forms binary form consists of two approximately equivalent sections although they may be unequal in length balanced binary form is when the two parts are of equal length and unbalanced binary form is when the two parts are not of equal length ternary form is a three-part form that is structured as statement contrast return this form includes a starting section a middle section that provides contrast and a third section that returns all or most of the first section let's go over some terms that apply to both binary and ternary forms sectional refers to a type of binary or ternary form where the first section ends on the tonic triad in the main key of the form continuous refers to a type of binary or ternary form where the first section ends with any chord other than the tonic triad in the main key of the form to reprise form refers to a movement or theme that consists of two repeated sections if you have two sections each with a repeat sign this is an indicator of two apprised form sometimes the repeat will be written out the minuet and trio is a sectional turn to reform because the minuet is played both before and after the trio the american popular ballot form is a sectional ternary pattern that many popular songs of the 20th century adhered to rounded binary forum is a form type in which the opening a section returns after contrasting material but in an abbreviated form this is also known as miniwet form or even a small ternary form the 12 bar blues is a forum type that typically consists of three four bar phrases here is the most basic harmonic pattern for the 12 bar blues also note that blues music often mixes the major and minor modes some terms that you'll also want to know are transition and coda transitions are passages that connect different themes or tonal centers a coda is a concluding section that can be used with any formal types an important topic to discuss is sonata form sonata form is basically a greatly expanded two rupees continuous ternary form sonata form consists of three sections the exposition the development and the recapitulation this form is also known as sonata allegro form there are many things to discuss about the sonata the exposition will present the important themes and it will involve tonal conflict between the two most important keys of the sonata it will have two tonal centers which means it modulates to a secondary key the development either develops off of the exposition's themes features sequential activity or introduces a new theme this section might move to some distant keys before preparing to return to the home key there is a term known as false recapitulation this refers to material that suggests the arrival of the recapitulation but that appears in the wrong tonal location toward the end of the development section the recapitulation will replay the sonata's important themes but it doesn't modulate to the secondary cape the sonata has a home key which is the primary tanaki of the movement and a secondary key that provides tonal contrast when the home key is major the secondary key is often the key of the dominant when the home key is minor the secondary key is often the key of the relative major sonatas also contain themes throughout primary themes establish the home key with at least one cadence in that key there is a destabilizing transition section between the primary and secondary themes that destabilizes the home key and allows the music to move to the secondary key modulating transitions commonly occur the secondary theme sets up the total contrast in the x position by establishing a secondary key by confirming it with a perfect authentic cadence in that key when you are in the recapitulation section the secondary theme will reconfirm the home key rather than the secondary key finally there will often be a closing section that ends expositions and recapitulations that is a very brief and basic overview of sonata form rondo form is a type of form that involves a refrain or return yellow theme that returns several times and it alternates with contrasting thematic material known as episodes here are the four common types of rhonda form rondo form is a type of form that involves a refrain or returnello theme rondo form is a type of form that involves a refrain or returnello that returns several times alternating with contrasting thematic material known as episodes here are the four most common types of rhonda form that you will encounter the final a section of a rondo is often treated as a lengthy coda sonata rondo form combines elements of rondo form and sonata form sonata rondo form resembles a sonata with an extra return of the primary a theme after the exposition and another after the recapitulation it is different from the seven part rondo in that it develops earlier material in the c section and that is a general overview of larger forms in tonal music let's talk a little bit about popular music this includes broadway show tunes 10 pan alley songs jazz standards folk music parlor ballads and the blues first let's go over the different sections and elements of a popular song that are commonly encountered a riff is a repeated instrumental motive a refrain is the section of a song that recurs with the same music and text a lot of songs contain an introduction the verse is the section of a song that returns with the same music but different text it's the storytelling part of a song the chorus is the section of a song that is repeated each time with the same or a similar text and the chorus often contains the song's hook which is the most catchy or memorable part of a song many times the hook contains the title of the song the pre-chorus is a short passage of music with text that comes between the verse and the chorus and the post chorus is a short passage of music following the chorus that prepares for the return of the verse an instrumental break is an instrumental section in the middle of a popular song where several instruments are featured a solo break is an instrumental section in the middle of a popular song where one instrument is featured an instrumental interlude is a passage with new music that serves as a transition between or a change of pace from other sections the bridge is a contrasting section in popular music that prepares