The Coltrane Fractal

thank you so much everybody for watching I recently hit 200,000 subscribers on this channel which got me thinking what does the sound of 200,000 notes played within the span of six seconds sound like well apparently they make the sound of the first eight bars of John Coltrane solo on giant steps when you zoom into the piano roll you see thousands and thousands of notes each belonging to a smaller iteration of the solo this is an example of something I call a musical fractal a demonstration of the polyrhythmic nature of melody if you want to learn more about the math and technique of creating your own fractals definitely watch my video on fractals where I demonstrate the whole process on a simple Mellish it's basically an elaborate post but I think it does a decent job of demonstrating an idea that every crusty old jazz man will tell you melody is like the same thing as rhythm man the song Giant Steps was composed as an improvisational for John Coltrane to explore something called multi tonic systems key centers built in major thirds equal distances from one another will take short clips of his recorded solo and then will speed those clips up 4,000 times their original speed these MIDI clips will be going by so fast that your ear will not be able to receive in between this beautiful thing as a waveform this is similar to how a wave table synthesizer works because the MIDI clips are all of the same a melody they will have a necessary periodicity to produce pitch when they're sped up if there were all different melodies it would just sound like noise when the sound of the clips hits your inner ear a structure called the basilar membrane will vibrate in sympathy with the total number of Clips hitting it per second tiny hair cells and the inner ear will convert that acoustic information into electrical impulses that the brain can then interpret just the same way that a microphone will pick up sound waves to be either amplified or recorded what happens next I think is pretty incredible and also not that well understood our ears can do that really quickly I'm afraid we need to use let's take these two sine waves one vibrates at five hundred and twenty times per second and the other vibrates at six hundred and fifty times per second your ear automatically calculates the ratio between the two of them as five to four this is the interval of a major third because five against four is a simple ratio with simple integers our ear accepts it as a pleasing sound our ears automatically do what our conscious brains might have to labor over quickly calculate ratios between two separate pitches and boy can they do it quickly thousands of notes per second can be processed by the brain with the right sort of math behind it this particular musical fractal the one based on the John Coltrane solo is a little bit harder to put together than the one for all-star just because it uses all twelve notes of the chromatic scale we'll need to find whole integer ratios that relate back to a root for all 12 notes of the chromatic scale in order to find the harmonic poly rhythms definitely check out this video if you haven't already unfortunately unlike last time we cannot just simply look up this information on Wikipedia now I'm sure there's some fancy math that we can do to calculate those integers but though Wikipedia lists that we were referencing earlier already has the Wikipedia list that I referenced earlier was just looking at seven notes of the just intimated diatonic scale not the chromatic scale this problem definitely stumped me because well I'm a musician and - not a mathematician refreshing myself on basic algebra and Khan Academy only got my so far but then I thought well maybe the answer lies in the harmonic series well maybe the answer lies in the harmonic series the harmonic series also known as the overtone series is based upon simple multiples of a fundamental so if your fundamental is a hundred Hertz the second harmonic will be two hundred Hertz the third harmonic will be three hundred Hertz just take whatever the frequency of a note is multiply it by a number and then you get that number harmonic so easy even a musician can do it we hear all of the different harmonics as different pitches and intervals in relationship back to the root our brains process the differences between harmonics as musical intervals the ratios between two of them create a harmonic interval for example the distance between the fifth harmonic and the fourth harmonic creates a five to four ratio or the ratio of a major that we heard earlier major thirds are in our system of Western harmony but other intervals aren't like the distance between the seventh harmonic and the fourth harmonic these intervals between notes get smaller and smaller as you go higher but they never stop the harmonic series in theory goes on into infinity so if we just went up high enough we could find all the twelve notes of the chromatic scale and then apply it to our musical fractal all we would need to know is just the numbers of these harmonics and then those numbers are the total number of MIDI clips we'll need in order to create our chromatic giant steps Solo in trying to figure all this stuff out I found an interesting paper by the bassoonist Johnny Reinhard which proposes a system of tuning based upon eight octaves of the harmonic series all the way up to the 250 6th harmonic enlists all of the unusual intervals you can create some of my favorites include the howling dominance the hyper leading tone major 7th and my personal favorite the almost major six you are so close major 6th you're so close in all of this though we can find pretty close approximations of all 12 notes of the equal tempered system it took these and then created this table of interval ratios the numbers on the right or how many MIDI clips of the first eight measures of John Coltrane so long giant steps we will need to create and play back within a given amount of time so that when we speed it up will hear that note so if we play 57 MIDI clips within the span of 32 MIDI clips it will one create a crazy complicated 57 to 32 polyrhythm when we play it slowly and to sound like a minor 7th speeded-up I went about manipulating large numbers of MIDI clips and recombining them based upon all of the individual notes from the John Coltrane solo when we start speeding it up you slowly start to hear the horror of notes recombine into the solo this is the testament to your ears incredible ability to perceive ratios between frequencies [Music] [Music] so our ear calculates these ratios almost instantly but we don't really know why this occurs we don't really seem to have that same ability when it comes to light frequencies for example consider this versus this noticeable for sure but not really jarring but if you listen to this versus this because our brains detect a more complicated ratio in the second example our ears immediately perceive it as being more dissonant than the first example this fine tuning of our ability to do oral math is why the Coltrane fractal works the range of human hearing is about 10 octaves from 20 Hertz to 20,000 Hertz certain marine mammals like the harbour porpoise can hear up to a hundred and eighty thousand Hertz or if we wanted to program it a hundred and eighty thousand Coltrane solos per second musical perception is a pretty amazing thing because of how unique it is to the physical makeup of our bodies we literally make music for ourselves and how our brains perceive the world of sound around us maybe that's one of the reasons why music feels so personal I do think that is a nice gesture that sound recordings of human music were included on a golden vinyl sent out with the Voyager 1 spacecraft but if there are aliens out there their ears will need to be as fine-tuned as ours to the frequencies of the music that we create otherwise to them it will just be noise hey everybody thank you so much for watching my name is Adam Neely I have a new video coming out every Monday if you enjoy what I do please consider joining my patreon because it's through my patrons over at patreon I'm able to do this every week so thank you so much for watching and until next time

Channel: Adam Neely

Views: 1,018,191

Rating: 4.943665 out of 5

Keywords: 200k giant steps, Q+A 26, Cat Piano, TRITONE, gay vlog

Id: J98jwtm5U4E

Length: 9min 11sec (551 seconds)

Published: Mon Jul 03 2017

Reddit Comments

[u/sachio222]

I'm afraid it's not our ears doing literal math. It's based on waveform physics. It has to do with the symmetry of the interference between multiple waves. If you have waves that fit a ratio neatly due to the peaks and troughs lining up at relatively regular intervals, it will sound relatively clear, if you shift the frequency of one of the waves however, it will not have the same neatly occurring interference patterns. He makes it out to be mysterious calculations, but it's really the mechanical patterns of air pressure waves

[u/Kake_Mace]

adam neely is great

[u/[deleted]]

My brain hurts... I think that may be the feeling of it growing 😂

[u/doom_chicken_chicken]

I really like Adam Neely, he's very likeable and cares and knows a lot about music and really makes it fun to learn about.

[u/AugustusMarcus]

I remember when I saw that, it still doesn't sink in. What an amazing thing.

[u/trevorcorylahey]

So when it is hyper sped up, we are hearing the note that of the key basically? and the key changes match the solo in a larger structure?