Mathematics of African Dance Rhythms

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>> From The Library of Congress in Washington, D.C. >> David Plylar: Good evening, everybody. Thank you so much for being here at the next event in our Video Discotheque Series, which has already been a nice -- we've had a nice run of events this week and actually since April 12th was when we started. I just wanted to let you know about a couple of upcoming events and then just a short introduction about tonight's talk. We invite you to come tomorrow at 12 p.m., we have a Veterans History Project talk at noon in the Whittall Pavilion, that'll be kind of a panel discussion. In the evening in this same room is a screening of House Party at seven o'clock. And then on Saturday we have a Symposium that starts at one, and then we have the Gloria Gaynor events that start in the evening. Now you may or may not have tickets to those events, they sold out very quickly. If you don't have a ticket we do have the possibility of getting in, there will be a space-available line that will start forming for each of those events if you'd like to still attend, and we'll try to get everybody in that we can. Tonight I'm really pleased to introduce Martin Scherzinger, he's a Professor of Media Culture and Communications at New York University. He's going to speak to us about various issues of mathematics, of African dance rhythms. And one thing I wanted to mention is what does this have to do with Disco? One thing that we wanted to do with some of these extra talks is to expand the context of what we're talking about with different types of dance musics and how they are still relevant contemporaneously and to Disco and to other cultures. So I'm really pleased to introduce Martin. He's a fascinating person, also a composer and performer, so it's great to welcome you. Thanks, Martin. [ Applause ] [ Music ] >> Martin Scherzinger: Okay, hi, everybody. I'm going to let this roll visually while I introduce the subject. What you have in front of you is a performance, a reenactment from a scholar who is doing some research in the region from the upper Volta, and the dance that you see is an ugbeckor [Assumed Spelling] dance, which is traditionally a war dance in Ghana. And I just want to talk a little bit, just to introduce this, about how the rhythms that you hear in the background are constructed. So we have a number of different kinds of drums. We have a Kagan drum, we have a Kidi drum, we have an atsemiru [Assumed Spelling] drum, and as well as a gankogui, which is the bell pattern that you hear prominently. Just very briefly and schematically all of these rhythms are a little more complex than the way I'm going to introduce them. They tend to be organized in what Western people would understand is different metrical frameworks, okay? That means that the Kagan drum would do something like this, and I'm just going to ask you to take a look up at the board if you can. You can think of this as a short, long, short, long, short, long, short, long. So Kagan, Kagan, Kagan, Kagan. Sort of in sense organizing things in threes, one, two, three, one, two three, one, two, three, one, two, three. At least from the perspective of a Western ear. A drum like Kidi would be doing something like, dit, do, dit, dit, do, dit, do, which is organized a bit more like, okay? So something like that before it repeats, right, which is in the West says something like that would be one, two, three, one, two, three, as opposed to one, two, three, two, two, three, okay? So we layer these two different drums more or less differently. Now again both patterns are more complex in practice, but this is their signature sort of placement in which they work. The bell pattern that you hear is a very common bell pattern, a 12-8 bell pattern, which I'm just going to play now in slow motion so that you can hear that part of the ensemble for special attention. [bells] It's a seven-stroke bell pattern, one, two, three, four, five, six, seven. It happens in a field or in what we might call proct [Assumed Spelling] time in a field of 12. Subdivided as two plus two plus one, two plus two plus two, plus one. Okay, so let me just illustrate that this way, okay? Um, bum, bum, ba, bum, bum, one, two, one, two, one, one, two, one, two, one, two, one, one, two, one, two, one, one, two, one, two, one, two, one, two, one, one, that kind of thing, okay? I want to just draw that one up in notation to give you an example of a striking, what we might call a correlation between an African practice and a Western technical instrument, okay? We've got one, two, one, two, one, one, two, one, two, one, two, one, two, one, okay? Everybody sort of get the notation, right? For those of you in the back it's not crucial and try to work with the ear, but visually I put it this way because what's striking about it is two things. The first is that there's two longs, a short, then three longs and a short, right? So there's something a little asymmetric about this, right? In other words, when you have a field of 12 and we have 12 pulses here. Why? Because we have that and then there's a space, space, space. If I count up the dots I get 12 micro pulses against which seven are struck. So we have seven elements in a field of 12, that's clock time for which seven stand out for special attention, okay? The relationship of seven and 12, think of days of the week, think of the annual way in which we organize time. This is something that is contemplated a lot globally, okay? But the thing that I want to draw your attention to is by being a little bit asymmetrical we can sort of split the pattern into two halves. The first half, which is long, long, short, and the second half, which has the three longs and a short. In other words, the boundaries happen in a slightly asymmetrical way, okay? So with 12 you can multiply and subdivide and so on into three by four, four by three, six by two, two by six, or which is important because it can do all those things, but it can do another thing, which is common in African music which is to say you take your 12, you take your symmetry and then you off center the symmetry by one. So you might call it N minus one, N plus one. So if we've got 12, six plus six, now we have six minus six, six plus six, five plus seven, right? And if we count up the dots, one, two, three, four, five, and then one, two, three, four, five, six, seven -- I should have put another dot in here, ran out of paper -- we have exactly that structure. Now just something to bear in mind here is that this is not just a rhythmic structure, but if you were to put this into a pitch field, in other words, A, B, C, D, E, F, like on a piano, we get exactly the structure of the modern piano, right? Instead of long we have a tone, so it's long, long, short, long, long, long, short. We have a tone, tone, half tone, half tone, tone, tone, tone, half tone. It's the white notes on the piano, okay? If I were to fill in the green notes, we'll confuse colors tonight, that is the black notes on the piano, okay? Something to think about why? Because the piano is designed in such a way, in the 18th Century when they sort of came to standardize the modern industrial piano it's designed in such a way that it's capable of very easily modulating from one pitch area to another, okay? So you can move from C major to, say, G major with very little -- with tweaking the system just a little bit. In time you can also modulate from one place to another place fairly easily, and I'll explain that in more detail as we get into this lecture a little later. So that is an important sort of feature and common characteristic that it has as a mathematical structure that incarnates in African rhythmic practice as a timeline pattern and in Western practice as a technical device for music making, which has been, you know, had a great monopoly of thinking and music in the West. Not an insignificant instrument, the piano, especially if we consider its afterlife in MIDI [Assumed Spelling], which is a software that basically incarnates the assumptions of the piano into code. Okay, so these are just some of the features that I want you to remember as we move on through this lecture. That we have here a sense of staggered downbeats, different rhythmic cycles that we can say have a different kind of downbeat. We have the principle of N minus one or N plus one, asymmetry, right? And we have another principle that I just want to quickly draw your attention to, which is that the rattle pattern, the rattle player is doing something that supplements the gankogui in the following way. If your gankogui is doing this -- going to keep these pens nearby, I'll need them -- if your gankogui is doing this, dum, bum [beats] your upshashir [Assumed Spelling] -- just using a [inaudible] bottle here -- your upshashir player is going to more or less for most of the pattern inhabit the spaces of what the gankogui player has occupied. So if that is a space after the beat, okay, so [beats] [rattle]. These are the black notes of the piano, okay? One, two, one, two, three, one, two, one, two, one, two, three, okay? One, two, one, two, three, one, two, one, two, one, two, one, two, three, okay? I may have rushed a little bit quickly through things and I'll recap them again as we move further into this lecture. But for now I want to jump to -- that was the northwestern part of Africa -- now I want to jump to the southeast. Take a look at this dance, called Nyungwe, Mozambique. [ Music ] Okay, very interesting piece of music making, right? In South Africa before the days of liberation, in the age of Apartheid, we used to say this was music called for one man, one note. You had a set of pipes, maybe three or four, with a different name and you would play one note at a time in which other people would play different notes, okay? That particular piece is called Uzungwa Gona [Assumed Spelling], which means something like White Man Sleeps, and there's been an interesting set of compositions based on it. This is an old transcription from when I was still there, so I apologize for that, but what I want to quickly do is show you how this music is put together, okay? Again, we're in Mozambique. The first part is called korirambu [Assumed Spelling], the second pakirakabambo [Assumed Spelling], and then enbitae [Assumed Spelling], okay? And the way this is put together is that the first part will sing something, blow something, and then breathe. So it's sing, blow, breathe, sing, blow, breathe, sing, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo. Okay, that's the first line, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo. The second part, pakira [Assumed Spelling], yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo. And then kabambo [Assumed Spelling], yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo. And enbitae, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo, yahoo. Okay, for give my terrible singing, but you get the point. So what happens here is that what's interesting about this is if we design