Dr. Donald Byrd
"Math is Music is Art Symedicity: A Theory of Music"
Cornell University, Ithaca, NY
December 4, 1998
This presentation took place as part of the Cornell University Lab Ensembles Fall Concert (Karlton E. Hester, Artistic Director)
Donald Byrd: I brought all my winter clothes because I'm from the Midwest. I was stationed at Sampson Airforce base the next town over, and I don't remember December being like this. I was sweating all day today. I can't believe that this is December at Cayuga Lake.
We have been involved in something, we meaning the African studies department here, James Turner and with Dr. Karlton Hester, and my handy man here, Bill Johnson, we've all been hanging out, working together. Up here has been very fertile territory for me because we started something and it looks like its going to go worldwide, and its very timely. We're doing a thing called "Math is music is art" and what that's about is teaching music through math and math through music. This was something that I got involved with when I was eighteen years old, and I left Detroit, Michigan, and I came here to Sampson Airforce Base, and then I went down into New York City. I found that there was a new way of doing music through mathematics. At that time in 1950, everybody was turned off by it and a few were turned on by it. I was first introduced to it by a professor at Columbia University, where I later on got my doctorate. He had this system that a lot of people in Hollywood and in the studio in New York City were involved in. Its called the Schillinger system of music.
Joseph Schillinger was a math professor at Columbia. He was showing people how to play through using mathematics. That sort of stayed in the back of my head, and I tried to figure out a way, how could I improvise and use mathematics simultaneously. Later on when I met John Coltrane, who was one of the titans of this twentieth century, you can say he is one of the titans of the twenty-first century, because his music will go on forever, that I introduced John to the Schillinger method, and some of the other methods that were being used at that time. Like I said, it stayed in the back of my mind, and I used to write compositions based off of this kind of system, and like I said, a lot of people were turned off by the Schillinger system. It was a little bit in advance of its time. There were classical composers and pop composers who had used this system. Prokofiev is an example of someone who used that, and I found out that Prokofiev is the one who was very much involved in math. And Stravinsky used it.
A lot of people were flirting with it in how they were approaching music. Then some of the jazz and pop people were involved in it. Eubie Blake used to use it in his writing in the 30s and 40s. George Gershwin used it and studied it. Parts of Rhapsody in Blue and Porgy and Bess employ this technique. Then I was introduced to it in the 50s, and people like Quincy [Jones], and quite a few other jazz musicians, like John Coltrane and so forth became involved in it. So then with what is happening today in America, it seems like its kind of timely because Karlton Hester and Bill Johnson, we have been talking about this for the last three or four years, and I've started testing it in public schools, just recently, I was in my home town Detroit, and there was a big organization there that is very much involved in education and training kids. A Catholic priest, I didn't get a chance to meet him before he died because I just became involved in this organization a year ago, and he died a year, a year and a half ago. But he has an incredible organization over there. If you're ever in Detroit, go to Focus Hope and look at this educational institution and what they're doing.
I just found some figures over there, that the people that they take from the inner cities and some of the economically deprived people are going to this school. If they graduate from the program, then the industries, auto industries and other industries, will hire them at the same rate that they will hire people from MIT, and they will start them off at a salary about 2-3,000 dollars higher than people graduating from MIT. Students graduating from MIT average somewhere around $45,000, at Focus Hope, their starting salaries are averaging around $47-48,000.
So they asked me to come and to introduce this pilot program, and they gave me four intermediate schools to do this program, and two high schools, my high school, Cass Tech, and Henry Ford High School. And I was very surprised and happy to get the type of attention, enthusiasm, and interest in this program, and we are trying to introduce a program like that around here in Ithaca. There are a couple of people who are planning to do something at the Lou Gossett School, I was supposed to have done something there this week, but my man had some problems, and didn't allow me to do that, but I will be back to do this thing. I have been asked by John Conyers to do this in the state of Michigan. Also they're asking me to do in the state of Ohio, and also the state of Delaware where I'm currently employed at two schools, the University of Delaware and Delaware State University. So I wanted to show you some of the things. You see what I found out here is that some of the students here are so fast. We got involved in something last night, and I didn't realize that I had them up until damn near 2 o'clock in the morning. But that's my usual thing, because I'm so used to hanging out all night long. See I don't function during the day. During the day, I have to get back in my box. Then I'm like all the players. Like Coleman Hawkins, he says he can't play jazz while the sun's shining, and I agree with him.
