This diagram shows relationships between the sixteen ways to tune a diatonic scale using just intonation. Each arrow in the diagram represents moving from one tuning to another by shifting a single note by a syntonic comma. The arrows point in the direction of raising the pitch of the note. The diagram has a loop: once all seven notes have been raised by a syntonic comma, one has returned to the same tuning structure that one started with, just a tad higher.
I've made diagrams for each of the sixteen tunings, showing the just tuned perfect fifths, major thirds, and minor thirds. In this first tuning, for example, there is no arrow from G to D. In conventional equal tempered tuning, every interval of seven half steps is the same. In just intonation, not all similar intervals can be tuned the same. In this first tuning, the G-D interval is tuned to a 40:27 frequency ratio, and will sound rather harsh.
Here is an example of tuning 1. I used 87edo to create these examples, rather than just intonation, because my algorithmic composition software works mainly with edo. This software uses weighted random choices to decide what pitches to play. The weights are computed based on the consonance or dissonance of intervals between related notes. So with tuning 1 for example, the program will not very often put a G near a D. It will much more often put A and D near each other.
Here is an example of tuning 2.
Here is an example of tuning 3.
Here is an example of tuning 4.
Here is an example of tuning 5.
Here is an example of tuning 6.
Here is an example of tuning 7.
Here is an example of tuning 8.
Here is an example of tuning 9.
Here is an example of tuning 10.
Here is an example of tuning 11.
Here is an example of tuning 12.
Here is an example of tuning 13.
Here is an example of tuning 14.
Here is an example of tuning 15.
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