Techniques of Polytempic Polymicrotonal Composition

 "Irrational" Time Signatures What Is a Whole Note? Technically, it is assumed that a whole note lasts four beats. The whole note, lasting four beats, has been a law of music since mensuration was gradually developed and codified throughout the Middle Ages, up to the present day. We simply accept that the value of a whole note is equal to four counts, with one single beat lasting those four counts. This, then, becomes the entirety of the measure (bar) and is called Common Time , or 4/4 time . But the truth is that a whole note really does not mean anything at all. One could argue that a whole note lasts a full measure. But what does that mean? If we stipulate that a whole note, at 100 BPM, is the set tempo, then how do we really quantify the whole note? Each 1/100th part of this whole note lasts approximately .6 seconds.  Theoretically, the whole note could last forever. Ostensibly, a time signature is needed to give a quantifiable value to the whole note. Therefore, the wh...

 More on the Divisions of the Whole Note, in a Cowellian Sense " Decimal Rhythms " While in Champaign back in 2007, I was given a notebook. Since I had nothing but time on my hands, I began ruminating about the divisions of the whole note. Borrowing (as the best of us do) from Cowell , I wrote out a schema for a 'newer' approach to non-duple-based rhythms . I wrote this:           Figure 1. A figuration of Decimal Rhythms Figure 1 is a common-time bar of decimal rhythms: one third-note , at 33.3% of a whole note; one twelfth-note , at 1/3 of a third note of 11.1%; an eleventh-note , at 1/11th of a whole note, at 9%; a seventh-note , at 14.3%; and three tenth notes , obviously at 10% x 3 = 30% of a whole note. These add up to approximately. 97.7% of a whole note, or the 4/4 measure, is indicated. An outline of the Figure 1 decimal rhythmic measure is shown below in Figure 2.     Figure 2. An outline of the decimal measure is hidden   ...

  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...