So, anyway, we were fooling around with some things. To give you an idea, you know that music is an international language. So is mathematics. You probably know more about it than I do because I've had to go back and reorient myself because the operations and procedures and the language has changed since I studied Algebra and geometry in high school. A lot of the reason why is that most music schools - hardly any music schools in the country anyone teach music through math. I've taught at many of them, Oberlin, North Texas, Rutgers, Queens College, Howard University, North Carolina Central, and at all of those schools, I've started, or helped to start the jazz programs; that's been my thing, starting jazz programs in universities throughout America. You see, every time I've taught at these various schools, Juilliard, and all that, I've never seen anyone teach music through math. And today it's still the same thing. In some cases, they will recognize that Pythagoras had some involvement with the music system, about acoustics, about the overtone series and things like that. But when it gets to melodic lines, the harmonization and so forth, the music departments are reluctant to incorporate this, they're still dealing with, 14th, 17th and 18th century harmony, and music has moved way past that, and I'm sure even now going into the 21st century, that you have a lot of composers that I'm not even familiar with that are using all of these new techniques in electronic music and other things, probably using computers and so forth, that they're really going way out there in space.
Mathematics is not only universal, but its interplanetary and galactic. They were talking about this relationship to the world and to the planets. So I don't see why we're so reluctant to teaching this and getting involved, when you have in America today schools such as those in New York where they had to go and hire quite a few of the math graduates in places like Austria to come and teach in the US because of the lack of applicants and so forth applying for jobs, as far as mathematics is concerned. So that is a big thing in education.
The other thing I find that is really critical is the fact that America scores the lowest in mathematics out of all of the developed nations in the world today. So I was thinking, how could I relate this to kids and people, and make them interested in it because all of these numbers, everything today involves numbers, your social security, your driver's license, pilot's license, everything has a number, so how can we orient and reorient people to get them to really examine mathematics and see the importance of it. So what I've done is see if I could do it through music. And I will get my friend Douglass Huang . . . I wrote some piano pieces for children, and they deal with mathematics.
When you get a kid, a kid doesn't know anything at all about what's difficult, what's hard, and its only when he gets to school that everybody starts teaching him, don't do this, don't play this, you're not supposed to play that high on the trumpet, because that's not the way its supposed to be played. Everything is don't, and by the time you've graduated you know what not to do and you have to figure out what the hell am I going to do, and everyone is trying to create something, but how can you do that if everyone is constantly telling you, don't do that.
So what I have gone back to doing is just exploring everything, I do what sounds right to me. I'm sort of following in the footsteps of Duke Ellington. He played music that appealed to him. He wrote chords because it sounded good to him. He orchestrated them and put different colors and so forth, he would mix all the instruments. If he had a chord, he would take the trumpet section and put each one of the trumpets on a different note, using a different mute. So that means that when you put a straight mute, or a cup mute, a wa-wa mute, a hat mute, a plunger, on each one of the different trumpets, and then you would tell them, okay, play the chord. Well that chord is going to scream and make sounds that you have never ever in your life heard. But who says you can't do that? If you go to a traditional music institution, they won't let you do that. Seriously, you won't see a symphonic player come into the New York, the Boston symphony, Baltimore, any of the symphony orchestras with a plunger. (Laughter) They will be found in the basements and in the toilets of the homes, not on the Carnegie Hall, Lincoln Center, Kennedy Center, places like that. That is not part of your equipment. Then, Duke Ellington turns around and uses all of those things. But that's what makes Duke Ellington different from everybody.