for the the bridge is a contrasting section in popular music that prepares for the return of the chorus the build is an increase in intensity that anticipates the chorus the drop is the return of the full texture in the chorus of a popular song finally many popular songs have a coda which is the concluding and ending section of the song let's go over some additional elements of popular music extensions are pitches that are added to a triad or seventh chord these include the added six added ninth added eleventh and the added thirteenth power chords are chords that feature only the root in the fifth they are missing the third for example a c5 is a power chord that contains the notes c and g these chords are often played by electric guitars and they typically move in parallel motion we also have sus chords the sus 4 chord is a chord with a fourth above the bass instead of a third the fourth does not necessarily resolve we also have sus 2 chords a c sus 4 chord contains the note c f and g and a c sus 2 chord contains the note c d and g the blues scale is a collection of notes from which performers can choose when improvising a blues melody these include scale degrees 1 lowered 3 4 raised 4 or lowered 5 5 and lowered seven because the blues scale contains the minor moodle scale degrees of lower three and lower seven it blurs the distinction between major and minor when it is used as the basis for improvisation against a major key blues progression a shuttle is the alternation of two chords in a popular song and a loop is when there are three or more chords that are repeated in the same sequence and harmonic rhythm finally let's go over some common song forms of popular music quaternary song form is a song form consisting of four usually eight bar phrases the first two phrases begin the same they may be identical or they may differ at the cadence they are followed by a contrasting section or bridge and then a return to the opening material this is also known as 32 bar song form or aaba form first refrain form is a typical form of early 20th century popular songs and where an introductory verse that is possibly modulatory precedes a chorus that is often in quaternary song form simple verse form is a song form that only has verses verse chorus form is a songwriting structure built around two repeating sections which are the verse and the chorus this is the most common form for songs today simple verse chorus is a song form where the verses and the choruses have the same music contrasting verse chorus is a song form where the verses and choruses use different music here is a very common song form that many songwriters use when writing popular music now it's time to talk about one of my personal favorite topics in music theory mode mixture which is also known as modal interchange this is an excellent way to provide more color to a musical passage mode mixture refers to the use of tones from one mode in a passage that is predominantly in the other mode in other words if you are in a major key mode mixture is when you borrow tones and chords from the parallel minor key and vice versa borrowed chords are chords that result from the use of mode mixture these chords will contain tones from the mode opposite the mode that you are currently in first let's go over the borrowed chords in minor remember scale degrees 3 6 and 7 are what differentiate a major scale from a minor scale minor keys offer fewer opportunities for colorful and surprising changes of mode because there are two versions of scale degrees six and seven that are commonly used in minor pieces of music you can use the unaltered six and seven scale degrees or the ray six and seven scale degrees remember how we raised the 7th scale degree in the minor mode which results in a major 5 chord and a 7 diminished chord as a result we can say that the 5 and 7 diminished chords are borrowed from the parallel major if we are in a minor mode and we raise the third scale degree to borrow it from the major mode one of the possible chords that we end up with is known as the pickerty third this is simply a tonic triad that is borrowed from the major mode for use in minor composers and songwriters would often use this to end their pieces that were in minor keys it provides a nice contrast and a resolution to end the musical work the pikerty third is indicated by an uppercase roman numeral one if you are in a minor key and you see an uppercase roman numeral one you know that this is a picker d third now let's get into borrow chords and major if we take the lower third sixth and seventh scale degrees from the minor scale we attain many possible borrowed chords that we can use most borrow chords in major involve the use of the lowered sixth scale degree remember the flat simply means to lower that scale degree not to literally add a flat the four commonly used borrowed chords that result from the lower sixth scale degree are seven diminished seven minor four two diminished and two half diminished seven two half diminished seven can also be analyzed as a minor iv chord with an added sixth when this chord is followed by a major one chord it creates a darker type of plagal cadence sound when you use the lower third scale degree some of the commonly used borrowed chords are minor one flat six and minor four seven and when you use the lowered seventh scale degree you get chords like flat 3 and flat 7. notice that the roman numerals for the borrowed median submediant and subtonic triads are preceded by a flat this indicates that the root is lowered you need to use the flat in your analysis regardless of the actual accidental that is found in the notation for example if you're in the key of a major and you have a flat six chord this is an f major triad and the root of this chord is an f natural a commonly used chord progression that is used to end pieces of popular music is flat six flat seven major one this is known as an aeolian cadence by using mode mixture and pieces of music songwriters and composers are able to enrich their melodic and harmonic palette with more expressive possibilities and they're able to add all sorts of amazing colors to their compositions the dominant chord can be approached in various ways one way that it can be approached is by the