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...

  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 ...