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Dodecaphonic Etudes
for various instruments

Work nos. 15, 157, 245, 246


    One of my professors at college was very fond of a story about a painter who used to be a mathematician, and quit "because he realized he didn't have enough imagination to do mathematics – only enough for art". And although circumstances led to me getting a degree in applied mathematics, I always felt like that painter. Years later, when I became a composer, no matter how hard I tried, it was impossible for me to truly understand complex 12-tone music; when I set out to create my own 12-tone piece, I decided to use a randomly generated row, and limit myself to its four forms and their transpositions – no clever symmetries and such.

    So the music employed the rows as symbols. The first etude had the row stated several times, then an incomplete statement ends the piece, like death. In the second etude, the row is always stated as is, but it exchanges its first and last notes for the second statement, then that form exchanges its 2nd and 11th notes for the third statement, etc. Eventually, the last statement is a complete retrograde form of the original. At the same time, the first few statements each employ a distinct pattern of (almost serial) durations, the last then go through the same patterns in reverse order. I thought of it as a kind of mirror inside a mirror.

    I got the inspiration to complete the next etude in early 2023, after composing a few somewhat "mathematical" pieces – Taşlar Yerine Oturmuş for solo pipe organ, loosely based on the concept of Shepard tone, and Study V for MIDI-controlled piano, which superimposed a number of duration patterns in ways impossible to play for a human. The solo pipe organ etude keeps the same arrangement of tone rows (prime followed by retrograde in the keyboard, inverse in the pedal) but goes through three permutations of duration patterns, the one first heard in the pedal rises to the right hand part by the end of the piece, like an emergence of something new from an unchanging structure seemingly incapable of producing anything new.

    The fourth etude was composed immediately after. Here too there is an emergence of something new, but it happens because something old is dying. The prime tone row used in the piano part keeps losing notes, which end up going to the saxophone part. At first, the saxophone only has the 12 notes of its row form to play, but with each new row statement come notes taken from the piano. It becomes 14 notes, 16, 18, eventually 24 notes to play, and the saxophone part becomes more and more complicated. At the same time, the missing notes in the piano are substituted with notes from a single inverse form of the row, which finally appears in full at the end of the piece. The slow process of the piano rows eventually ascending into the "sky" of saxophone was another type of death image.

    Each etude comes with a "deep meaning" epigraph from literature, or a quote from some historical figure; this extra ponderousness tips the pieces over and prevents them from being too full of themselves – otherwise all this abstract matter, death concepts, etc. was becoming a bit too much for me.

    Dodecaphonic Etude 1 – PDF score   Dodecaphonic Etude 2 – PDF score   Dodecaphonic Etude 3 – PDF score   Dodecaphonic Etude 4 – PDF score

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