this in such a way that we just call it that they sing, ya, and then this bland note fu, right? And the second, the third time point is a breath, okay? And we sort of line up our singing and our blowing in that kind of way. We can say that korirambu does this kind of thing, yafu, yafu, yafu, yafu, okay? Pakira, you will notice, starts with a breath, okay? Actually, you know what, I'll keep it all in red. Starts with a breath and then begins with a ya, okay? So breath, ya, and so on. Okay, enbitae, down at the bottom, begins with the fu. Et cetera, okay? So again we have this notion that each of them seems to start at a different part of the beat, that's on the first, that would be on the second and I put it in inverted commas, and this would be in some sense on the third, two beats missing, and then on the third where you start with your ya. Okay, what's fascinating about that is that we've got that same multi-metric situation. In other words, the down beat for each performer would happen at a different place, okay? What's interesting musically is that what you hear is not exactly what's going on meteorically because what comes to the ear is a different thing, it's a kind of phantom baton that is designed out of all the ya's being put together, right? So the ya gets thrown around between different performers. So you're kind of going ya, ha, ya, he, ha, ha, being thrown around two different performers, and your flute part, your pipes are doing the same thing but within the spaces of that. Okay, so that's the first thing. So you're generating melodies out of this is the formic principle, right, this is the zoetrope, where you spin a photographic image fast enough and the eye cannot not see movement, right? This is music of full stops that becomes lines, but nobody is fully creating those lines, they get passed around. This technique was used by various composers in the '60s and '70s when ethnographic recordings made their way to the United States and to Europe and very often to great avant-garde effect. Somebody like Luciano Bario [Assumed Spelling] takes a very similar style from horn music that was recorded by Sinclair Arum [Assumed Spelling] and rocks music in a heterophonic style, which became very, very interested -- people in the West became very interested in this and, in fact, philosophers like Dulars [Assumed Spelling] and Guatari [Assumed Spelling], kind of left wing philosophers thought this was a way of organizing political life and then that became a kind of metaphor for organizing for political life in many philosophies and political philosophies to follow, which is interesting, all the way up until today. It's kind of hidden genealogy for this kind of thinking. How do you hold this multi-metric situation together? If I ask just this room to go yafu, and we all start at a different time we are really not going to do a great job and I can anticipate that. And the way you do it is to organize your dance step in a way that everybody is equally in and not in on the beat, okay? So if it's going yafu, yafu, okay, so one, two, three, one, two, three, one, two, three, one, two, three, one, two, three, one, two, three, one, two, three, right, there's three elements, yafu and breath. Your dance happens in four's, so it's yafu, yafu, yafu, yafu, yafu, yafu, yafu, yafu, yafu, yafu, yafu, yafu, okay? You're on the beat and off the beat at different times, right? And because of that the beat floats amongst the different performers and is able to bring them all to the same kind of place. Now as you saw from the actual dance it's a lot more complicated than that, but when you're teaching a four year old to get it right you make sure that you're dancing in four's, when the music is structured in staggered three's. So everybody with me? Okay, so that's more or less another lesson we take away because though the music sounds very different it has some things that are similar. What are the similar things? Multiple entries, right? Different metric downbeats, if you like. Interlocking, which means be in the spaces of each other to create melodies that float amongst you. In the case, remember the gankogui upshashir in between the gankogui? And the third principle, which one might just call polyrhythm because in a sense my feet are moving in four's, one, two, three, four, but this is moving in three's even though the three's are staggered, okay? So those are the three sort of broadly speaking principles that I'd like to introduce to you to now before we change to a completely different time and place. [ Music ] Okay, probably one of the most famous samples in the history of music or history of popular music in America, okay? The Amen Break, which was a B-side tract called Amen Brother by the Winston's. This is now 1969, this was a short fragment of what was called The Break, which is when the music starts playing and for moments the rhythm is exposed and in the words of Steinski the music takes its coats off and you get down and get funky and so on and so forth, right? That, in addition to James Brown's Funky Drummer, was probably the most frequently sampled music in the 1970s. As I say, this particular moment I'm going to try to tie back to some of these African principles, and then I'm going to try to make a more or less speculative argument about how these things got here and what happened along the way, how did we translate some of the values from one place into another place, right? And that's not always a happy story, there's some, how shall we say, tragedy involved in this moment of great transition across the Atlantic. But let's just get straight into it and ask some questions of funk music, right? What are some of the techniques of funk? And I want to introduce you just to two very simple ones. The first one is sometimes called shifting or pushing something on to the metric offbeat, right? Which is just a question of if my beat is here I emphasize the space between [beats] okay? The second is shaping, sometimes called shaping the beat or extending it in time, but extending it somewhat. So if the beat is here [beats] I now go, okay? We're going to get to how that is actually sublimated into that particular rhythm that you heard, but for now I just want to play some very obvious examples of both so we can get this slowly. Here is Rufus Chaka Khan, 1974, Tell Me Something Good, shifting the beat to the metric offbeat, okay? [ Music ] Okay, everybody get the point? What makes this feel the way it does is precisely this shifting the on and the offbeat. You could actually step on both and it would give you decent movement, right? It doesn't script you or conscript you into one way of dancing, you can be on or off the beat. Same year, 1974, here's a way of shaping time. Actually, let me just remind you what -- you know, what, we'll do another shifting time, but to remind you that this isn't just a question of like pulses interlocking. You can have entire rhythmic configurations kind of being pushed over by half a beat, that sort of classic 0.5 or something, right? So the classic funk kind of drumming often does this. So if you listen to the following passage, this is Tower of Power, Scrub Case 1974, you will hear a short rhythmic motive that sort of go dum, da, da, da, da, dup, da, da, dup, da, da, da, dum, ta, dum, dum, dem, dem. And then it will delay by 0.5 that same dup, da, da, da. Okay, so if you can hear that, four measures of funk drumming, Tower of Power, 1974. [ Music ] Everybody get the point? [ Music ] Okay, so the entire sort of, as it were, the passage, the rhythmic configuration, dup, da, da, da, dum, ta, dum, that gets pushed over by 0.5. Did anybody hear that? Okay, let's do it one more time. [ Music ] Okay, so I came down. [ Music ] Where that little rhythmic fragment started again, but the drummer waited just half a beat and that would lead us into the rhythm of the one. Okay, it's as if it came a little early, came a half beat early, right? And that is very sort of more sophisticated way of shifting the beat, okay? In Disco music, of course, this shifting became a kind of dominant feature, it almost became a characteristic sound which was associated very often with the high hat, so think Donna Summer and so on and so forth. The prominent high hat that happened within the spaces. This is just a digital audio workstation sort of showing how you place the high hat within the context of an ongoing beat using Disco as you're trying to invoke Disco and stylistic. [ Music ] Now we have it here. [ Music ] Okay, now we've entered into the reign of Donna Summer. [ Music ] Okay, so we've sort of got the idea of interlocking or shifting, right, being in the space of something else, the shift of 0.15, 0.5 in a beat. What I want to now turn to is the shaping sound, which is to say instead of having just the beat go you have another beat going, but that's like stretched. [beats] Okay, and this made its way also both through funk into Disco and then ultimately into the mainstream sort of dance musics of the late '80s and into the '90s. I want to give you one example, this is from Tim Moss, so we're now already in the '90s of techno music just to again get the conceptual point across. It starts out with a symph that is very prominently giving you a slow beat against which a quicker one or the primary set of beats is going to join. [ Music ] What, we're musically doing this I'd say one, two, three, one, two, three, one, two, three, one, two, three, one, two, three. Because the real beat is heavy. [ Music ] Then the DJ will bring in the underlying beat. [ Music ] Okay, in the music world people sometimes call this grouping dissonance. As far as I'm concerned, we could call it a metric dissonance. It's like two elements or two parts of the layering are aspiring to different ways of counting time, right, but you do it simultaneously and they go in and out of phase with each other. Think about building a brick house with different size bricks or something, clearly they're going to go out of phase and come back into phase with one another. By the time we get to the late '90s this becomes quite a refined technique for the needle droppers and the refined DJs. This is some IDM music, which began or so-called intelligent dance music coming out of Detroit, but making its way through to the UK and so on. Mark Butler has written a remarkable book on this. I'd like to show you that what we have here is both a shaping and a shifting of the beat, okay? So take a listen to this passage of music. [ Music ] Okay, now listen to the way he drops the needle into this texture. We expect the beat. [ Music ] That's where we expect the beat. [ Music ] So it's both shifted the beat or turned the beat around, as the saying goes, and it's shaping the beat by de, dum, de, dum, de, dum, which is the slower beat within a beat. It's like having two cycles of a different size rotating simultaneously, you know, a 24-hour day and a 28-hour day somehow, simultaneously unfolding. Okay, and by 1999 -- I'm going to give one more example, this had gone thoroughly mainstream, so