Suppose that a musical monochord sounds at frequency F.  Stopping the string at two places, so dividing it into three segments, causes those segments to sound at frequencies A,B and C satisfying 1/A + 1/B + 1/C = 1/F.  

Now if one plucks the stopped monochord at a random place, the lowest of the three frequencies (attached to the longest segment) will sound with the highest probability, and vice versa.

As this piece develops, the stopping of an imaginary such string evolves so that the mathematical entropy of the random process stays approximately constant but gradually increases (until the stopping points divide the string into three equal parts).  A graph of this looks like a tight triangular spiral.

Finally the durations of the notes correspond, by design, to the probabilities at any given moment of the three frequencies --- but in a different way in each of the three voices.  A high frequency (unlikely note) in the first part grants the next note a long duration; in the second part a high itself gets a long duration; and finally in the third part a high note grants the previous note a long duration (so, from a listener's perspective, a long duration in that part heralds a high frequency coming).   This presents the listener with a counterpoint contrasting three different but related music logics.  

Another version of the piece works almost the same way, except that low frequencies correspond to long durations.

A score for an 12-tone equal temperament approximate version dates back to the late 1970's, but never received a performance.   This MIDI realization realizes the pitch relationships quite precisely, and perhaps supersedes the piece originally conceived for human players.   


Trio Entropicum (first version)

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

Please don't spam this account!

To all concerned: 
I am announcing publication of my new book, NOW AVAILABLE:
https://www.routledge.com/Maqam-Melodies-Pitches-Patterns-and-Developments-of-Music-in-the-Middle-East-and-other-Microtonal-Writings/Thoegersen/p/book/9789815129052
My book, Polytempic Polymicrotonal Music, is available on Amazon. 
https://www.routledge.com/Polytempic-Polymicrotonal-Music-The-Road-Less-Traveled/Thoegersen/p/book/9789814968294

I have a new album out through Magic&Unique Group Records on Spotify and other digital streaming platforms:
https://open.spotify.com/album/5qWHmcvyAemvVn2TJH1bio?si=OD5TmPptQ-ypr8WOI0EZKA&nd=1

https://whitecentipedenoise.com/products/peter-thoegersen-facebook-cantos-cdr-flea
My CD via Flea label has been out since April, 2021, featuring the wonderful Lore Lixenberg singing over my microtonal piano accompaniment
Hope you enjoy it!

https://www.newworldrecords.org/collections/vendors?q=Peter%20Thoegersen

From the liner notes on my CD now available on AMAZON and New World Records:
"The author of these notes has spent his life explaining radical music, and the music on this disc may be the most radical I've ever written about. Peter Thoegersen (b. 1967) is not yet a name known to the music world; not for any lack of connection to other famous musicians, but because he came to composition late, and because his artistic aims are so broad and complex that they have taken years to evolve. His aesthetic is well defined, and he is upfront about having a name for it: "Polytempic Polymicrotonal Music." That means he has musical layers simultaneously moving in different tempos, plus, even more radically, that he has different microtonal scales playing at the same time. Few composers have aimed at such fervent and heterogeneous multidimensionality. And yet, while Thoegersen's music can seem overwhelming at first, running through it is a level of charm and simplicity that belies the initial impression.

In total, these three pieces emphasize a particular side of Thoegersen's output. The image his music creates of ornately mathematical structures filled with intuitively friendly melodies maps on to the personality of the man himself: outspoken and acerbically ruthless in his musical opinions, Thoegersen is also marked by a jolly sense of humor and an inexhaustible love of cats and other animals that make him ultimately less imposing and more personable than he might seem at first. The same can be said for his music. And by going further than anyone else has gone in terms of this particularly American concept of fusing the polytempic with the polymicrotonal - extending and combining the conceptual worlds of Ives, Cowell, Nancarrow, Partch, Carter, even Frank Zappa and many others - he has created a special place for himself within American music."                                                             

-Kyle Gann (from the liner notes)

Trio Entropicum (first version)

David Victor Feldman