colorful neapolitan chord this chord is a major triad that is constructed on the lowered second scale degree for example in the key of g major and in the kia g minor the neapolitan chord would be an a flat major triad when you're analyzing music this chord is abbreviated with the letter n or a roman numeral flat 2. the flat doesn't literally mean you're going to have a flat it simply means you're going to lower the second scale degree and build a triad off of that this chord is most often found in the minor mode and it's usually in first inversion which is why it is often referred to as the neapolitan vi chord here are some important characteristics about this chord this chord has predominant function when you include this chord as part of a four part arrangement it's usually best to double the third of the chord the neapolitan six chord likes to move to five or five seven sometimes a secondary seven diminished seven of five will appear in between the two chords the neapolitan six chord also likes to resolve to the cadential six four in this case you need to use parallel fourths to avoid parallel fifths the goal of the lowered second scale degree is to resolve to the leading tone finally this chord is usually preceded by six four or one let's look at an example let's say we're in the key of c minor and we have a neapolitan six moving to five seven and then to one the neapolitan six chord is a d flat major triad in first inversion so f will be in the bass this chord will contain the notes d flat f and a flat and we're going to try to double the note f which is the third of the chord here is a good voicing of the chord f f a flat d flat remember the lowered second scale degree wants to resolve to the leading tone so d flat is the lower second scale degree in the key of c minor d flat is going to move down to the leading tone which is b natural this is how you would resolve this neapolitan six chord sometimes the neapolitan chord might be tonicized an example of this would be a 5 7 of the neapolitan keep in mind that borrowed chords and the neapolitan can be used as common chords in their modulation this can make it easier to smoothly modulate to a distantly related key borrowed chords and a neapolitan chord are excellent ways for composers and songwriters to add some more color to their music a tritone substitution is an example of a chord alteration that is used in music especially in jazz performance the tritone sub replaces a five seven with a major minor seven chord that is a tritone away this chord is basically a neapolitan chord with a minor seventh added this chord can be indicated as flat 2 7 5 7 a flat 5 flat 5 7 of 5 or even a sub 5 7. the tritone sub works because its tritone contains the same enharmonic pitches as the tritone of the respective five seven chord that it's substituting for look at this example we're in c major and we have the five seven chord next to the tritone sub in the 5 7 chord the tritone contains the notes f and b in the flat 2 7 chord the tritone contains the notes f and c flat so the tritone in the two chords is n harmonic when the tritone sub resolves to a one chord it will not follow the typical principle of the seventh resolving down and the third resolving up instead the tritone of this chord will resolve the same way that the tritone of the five seven chord it is substituting for will resolve also it's common to add a sharp 11 to the tritone sub because that note is the root of the original 5 7 that it substitutes for it also allows you to avoid parallel fifths if you put it in place of the fifth of the tritone subchord take a look at this example we have a tritone sub chord resolving to a one chord in the tritone sub chord we have the notes d flat f g which is the sharp 11 that's replacing the fifth of the chord and c flat this tritone is going to resolve the same way that the 5 7 chords tritone would be natural would resolve up a half step to c and f resolves down a half step to e here c flat which is n harmonic to b natural is going to move up a half step to c natural f is going to move down a half step to e g which is the sharp 11 is going to stay as a common tone and d flat is going to move down a half step to c natural tritone substitution is another option that musicians and composers have to make their music stand out and to add some more color to it approaching a tone by a half step is a good way to emphasize it if we approach the dominant scale degree by half steps from above and below at the same time this results in a strong approach to the dominant these two approaching tones will form an interval of an augmented sixth augmented sixth chords contain the interval of an augmented sixth which is formed by simultaneously playing the tones that are a half step above and below the dominant scale degree this gives you the lowered sixth scale degree and the raised fourth scale degree this predominant chord approaches the v chord or the cadential six four usually the lowered sixth scale degree will appear in the bass and the raised fourth scale degree will appear in an upper part there are a few specific types of augmented six chords the italian augmented six chord is formed by adding scale degree one to the augmented sixth interval in a four part texture the tonic pitch will be doubled the french augmented sixth chord is the same as the italian augmented six chord but with an added scale degree 2. this chord sometimes occurs in popular music and in jazz music it's a major minor 7th chord with a lowered 5th the german augmented 6 chord is the same as the italian augmented 6 chord but with an added lower third scale degree flat three simply means that you are taking the third scale degree from the minor mode in a minor mode this note occurs naturally in a major key this note will be chromatically lowered it isn't uncommon to encounter parallel fifths when the german augmented six chord moves directly to the v chord however these parallels aren't considered objectionable because the ear is too focused on hearing the resolution of the augmented sixth sometimes you might see the german augmented six chords spelled differently you might see a raised second scale degree instead of a lower third scale degree when this chord moves to a cadential six