Thelonius Monk -- sometimes, if he played the wrong note, Monk would say, all right, leave that in, because it sounds good, and it made him hear something like he had never heard it before. And that's what we're always looking for. I'm looking for a note, a chord, a sound, anything that will make me think differently and throw me into another orbit, or something. That's the way Miles was. Herbie Hancock was playing a chord one time and played something wrong, and then Miles came and played during his soloing, he played some notes and altered them so that they started right. So, that's what you're always looking for, how can I resolve this, how can I make this note move there. Its how you move into something and how you move out of it that's important.
Through mathematics, I found something in my training of higher mathematics, which is like arithmetic, division, multiplication, and substitution, (laughter) that's about as high as I've gotten (laughter). But when I found out something the other day, about higher math, like the associate and the commutative operations and values, I found something slick. When I found out that a + b = b + a, I said oh really, and I tried that with some chords, and you know what, the damn thing works. Then I went into advanced math, the associative, a + b + c = c+a +b. Again, it worked. And so now I'll show you how I did it, using numbers.
Now, I took this tune, "Visions", and I just took a low chord, this is a thing I wrote for John Coltrane a long time ago. I made more records with Coltrane than Miles did, over 14 albums with Coltrane, and here was something a little simple that I did, but then I took one little harmonic, and changed it, to get a distinctive character. The first 16 bars are very simple, but then I used a technique, like Mozart and everybody used, and people like Verdi. Verdi wouldn't teach you the opera until the last minute because he didn't want you to steal the arias. So he taught his solo parts just before they got ready to do the.
Music has to have surprises. Music is a drag if you know the end before you've ever even heard the beginning. So you've always got to put a hook in there, that's what we say in the recording industry. Something that makes you hear something and say, "you know what, I've never heard it like that before, that's different." So, I've been writing these pieces for children because they don't have these preconceived notions about what's good or bad, music or noise, and stuff like that. So I want to introduce a children's piece, a simple little piece, and see what you think of it.
(Douglass Huang plays "Child's Prayer")
What I did there was just to develop some chords moving in contrasting motion, and then at the end I played a chord, and made up a sound that incorporates every note in the chromatic scale. Doug would you just play all the notes of the chromatic scale?
(Douglass Huang plays)
You see that's the harmonization of every note in the chromatic scale. You see there, what is critical, depends on how you place it. That's what I learned through involving mathematics, is to put notes in a logical sequential pattern, and it comes out as music, and its logical. You see logical people will do logical things. Illogical people do illogical things. I employ all of the simple harmonic techniques that I've learned in composition, in everything I do, there's nothing new or different. If I use the associative fashion, I can play that chord or that sound up, or I can play it backwards, and it's still going to come out the same way. If I took all of those notes, mathematically, and rearranged them, and permutated them, its still going to come out. But you see very few people ever think about taking a piece of music, or taking a sound, and say, ok, how can I rearrange this? There are two ways that you can approach this, you can either approach it in an intuitive fashion, and you'll be sitting there guessing, trying to figure out what to do, and it will take you years; you might come up with something, you might not. But if you employ the scientific way, the empirical fashion, then you can sit there and do it mathematically and come up with all of the permutations that come out with it, and as the kids here said when I asked them about some chords. I asked them, "How many different ways can you do that?" And it reminded me of when I was at Oberlin Conservatory teaching this, and their reply was the same, "big numbers." So you don't want all of these musical combinations. You still have to use musical taste and say, you know I like this, this is a hip sound, this is cool. I don't like that. But at least, you can come up with all of these variations and combinations like that.
Another composition that I wrote like that for children. This is "Visions".
(Douglass Huang plays "Visions")
That's all it is. When I did that, I used just a simple mathematical formula. Its minor third, perfect fourth, minor third, perfect fourth, minor third, perfect fourth. But then I put a variation, I put, minor third, perfect fourth, down a half step, down a half step, minor third, perfect fourth, down a half step, down a half step, and it brings you back to the octave. Doug can you play that.
(Douglass Huang plays)
And then play it in retrograde backwards.
