Techniques of Polytempic Polymicrotonal Composition

 Applying Prosody to a Microtonal System What is Prosody, and what the Heck does it have to do with Microtones?   Although Leonard Meyer created a musical analysis approach using simple prosodic elements from the analysis of poetic syllabic feet, I have always been interested in prosody and its close relationship to song and music in general. This morning, as my cat Maximus attacked my face while I was trying to sleep, I had an idea concerning the use of prosody with regard to microtonal systems.  Fig. 1. Disyllabic permutations as applied to microtonal voice leading and pitch cell organization In prosody, poems are written syllabically in a meter, such as in iambic pentameter .  Most English classical poetry is written in iambic pentameter. Take Milton's Paradise Lost , for instance. This epic poem is entirely written in a foot resembling: ∪ — where "∪" is the unstressed syllable, and "—" is the stressed syllable. There are three categories of syllabic feet: ...

  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...

  Why is this Philosophical Question Relevant?  CHOICE AND INTENT During post-war music composition , the chaotic and hapless state of the geopolitical arena had caused ontological shock to people around the planet. People feel out of control, as they are starting to again, today. One way to deal with feeling helpless is to immerse oneself in some kind of system of control. Schönberg had created his system after the Great War, in the 1920s. Arnold, in fact, served in that war. One interesting outcome of Schönberg's system was the abnegation of personal choice; systems became paramount. This led to total serialism , and Cage's chance operations similarly showed another aspect of the dethroning of one's own personal choice. As though the composer's personal druthers were to be removed at once.  Polytempic Polymicrotonality , a non-system system, encourages choice and intention. Out of 5000 Scala microtonal scales, one MUST choose. Out of unlimited tempi, one MUST choos...

  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 ...