four this is because when we read music we tend to expect raised notes to ascend and lowered ones to descend also note that the german augmented 6 chord is enharmonic to the 5 7 of the neapolitan you might encounter german augmented 6 chords in lead sheet symbols they will be indicated as a major minor seventh chord on the minor sixth scale degree for example in the key of c major a flat seven to g seven is a german augmented six chord resolving to five seven the a flat seven chord is a tritone substitution for five seven of five because augmented six chords are linear sonorities that don't have a root they technically cannot be inverted as a result the base position of these chords does not need to be indicated in the analytical symbol one final thing to note is that the augmented six chord can result to other scale degrees besides five when we write an augmented six chord we are basically implying that the augmented six is going to resolve to scale degree five if you have an augmented six chord that resolves to something other than scale degree five you should indicate what scale degree the augmented sixth is resolving to let's go over enharmonic spellings and then harmonic modulations and harmonic spelling involves writing a note as its enharmonic equivalent this technique is used by composers to indicate in which direction a pitch will move this makes it easier to read the music remember raised notes usually ascend and lower notes usually descend spelling changes might change the chord visually but it doesn't change the sound function or analysis of the chord sometimes a composer might respell an entire key to make it easier to read for example if f-flat major is tonicized in the middle of a piece the composer might notate it in the key of e major another example would be if a piece in g-flat major moved to its parallel minor instead of writing the minor section in g-flat minor which would have double flats it could be notated as f sharp minor which has three sharps they're both enharmonically equivalent enharmonic reinterpretation is the technique of treating a chord as if it were spelled in a different key as part of a modulation there are four scenarios that are used in tonal music that can be reinterpreted and harmonically in a different key the major minor 7 chord can serve either as a 5 7 or a german augmented the major minor 7 chord can serve either as a 5 7 chord or as a german augmented 6 chord the fully diminished 7th chord is symmetrical where every note is 3 half steps away from the next as a result any tone can serve as a leading tone for example g sharp diminished 7 is enharmonic to e sharp diminished 7 which is enharmonic to d diminished 7 which is n harmonic to b diminished 7. they may be spelled differently but they sound the exact same the augmented triad is also symmetrical where every note is two whole steps away from the next as a result any tone can serve as the root for example c augmented is n harmonic to e augmented which is enharmonic to g sharp augmented or a flat augmented finally you can respell both notes of one of the major thirds of a french augmented six chord to convert it to a different french augmented six chord and this allows you to modulate to a key that is a tritone away enharmonic modulation is a modulation in which a chord that is common to both keys is reinterpreted and harmonically to fit into the new key here is an example of an n harmonic modulation from f major to a major take this chord the five seven of four an f major that contains the notes f a c e flat let's reinterpret this chord so that we can move to a major we can respel that chord as f a c d sharp now this chord is a common chord in f major and a major it sounds like a 5 7 of 4 in f major but it's literally spelled as a german augmented sixth chord in a major this chord now allows us to modulate from f major to a major because it's enharmonically reinterpreted if you are analyzing a piece of music and you encounter two chords that sound the same but are spelt in two different ways that is a sign that the chord is functioning in two different ways make sure you are wary when you encounter chords in music that can be enharmonically reinterpreted there are some aspects of tonal harmony that are less fundamental yet still important to go over around the time of impressionism added no chords became a standard part of the vocabulary of western music for example a triad with an added sixth let's say you have the following chord progression in c major the first chord contains all the notes of a two six five chord however the seventh doesn't resolve the way a seventh typically would instead this chord is functioning as a four chord with an added six and this chord resolves to 1 through a pagal cadence we also have the 5 subsets chords which contain the same scale degrees as those found in a 3 6 chord however these chords have dominant function if you use a five or a five seven chord with a substituted sixth the sixth should leap down to the tonic in other words scale degree three resolves to scale degree one we also have dominant chords with a raised fifth this results in an augmented triad or an augmented minor seventh chord these are known as augmented dominant chords by using the raised fifth this creates a leading tone to the third of the tonic triad when in a major key remember approaching a tone by a half step is a good way to emphasize it look at this example in c major we have the five augmented chord that contains the notes g b d sharp g stays as a common tone b is a leading tone to c and a d sharp is acting like a leading tone to e also although the five augmented or the five augmented seventh in the major mode is n harmonic with the five sub six or five seven sub six in the minor mode they have different resolutions secondary dominance can also appear in augmented form the most common is the five augmented a4 or the five augmented seven of four in tonal music thirds are stacked to produce triads and seventh chords if we continue to stack more thirds to a seventh chord we end up with ninth chords eleventh chords and thirteenth chords we notate a major ninth as nine and a minor ninth as flat nine when a ninth would be used in a tonal era it would often disappear before the