A few years ago I was reading about modes - Dorian, Locrian, etc. - in W. A. Mathieu's book
Harmonic Experience. I got the idea there that modes have distinct tuning, though I didn't manage to work out seven different tunings. More recently I have been contemplating the trade-off between tuning freedom and compositional freedom. A dense network of interval relationships constraints tuning, but gives a composer many options for harmonic movement. A sparse network allows more tuning options, e.g. for more precision. But a sparse network gives a composer fewer options. Thinking about sparser tuning networks brought to mind again the question of modes and how they should be tuned.
I can't say that I really understand how modes should work, but I have found a nice cycle of interval networks for diatonic scales: seven different ways that a diatonic scale can be tuned with just intonation. Do these interval networks correspond to the tradition modes, Dorian etc.? Probably not! But the notion of modes can operate in multiple ways. Perhaps what I describe here could be a fruitful alternative approach.
Here the green arrows represent perfect fifth, the blue arrows are major thirds, and the red arrows are minor thirds. This tuning corresponds well to a natural minor mode. Three minor chords, rooted on D, A, and E, can be just tuned with these relationships. I have used my algorithmic composition software to construct examples for each network, in 53edo which is very close to just intonation. Here is an example composition using this first network.
This second network corresponds to a major mode. The D has been raised by a syntonic comma from the previous network. That's how this cycle works - one note at a time gets raised by a syntonic comma, shifting its position in the network, until all the notes have been shifted and the network returns to the starting configuration. Here is an example composition for this second network.
Next the A is raised by a syntonic comma. The slight shift in tuning is not what is important, but rather the way this shift in tuning changes the interval network, which then constrains composition in a different way. Here is an example composition for this third network.
Now the F is shifted up. There is not a single path possible to cycle through interval networks in this way. The path I have chosen looks the most natural to me, but some further exploration could be worthwhile. Here is an example composition for this fourth network.
E is raised next. Here is an example.
Next is C, and an example.
B is raised next, producing this example.
The final note to be raised by a syntonic comma is G, which returns the network back to its starting shape.