So I'm running into several qualms with sagittal chord names. Assuming we already know what to call accidentals, we have Pai, Pao, Pai-flat, pao-sharp. Here's my proposed system based on Cam's system with a few modifications for special chords. This post is mainly for 22 TET but applies to everything as well I guess.
1. Chord names begin with Root which is exactly the same as the note name (duh but it's good to clarify this.)
2. Immediately following the Root is the suffix pertaining to the third of the chord. Major chords can have one but don't need a suffix.
Example, C Minor has a minor third. Gmaj9 has a major third. F is a F major chord etc...
In addition, there are suffixes which effect the fifth as well such as augmented but we'll talk about that in a bit.
3. If no third exists, then a 5 is placed after the Root. G5 has no third at all, it's just a power chord on G.
4. Immediately following the suffix for the third is the suffix for the quality of the seventh. When we the seventh is the same quality as the third i.e. it's a fifth away then we only need to name them once. Example Gpao7 has pao-maj3 and pao-maj7 in it.
5. Chord names are based on how they FIT in a scale rather than a harmonic interpretation. That means C major in 22 EDO is C E G not C E
G. I also think the 7th chord should NOT be 4:5:6:7 in tunings like 22 EDO because it should be the chord that exists in superpyth as the dominant chord. Making C7 as C E G B
. This makes it consistent with the chord notation. 4:5:6:7 in 22 EDO would be called a "harmonic-seventh" or "major-minor-seventh" which since it's so common having some kind of symbol such as "$" to be harmonic. Otherwise just say "h7" or "Mm7". This chord also is a C-pao dominant seventh.
6. Alterations to other chord degrees are done so by the accidental as well. Cmaj7pao5 = C E
B in 22 EDO. To make names shorter ^ and v can be used in chord names. The same chord can be written Cmaj7v5.
7. When the name of a chord becomes confusing, use "Root" possibly "Dot" or a CLEAR HELD pause to distinguish. Example C
7 vs Cpao7. THIS IS COMMON PROBLEM WITH THE NAMING SCHEME. A dot can be used in confusing chord names. So the two chords would be written C\!7 as C pao seventh and C.\!7 C pao major seventh.
BUT another possibility which may work well is NEVER using those as modifications but instead using the letter by itself of the accidental. so C\!7 = C Pao-Seventh, but C major with a pao-seventh is Cp7. Pronounced C "Pee" "Seventh" and C-"Pao" "Seventh". I think this may be a good way to avoid this confusion.
8. Augmented and diminished should refer to their literal meaning of stacked major thirds or stacked minor thirds. In 22 EDO, an augmented chord is C E G
#: and a C diminished is C Eb G
b: . IF we feel these get confusing, it might be better just to use explicit alterations to the 5 at all times and avoid confusion altogether. C diminished is a C minor pai-flat5 or possibly
Cm^b5. C augmented is a C major pao-sharp 5 or C.v#5 .
9. Slash chords are indicated normally with slash marks BUT in ascii we bracket each side of the chord. G7/B
written in Ascii looks loke [G7]/[B\!].
10. Major and Minor are based on a stack of fifths. The 11th harmonic is notated as a raised fourth so in 22 EDO it's a pai-11 or ^11.
That should cover everything, but tell me what you guys think.