chord it is part of resolves for example if you have a five flat nine chord which is a five seven chord with a minor ninth the ninth would likely resolve down a half step to double the root of the v chord 11th chords and 13th chords became more prominent around a time of impressionism figured bass symbols for all these extended chords wouldn't be very practicable especially since inversions of these chords are not as common as inversions of triads and seventh chords if you want you can use parentheses to indicate the inversion of the seventh chord part of the entire extended chord the majority of diminished seventh chords function as leading tone sevens however there is a diminished seventh chord that functions in a different way the common tone diminished seventh chord is a diminished seventh chord that shares a tone with the root of the chord that it embellishes this chord is basically used to expand another chord we label this chord as c t diminished 7. this chord may be spelled in any manner which means it has no theoretical root the function of this chord is simply one of embellishment and it has weak harmonic function as a result when you include this chord in a roman numeral analysis it is usually put in parentheses to indicate that it has weak harmonic function this chord usually embellishes and progresses to 1 in major or 5 or 5 7 in major this chord also usually acts as a neighbor chord or a passing chord if you are reading a lead sheet and you encounter a diminished seventh chord that seems to resolve incorrectly see if it shares a tone with the root of the chord before and or after it if so it is probably a common tone diminished seven chord finally the common tone diminished seventh chord that embellishes the tonic is n harmonic to seven diminished seven to five so you have to check to see how the diminished seventh chord is functioning and resolving before deciding how to label it composers of the late 19th century and early 20th century saw chord progressions where the chords had close relationships with each other mediants are a good choice for this remember diatonic triads with roots a third apart have two common tones the chromatic median relationship is the relationship between two major triads or two minor triads with roots a minor third or a major threat apart for example a c major triad and an e flat major triad these chords do not belong to the same diatonic collection here we have examples of chromatic medians to the c major triad the doubly chromatic media relationship is a relationship between chords that have roots a minor third or a major thread apart they are of opposite modes and they share no common tones for example c major triad and an e flat minor triad here we have examples of double chromatic medians to the c major triad these chords can be enharmonically a major throw to part for example an a flat major triad and an e minor triad because the a flat major triad is enharmonic to the g sharp major triad chromatic median progressions allow for very smooth voice leading connections these chords are often used as part of common tone modulations when analyzing late 19th century and early 20th century pieces of music music theorists will often look at the total voice leading distance which is determined by adding together the total number of half steps that each voice moves from the first chord to the second this measures the smoothness of the voice leading motion between one chord and another chromatic mediant relationships are used to move from one transitionality to another to temporarily blur the sense of a prevailing key and to use a method for composing chord progressions other than the circle of fifths musicians might consider a lot of the topics on chromaticism to be things that complicate the harmonic system however there is one main tendency that can summarize most of these chromatic elements a lot of chromaticism is used to intensify the sense of resolution from one chord to another by narrowing the distance between pitches in a given line for example using a five of five chord in place of a two chord in a two five one progression brings scale degree four closer to scale degree five also if you have the chord progression minor 4 to major 1 which involves mode mixture this brings scale degree 6 closer to scale degree 5. once the late 19th and early 20th centuries arrived many compositions began to add in complexity and they resist easy comprehension there is less focus on the harmonic progression and more focus on exploring the entire collection of chromatic pitches and using conjunct linear motion and smooth voice leading between chords if there is a passage that doesn't allow the listener to feel secure in any particular key it is better to use lead sheet and base position symbols instead of roman numerals when labeling chords roman numerals are mainly used in tonal harmony to indicate the function of various chords in a passage if you repeat the same chromatic media relationship a few times it will return to the same chord from which it started this is known as a median chain for example if you start with a c major triad you can move from c major to e flat major to g flat major which is n harmonic to f sharp major to a major and then back to c major major minor seventh chords can be used in a minor third median chain and this version will create two common tones which results in very smooth voice leading you see that in this example here where we move from an e flat seven chord to a c7 chord here we have two common tones surprisingly moving from a major minor seventh chord to another major minor seventh chordae tritone away can be smooth as well in this example we're moving from c seven to g flat seven here the note e natural is enharmonic to f flat so we basically have two common tones in music we also have what's known as a third substitute which is a chord that can be used in place of another chord whose root lies a third away as long as it shares two common tones and a common function with the chord it is substituting for for example six can substitute for one two can substitute for four and even three can substitute for five sometimes during the late romantic period of music composers began to use familiar chord types while exploring new