Techniques of Polytempic Polymicrotonal Composition

  Continuation of part XIIIa: Trisyllabic and Tetrasyllabic feet for intervallic cells As a continuation of part XIIIa, I will provide more notes and examples of prosody as applied to voice leading , intervallic cells, and a type of loose pitch organization as applicable to any microtonal system used in polymicrotonality . The most important aspect of this technique is the specific use of the ultrachromatic cell , prescribed as the unstressed unit "U." According to which smallest intervallic unit your microtonal system is using, for example, the 92.3 cent microchromatic interval of 13tet , becomes arsis U. (All this is presented in part XIIIa) Thesis "—" then contains the remaining group of intervals still within the microtonal system, but are larger than a microchromatic step. Therefore, the third microtonal scale degree , or larger, will be considered as skips, leaps, and jumps to other pitches. The reader may interpret these other larger intervals in the fr...

 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: ...

  Compression of Harmon y in Polymicrotonality One technique regarding the gradual compression of micro-intervallic structures in the microchromatic line is shown below, in Figure 3, from my String Quartet 12 , Big Bad Mother Fucker From Outer Space, 2019.  Figure 1. Tuning Legend from String Quartet #12 String Quartet 12 is explicitly polymicrotonal , with microtonal systems in full, except for the last one. We start with 20tet at 60 cents, 22tet at 54.5 cents, quartertones at 50 cents, and lastly, 18 of the 26tet gamut , at 46.15 cents. Since a starting pitch needs to be chosen for further divisions of the octave of a pitch class set , and inclusive of all other pitch classes within that octave, and for all microtonal systems within the given octaves of each system, I chose C as "1/1" as indicating the "untouched," pure beginning pitch. In this case, the pitch C is from 12tet and is 261.6 Hz. Any pitch class can be used, including a starting pitch up the over...

More on Contrapuntal Tempi...  Polytempo as Static vs. Dynamic and Fluid Tempo has throughout Western musical history been thought of as a single-formed containment system for music, perhaps except the isorhythms of the Middle Ages, which actually had nothing to do with tempo, but marked the beginning of the awareness of the potential of several strands of musical thought working simultaneously, as in color and talea , that could conceivably be a thought-form precursor to polytempo . Additionally, and unrelatedly, many motets were written with differing text languages, also not related directly to polytempo, but actually more to polymicrotonality ; the different languages presented in polytextual works offered different vowels, phones, phonemes, and glottals--imperceptible at the time, but today would actually count as polymicrotonal by closer examination. It is here that I must declare that, for me, polytempic polymicrotonality is really nothing more than an attitude; an aesth...

  The Idea of Fuxian Counterpoint of Tempos In looking over what music I have composed over the years, I have noticed a desire to independently vary the tempi of all constituent parts, not unlike Nancarrow did in his Tempo Canons .  I think that the amount of freedom Nancarrow had in making huge punch-rolls for the player piano , gave him a sense of total control over his materials. Although it must have been enormously painstaking, I am sure that after mastering his approach to this, he had way more freedom to calculate tempic relations to which even our modern-day sequencers and notation programs can not even compare. Not being a computer language programmer, I have to hassle with Finale or Dorico , down to the minutest detail, just to get a bit of cooperation from these programs to compose polytempic music , only to then obtain a halfway decent playback.  Elliott Carter also had huge pre-compositional notes and scores pasted on his walls for the calculation of large...