when people were dancing raves and so on and so forth we often had these kinds of techniques. So I'm actually going to try to draw this up on the board because it's -- try listening to the different layers because it's shaping and shifting on numerous levels. I'll draw it up and speak across the actual track. So here we go, Almac Twins, Almac Head [Assumed Spelling], sorry. [ Music ] You've got the beat. [ Music ] Okay, but the symph is prominently off that beat in this phase. [ Music ] Okay, I'm going to go back, this is what happens next, so that we call shifting of the effect. What was once just a gentle high hat is living up to the beat and Disco has now become a prominent [inaudible]. [ Music ] Listen to what happens now. [ Music ] It's becoming more prominent. [ Music ] Sort of doing its own thing, and there's another layer which is doing this. [ Music ] Okay, in fact, the drum, the main sort of beat that hold it together they remove so that you can hear all this. This is like that break that you used to have in funk music, now you remove the basic element and just allow all these rhythmic sort of ambiguities to come to the forefront and then dancers often speak of flowing and trancing, whatever. You know, the language there is interesting how to describe this. But what I want to show you just very quickly is that the first thing is that prominent symph in the spaces happened in the space of the beat, right? It was somehow punching in between. The second layer went across that in three's, so this was all in two's, and then this went into three's, okay? But this one went chun, ja, chun, ja, chun, ja -- this one actually went into the space of the space over here, okay? So you have all these various elements that are suddenly starting to sound a little bit like an African ensemble. Very little harmonic change and all sorts of rhythmic complexity that the DJs are bringing and filtering and figured rounding in ways that are attentive to the audience's reactions. So how did we get there? Well, let me start very quickly by going back to Africa. This time just South Africa. And again it's hard to measure exactly how these things transferred from one place to another, but what I do want to say is -- and it's hard to map because the place, South Africa, for example I'm South African and so on, obviously a hybridized South African, hybridized African, if you like. And so, too, is the music deeply hybridized. So it's quite difficult to look at contemporary music and find just this irreducible stamp of Africanus because it's become part of the record industry, the radio, emergence of radio, the globalization of culture, very quickly hybridized all of this. So what I'm trying to get at is some of the pre-hybrid forms of music making which were equally complex and non-static, but there is a sense in which they functioned across a different type of modality. But even in the hybrid music of South Africa, this is back to when I grew up, turning the beat around was a common thing. It is almost like even in popular music it was modeled on Western music you hear this sort of ease with which the beast gets turned around. Here is Inzie Zamoya [Assumed Spelling] playing a Marabi music, in fact, this piece of music is called Marabio [Assumed Spelling]. Sorry, attempt to hit that button. [ Music ] That's where you can move. [ Music ] Moving into all sorts of dance things that are like MiteMite [Assumed Spelling], which is associated with [inaudible] and I'll talk about that when we talk about [inaudible] next time, but that's like to walk like a duck and so on and so forth. So this is a sort of association that goes along with this, but it's clear that turning the beat around is not a big deal in the South African popular music even of the modern hybridized sort. Okay, now a speculation, how did this get here? And I want to just take a sort of detour through certain soundscapes, such as the sites such as the Bronx where arguably we can find the origins of Hip-Hop and argue that the actual sounds that were out there in the streets, in the parks, in the dancehalls, on stairways and so on and so forth, actually carried an imprint of this music by way of the Africarribean. Okay, this is actually an argument that's very well made by a colleague of mine called Mark Katz [Assumed Spelling]. If anybody wants to read up about that exact connection. I think it's a compelling argument. I lived in New York for a long time now and when I lived up in Harlem it was clear that if you left your apartment on a Sunday or Saturday or a Friday, maybe even a Thursday in summer these soundscapes are very prominent, right? There's different competing groups that still have traces of all of this. And it seems to me that that sonic geography has something to do with what people felt was a certain appropriate way of beating. So here's an example from a novel, written by Allen Jones, this is in the 1950s, the book is called The Rat That Got Away, and here he's describing the soundscape of a certain sort of area in the projects. The Patterson Houses at night were alive with activity, he says, and alive with sound. Music was everywhere, coming off people's apartments and on project benches. One side of the street he would have people who brought out portable turntables with two big speakers. That's already in the 1950s. Cool hoke [Assumed Spelling] only starts, you know, a good 10 years later. And on the other side you could hear some brothers singing a Frankie Lymon song. But the one constant every night without fail was the sound of Puerto Ricans playing their bongos in local parks and playgrounds. The steady beat of those drums was background music to my living reality. Renee Scroggins, 1970s, describes the Bronx in very similar terms. Every summer in St. Mary's Park you would have some Latin gentleman in the park with some Coke bottles, a cowbell and a set of congos and it was our summer sound. Okay, so that's by way of speculation about one place where something moved from the African by way of the Africarribean into the soundscapes of the United States and then into popular music of various sorts, from funk to Hip-Hop through Disco and so on. That break beat was the most sampled or played with on vinyl on a certain kind of turntables. Of all sounds it's probably the most popular. And the argument is that when you make a recording this is the phonograph effect, when you make a recording of something it's different to being live. If you're live you can adjust to your audience, you can look at them, you can slow down, speed up, you can extend the break if they're getting down and so on. How do you do that if you've got it on vinyl because on vinyl you always keep things shorter, right, even if you're like recording Chopin or something like that, you know, live I can do that, I can really hold that silence, right, and people will wait. A phonograph always compresses it, you can't -- you don't see that silence so, therefore, you shorten it. And so the break was relatively short. Well, how do you extend that if people are getting down? And you're just basically creating a party. Well, one thing you can do is have two turntables and needle drop or pull it back, which is their way, that particular technique emerged from. So it was a kind of production, creation, and then became a kind of music stylistic of its own. In fact, Colverk [Assumed Spelling] used to toast over this, which is a Jamaican thing to do, perhaps to cover up some of the little mistakes. So it's an interesting story about how this all comes into the soundscapes of our parks and so on. So I want to get a little bit into this, into the claves [Assumed Spelling]. Demonstrate, which is the Africarribean that I'm referring to here, and demonstrate how these take up residency, these patents take up residency in various contemporary styles. And you should be able to recognize them, I'm trying to in some sense give some irrefutable sort of styles here. But here is the sound of the 3-2 sound claves. And when you think of the claves think of that gankogui [inaudible] that we did a little bit of work on, that looked like the piano, that's the one I'd like you to think of when you think of the sound claves and then we will talk about the relationship it takes to the African original. [ Music ] Okay, it's three on one side and two on the other, right? So one, two, three, four [beats] that kind of thing, right? Remember there's black notes on the piano, right? Five things happening in a field of 12 or five things happening in four big beats, five beats in four, okay, trying to make five things happen in that space. This one happens in this particular way, so it's one, two, three, one, two, one, two, three, one, two, okay? If I speed that up just a little bit, so dun, dun, dun, dun, dun, dun, dun, dun, dun -- I find it here. [ Music ] This is the block party call to ... [ Music ] Okay, I hope we all know that particular piece of music, okay? There were many variants of this particular pattern and I'm not going to have the time to do it all, right? But we have in a sense three on one side and then two on the other. The beat falls sort of in between all these things, right? And then sometimes on these things. So there's the beat, dah, dah, dah, dah, dun, dun, bum, bum, bum, okay? That's kind of how this pattern works. If I were to just to delay this one just a little bit I get the rumba, okay? If I delay this one just a little bit I get the bossa nova. I can also delay both a little bit and I get also a very interesting pattern. So the original song pattern, something like this. Okay, here's the beat. [beats] Rumba, I'm going to delay the third of those. [beats] Everybody hear that subtle difference? Okay, so instead of I'll play them one after each other. [beats] Okay, bossa nova, now I'm going to delay the other side of it. [beats] Again, I'll play now the sun [Assumed Spelling] and then the bossa nova. [beats] Sorry, that was the wrong way around. [beats] I could do both. [beats] Now I'm almost playing exactly five equally spaced things in the field of four, but we are locked into four-four time, which is undermining that a little bit. If you slow down, for example, the rumba pattern from [beats] but slow it down [beats] you get something like this. [ Music ] So the bass drum. [ Music ] Okay, I raise it because when we look at Hip-Hop, you know, often in the popular media or at universities. You know, I teach at a university. We often look at the voice, the importance of voice, politics, culture, storytelling, imagery, et cetera. What we don't often do is just listen to the pure grammar of how are these beats put together and where do they come from, right? This is clearly a slowed down kind of rumba, right? And the girding through the bass drum, the feel of the song. It is essentially important and throughout the first decade of the 21st Century I challenge anyone in the room to find me seriously sort of popular Hip-Hop that didn't have a mark of some of this kind of claves pattern built into the underground of that particular