Techniques of Polytempic Polymicrotonal Composition: Counterpoint of Tempi, part IV AND IVA, new composition Symphony IV.

 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-scale rhythmic patterns. There is freedom in paper and pencil. Taking paper and pencil to a roll, or a wall, gives one an expansive view and feeling, while the computer screen is small and boxy and gives a feeling of claustrophobia. Yet, I have become a 21st-century composer, dependent on these very good, but limited, commercial programs, and it is with these that I must hassle.

Nancarrow paved the way for independent tempo acceleration and deceleration. Nancarrow employed these techniques in his numerous Player Piano Studies, and I am eternally grateful for his work. 

I differ from Nancarrow in that my harmonic language does not predicate itself on convergence points or big cadences. My particular music is not obviously "goal-oriented", which is frustrating to listeners, now, but I am sure that this will be forgiven over time. 

I, therefore, suggest using Fux's four types of contrapuntal "motion" for tempi. Let me explain: 

• Parallel motion would be the equivalent of two tempi moving at the same rate.
• Similar motion would be the equivalent of two or more tempi moving at different rates in either acceleration or deceleration.
• Contrary motion would be two tempi moving in opposite momenta, i.e., one voice quickens while another voice slackens.
• Oblique motion would be a steady tempo against either an accelerating or decelerating tempo. 

I do not think that Nancarrow thought of tempi in this way. I believe Nancarrow was unifying his music with strategic CP that brought a sense of completion and structure to his wild and brilliant ideas. 

As per the species of Fuxian counterpoint, the point is moot, since the polytempic lines are already in a state of florid counterpoint, such that the offset notes already appear to be "ligatured" and syncopated. But this is where the harmony provided by disparate tuning systems gets interesting. 

So, in line with Fux and the "species" of counterpoint, loosely applied to polytempo, I see first species as two-voice tempus contra tempum, as punctus contra punctum was applied as note against note in the first species of counterpoint. But, in the case of polytempo, there would only be two tempos that could satisfy the condition of tempo against tempo, only in two voices and no more. Similarly, the second species would involve three voices of polytempo, while the third species would involve all four voices in "florid" polytempo. 

Figure 1. From my notebook, ideas of the framework of polytempo abound

It is July 31st, and I probably should have made this a new entry. This is a work-in-progress for polytempic Symphony IV, below, in a few photos. I shall not enumerate them, as they are all fairly self-explanatory. Note, however, the third photo down, showing similar, contrary, and parallel motion of tempi. The additive arithmetic and geometric means of controlling the tempi depend on manipulation of Finale's time signature and tuplet tools, as the global tempo function becomes totally irrelevant in polytempic composition. One measure to a page, controlling the pulse through time signature tools, figuration, and phrasing come later, as do meters, which are all drawn in. This ensures that Finale's "reflow staves" automation can not destroy the hard work with 'flying graphics'. 

Part IVa, new work with contrapuntal tempi, Symphony IV.

Figure 2. Tempo List for Symphony IV

Figure 3. Tempo List continued

Figure 4. Planned Sections Featuring the Tempic Contrapuntal Motions

(use of math for tempos)

Figure 5. Early Layout of Score

To be continued...