Techniques of Polytempic Polymicrotonal Music Composition: More on Prosodic Meter and Polytempo, part XIIId

 More about Meter

Poetic Meter, for me, is essentially music. Song. The art of songwriting. Although different, the art of poetic meter has a built-in logic that suits musical construction. Most of the time, songwriters, or composers of Lieder, or Art Songs, simply use the rhythms of the composition itself. Or the words of the poem may dictate the rhythms to the composer in a type of durch-komponiert style of writing, like Wagner or Schubert have done. As a matter of fact, prosody is a poetic analysis, much akin to musical analysis. Yet, there is a compositional system dormant and employable in this analytical system. Much like atonal analysis using set theory, or intervallic cell analysis, these types of techniques can also lend themselves to creation by working backwards. I have frequently composed music backwards, or even started in the middle of a piece. 

Figure 1.

As said earlier in this blog, poetic forms themselves are just as numerous and organic as musical forms. There are one-line poems called a monostich. To continue, there are distichs, tercets, quatrains, and pentastich poems with 2, 3, 4, and 5 lines, respectively. And on the other end, the lengthy epic poems use iambic pentameter, or the Greek dactyllic hexameter, as Homer used. Haikus use three lines in a 5-7-5 pattern, while sonnets use 14 lines ending in the Heroic Couplet.

Poets no longer use these older forms and instead write in free verse or prose. But for argument's sake, I am more interested in using the old poetic feet and meters as an unused resource for music composition. 

Nevertheless, Figure 1 displays the disyllable group working in various time signatures. The iamb, for example, would work great in binary meters, like 2/4 or 4/4, fitting evenly and without overlap. Iamb, however, would work unevenly inside a 3/4 time signature, resulting in the musical term hemiola, or a 2:3 pattern. It's actually a reverse hemiola, but I digress. The time signature 4/4 would result in the poetic meter of di-meter, repeating twice, neatly, inside the time signature. The longer meters would entail a string of prosodic feet, including the sub-groupings of the foot types themselves, already creating a nest of complexity. 

The key to this technique is that each syllable of the foot counts as one beat in relation to the time signature. The whole foot itself and its cycles, depending on the meter, would repeat at the end of its cycle, regardless of the time signature. In Figure 1, the 3/4 time iambic hexameter example ends on the third beat of the fourth measure. Results like this are what make this approach interesting for me. And, obviously, as the meters extend and the tri and tetra syllabic feet are used, the contrapuntal linear aspect becomes enriched while this behavior is contained within one tempo of one part against all the others in their tempi and constituent parts. The metric foot meter works in dissonance with the time signature, as well as the other voices of the composition. 

Down the page in Figure 1, there is a 9/16 example with dactyllic pentameter. The dactyl is a three-syllable foot, which corresponds nicely with 9/16, yet the meter is in 5-foot syllables per cycle, ending on the third syllable of the fifth foot in the second measure. Again, it's these little unhappy endings that fill me with glee, as one can either rest and re-align, or continue ad infinitum, waiting for that happy consonant ending. 

Figure 2. Poly schema in full

Figure 2 shows the full arsenal of the polytempic polymicrotonal schema. The microtonal systems chosen are 13, 14, 15, and 16 tone equal temperament. The note values are fifth notes, which operate 20% faster than the quarter note at 60 BPM. The corresponding time signatures equal the microtonal system's numerical ordering, at 13, 14, 15, and 16 fifth notes. The tempic BPMs were all figured according to cross multiplication, solving for x. The tempi are: 72, 78, 83, and 88 BPM, from top down. 

The characteristic intervals, as I call them, since the most defining aspect of each microtonal system happens to be its microchromatic interval, are: 92, 86, 80, and 75 cents per system. 

As for the poetic feet and meters used in this example are the following: violin I has iambic pentameter, inside its 13/5 time signature, resolves at the tenth beat inside the first measure, with three left to go, it begins again, ad infinitum

Violin II has dactyllic hexameter "outside" of 14/5, because its cycle exceeds the length of the beats of the time signature, and does not resume until the fifth beat of the second measure, and goes on ad infinitum

Viola has spondeeic heptameter, which has two complete cycles "inside" the 15/5 measure, and with a beat to spare at the last note of the first measure, begins a new cycle ad infinitum

And finally, the cello has an amphibrachic octameter, which is quite long, and exceeds the length of the first measure of 16/5 and renews on the ninth beat of the second measure and goes on ad infinitum.

As for the pitch and interval materials inside the schematic, it is entirely up to the composer, just as with choosing the systems, tempi, and everything else. 

Figure 3. Close-up of the schema

One may think I am stealing isorhythmic techniques from the ars nova and Philippe de Vitry, but I am not; the color and talea technique is about a repeating and specific rhythm, against a color of melody many times longer. This is not that. In fact, the meter does not specify rhythm, only increments of repetition, while the feet are unspecified about pitch and intervals. In fact, my system repeats groups of intervallic feet, and not isorhythms. So I hope I am vindicated for this potential theft of ars novae proportions. Also, I am not working from a "color" melody or cantus firmus. I am hoping these techniques with free use of interval cells will create a melody--four melodies, in fact, one per voice.