sound. So how would you render this pattern in an African context? What is different about these to the ones that we started with, right? And I want to get into this a little bit slowly, but let's just first have a demonstration of it. This is Mario Puchae [Assumed Spelling] again. This is the African Icefield [Assumed Spelling]. [ Music ] Okay, it's interesting because the beat should really be here. [ Music ] Okay, it's a slightly different feel, right? So consider the one goes like this [beats] that's our song, and this one goes [beats]. Okay, a little bit different to [beats] subtle, but it's a very different feel. And what makes them different primarily is that the one is what in the West is called four-four time or binary time and the other is in a kind of ternary time. It's going one, two, three, two, two, three, three, two, three, three, two, three, four, two, three. And the other is going one, two, two, two, three, three, four, two. And you're trying to fit the beats on and off the beat in the same kind of way, but in a different metric framework. Is everybody with me? And notice that this three-two claves is exactly what we had when we knocked off right in the beginning the spaces between the gankogui pattern. Here was that first pattern you heard. This is now the bell pattern, gankogui bell. [beats] [rattle] Africanized. [beats] [rattle] So I'm not going to even try to make that final translation, but you get the point. It's entrained differently, the way the placement of the beat is in a slightly different spot within the temporal spans that are provided by the music. Okay, this manner of rendering that three-two claves, quote-unquote, and it's completely back formation now because we're now going back to the earliest music that we have traces of, is part and parcel of something that's been sort of at work in African, how shall we say, temporalities for a very, very long time. I'm going to take you back to a Bucker [Assumed Spelling] ensemble, one might call it. Here's a string instrument called the venaluma [Assumed Spelling]. This is now Central Africa, and I want you to hear first that particular three-two and it's going to come in the form of a rattle, okay? And the string instrument is going to double it, so the string instrument will feel that pattern in the same way. Listen carefully. [ Music ] You might be sort of [inaudible] by the stick pattern that's in the foreground. [ Music ] One, two, three, four, five, six. One, two, three, four, five. One, two, three, four, five, six. [ Music ] Can everybody hear that? Okay. [ Music ] I think for the purposes of the argument tonight I just want to make two points about that. There's a third layer that I wanted to introduce us to, but for now I'm going to suspend that. What we have is the simultaneous unfolding of two patterns, both of which are structured through this N minus one, N plus one technique. [sounds] Right, that's the venaluma and the shaker. One, two, one, two, three, one, two, one, two, one, two, three. So it's five plus seven. One, two, one, two, three, one, two, one, two, one, two, three. [sounds] That's how you're dividing up a field of 12. But you also have the Dketo [Assumed Spelling], which is the sticks that you heard, not the clapping, the sticks which went like this. They went down below, short, long, long. [beats] Okay, we need to be asking a lot of questions right now because this is now going one, two, two, two, two, two. One, two, two, two, two, two, two. Six times. But what it's doing is as it sets up one beat for the first half it reverses that for the second half, right? And it does so in a way that recapitulates the N minus one, N plus one logic but on a much longer time scale. In this case 24, okay, if you add up all the three's and two's here we get 24. So you have two cycles, both organized through N minus 1, N plus one, running simultaneously and going on a phase with each other. Okay, so you need to keep your wits about you playing this music. There is no overriding beat or if there is one it is music to find the beat by or even music to rotate the beat by, which is something that we will get to hopefully at the end of this lecture. How do Westerners hear this music? Here's a fragment from Herbie Hancock's album, Headhunters, in which his drummer, Bill Summers, takes a short fragment of African music and begins a song called Watermelon Man that way. [ Music ] Okay, where did he find this? He found this on a UNESCO collection album that was recorded by Simpha Har Aram [Assumed Spelling], whom I mentioned at the beginning who is an Israeli ethnographer who went, commissioned by the French Government to go teach people in Central Africa to play the horn. And he discovered, of course, that people knew how to play horns in some ways much better than he did and he kind of found Jesus and stayed there for a number of years and made some of these fascinating recordings, which we now have circulated, right? This particular piece, there's a very famous article by Steven Feld [Assumed Spelling] written about how it circulates in a global frame, and we can talk about that as a slightly separate issue about when things become monetized and when they stay in a gift economy but we'll leave that aside for the purposes of tonight. What I want to draw attention to is the original recording which was listened to by Bill Summers, here it is. [ Music ] Okay, once again the one note, one flute, et cetera. These are by Bengali [Assumed Spelling] singers or players. In this area the rain forest is so thick that people often have to find their way by ear rather than by eye, so it's a very interesting soundscape and we have a lot of sort of intermediate linguistic coding through sound that might be music, as language might just be spatial, location and so on. So definitions of music are challenged by this, but nevertheless that's the sample. If we went deep into it you'd hear all the interlocking parts come in and so on. But what I want you to do is take a listen again to what Bill Summers hears in this music and how he feels the beat and then compare it, okay? And then I want to make a point about that difference, even with the same music. [ Music ] Where is the beat? [ Music ] Where is he feeling the beat? [ Music ] Anybody want to give it to me? I'm giving it to you. [ Music ] That's the beat, right? [ Music ] Everything is conspiring to that, right? Okay, now again I don't sing very well, but the way he more or less hears it in that band is bah, bah, bah, beepa, bah, bah, bah, bah, bah, beepa, dah, dah, dah, dah, beepa, dah, dah, dah, okay? The way it is entrained in the original context would be more something like bah, bum, ba, beepa, bum, bum, ba, ba, beepa, okay? Very different way in which it is heard as a metric phenomenon, right? And I think that difference has something to do precisely with this N minus one, N plus one thing I've been talking about, which is to say if you look carefully how this melody is structured, dah, de, dah, de, dum, bum, bum, ba, beep, bum. Okay, something of the ba, ba, bum, bum. [beats] Something of that claves Africanized pattern is embedded in the way the melody is structured, which makes it symmetrically malleable, okay? That is something now that I want to turn to in more detail and now this sort of math game is going to start a little bit more intensely, so far it's just been like introduction. But let me draw your attention to this, right? Here's our claves pattern, here's our gankogui pattern, excuse me, right? And these are the time points, zero, one, two. In set theory in math you start, you count from one to 12 by starting with zero, so forgive me, that's a convention, but it's zero, one, two because nothing has happened yet, like time 0.0, right, we start at zero. So zero, one, two, three, four, five, six, seven, eight, nine, 10, 11, right? That is 12 time points, this is clock time, it's as if it's going one to 12, but zero is 12, okay? so zero, one, two, three, four, five -- well, where do the beats fall on this, right? I remind you now, dum, dah, dah, dah, dah, dah, dum, right? That is the pattern. The beat can fit anywhere within that pattern. Why is that? Let me play the pattern and let me play you some of the possible beats, okay? [beats] Easy enough. Why? I align the first two notes with the beat and then I keep the beat going and this thing knocks on and then off, just like we heard in that music of Central Africa, right? Or I can start by placing the beat in between those notes, the first two, right? Now instead of starting together I go [beats]. It's as easy to do. As many things are off the beat and on the beat within the cycle. I could also extend the beat, quote-unquote, shape it, have a longer beat instead of having dong, dong, dong, have it dum, dum, dum, okay? [beats] I could take that place and shift it over one and have the longer beat but one pulse later. [beats] Basically, I'm giving you a phenomenology of an algorithm here. No matter where I put the beat and no matter how short or long I make that beat the pattern has the capacity to entrain that beat with equal validity. Now that might not have quite of made sense and here's the sort of formulation of it, but what happens when you entrain -- these are the binary times, on, off, on, off, on, off or off, on, off, on, off, on, on, off, off, on, off, off, on, off, off, or shifted one on, off, off, et cetera, and this is the third permutation. Each of those coincides and uncoincides the same number of times. So to design a pattern like that takes some doing. There are one or two within a span of 12 where you have seven pulses, where you can design a pattern that entrains with equal validity for every possible time signature, okay? There aren't that many. It's actually kind of a math problem, which is why I'm absolutely convinced this isn't just music of the body, but music of the mind. That's probably the biggest lesson to take away from today. I won't explain this level except very briefly for those of you who are tuned into this kind of talk. The zero, three, six, nine is moving across the time steadily from zero, to three, to six, to nine in ternary time, okay? That's what that means. The bold on zero and nine is when the beats are on and off. Two of them are on, two are off. If I shifted and rotate it to four, seven, 10, one, two are on, two are off, a different two. And the same thing, there's three on and one off in the lowest layer. If I go look down the columns I also get it maximally distributed, okay? So the on and offishness with seven pulses within a field of 12 is maximally metrically ambiguous, okay? Remember that this is also the structure of the piano, which has the capacity to modulate from one place to another and for you to be able to position, find yourself in the music, you know where you are in the music, musically speaking, not the words. Because of certain properties that it has mathematically. The colophony of the diatonic system, which has to do with every interval appearing a different number of times. That's probably a