An outstanding Ukrainian composer has been working on the method of algorithmic composition since the 1960s. In the lecture for the Pandemic Media Space Project, Leonid Hrabovsky talks about the idea of a new book, invention of his own rhythmic and polydiatonic vocabularies, coding programmes, and actually how his music is created with their use.
Here’s the short explanation about my system of algorhythmic composition. I have to warn everyone about the fact that this explanation requires much more time than a 45-minutes lecture, or an academic hour, so everything will be explained, absolutely shown and proved in my book I started last year. The book will be named “Technique of my music language”, dedicated to the memory of Olivier Messiaen and Iannis Xenakis.
First of all I have to explain how and when I got to the idea to start my own system of composition. At the mid time of the 1960s there were mainstreams in European music especially in East Europe where a part of musicians went into sonoristic concept, most essentially it was donel in works of Penderecki, Górecki and especially underestimated Polish composer Kazimierz Serocki. So I myself paid a good price for a sonoristic concept composing several works between 1964 and 1967. But at the end of that I got to the conclusion that sonoristic concept doesn’t allow you to build expanded symphonic forms in a sense of great form and developing, with changes, with time. And looking into face representatives of 20th century literature, cinema, visual arts, I got to the conclusion that there should be something like a system that incorporates all elements and turns them into the unity. And especially big style requires a big and rich vocabulary and expanding one.
So at the very time I got ideas about those issues. First issue of “Res Facta”, Polish not maybe a magazine, but an anthology of texts, was devoted to contemporary music (RES FACTA. Studies in Contemporary Music (Kraków/Polskie Wydawnictwo Muzyczne, 1967-1989. It was the first journal in Poland to publish articles by composers, musicologists and critics who have later been recognized also by subsequent generations of Polish artists and intellectuals — D. S.). In this first issue I for first had seen the famous text of Olivier Messiaen, the “Technique of My Musical Language”, also the article of Xenakis about his new idea about sieves. I had no idea what it this means in his vocabulary yet but I only understood how he turns from his pure highly abstractmathematical concept probably to some diatonic ideas. Because it it seemed to be certain in some combination of intervals, making something between scales and the arpeggios and so on.
And also some ideas in this “Res facta” issue were devoted to the usage of random numbers especially in commercial art, in advertising. So I started to think how I may also build the diatonic things, because diatonics as Olivier Messiaen and Xenakis seemed to me much more unexplored yet, in new conditions. If this would be combined and united with techniques of random numbers, known in America as the “mapping techniques”, with some diatonic rows I have made myself and some rhythmical systems a bit later… So I started to build 7-steps diatonic model. I started to build them step by step, each step – a b c d h d f g, were explored in flat, in natural and in sharp. All that combinations gave me about 365 rows, after I eliminated everything that contained enharmonism, like g-flat, f-sharp and so on. These 365 7-steps rows I changed in 7 groups, of lengths like the piano keyboard and I obtained 104 polydiatonic rows from bottom а to top с and back.
So these 104 comprised was my very first vocabulary of my system pitch sources.
Then I turned to the rhythm and also started from skratch. At this time appeared the book about rhythm by Russian musicologist Valentyna Kholopova. She says there are two kinds of rhythm, accented one and time measuring one. I myself got to the idea that there would be three groups of rhythm: one rhythm is tied one, a group of syncopated ones, and then the third group of broken ones. I obtained about 2041 rhythmic figures of different structures or different proportions of syncopated ones, dotted and so on. This was my very first foundation for work with rhythm and in full for the first time it was used when I composed my piano piece Für Elise.
I have to show you first how it was looking in my working sheets in the 60s. First page of my 104 seven-step chains . Then I included in my list also as additional source of rhythm decî-tâlas which were used by Messiaen in his rhythmical vocabulary.
It was much later when I was already in America and everything was described here. Previously it was a work with pen and paper, coloured pencils and so on. Only in America after coding in list of computer programming language named Lisp, it put into action all that vocabulary rhythms I created there. I coded them — like that ♬like letter s, ♪ like letter e, ♩ like q, half-note like h and whole note like w.
This full vocabulary of my rhythm is now expanded to 8164 rhythm figures.
I’ll show you a bit how look the polydiatonics changes like that I name them pitchains, Here is the polydiatonic at least 104. This is the source itself. But then how to operate with them? I have come to the conclusion that there are two ways to operate with my pitch system. One is to extract short fragments of different length. In computer language this function is named SUBSEQ. Second method is to extract isolated ones and combine them, regroup them in pitch, in octave, in position and so on.