(Douglass Huang plays)
And then see there was one time when there was contrary motion going up and coming down. Its just the same backwards.
You can take any series of numbers. I can take that minor third, perfect fourth, down a half step, down a half step, and if I turn it into an algebraic expression, it would be, 3 minor thirds + 3 perfect fourths + 4 half steps. So really that could be a + b + c, and then playing it backwards would be c + b + a, or it could be b + a + whatever, or c + any arrangement that you play. The point is to go from one octave to the other octave. When I put a slick beat to it, and push it up to about 96mm, and if I said (beats and sings pattern), some kids in Detroit said, would you do some rap to that? You can put it anyway you want to put it, its still going to come out the same way.
I'm one of the most sampled artists in America. They use all of the music that I did in the 50s, 60s, and the 70s behind people like Tupac, and LL Cool J. I'm one of the first to take bebop and mix it with hip hop and guru, and gangsta rap, and stuff like that. I'm into all that stuff. The music I did with a group called the Blackbyrds, out of the sixties and seventies. There's a new movie out called Slam, it has my music in there. So, when you put down something, and its really slick and constructed right, something like that can be sampled and used forever.
Now the way that I introduce this
curriculum and everything like that to young people, I wouldn't dare come in
talking about some bebop, they don't know a thing like that, that's for older
people. What I do is come in and say, how many of you are into DJ Premier, and
gang style, and right away, that's my hook, I got them after that. I can take
them anywhere I want to take them, take them all the way to college calculus.
Because then they can relate to something like that.
I took Blackbyrds to Detroit and then I started doing some of the things there that I've demonstrated for some of you. Some of this is going to be published in the Call and Response journal, the first issue's coming out soon, and I think its going to be a little bit different. You're going to read articles in here (holds up an issue) that have a perspective that I don't think you are used to seeing and hearing.
Something else I've done for the kids, I've taken that line I've shown you and, using the x and y axis, turned it into graphic. Now I can take this same thing, and turn it into a picture, and I have evolved patterns from that. In other words, I've taken this from math or music into visual art, and now I'm into fractal music and fractal designs.
The point is that with using numbers and mathematics, there is no end to what you can do. The other thing is that I just employed the federal mathematic standards, which involves this program too. I used the guide handed out by the federal government for New York State. So I incorporate everything. Geometry, patterns and designs, I teach students all of the different shapes. See, once you've got a kid interested, and you can show him how to do anything. I can take his telephone number, and I can take his social security number, and I can take that and use the horizontal aspect of it, and turn it into a rhythm pattern. Then I can take it and turn it up from a vertical standpoint, and make a melodic line out of it. So I can take the outline of the city of Detroit, the Ambassador Bridge, New York City, and turn it into a piece of music. I can take their phone numbers, how much money they have, talk about percentages, fractions, anything. You can do anything you want with it. And then you can relate the operations the same way. I can take a plus or a minus and do the same thing. If you add something to it, that's a plus, in music you just add a sharp. If you take it and you put a flat before it, you subtracted something from it, that's a minus.
Then you can take all of the different notes, take a line with all eighth notes, and put them in different spots, and go into syncopation, and that's like percentages and decimals. You can play games all day long with it. That's if you really want to get involved. Not that this will teach them to go into space, or something like that, it might help them. The point is that you can work with them. This is just another perspective, another way of approaching it. Let's take a simple line like the one in the song Doug just played, and show you the permutations on it. This is the tune that I did called, "Toussaint" that's my middle name.
(Douglass Huang plays)
This is also shows what you can create using a minor third and perfect fourth, and different permutations of it. Take a minor third, perfect fourth, you can move it up a half step, you can move it down a half step, you can make it resolve into another minor third and perfect fourth, and so forth. This is just with those two intervallic structures. Those two numbers--minor third, perfect fourth. This I developed into a clarinet concerto. But we'll just play the lines a little bit:
(Douglass Huang plays)
The piece goes on and on and on. You see there's no end to what you can do. You can put it to rap. If I had to write a movie score, which I've in the past, I can put that into certain sections. Then if I had to, for instance, a lot of the old cartoons and the old TV shows of the sixties and the seventies, where you had to play (sings) Now here you have to take that theme, and you have to use that theme through the whole television show. Here's where you really have to play a mathematical game. You've got to take that one simple theme, and you can never vary from that, you have to use those notes, but then you turn the different rhythm patterns and things around like that. That's how incorporating this stuff with the kids.