little jargonish, but for similar reasons this particular mode of entrainment or of patterning permits any of many types of entrainment or maximal metric ambiguity. Okay, I'm going to go into a slightly more speculative mode. I'm hoping that I haven't lost folks just yet. What you see on the left is Pingala's Metaprastar [Assumed Spelling], which is the Mountain of Jewels which he thought up many thousands years ago which is also known as Pascal's Triangle, but it also emerged in the context of a certain pneumonic device for memorizing Sanskrit passages that were opaque and so on and so forth and you didn't know the meaning but you could memorize through rhythm. And he designed this Metaprastar, which gives you the binomial coefficients. It also gives you the fubinache [Assumed Spelling] series if you slice through it in different ways and so on and so forth. So that's India, you know, what is it? Is it 6,000 years ago, I can't quite remember the date right now for that. It's on my notes, but I don't want to look. Pascal, we don't know if it's just a translation or if he actually reinvented it, could have reinvented it. And what I want to draw your attention to is this layer over here, one, three, three, one, just for the time being. There's a Sanskrit sort of recitation [foreign language] which was supposed to be a way of memorizing that layer of Pingala's Metaprastar. I want to compare it to the African rhythmic patterns that you have on the righthand side, but let me go there in more detail. One of the clapping patterns that's associated with enbitozamazima [Assumed Spelling] music is very similar to the gankogui pattern that we listened to. The gankogui remember had seven in the field of 12 and they looked a little bit like this. Okay, the gankogui and I've rotated it a bit, okay, started over here. Dum, bom, ba, bom, bom, bom, bom, ba, bom, okay? One of the clapping patterns that holds an ensemble in Zimbabwe together, which we will get to, has this kind of character. It fills in exactly that, but it fills in one of the beats over there, okay? So the pattern that you clap while this ensemble is going on sounds something like this. [claps] Okay, why is this pattern interesting? The first thing is we have in the mbira, world of mbira an equal problematic kind of way in which people are all on potentially on different downbeats and they're interlocking like this. So when you're playing the other person is quiet. It's a very difficult scene to hold together. So having a pattern that is maximally metrically ambiguous helps. But it's more, what if you get lost in this ensemble? What if for a minute you're just one beat off? Where is that beat when all the sonic input that's coming from the other members of the ensemble is pointing you in the wrong direction? Well, here's one technique for doing that and, again, there are two possible rotations here in math. This one is the one that's used in Zimbabwe. If I ask the question, which Pascal kind of asked, about how many ways are there of ordering say two elements in a field of say three spaces? So binary, think zeroes and one's or think dits and dahs, Morris code, or think longs and shorts, African patterns. How many ways are there of ordering say two, zero and one elements in a field of three spaces? Okay, so what I mean is we've got two elements, long and short. We've got three spaces to put them in, and there's a number of ways, a fixed number of ways that those can be ordered, right? We would call this two to the N, right, two things binary to the power of something, in this case three, okay, two to the power of three. Like this is what we would do. How can you create a sonic pattern that imprints that mathematical value, okay? So that if you get lost in the ensemble you know in an instant where you are. You don't want to wait, where is the beginning? This whole beginning thing was already problematized by the music, itself, so how do you position and find yourself? Well, consider that the two ways, the ways in which you can order two elements in a field of three would include, let's say longs and shorts, okay? We could have three longs, we could have three shorts. Everybody with me? You could have two longs and a short and then we have to recognize that there are three ways of ordering that. Long, short, long and short, long, long, right? So we have three longs over here. Here we have two longs and a short, so we go long, long, short. Long, short, long. Short, long, long. Just spelling it out. The other third permutation would be having two shorts and a long. Let's just do the same thing. Short, short, long. And now we'll rotate that in its threefold way and we get long, short, short. So short, short, long. Short, long, short. Long, short, short, okay? Notice that this is one, plus three, plus three, plus one. It's two to the power of three, which equals one, two, three, four, five, six, seven, eight, okay? That's what's going on and these are known as binomial coefficients. How would you encode that in sound? Well, let's take a look at this pattern, let's just call it off or three elements. The first three we can call them long, long, long. The second three, long, long, short. The next one, next three is long, short, long. Let's go up here, the next one is short, long, short. Then we have long, short, short. We have short, short, short. And then we have short, short, and we've got to spin it around this side, long, and finally short, long, long. One, two, three, four, five, six, seven, eight groupings. And what are they? Long, long, long is over here. Short, short, short is over here. Long, long, short. You can figure it out, but they're distributed right across that pattern. This means that as soon as you hear any three pulses you are exactly precisely located within that pattern. So your clappers are not just sort of having fun and, you know, they're actually guiding in a sort of metronomic way where you fit in to the pattern. Given that a big conductor pulse would just be absolutely disruptive, it would simply pick out one part of the performance that's actually multi-metric. Let me skip this, but the composer, Steve Rush [Assumed Spelling], actually took one of these similar related pattern and turned it into minimalist -- it was one of the founding moments of minimalist music. I'd be happy to entertain that in question time, but let's -- it circulates at this point as an ethnographic text. He read a lot of transcriptions through A.M. Jones, the Reverend Jones who had done a lot of work in Africa and so on. There's a long story to be told here about how things get. It's not just the Africarribean, there's different stories, and I haven't done that justice but I want to get you attuned to some of the issues. In fact, he wrote that piece and there's a sketch that he wrote and he considered it to be too African, he wanted it to sound more original, but he nevertheless stayed with the African pattern. Why? Because in a permutation setting you can't mess with these change of digit and everything falls away and the interest is considerably less. So briefly I want to just talk about African mathematics in general. I'm not an expert in the entire field, but I do want to draw your attention to it, just a couple of features of current research in this. Such as that into the archaeological sort of remnants of mathematical practice. In other words, when did we as a species begin to think mathematically, like when is the first baboon fibula not used as a tool but used as a counting device? And the oldest ones emerge as expected, in my view, from Africa. This eshongo [Assumed Spelling] bone that you see here is 8,000 years old. There's an argument about whether it's 9,000 or 7,000, you know, it's not my debate, but it's a long time ago and it predates a lot of numeric thinking. There's also the Lebombo [Assumed Spelling] bone in South Africa. What I just want to draw your attention to is not only like if you look at the markings that are on here, it's not just that we have a prime quadrant on the left which equals 60, we have certain kinds of ratios in the middle, and you can figure those out. But this one interests me because it's 11, 21, 19 and nine. This looks like decimalism in the form of N minus one, N plus one, to me, but I can just speculate at this point about how that kind of thinking gets to be amongst us as a species. Okay, so I want to end with two more genres of music to really get down more seriously into the way in which African patterns articulate very interesting mathematical worlds. Remember I talked about shifting and shaping or being off the beat or turning the beat around, and the other one extending the beat. In Africa there are considerable traditions that do both of these things. I want to turn you now to a kind of a region called, today called Uganda, that in some sense is a tragic place because when Motona Bota [Assumed Spelling] came into power in 1961 I think it is they soon after, he had the cabaco and the luberi [Assumed Spelling] court sort of destroyed and terminated, right? The cabaco is the former chief, as it were, it's a terrible word, but cabaco, okay? And in this court there was considerable music played, 24-7. It was a semi-urbanized area, said to be the source of the Nile, there are competing sources of the Nile, but it had a certain kind of stature. It was in pre-Colonial times. However, because of the way Colonial rule works very often what you do is politics, we're in the politics capitol, what you do is you amplify some part of your enemy, right, you separate and divide and rule. In direct rule you give your chieftans a little more power than they might have had and then they become corrupted in some sense or are seen later by the resistance fighters as complicit, right? We have this debate constantly at play. Unfortunately, this meant that the complicit court was then ended and all the instruments were burned and so on and so forth. So it's a fairly tragic environment. But, fortunately, there's some small positive affects of Colonialism, if one can say it that way. And Hugh Tracy [Assumed Spelling], who was commissioned to actually make recordings for the Rhodesian Government at the time, kind of reeked out, a little bit like [inaudible] and really got into it. He wasn't just doing it as a job anymore, and discovered this great universe of cultural making and made some recordings before the luberi court was ended. And so we have a few fragments of Hugh Tracy asking to demonstrate how this music works. Now this is interlocking music, but of a highly virtuosic character. What happens in this music is that across a single xylophone, known as the amadinda [Assumed Spelling], a performer will play a certan pattern. Bong, bong, boo, be, bom, bom, bom, bom, bom, bom, bom, bom. Very simple, but with octaves, not what you might expect. And the reason is because on the other side of the instrument another performer is playing in the spaces of that first performer, a pattern of a different length. So you're now nesting into one pattern of another, right? And