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   ...