Now I'd like to open it up to the floor. Sir:
(Audience member: "Can you talk a little bit more about how you can use mathematics to construct rhythms?")
Simple. Lets start off with a simple thing. Beethoven's fifth goes how (Nah nah nah nah). During the second world war that was an unbelievable thing, because what else did it imply?
It was taken out of the Morse code, and it was dot-dot-dot-dash, and that Morse code represented V, and V was used for Victory, or in Custard's case, that stood for, there's only two of us left. No-sorry. So you can take that. Or Mozart (sings) But that's a mathematical formula. If I took your social security number, and I said 1 = the eighth note, like I've done here on the graphs and things like that. If its two, two eighth notes would equal to what in 4-4 time? A quarter note. Three eighth notes are equivalent to a dotted quarter. Six eighth notes are equivalent to a dotted half note. That's how you can make your rhythm patterns. You can use it with sixteenth notes, you can put it in 3-4 time, you can put it into any metric system. Now, turn it into a vertical thing. That's where you can with your math, you can change the operation from base five, to base 7 or 8. We use base 10, right? If you change it to base 12, base 12 would be equivalent to what in music? The chromatic scale. Then you start playing games with those numbers. Then you can take the same thing and play numbers with the alphabet. 26 letters, so you've got 26 numbers. That's in the first row of the alphabet. Then you can do the same thing with the chromatic scale. You've got one octave, 12 notes, 24 second octave. The horizontal line will now become your rhythm pattern. You turn it this way, and it becomes your melodic line. Cool? That's it.
Any other questions?
(Audience member: "I just recently read Bill Cole's biography on John Coltrane, and he's discussing that during the writing of a love supreme, Coltrane had started to research some Indian philosophy, and utilize the concept of the triplet, . . . In some of your music I think I picked up not only just math, but history and culture also in that piece he just played "Toussaint L'Overture" Can you expand on some of those ideas?")
Well, concerning Coltrane's spiritualism and so forth . . . You know Coltrane has become a religion. In San Francisco, he's treated as a saint. There's a church out there. The only thing I can say is this. I knew John Coltrane. I met him in the 11th grade in Detroit. I skipped school one day to see Dizzy Gillispie, and that's where I met Coltrane. Coltrane and Jimmy Heath just joined the band, and I brought my trumpet, and he was sitting at the piano downstairs waiting to join Dizzy's band. He had his saxophone across his lap, and he looked at me and he said "You wanna play?" So, he played piano, and I soloed. I never thought that six years later we would be recording together, and that we would be doing all of this stuff. The point is that you never know what happens in life. There are people who knew him better than I knew him, people like Elvin Jones, who they said that they don't know him either. And here he was with Trane every night. You never know. I never thought that he would be emulated like people today. Sax players and everybody today still loves him and believes in him, and copies his style of music. That to me, like I told you in my opening statement, when you talk about titans and genius, is what my definition of genius is: people who come into a situation, and change the direction of it forever. And forever is a long time. And that's what he has done.
Today Coltrane has been dead for thirty-some years. I never would have dreamed that he is what he is to the world. He change the way that that instrument evolved. There have been many sax players, clarinet players, who have played an instrument and who have been outstanding. But that doesn't mean that they changed that whole style of music, and I don't mean one type of music, I mean in the world. When somebody does that, that's something special. People like Coltrane and Charlie Parker, changed the direction. I want to play something.
I just want you to hear something. (Asks the sound engineer) Is that set up? Would you run it? We're one year from the end of this century. This was created here in America, and this changed the direction of music in the world. I brought a composition that changed the direction of music in the world. The most popular man in the world, still today, is Louis Armstrong.