this happens at very high speed, sometimes 600 pulses per minute. This is very seriously high speed. And what happens as a result is that because of this interaction notice this is actually from Kubeka's [Assumed Spelling] work, he made a depiction of this. Kubek is another interesting Viennese scholar who went and moved to Africa and so on, settled there. He made this depiction back I think it's in 1970s around his research, goes back to the '50s. A very interesting guy. Here is umwawuzi [Assumed Spelling], here is umwanazi [Assumed Spelling] playing on opposite ends of this xylophone called the amadinda [Assumed Spelling], right? And what happens, of course, if you play piano, think of two people on the opposite ends of a piano playing within the same register and never touching each other, right? You can't touch anyone because technically you're going to dampen the wood, right? So you're always going to be off when the other player is down, but you're occupying the same what in music is called the register or the same area of your keyboard, right? You're both coming down in that same area. It's not like base and treble, you're actually both in the middle. The music that comes to the ear is radically different to the music that's actually being played. The motor image of the performer doing this is very different from the audial image, which is construing this again using that phonic zelatrope [Assumed Spelling] technique by putting patterns together that are like phantom patterns. And these are taken out by a third performer, umaqanazi [Assumed Spelling], and the part is called the ookonira chunak [Assumed Spelling], and pulled out for special attention as a kind of resultant or inherent pattern. So the concept of inherent pattern or resultant pattern, which emerges in a lot of Western composition, again of the avant-garde sort. I will not bore you with those details, but that is actually an African concept of ookonira, to bring something out that nobody is playing, right? Take a listen to a short fragment, as I say these are compromised recordings, very short, didactic almost, at a long time ago. [ Music ] Your ear cannot follow that line, it can only hear the results. [ Music ] And that's the knocking brought out, the ookonira, where he's doubling the resulting pattern. [ Music ] Okay, we'll stop that one there. Very briefly, the music gets even more virtuosic with the akadinda, which is to say now you can also sometimes place two beats within the space of one and so long as you never touch the other performer. Take a listen to how this sounds in its more virtuosic form. [ Music ] Second part will come in. So far so good. Now the spaces of the spaces will be filled. [ Music ] Sometimes two beats, sometimes one. [ Music ] Okay, one wants to continue, okay? The very last music that I want to introduce you to is that of the [inaudible]. I've spent considerable time with this music. I learned how to play this before I learned how to play the piano, which is why I find the piano so fascinating as you can tell. But here it is and this is the last of the points I'm going to make, because I want to get into what's actually going on in those inherent patterns? Right, where is the beat? It's very, very difficult for a Westerner to place a beat there because in some ways the question concerning the beat is itself put to question, right? And that's perhaps what's at stake in this music, if you just hear water flowing or something like that you're not doing enough with your ears to open them to this field of possibility. Okay, here are what one might call three keyboard interface designs, right? How is the technology designed? And the reason I take this as a very interesting starting point for thinking through history and thinking through math is because in some ways once the interface design gets settled into a fixed structure it carries a kind of history and it doesn't get changed as quickly. When things become standardized it tells you something about that culture and how it standardizes, how it construes the body, right, as an interacting medium. So machine learning, all of this, how is the body construed in relation to the machines with which it interacts. We will always [inaudible]. The point is not that there's natural people over here and technological -- no, we are always technological. We automate fire, we're technological, we sit back, okay? We can watch things happen for us. So this is not the point. The point is how do different machines, how do different algorithms comport the body in its behavior? So take, for example, Qwerty, the typewriter, right, Q-w-e-r-t-y, where did that come from? Why Qwerty? This not how the piano is designed, which is also a typewriter, it's a typewriter for sound, it's a music inscription device that works like a phone, too, lots of slices that make melodies. Why are typewriters designed that way? They seem both efficient and inefficient, right? They're inefficient because you're kind of going back and forward, right? Why don't we just stroke through, like t-h-e should be, you know, it shouldn't be like ta, ta, ta. Why is it back and forth? Why does that interlock? Because the hammers would come flying into the same sort of end point, same focal point, and you didn't want them jamming. So you don't want people playing like a piano because the piano is in parallel hammers, this is in hammers that all have the same destination. You didn't want that clogging up. So you build in an inefficiency and make sure you interlock it a lot, right? So we get Qwerty. And then what happens is the theory of ergonomics or whatever it was that the engineers were working with have to take in account the 10 fingerishness and then they have commitments about what these fingers can do. And the commitments are usually these four in the West, these four are really good, they're facile, and this one is kind of bulky and stupid, maybe it just has two, you know? Whatever the reasons are, ergonomics and so on, you construe these as being more facile or quicker. And so early pianism, the piano, actually didn't even -- eliminated the form, right, you were supposed to do this. Plus it emphasized righthandishness. So we have in the piano high notes on the righthand side, low notes on the left-hand side. The very sort of, how should we say, scalar way of organizing pitch as well as time, but that's a different issue, okay? So instead of the circular one or symmetrical one this is a scalar one, right? So from left to right, it's a kind of darkness over here. And why did you put this slow stuff, why did you put the base notes in the left hand? Because the argument was that the left hands are slower because we're all righthanded. Well, I mean that's the sort of bias of technology. One needs to look at the values built into technological designs because if you happen to be lefthanded it's tough luck, okay, because there ain't that much music that really -- that's not entirely true, but generally slow movement in the left hand and then faster up here. And plus on typewriters it was like the space bar, which was huge and bulky, and you really eliminated one, you didn't even need it, but there seemed to be so transient, you know, you can just hit that space bar easily with the thumb, right? Same thing with pianism, it comports the body in a certain way and then we respond and we get really good at typing and playing piano. And so the model is, the engineers who are designing these systems are flattered and they think, yes, we must have been right about the body. So we are the order of complete for the incomplete algorithm in some funny way. But what I want to draw your attention to is that that's not the only way of designing music inscription devices. So if you just take look at the metepa [Assumed Spelling] over here or the [inaudible] over here, the difference is that your low notes are more or less in the middle of the instrument and the high notes fan off to the side, right? So it's kind of reflective of the symmetry or semi-symmetry of the body, itself. I'm not arguing this is better, it's just a different way of organizing your digitorum, right? And what's interesting is, I was going to bring it but it's too complicated to sort of play in the context of this environment, but if you were to play like a scale on this, because there's seven notes before the octave recurs in this instrument. You'd do something very strange, you'd have to start here, jump here, jump all the way across there, back there, back there, back there, back there, back there, back there to play just da, da, da, da, da, da. You'd be going -- it's very cumbersome to play. However, jumping by a fifteenth or by octave is very easy to play, okay? So it's construing the sounding forms that come out of this interaction with the body are very different as a result of that. No less facile, no less eloquent and so on and so forth. The other important thing about the mbira [inaudible] is that there's a division of labor between two performers, right? So where one performer is playing on the beat, the other player plays in the spaces of that beat, right? So this is not -- it's like the amadinda, you don't play simultaneously, you play and nest your performance in this kind of way. So where you're on, the other performer is off, okay? Let's listen to actually a solo performance by Gwanzuto Gwenzie [Assumed Spelling] just opening to hear some of the rhythmic complexity that emerges within this environment. [ Music ] Okay, again, pretty interesting patterns emerging out of this instrument. They say the mbira players that there's more that comes back from the instrument than what they put in, okay, that something starts to happen that's not under their direct supervision and it's music associated with the ancestral spirits and [inaudible] music of the ancestral spirits. I want you just to focus in -- this is going to be the last point for the night and I do appreciate you staying the course -- notice that the left-hand thumb is the one that is charged with two manuals, while the right hand has only got one manual. This is a reversal of the psychology of asymmetry in the West, that we're all righthanded and our technology is designed around righthandedness. This is in some sense constraining the left hand as being the dominant hand, okay? That's the first thing to take into account, there are different ways of understanding the human body and we can become just as virtuosic in different arrangements. But the second point is the final point, is I want you to take note of just what could possibly happen when you're only working with the left hand going up and down between these two manuals, okay? And remember that there's a second player in the spaces of the first player. And this is where I'm going to ask you to take a look at one more diagram because it's perhaps the most important point of the night, okay? Which is if the first player, the arrows up indicate what one player is doing, okay, so the arrows up are when one player is going ding, dong, ding, dong, ding, dong, ding, dong, ding, dong, ding, dong, okay? So