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...