possibilities for harmonic progression outside of the traditional diatonic system simultaneity refers to traditional sonorities that are used in a non-traditional manner again using roman numerals for such chords might not provide much insight into what is happening behind the progression that is occurring when it comes to advanced tonal writing you can basically connect any two chords together that you want in a smooth manner as long as you incorporate inversions don't limit yourself to the diatonic collection and don't restrict yourself by the traditional preparations and resolutions of dissonances many late romantic composers made wide use of sequences a chromatic sequence is a diatonic sequence that is transformed by substituting chromatic harmonies for diatonic ones or by chromatic embellishment for example we can have a sequence that keeps moving up by whole steps such as c sharp major to d sharp major which is then harmonic to e flat major to f major to g major and then to a major there were composers who would include chromatic bass lines in their compositions and they would use familiar chord types above the bass lines to harmonize them an omnibus is a progression that is used to harmonize a chromatic baseline many times an omnibus progression features voice exchange it is usually best not to analyze every different chord combination that occurs in an omnibus progression for example here we're in c major and we basically have a 5 7 chord that is embellished through a chromatic bass line that moves to a 5 6 5 chord instead of analyzing these three chords as a german augmented 6 chord 1 6 4 and another german augmented six chord in d minor it is best to just consider this all a five seven chord that leads to a five six five chord and those are just a few of the advanced techniques and concepts behind tonal harmony from the later part of the common practice period around the turn of the 19th century into the 20th century composers became aware that the traditional tonal system was being stretched to its limits as a result they saw alternative methods and concepts to go about composing and arranging music some elements that they thought about modifying included scales chord structure harmonic succession rhythm and meter and even musical texture post-tonal music is considered music that has been composed since the general decline of tonal harmony around 1900 an important part of post-total music is impressionism impressionism is a term that was originally applied to a style of painting that began in france in the late 19th century around this time composers became more fascinated with color mood and atmosphere and emotions and they sought to depict these things in their music through new uses of harmony instrumentation and rhythm as a result the term impressionism was also applied to music a lot of early post-tonal music is still easily accessible to the tonally oriented ear however the compositional style of early post-tonal composers such as claude wc and maurice revell defy the traditional tonal expectations when it comes to analyzing early 20th century pieces of music music theorists look into the piece to see if it has a tonal center or centers and then they ask themselves how is this accomplished or avoided we are going to end off this music theory review video by examining some of the techniques that were used by post-tonal composers in their compositions the use of diatonic modes in music is a very cool concept a mode is a type of musical scale with distinct melodic characteristics the diatonic modes are the seven scales or modes that can be formed by building a scale using each of the tones of a major scale as a different tone center in other words the modes involve taking the pattern of whole steps and half steps of the major scale and starting the pattern from different spots let's go over the various diatonic modes that are possible the ionian mode is the same thing as a regular major scale the dorian mode is a natural minor scale with a ray 6 scale degree the phrygia mode is a natural minor scale with a lower 2nd scale degree the lydian mode is a major scale with a raised fourth scale degree the mixolydian mode is a major scale with a lower seventh scale degree the aeolian mode is the same thing as the natural minor scale finally the locrian mode is a natural minor scale with a lowered second scale degree and a lowered fifth scale degree the modes each have a unique sound and they are used by composers and songwriters to create different colors in their music make sure you memorize the properties of each of these modes the modes can be arranged in a relative order of brightness this is based on the number of major or augmented intervals above the mode's tonal center here is the order of the modes from brightest to darkest over here i have spelled the diatonic modes that correspond to the white keys on the keyboard remember the diatonic modes involve starting a major scale from different places the c major scale only uses the white keys if you start the c major scale from different starting points you get the different diatonic modes and they only use white keys in this case since they involve the same exact notes as the c major scale and over here i spell the diatonic modes each starting on the note c so that you can see how each mode can be built on the same note when it comes to the diatonic modes you need to be able to spell them and recognize them make sure you know the properties of the different diatonic modes and use the major scale and the natural minor scale when spelling and determining modes let's do an example of each let's say you have to spell a flat lydian first give yourself one of every note letter now you have to know your properties what is lydian lydian is a major scale with a raised fourth scale degree so start by building your a flat major scale your a flat major scale has the notes a flat b flat c d flat e flat f g and a flat now we need to take this and raise the fourth scale degree the fourth scale degree is d-flat so instead of having a d-flat it'll just be a d-natural and that is the a-flat lydian mode let's say you're given this mode and you're asked to name it the starting note and the ending note are both b so this mode is based on the note