let's say that that is a blue pattern over here, going up, down, up, down, up, et cetera, okay? The other player -- so that's arrows up, so I'll just make sure that that's the same as what you see on the PowerPoint. The second player is playing in the spaces of the first player, but let's say the second player is doing something also very simple but a little different, okay? Instead of going ding, dong, ding, dong, ding, dong, ding, dong, ding, dong, he's going dong, ding, dong, dong, ding, dong, dong, dong, dong. We would call that two-four time, dong, ding, dong, ding, dong, one, two, one, two, one, two. And then this one, so one, two, three, three-four time, okay? So I'm going to do like a three-four time in between and this one is going to be in black, happening in the spaces so we'll start here. Okay, et cetera, okay? So what happens is this player is going down, up, down, down, down, up, down, down, up -- and this one up, down, up, down, down. But the ear is picking up that layer, so you might be playing like this but the ear is only picking out the bass line, okay? Because the ear, this is the film, this is the movie, right? Where these are the slices of sound that are coming to the ear. And so what happens is the pattern -- I'm going to get a red pen, actually, I'm going to have to redraw this diagram because I didn't give myself enough space. But what I do want to do is show you that this is what the ear is listening to. First, that particular configuration, and in the top it's listening to the other notes, okay? So I'm going to do this just one more time, okay? So we're going up, down, up, down, up, down. And the other one is going down, up, down, down, up, down, down. Correct? Okay, everybody got that? This I claim is what we hear, right? And this pattern could be written as two beats absent, one beat absent, two beats absent, none, okay? So what I hear is something like dum, da, dum, da, dum, da, ta, dum, ta, dum, ta, ta, dum, ta, dum. So instead of hearing bing, bong, bing, bong, bing, bong, bing, bong, which is the first player or hearing dum, da, dum, da, dum, da, dum, dum, dum, what I hear is -- put these down, too many pens -- [beats]. Even though each player is doing something much simpler than that. From the perspective of Western theories of meter what was binary time before, dum, dum, dum, two-four or one dum, dum, dum, dum, three-four, becomes ternary, becomes dum, da, dum, da, dum, da, ta, dum, ta, ta, dum, ta, dum. Okay, that's the first thing, so there's a transformation of time that happens that neither player is in, okay? And that an emergent pattern that appears out of this. Why is this fascinating? Because if you change the smallest detail in your movement totally new patterns emerge that are not under your direct supervision. So if you're doing up, down, up, down, up, down and now suddenly you do what you teach people from the 101 of improvisation on this instrument, not up, down, up, down, up, down, but down, up, down, up, down, up -- it transforms the pattern completely. Why is that? Take a look at the second square. The first arrow down is doing exactly like the diagram up here, it's down, up, down, down, up, down, down. Again, down, up, down, down, up, down, down. That player has not changed at all. The second player instead of going up, down, up, down, up, down is going down, up, down, up, down, up. The emergent pattern over here, which that's the form, is very different to that form. And all I've done is change my sticking. So from a vertical motion I've produced -- this is like typing into a system and the code gets scrambled, right? You're not typing what you think you're typing. This is ventriloquized music, has something to do with ancestors appearing, okay? This is not how you would design a system for ancestors to appear, okay? And the final point is the very last point of the night, is that the curious thing about these patterns is that if you look at what emerges from here, dum, ta, dum, ta, ta, dum, and you were to look at this pattern does that appear anywhere in this pattern? The answer is yes, but six time points further, where you see the arrow here, dum, ta, dum, ta, dum, ta, ta, dum. So a pattern that is fixed has managed to dislocate itself or be set adrift from the meter and has shifted over or metrically modulated to a place elsewhere in that pattern, right? But not in a way that you might expect. This isn't I'm going to start a canon and then you're going to follow me like six beats later with the same music. But rather I'm going to simply change the smallest detail in the way I'm moving my form. And suddenly it throws this new voice into alignment, misalignment. In other words, it's not just the transformation of pattern that happens, but it's transformation that recoups similar to it, right? A similar pattern reappears as a phantom pattern, but dislocated from its reigning beat. Small wonder that the mbira players are going to say they hear something more than what they are putting in, okay? And what they hear, what these patterns are, just like in the ocarina [Assumed Spelling] is when they start to sound like a flute which has to do something with the harmonics and something to do with these inherent patterns, the ancestors come. Something is speaking because now you're typing into a typewriter making complete sense, it scrambles the code into a higher order coherence. It's talking in sentences but they're not yours. And I'll end there. Thank you. [ Applause ] It's eight-thirty so technically we're at the end, but I'm happy to entertain questions even if they don't make their way into whatever the format this gets delivered in. I think the first question was there, so I'm just going to do this, okay? I've seen five questions, I'm going to go one, two, three, four, five, is that okay? All right, thanks. >> I think you skipped over, I mean you skipped over a few slides, but there was one that had like [inaudible]. >> Martin Scherzinger: Yes. >> So I was wondering? >> Martin Scherzinger: Okay, those are symmetrical patterns that are drawn in sand in Angola, a tradition that barely exists anymore, to sonar patterns where you have to make your way through a series or a gridded kind of set of matrix and then find your way and create patterns of imagination and so on and so forth, but they have to be symmetrical in these ways. So it's a trick, it's a trick, it's a math trick. This was actually a secret kind of group, quite patriarchal, and so this is one of the tragedies though of African mathematics because the way in which you got important information was not necessarily through this principle of copyright, which is how one does it in the West, but by abolishing all evidence so that you can retain authority within smaller kind of secret societies. So it's one, it's an area of great interest and also in some sense tragic because how do we reconstruct these great mathematical traditions when part of the project was to eliminate the archive? And in the West we can talk about copyright as a way of giving authority to certain voices and that, too, is a system that has great affordance but also limits, there are serious limits, especially if we look at how some of the biographies of these sounds work, right? We have this music from Africa that is authored there, but then when it's taken up by Western musicians suddenly it becomes copyright worthy, right? That's another very important question, but I'll leave it at that. That's where that's from, Angola. Gerhart Kubek [Assumed Spelling] writes about it beautifully. Gergli Legetti [Assumed Spelling], who is a Western composer, also part of the avant-garde, he was like a highly funded composer of Europe, drew great inspiration from these diagrams, as well, when he Africanized his piano techniques and that's a very interesting new kind of piano sound that comes out of his because of this encounter. Hi. >> Can you talk a little bit about South African inspiration [inaudible] where did ancestors come up with these rhythms [inaudible] and everything around them, somewhere out in the bush, an orchestra in itself. I'm just curious if there's things, mathematical connection with things that are in nature that sequence in with these rhythms that are used? >> Martin Scherzinger: That's such a nice question, but it really is too big for me to engage. And I have to say that my focus is quite narrow. It's deliberately narrow because of my own biography and my own biographical sort of relationship to the land, which means I grew up in Apartheid and one of the dangers of organizing people according to cultural identities was that it very quickly becomes hierarchized. So I felt very suspicious about that from the beginning. I could see in some sense as a child unfolding before me great injustice simply because of the way people were being understood to be. And so for me understanding Africans as having very connected to dance and embodied and so on was a way of disavowing the intellectual work that was built into this. So when the question of environment comes up I'm a little -- I back off a little bit only because of that, because it's the idea that people are more natural or something. However, there's very interesting work being done that. I mean Steven Feld [Assumed Spelling] has done some very interesting work, looking at how soundscapes impact how people organize time. And you know anybody who has been to Africa, I mean it's an incredible soundscape, and just the simple rhythms of open space are something to behold. So it wouldn't surprise me if there's some kind of connection. The archaeology and all of those kinds of questions are extensive, you know, how tuning systems emerged. Most of my work that I've done in this region has nothing to do with rhythm, partly because I shy away from the idea that Africans have a special endowment for rhythm or something, and I use the pun intendedly because there's this cliche that comes with it. In fact, [inaudible] music is more noteworthy for me because of its profound harmonies and the way harmony works through space, which is a kind of fractal logic, which would have just been a little too difficult for an open forum like this. It's a more strictly mathematical set theoretical world and I would have had to start there and I would have maybe got a point or two across in that time. So I didn't do it, but imagine there's no rhythm in African music, imagine there's no dance, and now you're just left with certain tuning practices and harmonies and you get results that are even more mathematically compelling. I'd be happy again to talk right after if you're interested in that part. So I was always drawn to how this music is thought because the people, you know, we were raised in interesting ways in South Africa. I was raised by partly by my older sister and a maid, right, so I didn't ever understand this as being a kind of distinction, that I was encouraged to in the classroom, in our education system. Of course, I benefitted from white education, but at the same time