I was barely out of my teens when I met Tom Johnson in NYC and we started exchanging ideas about music and mathematics.  We continued doing that for more than four decades.  He left us on the last day of 2024 and I miss him greatly.  

One of his enthusiasms was "logical music."   Now this might seem a category error - after all, shouldn't it be be arguments and proofs, and not works of art, that are logical or not?  

Actually it turns out that formal logics in themselves just don't care about truth and correctness. Rather they're just oblivious rule-based systems that produce new thing from old things.  Well, sometimes they always produce new true statements from old true statements, and then that's very useful. So those kind of  logics are what people think of when they hear the word. but really the realm of logic is actually much larger.

So I understand Tom's program thusly: instead of having rules bound and bind our art, and also instead of attempting to reject rules altogether (if that's even possible), how about making works of art that, by design, faithfully project faithfully their own sui generis and hopefully intrinsically interesting rules?  With music, that means that both the sounds and the rules, so the logic, become potential objects of contemplation.  

Consider the duality of mind and brain, two distinct things with nevertheless thoroughly entangled existences.  So likewise the sound and structure of music.  By itself that's not new of course, music has had structure for millennia.  But treating musical structure as a first-class aesthetic object for contemplation by the thinking/listening subject, that was new.   Now structure could be more than a mere package or organization for the sonic experience, more than the mere bottle for the wine.  

My Elegy here is based on the fact that (11/8)^37 = 2^17 very nearly (the discrepancy is about .07%).  Both the rhythm and the harmony of this piece project this coincidence.  All the details emerge logically from the effort to project this little arithmetic coincidence.  

While the generating interval 11/8 is approximately 5.5 half-steps (actually more like 5.513), so roughly midway between a perfect 4th and a tritone (11/8 is the freshman sum of 4/3 and 7/5), if you pay close attention you will hear that the *logic* of this piece is actually not the logic of quarter-tone music, even though moment-to-moment it might have a sonic quality similar to quarter-tone music.  The faint, high-pitched wood-block type sound keeps track of this.  As Tom would say, "Just count the notes!"

Cover art from Tom's great book, Imaginary Music: 
https://www.editions75.com/pdf/books/Tom_Johnson_-_Imaginary_Music.pdf

Elegy for Tom Johnson (in 37TET)

polymicrotonal weirdness with max msp, 2018

PolymicroEtude7

This, my second mixed Trio in poly, features 17-19-21-23-25-28-31 seven note scale in the cello, that loops 6X against two polyrhythmic contrapuntal 24 unequal Pythagorean scale of al Farabi in the piano, and Ben Johnston's 6th Prime row of 25 unequal per octave, in the Clarinet. The interplay is finely thought out and responsorial. The poly trio is a new form I am experimenting with for more transparency for the contrapuntal interplay between the instruments in polymicrotonality. 2025

Mixed Trio in Polytempic Polymicrotonality #2

fucked up mess

Twist

This piece is an outgrowth of the previous sextet that is now a NONET, with English Horn, C Trumpet, violin, viola, cello, 2 marimbas, guitar and piano. This is fully polytempic, but is only standard tuned, no microtones. (unless of course 12tet in-itself is already microtuned as it deviates from just overtones) . This piece is sprightly and alive, quite the opposite of its composer, so that remains an enigma. 

Just Shut the Fuck UP, it's a Beautiful Day Outside and I have a Boner, so don't ruin it.

Like a wild Klezmer orchestra, everyone is going dixieland Mad with pdlytempo and polymicrotonality, for piano, guitar, violin, viola, cello, 2 marimbas, English horn and Trumpet. It's a mad drunken bar fight but, fun, a fun mad drinking bar fight. No one lives! Composed today and all week. This is related to the Boner happy day piece. You're welcome. 

Polymicrotonal Nonet I

This music is about how we are all fucked and Trump will destroy the Earth, as I've been fucking telling you idiots for the last ten fucking goddamned years and you just sat on your ass doing nothing. Happy Death. 2025

Nonet in Polytempic 12tet, updated version, for English Horn, Trumpet, Violin, Viola, Cello, two Marimbae, Piano and Guitar

Music for English horn, trumpet, violin, viola, cello, two vibraphones, guitar and piano. Tunings will be discussed later. Working on score, still. This piece is constantly evolving. 2025

Polymicrotonal Nonet, without Polytempo, version 2, for Violin, Viola, Cello, English Horn, Trumpet, 2 Vibraphones, Guitar and Just Piano

Totally synthesized version of nonet for acoustic instruments, all with samplers. Relax and enjoy, or I'll kick your fucking ass. 

Nonet synthesized, Version III

2 Trumpets, Horn in F, Trombone, Tuba in 99-98-97-96-95 ratio tempi relationships with "large" quarter and eighth tone modulations. Quasi tripartite form in a Schoenbergian sense in that there is no tonic-dominant axis for formal constraints, yet the microtonal modulations act in place to delineate form. Simple retrograde is employed to a general singular "diatonic" line multiplied and displaced by the pdlytempo. This is not phase music. This is still polytempo but at micro rhythmic gradations. Each tempo is marked by a .5 beat difference between the five parts. There is no convergence, only separation, like our country. Frankly, like the world today.

Polytempic Polymicrotonal Brass Quintet

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

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Elegy for Tom Johnson (in 37TET)

David Victor Feldman