User:Unque/15edo-Chords

In standard Western Classical Theory, chords are made by stacking different flavors of Thirds. In 15-EDO, this approach doesn't work as consistently as you may expect... So, how does one handle chords in 15-EDO?

When creating chords in 15-EDO, I tend consider the sum of the stacked intervals to be more important for the chord's function than the values of those intervals; for instance, 4+5 and 6+3 both have a sum of 9, so the chords [0 4 9]\15 and [0 6 9]\15 would be placed into the same category despite having completely different step sizes.

Here, intervals borrowed from the equi-Pentatonic scale (5-EDO) will be used as the "target" intervals - those are steps 6, 9, and 12 of 15-EDO. Two intervals that add up to 6 form "Suspended" triads; intervals adding up to 9 form "Pathic" triads; and intervals adding up to 12 form "Metallic" triads. Note that these names are idiosyncratic, and do not reflect any mathematical or harmonic properties of these chords.

Additionally, the target intervals can be Augmented or Diminished if they are raised or lowered by one step of 15-EDO. Intervals adding up to 7 form "Suspended-Augmented" triads, intervals adding up to 11 form "Metallic-Diminished" triads, etc.

To indicate a specific chord of 15-EDO, the idiosyncratic category name need only be suffixed with a number, to indicate the flavor of the central interval; this number is two less than the size of the step. Step sizes 1\15 and 2\15 are known as the Sublead and the Superlead, due to their nature as extremely tense intervals rarely used in chords; they can be indicated as a lowercase or capital letter L rather than a number.

For some examples of chord names:

• [0 6 12]\15 would be called Met4, or Metallic #4
• [0 3 7]\15 would be called SusAug1, or Suspended-Augmented #1
• [0 2 9]\15 would be called PatL, or Pathic Superlead.

Note that under this chord naming scheme, the inversions of a given chord will have a different name and function; for instance, the Pat3 chord can be rotated to form a PatAug2 chord, and again to form a MetDim4 chord.