b now let's compare it to the major scale and the natural minor scale b major has five sharps b minor has two sharps this example only has one sharp so is it closer to b major or b minor in this case it's closer to b minor so this is going to be one of the minor modes either dorian phrygian aeolian or locrian now in b minor our two sharps are f sharp and c sharp so here we have an f sharp but we don't have a c sharp so this means it can't be the natural minor scale it can't be the aeolian mode so which one is it well because we have a c natural that means we took the second scale degree which is c sharp and b minor and we lowered it the natural minor scale with a lowered second scale degree is your phrygian mode so this is b phrygian and those are examples of spelling and recognizing your diatonic modes let's go over some other scales that are commonly encountered in post-tonal music the pentatonic scale refers to any five-note scale the major pentatonic scale is built on scale degrees one two three five and six of a major scale the minor pentatonic scale is built on scale degrees 1 lowered 3 4 5 and lowered 7 of a natural minor scale the hiroy joshi scale is built on scale degrees 1 2 lowered 3 5 and lowered 6 of a natural minor scale any one of the tones of the pentatonic scale may be made to serve as the tonal center which basically results in modes of the major pentatonic scale you can also play a major or a minor pentatonic scale using the black keys of the keyboard black key pentatonic refers to the pentatonic collection that is formed by the five black keys on the keyboard music that only uses the pentatonic scale will sound harmonically static so it is seldom used as the basis for a full composition next let's talk about synthetic scales these are scales that do not bear clear resemblance to the scales or fragments of scales associated with the diatonic system the whole tone scale is a six note scale that is composed entirely of adjacent whole steps this scale has an ambiguous quality because of its symmetry and its lack of perfect intervals the augmented triad is the only possible tertian triad of this pitch collection whole tone chords are any vertical sonorities that can be derived from a whole tone scale such as an incomplete dominant seventh chord with an omitted fifth and a french augmented six chord the octatonic scale or diminished scale is an eight note symmetrical scale that is composed of a repeated series of half whole or whole half successions the hexatonic scale is a six note scale that is composed of a repeated series of half step minor third or minor third half step successions the lydian mixolydian scale is a major scale with a raised scale degree 4 and a lowered scale degree 7. just like with other modes any tone of the scale may be used as a tonal center to create different musical colors over here i have examples of all the scales that we just talked about all built on the note c you can use this as a reference the use of chromatic saturation in the 20th century would ultimately lead to dodecaphonic music which was music composed using the 12 tone method let's go over some post-tonal chord structures that you should know about let's start with extended tertian harmony extendation sonorities which are also known as tall chords include 9th chords 11th chords and 13th chords they are used as an extension of traditional tonal harmony and they can be used in functional and non-functional settings these are coloristic chords and the traditional rules of resolution might not apply when these chords are used it isn't unusual for a composer to omit certain chord members that create strong dissonances these extended chords are often indicated by lead sheet symbols now let's go over poly harmony a poly chord consists of two or more chords that are sounded simultaneously for example a c major triad heard over an f sharp major triad chordal units are the individual chords that are the components of polychords a split third chord is the scenario that results when both the major and minor triad built on the same root are used simultaneously for example an e minor triad heard over an e major triad when two or more key centers are heard at the same time this is referred to as bi-tonality or polytonality let's discuss a few more types of harmonies chordal harmony is a sonority that's derived from stacked fourths quintal harmony is a scenario that's derived from stacked fifths remember the perfect fifth is the inversion of the perfect fourth secundal harmony is a chordal sonority that's derived from stacked seconds if you have any collection of three or more adjacent pitches in secundal relationship this is known as a tone cluster a cluster chord is a chord that consists of three or more pitch classes with seconds separating most pitches from their neighbors finally let's relate chords to the pentatonic scale there are five possible chords that can be derived from the tones of a major pentatonic scale these include a major triad with an added sixth and ninth a stack of perfect fifths a fourth rich sonority an implied five nine core with a suspension and a diatonic cluster chord that's built from seconds let's go over some other concepts of post-total music starting with parallelism an early sign that music was breaking from traditional tonal procedures was when composers began incorporating a lot more parallel motion between chords a non-functional harmonic progression is a succession of chords that does not follow traditional or functional patterns or progressions this type of progression often involves parallel movement and parallel movement creates a sliding effect among chords as you see here in this example it's good to use lead sheet symbols when analyzing non-functional harmonic regressions let's talk a little bit more about parallel motion planing is the term that refers to the use of chords moving in parallel motion real planing is parallel movement of vertical sonorities where the numerical value and quality of the intervals remains constant this results in an unclear sense of a tonal center for example a chord progression like d sharp 7 c sharp 7 b7 a7 g sharp 7 is an example of real planing diatonic planing is parallel movement of vertical sonorities whose quality