I decided that it would greatly ease my writing if I were to write up a list of chords, all written in Sagittal, all relating to C. That is, every chord has an unaltered C in it, and I cycled through shifting each chord so that C eventually covers every chord tone.
I will also add more chords to the pages from time to time, and make corrections when I find them.
2018 update:
Using Dorico 2, I have created a more complete listing of diads specific to the Sagittal Athenian subset, which covers up to 13-limit pretty well and includes some 17-limit intervals. Intervals that require symbols not included in this subset are notated with ‘X’ noteheads showing the closest available interval. Dorico 2 makes this particularly beautiful because I am able to not only make custom accidentals that are easy to apply, but I also created a custom 224EDO which makes reasonably accurate playback of all of these intervals easy to get as well. I caught a few errors using playback. The 224EDO (set up where each 8:9 whole step gets 38 steps and each diatonic semitone gets 17 steps) realizes the quirks of just intonation pretty well. This diads listing is also instructive such that intervals that I expect to be related by some other simpler interval are shown with the symbols to be such. For example, 4:7 is a perfect fifth larger than 6:7. Checking for these relationships is another good way to error-check.
mixed sagittal athenian chord charts – diads
Here is a list of triads. I followed some guidelines to reduce the number of chords listed: no triads with span equal to or greater than 1:2 (except the very first); don’t count chords that are 1:2 inversions of simpler chords (thus, 3:4:5 is listed an 4:5:6 is not); every triad is written with one of 3 notes set to middle C. This last rule is handy considering how Pythagorean tuning works related to Mixed Sagittal. Each chord can be transposed to other chords that keep the same ‘vanilla’ reference note while keeping every accidental the same except for sharps and flats. For example, the 5:6:7 triad of A-C-Eb (with C as the middle note) transposed such that E is the middle note (thus, C#-E-G) adds sharps but the other accidentals stay the same in relative positions.
mixed sagittal athenian chord lists – triads
Andrew Meronek 