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...

  What is Polytempo?   What is tempo? First of all, we must understand what tempo is. So I will explore this topic as deliberately, naively, and as guilelessly as I possibly can, to ask the most basic questions without the pomp, rhetoric, and expectations of my doctorate, telling both me that I damn well know what tempo is, when in fact, do I? Jean-Baptiste Lully thought he knew what tempo was when he accidentally crushed his toe with his staff, pounding the tempo onto the floor while conducting Te Deum . Lully was 'tempoed' to death. There is no more concrete example of tempo than this. Now imagine three more Lullys pounding the floor at different rates of speed with their staffs. This is polytempo, and hopefully not the accidental polydeaths of the three additional Lullys.  Today's version of this would not be so much the conductor, but perhaps a drummer? Or more precisely, the click-track pounds the tempo into the ears of hapless musicians via headphones for them to p...