Techniques of Polytempic Polymicrotonal Composition

  What is JND? Just Noticeable Difference , which has nothing to do with just intonation , btw, is a psychoacoustic metric associated with the smallest interval detectable by the human ear . There is no point in making microtonal scales that can not be heard at their smallest division. Or is it?  The Greek schisma is a 2-cent interval created by subtracting the Syntonic Comma at 22 cents from the Pythagorean Comma , at 24 cents ( Ditonic Comma ). Ben Johnston used this 2-cent interval in his music. To truly hear a 2-cent interval, one would have to count the beats in between this narrow structure. I believe it was Marin Mersenne who discovered counting beats for intervals back in the 1600s, and this technique was discussed in Ellis-Helmholtz . Nevertheless, if Johnston used the schisma, then what stops the rest of us from using the cent itself?  Ellis-Helmholtz suggested the ten-cent threshold, while David Whaley , in his 1975 dissertation on the  microtonal ca...

  The Idea of Fuxian Counterpoint of Tempos In looking over what music I have composed over the years, I have noticed a desire to independently vary the tempi of all constituent parts, not unlike Nancarrow did in his Tempo Canons .  I think that the amount of freedom Nancarrow had in making huge punch-rolls for the player piano , gave him a sense of total control over his materials. Although it must have been enormously painstaking, I am sure that after mastering his approach to this, he had way more freedom to calculate tempic relations to which even our modern-day sequencers and notation programs can not even compare. Not being a computer language programmer, I have to hassle with Finale or Dorico , down to the minutest detail, just to get a bit of cooperation from these programs to compose polytempic music , only to then obtain a halfway decent playback.  Elliott Carter also had huge pre-compositional notes and scores pasted on his walls for the calculation of large...

  A Quasi Syllabus for this Blog Blog Ideas Contrapuntal Tempos, or a Counterpoint of Tempos  Divisions of the Whole Note  Divisions of the Whole Tone  Contour Creation/ Analysis of Polymicrotonal Lines Myriad New Intervallic Structures Harmony Resulting from Vertical "Cadence" Points- vertical structures Intervallic Compression of Polymicrotonal Systems Centricity Simultaneities Panmicrotonal Harmony: tonal vs atonal, or tonal sublation What is a Polymicrotonal Chord? Counterpoint of Microtonal Systems Pitch Organization   Pitch Cells vs Gamut Tetrachords Serial Techniques?  "Just Noticeable Difference" and Microtonal Hearing Composer Intent Nancarrow-Ives-Cowell-Marie-Xenakis Alternate Staves? Fatter spaces and lines for microtones?  Human Performance Strategies Manifold Electronic Realizations In many regards, these topics have already been broached in other blogs and may not require their own section...

Preliminary Considerations Dividing the Whole Note into Non-standard Parts Many ideas under consideration for a compositional system for Polytempic Polymicrotonal music are not wholly new. I have been influenced by many composers, theorists, and authors of works that are common fodder in the more arcane areas of music theory. Henry Cowell comes to mind. Amazingly, much of Cowell's work still remains unused and unexplored. Something as simple as fifth notes , or pentuplets , up to today, 2025 -26, really should be standard rhythmic practice, just as triplets are. But, they are not. Nevertheless, the division of the whole note into parts other than the binary divisor 2 should be in common use now. Anyone should be able to play pentuplets, septuplets , and nonuplets , as nonuplets are essentially a nested rhythm of three sets of triplets...So, not quite complex nested rhythms, but not merely duple rhythms based on the number 2. Human limitations, of course, limit tempo and speed f...

Although I have heretofore written two textbooks on this subject, I have yet to issue forth a methodology on writing Polytempic Polymicrotonal music . Up until now, my approach to composing polytempic polymicrotonality has largely been intuitive. The impetus for this enterprise came from my drumming background, playing four meters at once on the drumset . This gave birth to later ideas as a composer for myriad ways to synchronize four-part writing in a deliberately syncopated way that would preclude predictable alignment of harmony. The words " verticalities " and "simultaneities" come to mind.  The non-pitched inharmonically tuned drums have always been " microtonal "; the extension of this idea, for me, was to assemble an array of pitches that at first glance would have nothing in common, yet could be heard as an infinite set of tom-toms that could be represented by hundreds of microtonal pitches , other than the mere designation of high, medium, and l...