Techniques of Polytempic Polymicrotonal Composition

  What is a Whole Tone, and Why Divide It? Anaximander Anaximander believed in a concept called " unity ," wherein infinite divisions were possible, and apparently, this philosophy included divisions of musical intervals, such as the tone. Aristoxenus was also an advocate of this philosophical standpoint. "All and innumerable worlds are infinite in possible harmonies."  Conventional wisdom states that a whole tone is composed of two semitones that range from ratios 11:10, at 165 cents, all the way through 8:7, at 234 cents. Generally, the ratio 9/8 is the most accepted version at 204 cents. If we are not speaking about rational tunings or string lengths from the monochord , then we are referring to 12tet, where the whole tone is simply 200 cents.  Although I went through a bit of the history of tuning in my thesis, Polytempic Polymicrotonal Music: the road less traveled, 2012, I just want to discuss my personal thoughts on pitch.  I am not a tuning/temperament ...

  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...