Techniques of Polytempic Polymicrotonal Composition: Trisyllabic and Tetrasyllabic Prosodic Feet Applied to Polymicrotonality, part XIIIb and c

 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 framework of commonly known intervallic structures, such as major tone, minor third, minor sixth, etc., in a tonal sense, or not. It depends on how one designs these feet with respect to each tuning. Again, composer agency is paramount. The composer can no longer defer the act of choice to some anonymous process relieving him or her of responsibility. 

There will be many variations of standard large intervals. One aspect of using this prosodic system and simplifying it to just two major intervallic motions is to retrain the ear to listen to the differences between the large intervals and the microchromatic intervals. The point is to always remember that these are all microtonal systems, with different laws and landscapes. The fact that there will be multiples of "Major sixths" concerning the system involved needs to be reframed into a new context; these are adjacent to common-sounding intervals, but are not functioning as these common-sounding intervals. 

For example, take 27tet, whose arsis U = 44.4 cents. The G above C in 27tet is 711 cents. However, from an equal tempered diatonic white note perspective, the class of Gs range from flat G, at 578 cents, to sharp G at 800 cents, which is actually the same pitch as Ab in this system, since both Ab and G# can be assigned to 800 cents, just as in 12 equal. The point is that many shades of G can be interpreted as a fifth, none are perfect consonances; therefore, the function of the interval loses its meaning. This "out of tune" fifth simply becomes a different interval class of its own. 

Figure 0. 27tet, a difficult system to assign nominal ordering, as most microtonal systems are.

My goal is to liberate the numerous microtonal intervals, allowing them to have their own identity, rather than being discarded or confined to a "functional" identity within common practice harmony. If Schönberg liberated the 12 chromatic tones of 12tet, I suppose in my own way, I am trying to liberate microtonal intervals from underneath the functional hierarchy of tonal intervals. Perhaps the only true way of doing this is to use atonal rows on each microtonal system being used in any given piece of polymicrotonality. One outcome of microtonality is how the notion of absolute pitch becomes less and less important. What matters is the intervallic space. 

Ben Johnston used rows for his 53-tone system. Although Johnston used the 12-tone row paradigm within his 53-tone system, by chopping up the gamut into rows of smaller-sized pitches, as he did in String Quartet 3, with three row systems: a 12-tone chromatic row, a twelve-tone microtonal row, and a microchromatic 22-tone row. This was Johnston's treatment of microtonality. Serial techniques were still popular in his day, but today, everyone has flocked back to "Mary had a little lamb", microtonal über simplichkeit. 

Nevertheless, a beginning system for polymicrotonality is being outlined for you by applying prosody to microtonal systems. I do not recall anyone else doing this. I believe the only other musical use for prosody, other than poetry itself, was the use of prosody by Leonard Meyer for analyzing rhythmic structures in music. This is not that. 

Earlier in this blog, part XIIIa, I discussed how these metric feet can be applied to microchromatic lines. Please refer to part XIIIa, as it is all laid out there. Figures 1-5 are fairly self-explanatory, and although there are systems of pitch included with the intervals, the pitch is almost immaterial. The hovering about the smallest unit is the most important thing. Arsis establishes the character of each microtonal system through its smallest part. The microchromatic line, for me, is the most important aspect of these systems. The sheer compression of intervals bordering on the threshold of hearing. 

Figure 1. Trisyllables are three-interval feet, or units.

I suppose in the future I may invent another, more musical name for these units, but I rather like them. They fit here as they do in poetry. Another motion I have not discussed is that U can also remain as a cell with repeated notes. Therefore, U has three types of motion: up chromatically, down chromatically, and repeated notes. Unlike Schönberg, I will allow repeated notes anywhere in the music, even if that invites centricity, which I am not averse to. 

Figure 2. Trisyllable Examples, including contour lines.

If anything, these interval cells can jumpstart the blank page staring the composer in the eyes. One can even imitate the contours of each cell for igniting all that creative fury and angst. Weltschmerz. Stürm und Drang. 

Figure 3. Tetrasyllables, or four-interval cells

Figures 4., and 5.(below) Tetrasyllabic examples with contour lines

Unlike Fux or Arnold, I do not advocate exercises or any graded progression. Just leap in and begin. This is supposed to be about freedom, and the last thing I want is another heavy process-laden endeavor. You do not even have to read this blog. You could be at the beach getting sunburnt. 

Polymicrotonal Polytempo Music is in its infancy. 

Once rhythms are added to these interval cells, they become motives. One may start building motives like tinker toys and create a new Beethoven's 5th, the ultimate motivic tinker toy construction. 

METER. 

I keep forgetting to discuss meter because for me, it is so obvious. One can repeat these cells, just as in poetry, any number of times in a row, from monometer to tridecameter. Common Greek poetry in the Homerian epic style used Dactyllic Hexameter: [— U U] x 6. Classic English poetry used iambic pentameter. I even think the Canterbury Tales are in iambic pentameter. 

The best part of poetic meter and these intervallic feet is that these phrases will behave in contradistinction to the time signature. If you have a time signature in 9/8, and you have iambic pentameter, the poetic rhythm will dissonate with the time signature until it either resolves or it doesn't. And do not forget that each part will still be in a different tempo. There will be many moving parts to this. This is not whole note + whole tone music that drones for years on one fundamental with one just intoned chord. This is not "aum" music. This music represents real-life chaos while maintaining its integrity and its implicit and explicit order. This is a music of actuality, war, truth, and eventual peace. This music is about senators being arrested and Marines detaining civilians. This music is not the Tao-Zen-Buddhist spiritual perfection of Pythagoras. This is nitty-gritty Aristoxenus-Diogenes-Heraclitus "wake the fuck up" music.