Techniques of Polytempic Polymicrotonal Composition

  Microtonal Intervals and Harmony Figures 1-3. J. Murray Barbour 's Superparticular Ratios   from octave to schisma (added by me.) fig. 2 fig. 3 I am deliberately using an old textbook ( Tuning and Temperament: A Historical Survey , by J. Murray Barbour) list of superparticular ratios converted into cents values for a semi-comprehensive list of intervals for the effect of tabula rasa vis-à-vis the wealth of tuning and microtonal information available today.  Between Ellis-Helmholtz's On the Sensations of Tone , 1875, and today, a good deal of literature exists concerning tuning and microtones by hundreds of writers on the subject. This rather simple list of Barbour's helps me gain perspective on what I am attempting to convey about pitch relations and intervals without the extra baggage of thoughts, opinions, and tuning inventions since 1953, when this book was published.  What I have found myself doing in my own music is that I have made a mental separation bet...

  5000 Microtonal Scales Myriad intervals from a plethora of microtonal scales . Considering the wealth of information about this on the internet, this will oddly be my shortest blog entry. As I write these, I am trying not to recreate my own book, Polytempic Polymicrotonal Music , or start another survey of sorts. I would rather just get down to it, but I have to consider whether things are extraneous or redundant.  Ultimately, we are still at the precipice of the eternal argument between Pythagoras and Aristoxenus . Will we use rational unequal tunings , or equal divisions with or without octave equivalence into infinity? Answer: BOTH. I prefer to forget the position of either/or in consideration of a stance that embraces both of these paradigms. So, with precision and concision, I will adroitly say this:  There are choices to be made in polymicrotonal composition (you may use dice for this decision). If we consider the historical, theoretical, and cultural microton...