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)

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

Please don't spam this account!

I'm a multi genre composer and songwriter.👇

Follow me for downtempo, cinematic, (nu) jazz, ambient and other music! 

Aim is to have an impact on your mood :-). Enjoy!

Love, Peter

PhD Student - De Montfort University
M4C DTP

Improvisations for recorders and electronics
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Releases:

Markus Reineke: "Was soll schon passieren" (pan y rosas discos)
http://www.panyrosasdiscos.net/pyr271-markus-reineke-was-soll-schon-passieren/

Ashwood/Bourne/Holtz/Hoogeboom/Reineke: "We Trust You"
https://martinhoogeboom.bandcamp.com/album/we-trust-you

Reineke / Wilke: "Sun Chief Moccas" (Muteant Sounds)
https://muteantsoundsnetlabel.bandcamp.com/album/sun-chief-moccas

Reineke / Wilke: "Born in Nature (Graftings)" (arborescence records)
https://arborescencerecords.bandcamp.com/album/born-in-nature-graftings

Reineke & Matthies: "waves on shore" (darkpebble-bluewave)
https://darkpebble-bluewave.bandcamp.com/

Hoogeboom/Reineke/Sanna: "Okapi"
https://martinhoogeboom.bandcamp.com/album/okapi

Markus Reineke & Paulo Chagas: "Machado Sketches" (Zpoluras)
https://zpoluras.bandcamp.com/album/machado-sketches

Reineke / Wilke: "KURGES" (Petroglyph)
https://archive.org/details/petroglyph381Reineke_Wilke-KURGES

Markus Reineke, Frank Wilke: "Dream Incorporation" (Haze)
https://hazenetlabel.bandcamp.com/album/markus-reineke-frank-wilke-dream-incorporation

I'll follow you back when SC lifts the follower limit (!)
Loving listening to everyone's music on here :-))))))))))

Elegy for Tom Johnson (in 37TET)

David Victor Feldman