is determined by the prevailing diatonic scale for example a chord progression in c major like g f e minor d minor c is an example of diatonic planing mixed planing refers to parallel voice motion that can be explained neither by consistency of core type nor by the limitations of a single scale for example a chord progression like e g minor d f minor is an example of mixed planing now let's go over pandiatonicism pandiatonicism is the attempt to equalize the seven tones of the diatonic scale so that no single pitch is heard as a tone sensor a pandiatonic passage usually has the following characteristics a key signature an absence of accidentals free use of the seven tones of the scale that's associated with the key signature and an absence of functional harmonic movement and those are some other concepts of post tonal music to end off let's briefly go over rhythm and meter as it applies to post tunnel music this section is mostly going to be definitions and terms because there are tons of aspects of post-tonal rhythm and meter to explore remember some of the basics about rhythm the beat is the basic pulse of a musical passage tempo is the rate at which beats occur beats in traditional meters tend to group into regular patterns of two three or four beats each meter has a pattern of metric accents syncopations stress normally weak beats time value relationships can be expressed as ratios a hemiola is an interaction between rhythm and meter that implies a three to two ratio and symmetrical meters are meters that are based on regular recurring pulses subdivided into groups of two or three post-tonal composers sought to break away from some of the traditional aspects of rhythm and meter let's go over some of the things that they used more often an asymmetrical meter contains an odd number of beats with the exception of triple meter for example 5 4 meter and 7 8 meter a composite meter is a meter that is made up of recurring irregular subdivisions for example 3 plus 3 plus 2 over 8. a dotted bar line is used to show how long measures are subdivided into shorter segments mixed meter refers to the use of rapidly changing meter signatures composers would use displaced accents to shift the accent of a meter to a relatively weak beat additive rhythm is a process that gives the effect of unequal groupings of subdivisions being added together polyrhythm also known as cross rhythm is the simultaneous presentation of two or more orally contrasting rhythmic streams polymeter is the simultaneous presentation of two or more meters at once for example hearing seven eight and three four together ametric music is music that lacks normally perceivable meter composers of such works would often omit bar lines and time signatures tempo modulation or metric modulation is a method of changing tempo by equating a particular note value to another note value which is a proportional note value that is usually located in the next bar here's an example of tempo modulation we start off in 2 4 meter the quarter note gets the beat and we're hearing the beat at 60 beats per minute in this measure we have eighth note triplets in the next measure this indication here tells us that the speed of one eighth note of the eighth note triplet is the new speed of the eighth note you could also write this as the quarter note is heard at 90 beats per minute so that's an example of tempo modulation or metric modulation added value is a process by which rhythmic irregularity is created through the addition of a note value or rest to a rhythmic figure dots and ties can be used to change the duration of a note or a rest non-retrogradable rhythms are rhythms that are the same whether played forward or backward polytempo is the simultaneous presentation of two or more contrasting tempos an ostinato is a musical pattern that is repeated many times in succession iso rhythm is a rhythmic technique that typically consists of a repeated rhythmic figure in combination with a repeated pitch sequence of a different length the talia is a repeated rhythmic pattern in an iso rhythm the color is the repeated pitch series in an iso rhythm tempo canon is a canon in which the individual voices are presented at different tempos mechanical rhythm is rhythm that requires a machine for precise execution for example irrational tempo relationships like the square root of 2 over 2 or even e over pi one final thing i'll mention is that some 20th century composers use the fibonacci sequence to determine musical information this sequence is an infinite sequence of numbers in which each number is the sum of the previous two numbers the ratios that are implied by the sequence approach a golden ratio of approximately 1.618 to one and this golden ratio has been found throughout nature and has been associated with balance in the arts throughout the 20th century composers took it upon themselves to explore the musical elements of pitch harmony rhythm form texture timbre and instrumentation looking at these musical elements in a new light opened up an infinite world of musical possibilities and composers were only limited by their own imaginations and that concludes this music theory review video if there are topics that you still find challenging and difficult to understand there are tons of great resources out there that go over these topics in greater depth and detail also i didn't go over every single term and concept in music theory however this video should have given you a solid overview of the central topics of music theory that you need to understand in order to be successful please share this video with anyone that will find it useful and beneficial i'm hoping that it will give people a greater understanding and appreciation for music theory and thanks so much for watching

Channel: Lennon Ashton

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Keywords: Lennon Ashton, Music, Music Theory, Review Video, AP Music Theory, Advanced Placement Music Theory, Undergraduate Music Theory, College Music Theory, University Music Theory, IB Music, Tonal Harmony, Final Review, Tutorial, Study Guide, Music Theory Review, Music Review Video, Music Theory Review Video, Music Theory Video

Id: QAGUWiVC1ys

Length: 204min 25sec (12265 seconds)

Published: Tue Jun 30 2020