I've been delving for some time into a concept of music theory I chose to call "harmonic configuration".
I'm creating this page to gather resources about it or related topics.
For now, I’ll do this in a messy way and think about how to reorganize it later and add more factual resources.
The idea of harmonic configurations provides a way of analyzing harmony by looking at which notes are present or not, without assuming a root or tonal center.
Traditionally, we think of harmony in terms of scales and modes, each anchored to a tonic.
This view can become computationally complex when analyzing music automatically, because it involves many potential roots and modal variants.
Harmonic configurations bypass that by treating pitch collections as absolute sets, essentially binary patterns of included and excluded notes across the 12-tone chromatic scale.
If we only consider complete scales exempt from consecutive semitones, there are 57 of those "unrooted" configurations (while there are 33 "rooted" scales satisfying those conditions).
I'm speaking about this in French in a couple of videos:
This one speaks about musical modes in general, not configurations, but approaches music generation and introduces the concept of musical "biomes".
This one is the first that I made specifically about configurations, where you can see me struggle to explain and demonstrate the concept.
In this one, I explain how one can optimize calculations when coding programs requiring some understanding of harmony.
Here I am running a large set of classical MIDIs through a configuration analysis pass.
Later, I discovered some oddities in the distributions and talk about them a bit.
Here are some resources somehow linked to the present topic. Again, this is a draft and I hope to be able to order them in a more useful way someday.
Emanuele Di Mauro's théorie de la gravitation tonale (also in French) explores the same idea in detail, sometimes using different words than mine:
https://gravitation-tonale.fr/
YouTube account
I think this video explains the "traditional" 33 complete rooted scales without consecutive semitones pretty well.
A large table of chords.
A large table of scales.
Other unsorted links and references that were given to me or that might possibly have something to do with the topic:
Gammes, rythmes et maths
Allan Holdsworth lessons
The Forte number
Xenharmonic music
The Thesaurus of Scales
Some of my somewhat related work I sometimes talk about:
An old contextual harmonizer