my cultural wires got a little crossed. I forget who, was it you, sorry? >> The last recording that you played you had on the screen a picture of I guess a finger piano, a kalimba, and you called it a solo, was that a single person? >> Martin Scherzinger: Yes. >> Playing a single instrument? >> Martin Scherzinger: Yes, so that's Gwanzuto Gwenzie [Assumed Spelling], a remarkable player, absolutely remarkable player, who is basically imitating how it would be to play with two players. So I mean he's just a virtuoso, but if you put him together with someone like Ford Kwinda [Assumed Spelling] I mean things are really just unbelievable. You have to tune into it for a long time before you really get at what's going on there. These are all night spirit possession ceremonies and so on. After awhile it does feel like everything is just sort of automated, right? It's other worldly in that sense, but Gwanzuto is just a brilliant, brilliant, brilliant player and he made this recording because he came and took a visit to the United States. And you know that's what you do, you have your CD in your pocket and then you do your concert and so on. But traditionally you never play with one player, I mean in the context of mbira or an all-night ceremony you always play with a second player who is locking in, so that the whole thing becomes much more mysterious and phantom patterns can emerge. But, yes, a great player. I think, yes, sorry? >> How are we spelling, if I heard you correctly, the Angolan tusona? >> Martin Scherzinger: Yes, t-u-s-o-n-a. So a short question. >> And also the mbira in that other slide was I think on the right, I wonder where the other one [inaudible]? >> Martin Scherzinger: Yes, okay, that is called matepe, m-a-t-e-p-e, matepe. Matepe is, in fact, from the perspective of fractal logic that I've been working with, an even more interesting instrument than the [inaudible]. It is less played than the [inaudible] because it's basically what was once known as the Korekrre people, which is a dialect of Shauna [Assumed Spelling]. It's actually an independent language, but history has it that ... >> Korikori? >> Martin Scherzinger: K-o-r-e-k-r-r-e. Very few matepe playing families left in the world, but that is I think the Korekrre region is up in northeast of Zimbabwe or modern day Zimbabwe, an area that once controlled the salt pan, which for a landlocked land is gold, I mean you need salt. And it was once in my view a very dominant area culturally and then became in some sense impoverished through the forces of history, let's just call it that. And as a result of that the instrument is marginal today even in Zimbabwe, which is really interesting and kind of problematic because it is I think the source of much of the fractal reasoning in harmonies, but that was a different conversation but it's a fascinating instrument. Okay, one more question? >> How different is the matepe to the mbira? >> Martin Scherzinger: The mbira [inaudible]? >> Yes, because you said in the center you have your low notes and the high notes on the side? >> Martin Scherzinger: Yes, so that basic principle is the same, but you'll see all of the notes, the note configuration -- there are many more notes here, first of all, in most of them and then they're organized very differently. [ Inaudible ] >> Martin Scherzinger: If you can play the matepe that would be the place to go because the mbira [inaudible], here's the tragedy, remember I mentioned radio, too, where they were recording made for Africans to keep Africans in separate developed space, you know, so radio, too? Well, the mbira [inaudible] the one on the right happens to be the instrument that was the most played in the Colonial center then called Salzbury and the engineers didn't go that far, and so there's a great archive of mbira [inaudible] and the matepe sort of gets written out of history because it's a little too far away to travel so there's fewer historical recordings. [ Inaudible ] >> Martin Scherzinger: Yes, Stella Chuwachi [Assumed Spelling]. >> Is she still playing? Because I saw her here, there was some program, and I can't remember the name and it was all women. She and [inaudible] and others and it was really extraordinary. And they say she had to fight to be able to play the mbira because it's traditionally played by a man. >> Martin Scherzinger: Yes, it's a sort of patriarchal thing, but there have been some great woman performers. I mean Beulah Dyoko, who died recently, but she traveled with some really great players in the '90s. Beulah D-y-o-k-o, she died recently, but a magnificent player. I think perhaps better than Stella. Stella is kind of a little more hybridized. But, yes, it's a constantly evolving tradition. But the one thing that's interesting is that, as I said earlier, as a technology it didn't change much, like the piano, it sort of settled down towards the end of the 18th Century and then it reached its talus, right? I mean it tweaked a little bit, but the basic technical art lay, the interface design remained the same and it's that that becomes such an instructive microscope into history. >> You talked about how the music was created. My question is what did the dancers do with this? Can you look at one of these diagrams and know what the dancers would be doing? >> Martin Scherzinger: Okay, so the dancers do different things in different places, obviously, but take for example -- I'll just have to be brief so I'm just going to give you an interesting sort of schematic. Remember we started with the gankogui pipes from Mozambique, which was the second thing we did, but the dancers there remember move in a way that the instrumentalists are not playing, right? So they're going one, two, three, one, two, three, yafu, yafu, yafu, yafu. And then once that is locked in, once that felt beat is locked in, then there are all sorts of dancers with steps, such as 50 Boro [Assumed Spelling], which is a football. But you're feeling it in four, so you're not doing -- it's a bit boring, but you are feeling it in four. In the context of the mbira, which is sort of on, off, on, off, on, off, binary, right? Daka, daka, daka, daka, daka, daka -- and that's kind of basic principle. I mean here's a diagram that makes that apparent. This is if everybody is playing exactly the same thing. So ding, dong, ding, dong, ding, dong. And the other one ding, dong, and so but what comes to the ear is da, ta, da, ta, da, ta. Interestingly, what the [inaudible] does, which guides the dance step is not going da, ta, da, ta, da, ta -- now the music is in four, one, two, three, four, one, two, three, four -- it's binary, that's why, but the [inaudible] goes choo, choo, choo, choo, choo, choo, choo, choo, it's in ternary, right? And the dancers are going to move in ternary time. So it's kind of cutting across that again and, of course, the dancers become complex but the basic felt pulse is at, how should we say, at a kind of cross-current with the dominant musical input, okay? Again, I don't want to generalize this Continent. There are certain features, you know, it's interesting because even just the Nyungwe, which is close to the [inaudible]. I mean we've just got a simple Colonial border, almost a straight line separating them, so they're related but they've inverted that relationship of in the one we've got four against three, in the other we've got three against four, broadly speaking when it comes to the dance. But the question of dance is much bigger than this and the choreographic supplement is an important component of felt time, right? So I mentioned it sometimes and not always just for time reasons, but it's a great question. >> Is there anything I can look at or read that talks more about the dancing, any research? >> Martin Scherzinger: Yes, so my colleague, Kafi Agawu [Assumed Spelling], he's a [inaudible] musicologist, he write about Mozart and he writes about Africa, which is the way to do it because then you understand more the affinities and not just all the differences. Kafi Agawu, A-g-a-w-u, Princeton University, has written a book called Representing African Music, where he actually raises the argument that we need to be looking at the dance steps if we want to really understand how the felt metrics work. So, yes, what I was trying to suggest is that there's a number of possibilities and layers that vie for syntax formation and, of course, what the body is doing is one layer within that sphere. Yes? >> Can you go back to the slide [inaudible]? >> Martin Scherzinger: Okay, this one is interesting because ... >> Not that one. >> Martin Scherzinger: Oh, not that one. Oh, this? >> No, no, the secret, you talked about a secret communication pattern? What are those? I must have missed that sentence because when I look at that I see animals. >> Martin Scherzinger: Yes, yes, yes, that's interesting. So but what they are is symmetrical, they're sort of geometric shapes that are uni-linear, you cannot lift your stick or your pen if you like, as you create a symmetrical pattern through a series of gridded dots, right? And you then emerge with a pattern and, yes, of course, that's a lizard over there and so on and so forth, yes. >> So the dots are rocks on the ground or there's ... >> Martin Scherzinger: Holes in the sand, holes in the sand. >> Okay. >> Martin Scherzinger: And then you've got to step your way through it without lifting your stick and come up with a design. If you think about this mathematically there's some tricks that you have to know. >> Okay, I understand that now. I wasn't sure if these were dance steps or notes or what? >> Martin Scherzinger: No, this I didn't talk about because it's visual culture, all this is is an introduction to look, here's that bone, the ushango [Assumed Spelling] bone, and there's evidence that there's a sort of numerocic thinking in the region that predates most other regions of the world, at least in terms of archaeological evidence. I have a softer theory of this and that is that given certain problem sets people in different parts of the world might come up with the same answer. So I'm not saying that the piano, which came long after the gankogui pattern, I'm not saying that it derived from necessarily, I'm saying thinking in a certain set theoretic way with certain problems and aspirations in mind might lead you to the same conclusions, but I'm certainly not saying that mathematics was invented in Europe. >> Now that I know what this is I'm thinking [inaudible] part of the world. >> Martin Scherzinger: I think that's probably the next talk that's coming up with The Library of Congress, but, yes, so fantastic. I think we should probably close things up. Thank you for the great questions and thank you for your time. [ Applause ] >> This has been a presentation of The Library of Congress. Visit us at loc.gov.
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Channel: Library of Congress
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Length: 108min 49sec (6529 seconds)
Published: Mon Sep 25 2017
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