On Prosodic Feet and Microtones, Referencing the June 11th post. Part LX

 

Beyond Book III: Naming What Was Already There

Two posts from June of last year form the empirical foundation of what I am about to describe. The first, from June 9, 2025, introduced compression/expansion — the simultaneous compression of interval size and duration across four independent tuning systems and four independent tempos, realized as a polytempic polymicrotonal stretto. The second, from June 11, 2025, fused prosodic feet with microtonal voice leading, arriving at a key statement almost in passing: these interval structures are relative, not absolute, because they apply to all microtonal systems at play in any one given poly composition.

Both posts are now incorporated in Book III, recently submitted to Jenny Stanford Publishing. The book crystallizes the theory at a specific moment. But theory does not stop at submission.

Looking back at those two posts together, I can now name what they had already discovered.

The governing principle is Numerical Invariant Interval Class. The interval class — the abstract integer identifying a relational distance — remains invariant across all four tuning systems. What varies is its acoustic realization in cents. The number is fixed; the sound is plural. The June 11 post stated this without naming it: relative intervals, not absolute pitch structures, applicable to all microtonal systems simultaneously. NIIC is that statement formalized.

This produces a pitch organizational principle that is neither tonal, atonal, nor centric. As n increases toward infinity, absolute pitch class loses its theoretical primacy — no one can be expected to have perfect pitch for n equals infinity divisions of the octave. What takes its place is interval content. NIIC is its formalization.

The interval class is the set; the set is its interval content. The invariance manifests at every level of pitch organization simultaneously. The same numerical interval class content appears across all four microtonal systems at once, each realization acoustically distinct. Numerically identical; acoustically four different objects.

The second concept that has emerged I am calling the Society of Pitches, derived from the third to last paragraph of Emerson’s “Society and Solitude”: Put any company of people together with freedom for conversation, and a rapid self-distribution takes place into sets and pairs. All conversation is a magnetic experiment. Leave them to seek their own mates, and they will be as merry as sparrows.

I am transposing this wholesale into pitch space. The interval ratios are the personalities; the NIIC identities are the affinities; the self-distribution into sets and pairs is the compositional methodology. This is not aleatory — chance is indifferent to interval content. It is motivated autonomy: the freedom is real, the choices determined by the mathematics already inside the pitches.

The generative mechanism is call and response. I write a line first, then answer it with each of the remaining three voices in succession. The set is not determined before the music — it is precipitated by the unfolding of the lines. The composition generates the set structure, inverting the entire serialist relationship. The subsets that emerge are fossils of the voice leading, encoding specific contrapuntal events. Bach said a voice ends when it feels like it. The responding voice ends when the call has been sufficiently answered.

The prosodic feet from the June 11 post supply the micro-level motion grammar: conjunct unstressed motion as the smallest interval of the system, disjunct stressed motion as everything else. The desire of a pitch is now precisely describable at every level simultaneously — from the single interval to the complete subset structure — governed throughout by NIIC.

Book III is a waypoint. The argument continues.