Non-Diatonic

I hadn't realized how many ways the 12 conventional notes could be tuned in just intonation!There are so many possibilities with temperaments, with scale sizes... but even with this very restricted approach, there is a lot of room for exploration!

Many of the tunings will be oddly shaped with few options for harmonic movement. Many will be based on conventional diatonic tuning, with the usual seven note pattern connected by close harmonic relationships. The above tuning network does not fit the diatonic pattern. The core of the pattern consists of the two short chains of perfect fifths, C#, Ab, Eb, and E, B, F#. Either A or Bb could be added to make a diatonic scale, but both A and Bb are not directly related.

Here is an algorithmic example of this non-diatonic tuning.

This piece was created in 53edo, which is quite close to just intonation. The table above shows just tuning and also the 53edo approximation for this interval network.

It's simple enough to move A and Bb in the network so that diatonic scales are supported. Here E major and Ab minor will be tuned properly:

Here's a piece in this more conventional tuning.