User:Mike Battaglia

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I'm a jazz pianist and microtonal music theorist, and also a sysop on the wiki here. Some relevant links:

Music and Social Media


I've written many articles about tuning theory in the past 10 years on this Wiki, some of which are very much developed and others of which are little minor contributions. Below are some that I think are particularly notable, being the focus of my research at some point or another.

Musical Information Theory


In 12, I tend to think in terms of modal harmony quite frequently, particularly for the kind of post-bop jazz that I love to play, and these ideas are mostly my way of generalizing them to microtonal scales. There are dozens of pages that talk about MODMOS's at this point, so these are just the high-level starting points. A good book to summarize my thinking in 12 is Ron Miller's Modal Jazz: Composition and Harmony series.

Regular Temperaments

These are various writings of mine involving regular temperament theory. Much of the stuff I've done is collaborative and some of it is just really extending other people's writings (such as with the Zeta function), and I've noted that when applicable. I collaborated with many people, but probably most frequently with Gene Smith, Keenan Pepper and Ryan Avella (although my collaborations with Gene are a small fraction of the incredible work that he did).

High-level Stuff

Mathy Stuff

I've written so many little mathy things here and there that there's no point listing them all. Here's some selected that seem particularly interesting to me, and could be the launching point for another set of good ideas.

  • Subgroup Temperament Families, Relationships, and Genes - This was written after Gene passed from COVID-19, but is basically an expansion of his ideas regarding temperament families, extended to arbitrary subgroups. Much of it can be thought of as a birds-eye view of his "clan" project.
  • BOP Tuning - possibly an improvement on the TOP tuning, at least in some situations. This weights intervals by 1/(nd) rather than 1/log(nd).
  • Wilson height - another useful metric which happens to be involved in the computation of the BOP tuning, but seems to have other uses in looking for good commas in a subgroup-agnostic way
  • The Riemann zeta function and tuning - Gene Smith did the majority of this research; I extended some results later on the second half of the page
  • Chord complexity - much of what we do in temperament theory involves intervals, so here I show how the framework can be extended to include chords.
  • Munit - these generalize things like tetrachords, trichords, etc.
  • Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space - The stuff on TWp space generalizes other metrics that have been around for a while: the Tenney and Tenney-Euclidean norms, the Weil and Weil-Euclidean norms, the Kees and Kees-Euclidean seminorms, and even the Cangwu norm are all special cases of this general norm

The articles below are fairly minor contributions which extend some simpler ideas that had been floating around, and are typically collaborative with Gene and very much in the usual RTT view of things. These are mostly useful from a computational standpoint in doing temperament searches. I need to update some of this with later results involving the Weil norm and such, so this is also a note to myself.