I was sent on a tour of the world, by Philip Morris. That was a funny tour, we hit a different city every night, and we were promoting cigarettes. There were about thirty some people. Only two smoked cigarettes. But we got to see the world. It was really slick. The point is that everywhere I've gone in the world, everybody knows Louis Armstrong, there's no question.
(Audience member: "I was interested in the idea of collecting numbers from driver's licenses and phone numbers in order to have a lot of numbers, so that you can create something that goes onto infinity and encompasses everything and you can go anywhere with it. I was wondering if you thought about, there's this computer program called a "Pseudo Random Number Generator", which can generate more numbers than you can possibly collect by hand. One nice thing about the pseudo random sequences is that if you wait long enough, you can find any particular short sequence that you want. In other words, it encompasses everything, so it can go everywhere. So, one thing I did was that I mapped the numbers from a "Pseudo Random Number Generator" to notes, and I guess when I heard, I didn't think much of it, but it sounds like that's where to go")
Well see, you've hit on it again. That's all I've been talking about on campus is numbers. We are talking about the possibilities, big numbers. You used the expression, math and music is universal. You said intergalactic. He really tripped me out. But somebody was talking about, with the operations and the computer, where you can go from the binomial to eight. There's no end to it, by doing this program, you can also get the kids to write essays, and get them to think, that's taking them to the next level.
(Audience member: "I'm interested in what influenced you to start making recordings with electronic sounds. Especially in the early seventies with the Blackbyrd for instance. What were you listening to that made you start thinking of that? . . . like 'Bitch's Brew', or anything like that?")
When I brought in James Brown's records to Blue Note, they literally threw it out the window. I was put down by all of the jazz people, by all of the clubs and everything in America. When Tony Brown at WHER started playing my Blackbyrd album in Detroit, they had to re-service all of the rock stations in America because all of the rock people said, that ain't rock and roll, and all the jazz people said that ain't jazz. The people who got me interested the pop concept were the Miezel brothers of Englewood, NJ, who were my students at Howard University. They wrote ABC, and everything that Michael Jackson ever did, and they didn't want to be bothered with Michael. I was trying to teach them Jazz and Bebop at Howard,, and they were teaching me James Brown, so I think we both won. I started the Blackbyrds, and that's when Herbie Hancock started the Headhunters. Out of that, I had maybe 16-18 gold records, back to back. That's how it started. My latest thing is playing this music here and explaining this to you.
In Chicago, Illinois last year, when I played those tunes, "Child's Prayer" John Coltrane, and the other, "Visions" or something like that, using this mathematical system and so forth, they wrote in the Chicago Tribune (I forget the name of the other paper in Chicago), "Do not go and see Donald Byrd play." Then they said, "he doesn't know what he's doing, he's deliberately playing all wrong notes." That's what happens when you try something different. So now, I've introduced it, and the kids in Detroit have accepted it in every place we've been talking music and math ever since. They like it, so I'm going to stick with what I believe. I don't believe in following the leader. My thing is about creating music, not recreating music. If I were to do what most musicians are doing today, I would play music 50-100 years old. I don't play 100 year old music. I never did. When I had the Blackbyrds, they were putting me down but the records I sold out.. Now I'm doing this stuff with Hip Hop and Guru, they're putting me down , but our records are sold out again. So every time I do something, and lead the way into something brand new, everybody hates it. But I can't wait until they catch up to what I'm doing. So I'll see how fast everyone will catch on to what I'm saying now.
I'd like to ask this, in closing, what do you think about what I've said, and the way that I'm approaching music. Do you think that it can help kids, do you understand it, or what? Can I get some comments?
Anyway, that's what I believe in, and that's where my head is at.
So, we'd like to maybe do a simple thing. We'll take something and fool around with a line, and we'll close out this thing with a thing called " Bye Bye Blackbird." Anyway, I just wanted to take this opportunity to say thank you very much. You have really been receptive.
(Plays "Bye Bye Blackbird")
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