Heteromorphic Profiles

Howdy patrons!

Last night I completed another complicated bit of coding for the scale details: a metric called the "heteromorphic profile".

Near the bottom of the "Analysis" section there is a new metric called "Heteromorphic Profile". It's a three-part measurement of generic-to-specific interval "properness", as described in a brilliant paper by Norman Carey ("On Coherence and Sameness, and the Evaluation of Scale Candidacy Claims", 2002).

If you have a yen for opaque reading about set theory, look for it. It explains how you dissect a pitch class set, and look at every interval within it to compare if its generic "span" is coherent with the specific distance. It describes how a Coherence failure can be a contradiction, ambiguity, difference, or sameness... differences and samenesses are reciprocal so the profile doesn't bother mentioning samenesses. The profile describes, succinctly, whether you can hear two pitches with no context except knowing the scale (or, pitch class set) but not its height (or - in tonality jargon - the "key"), and know what generic interval (aka "span") it is.

This new property is available now on the scale detail pages, but I haven't written an explanation for it... the "Study Of Scales" essay is going to be in a kind of "code freeze" for a while and I won't make any changes to it until I have the longer, more meticulous and well-organized book-version of it finished. So for those who know what the heteromorphic profile is, we'll be able to look at it computed for any scale, but I'm not offering a more detailed explanation at the moment.

In other news, I have two new interesting theses to review! As a published theorist with a bit of a public exposure (and a contact form on the website), I occasionally get mail from explorers who have come up with a new idea and want to get a second opinion or a peer review. One of them has already gone through a few iterations, and is close to a state where it can be published. I'm a little swamped for free time right now, but if all goes well I might have some really fresh material to share, soon.

Cheers

Ian