This is an extension of chord symbols for microtonal purposes, assuming marvel tempering (225:224 tempered out). Most of it will work with just intonation. The base chord is a 4:5:6 triad. Pitch names can follow tricycle notation. The idea is that names look as conventional as possible but the chords are still pinned down more precisely. The tuning will depend on the temperament in effect.
| ⁷ | 9/5 |
| 7 | 16/9 |
| z | 7/4 |
| -5 | 13/9 or 64/45 |
| ♭5 | 10/7 or 36/25 |
| ♯11 | 45/16 (45/32) |
| +11 | 11/4 (11/8) |
| sus4 | 4/3 |
| ♯4 | 7/5 |
| +4 | 25/18 |
| ⁹ | 9/4 (9/8) |
| 9 | 20/9 (10/9) |
| ♭6 | 8/5 |
| 6 | 5/3 |
| ♯6 | 7/4 |
A "Δ" chord follows the major-seventh pattern, so these pitches are interpreted differently and may be implied (obviously the 7 is).
| 7 | 15/8 |
| 9 | 9/4 (9/8) |
| +11 | 11/4 |
| 13 | 13/4 |
As a variation, a "∇" chord follows the harmonic series, with pitch numbers referring to harmonic partials (with suitable octave equivalence). An "h" can also be used before a pitch number to specify the harmonic series, so "h7" as "harmonic seventh" or "z".
These symbols replace the third rather than adding a pitch.
| sm | 7/6 |
| _m | 32/27 (Pythagorean minor third) |
| m | 6/5 |
| n | 11/9 (assuming 243:242 tempered out) |
| _n | 11/9 (assuming 352:351 tempered out) |
| n_ | 16/13 (assuming 352:351 tempered out) |
| _ | 81/64 (Pythagorean major third) |
| S | 9/7 |
Subscript numerals show wheels as in tricycle notation. Triads by default follow consecutive ascending numbers modulo 3. A "⁷" is on the same wheel as the tonic and a "7" is on the wheel below. Other numbers can be placed at the appropriate place in a chord, so "C" could also be written "C₁₂₃" and "D₁m" as "D₁m₂₃". The other interesting variations are Pythagorean triads, which would be "C₁₃₃" and "C₁m₁₃". You could write neutral third chords as "C₁₁₃" and "C₁m₃₃" but there's no need as there's a special symbol for neutral thirds.
Generally, the interesting thing about non-consecutive triad voicings is that two pitches end up on the same wheel. The "_" is used to show this. so "C₁₃₃" is the same as "C₁_" or simply "C_" hence "_" works as a Pythagorean major third above, but that isn't its primary meaning. "C₁m₁₃" is the same as "C₁₁m₃" or "C_m" hence "_m" is another Pythagorean third.
An earlier version of this document used "n₊" for a 16:13, so you could say "₊" after the third means "on the same wheel as the fifth (would normally be)" and "₋" after the third means "on the same wheel as the tonic" and similarly in other cases, and that might be useful but I prefer the "_" now.
The sevenths are diminished in diminished chords but "⁷" and "7" still distinguish wheels. We have to distinguish minor thirds from augmented seconds, but assume that three 6:5 thirds plus a 7:6 add up to an octave, which is consistent with 126:125 being tempered out and the usual meantone. Tricycle annotations can give variations and outside meantone one third must be "bad" in a seventh chord including the octave (but might approximate 8:7 in magic temperament). A seventh chord will normally have a pitch on each wheel and a pair on the same wheel, so the "_" identifies that pair.
| dim | both thirds 6:5 |
| ds | 5:6:7 |
| sd | 7:6 6:5 (utonal 5:6:7) |
| dim⁷ | 6:5 6:5 6:5 (6/5 16/11 7/4 with 100:99 tempered out) |
| dss⁷ | 6:5 7:6 6:5 (6/5 7/5 27/16) |
| dim s⁷ | 6:5 6:5 7:6 (6/5 16/11 27/16 with 100:99 tempered out) |
| sds⁷ | 7:6 6:5 6:5 (7/6 7/5 27/16) |
| _dim7 | 32:27 6:5 6:5 (32/27 10/7 12/7) |
| dim_7 | 6:5 32:27 6:5 (6/5 10/7 12/7) |
| dim7 | 6:5 6:5 32:27 (6/5 16/11 12/7 with 100:99 tempered out) |
In magic temperament (generally 875:864 tempered out), 7:6 becomes 8:7 when both pitches are on the same wheel, giving us first class rotations and variations like
| _ss | 8:7 7:6 or 8/7 4/3 |
| _sm sus4 | 8/7 4/3 3/2 |
| s_s | 7:6 8:7 or 7/6 4/3 |
| sm sus4 | 7/6 4/3 3/2 |
| _ss♭6 | 8:7 7:6 6:5 (5:4) or 8/7 4/3 8/5 (2/1) |
| s_s♭6 | 7:6 8:7 6:5 (5:4) or 7/6 4/3 8/5 (2/1) |
| _sd♭6 | 8:7 6:5 7:6 (5:4) |
| d_s♭6 | 6:5 8:7 7:6 (5:4) |
| _sd6 | 8:7 6:5 6:5 (6:5) |
| d_s6 | 6:5 8:7 6:5 (6:5) |
| dim6 | 6:5 6:5 8:7 (6:5) |
| aug | 5:4 5:4 (9:7) or 5/4 14/9 (2/1) |
| Sag | 9:7 5:4 (5:4) or 9/7 8/5 |
| agS | 5:4 9:7 (5:4) or 5/4 8/5 |
| G | G B D₂ | 4:5:6 |
| G⁷ | G B D₂ F₃ | 4:5:6:9/5 |
| G7 | G B D₂ F₂ | 4:5:6:16/9 |
| Gz | G B D₂ E♯₃ | 4:5:6:7 |
| Gh7 | G B D₂ E♯₃ | 4:5:6:7 |
| G∇7 | G B D₂ E♯₃ | 4:5:6:7 |
| G9 | G B D₂ A₃ | 4:5:6:7:20/9 |
| G⁹ | G B D₂ A₁ | 4:5:6:9 |
| Gz⁹ | G B D₂ E♯₃ A₁ | 4:5:6:7:9 |
| G∇9 | G B D₂ E♯₃ A₁ | 4:5:6:7:9 |
| Gm | G B♭ D₂ | 10:12:15 |
| Gsm | G A♯₁ D₂ | 6:7:9 |
| I | 1/1 |
| ♭II | 16/15 or 15/14 |
| II₋ | 10/9 |
| II₊ | 9/8 |
| SII | 8/7 |
| ♯II | 7/6 |
| s♭III | 7/6 |
| ♭III₋ | 32/27 |
| ♭III | 6/5 |
| nIII | 11/9 |
| nIII₊ | 16/13 |
| III | 5/4 |
| III₊ | 81/64 |
| SIII | 9/7 |
| IV | 4/3 |
| ♯IV₋ | 25/18 or 11/8 |
| ♯IV₊ | 45/32 or 7/5 |
| ♭V₋ | 64/45 or 10/7 |
| ♭V₊ | 36/25 or 16/11 |
| V | 3/2 |
| ♭VI | 8/5 |
| nIII₋ | 13/8 |
| nIII | 18/11 |
| VI | 5/3 |
| ♯VI | 7/4 |
| ♭VII₋ | 9/5 |
| ♭VII₊ | 16/9 |
| VII | 15/8 |