This second method I use mainly in maybe exclusively in my piano piece “Für Elise” 1988. This way I worked long enough, also when composing my choral work “Temnere Mortem” on texts by Grygoryi Skovoroda for an a cappella choir in 5 and 4 voices, a bit later with other compositions.
Many things I have composed in the epoch when computers were inaccessible to me. Only in 2008 there came the time when I got some help and advices from one computer music guru named Michael Gogins, who pointed me to the LISP programming language which fit my needs and allowed full computerization to my system of composition.
Everything was done, including reprogramming, coding all my rhythmical figures, coding my intonation vocabulary and all my 104 pitchains as I name them. And I got to the conclusion that it should be very important to elaborate the system to operate with them. So in computer language I found some functions, I get them from the LISP. One function that allows me to obtain all my vocabulary, and, as I said SUBSEQ allows me to get fragments of a different length. Now I may try to show you the functions. So for each of 104 there are specific functions determined on pitch, on particular tone rows. This is how I work with that.
When composing “Concerto misterioso” in 1977, I turned to the collection of 518 folk songs recorded by Yavdokha Zuikha (Явдоха Зуїха), peasant woman from Vinnytsia region, made by folklorist Gnat Tantsiura.
Everything there is also coded in list but it is the daughter system named Common Music, elaborated by two American professors by William Schotstedt from Stanford University and also Heinrich Taube from University of Illinois, Champaign-Urbana. This is a system of coding pitches just from their music. Here “f4” means “F of 1st octave” in European system and so on.
Here is the system of 518 functions get from Zuikha pitchains. It allowed me freely, easily and fast operate with fragments of Zuikha. But until the 1990s I had to do everything by hand, and it took me millions of hours of work. Now it has changed absolutely. So this kind of folk music I use it in my system of algorhythmic composition.
My music is built of chained fragments I call streams. Oleksandr Schetynsky claims to name my system ‘the system of meta series’ but I still think it less remains any series because any series are somehow strictly limited in beginning and the end. But my streams are simply made to avoiding any repetition, everything new and new according to the maximus, what said Arnold Schoenberg still at the beginning of 20th century. For me, my streams take some contrasts and maybe some different moments of step by step changes. So I got to the idea of getting the system of Fibonaccization and de-Fibonaccization in my sequences of rows, sequences of pitchains and rhythm units.
So if you take one sound, then two sounds and you repeat one, and join then you repeat three and pitches to full row to 34 pitches and you can go again. This process of Fibonaccization may be taken differently: you start from the end of that row and then you take the last one, then two last one, then three last ones then 5 last ones, then 8 so your process is going in the opposite direction.
Then de-Fibonaccization is a reverted process. You get four kinds of processes somehow connected with ideas of Fibonacci row. This is one of the most imported elements of developing my materials.
Another one is second somehow related to the medieval notions of rhythm talea and color. You can find it in books of historic medieval music. So if you repeat one of the same row of pitches but under them are laying different rhythmical units, you get some very important variations of this material. And in the opposite sense, you take one rhythm and repeat it with the a different pitch sequence, you get some reversed and transformed version of previous music. So combine all that principles in some unity I got to the conclusion that having 42 designs of building particular small constructions, I may combine and append them into a big form.
This is my idea to build hybrid forms incorporated into smaller figures and into bigger units.
And the final question of lecture’s listeners to Leonid Hrabowsky was
‘When you apply algorithms, how far can you predict the outcome sound result, what are your expectations?’
I owe some of the ideas of my muses of aesthetics to a man who passed away last year, to Boguslaw Schaeffer, a famous Polish composer, theorist, visual artist… (One named him the Polish Stockhausen). He urged to explore the boundaries of music and to go further. It was one of his slogans and “Horizons of Music” – that’s the name of one of his books. He said that you should try things that you may even be shocked by, and things that will astonish you or come as a surprise. So I deliberately went for it. And it really was. when I went to “Concerto misterioso”’s first rehearsal I was worried and unsure of what I would hear. After all, there is a 9-voice polyphony and even the fact that it could be played with ten fingers… (Then Xenakis writes a separate stave for each finger, so he can, but I could not). I just relied on Stravinsky’s assurance that the composer always hears what he composes, at least by calculation, and so I approach it. I hear it approximately, but usually the details appear when the algorithm gives me this or that text. I can change it, of course, for example, when I composed my cantata “Temnere Mortem”, I didn’t change anything except the regrouping of notes in height, change of octaves and only. There was no change on my part. I believe that the method of random numbers and the assumption of a certain moment of chance is a creative process, and it can give unexpected interesting consequences.
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