- 2-dimensional tuning spectrum
- 3rd-tritave temperaments
- About harmonics
- Bimetallic MOS
- Chromatic pairs and how we define haplotonic
- Heuristics for picking a nonstandard basis of JI subgroup
- Just odd intonation
- Layouts
- MOS tree with continued fraction
- No-1s odd-limit consistency
- Random lists of temperaments by generator size
- Related to 1729/1728
- SandBox
- Semitritave
memo
12ET-complementary comma pairs (e.g. syntonic-schismatic relation)
| M3 or d4 | A: 4*P5=M3+2*P8 | B: 8*P5+d4=5*P8 | Remarks |
|---|---|---|---|
| 32/27 | 2187/2048=[-11 7⟩ | 256/243=[8 -5⟩ | A/B=[-19 12⟩, A: (7edo), B: (5edo) |
| 6/5 | 135/128=[-7 3 1⟩ | (64/63)^2*(245/243)=[12 -9 1⟩ | A/B=[-19 12⟩, A: Mavila, B: Superpyth |
| 11/9 | 729/704=[-6 6 0 0 -1⟩ | (64/63)^2/(99/98)=[13 -6 0 0 -1⟩ | A/B=[-19 12⟩, A: Meanenneadecal?, B: Supra |
| 8192/6561 | 531441/524288=[-19 12⟩ | 1/1 | A: (12edo) |
| 5/4 | 81/80=[-4 4 -1⟩ | 32805/32768=[-15 8 1⟩ | A*B=[-19 12⟩, A: Meantone, B: Schismatic |
| 81/64 | 1/1 | 531441/524288=[-19 12⟩ | B: (12edo) |
| 9/7 | 64/63=[6 -2 0 -1⟩ | 59049/57344=[-13 10 0 -1⟩ | B/A=[-19 12⟩, A: Archytas clan, B: Septimal meantone |
| 4/3 | 256/243=[8 -5⟩ | 2187/2048=[-11 7⟩ | B/A=[-19 12⟩, A: (5edo), B: (7edo) |
Q: Mavila must have the fifth flatter than 7edo's, why be placed between 7edo and 5edo?
A: I wrote the 32/27 in this table as a monzo-ish value. 32/27 constructed of P5 & P8 will much sharper when flatter P5 situation.
| (3/2)^(1/2) | 2187/2048=[-11 7⟩ | 17-comma=[27 -17⟩ | A/B=[-38 24⟩, A: (7edo), B: (17edo) |
|---|---|---|---|
| (3/2)^(4/7) | 531441/524288=[-19 12⟩ | 531441/524288=[-19 12⟩ | A*B=[-38 24⟩, A: (12edo), B: (12edo) |
| (3/2)^(2/3) | 256/243=[8 -5⟩ | [-41 26⟩ | B/A=[-49 31⟩, A: (5edo), B: (26edo) |
temperaments with septimal tritones
| Fifthspan | -8 | -6 | 4 | 6 | Remarks |
|---|---|---|---|---|---|
| Septimal meantone | 32/25 | 10/7 | 5/4 | 7/5 | Good 4:5:7 in 10 fifthspanp-p |
| Dominant | 32/25 | 7/5 | 5/4 | 10/7 | inaccurate |
| Schism | 5/4 | 10/7 | 80/63 | 7/5 | inaccurate |
| Garibaldi | 5/4 | 7/5 | 80/63 | 10/7 | Good 4:5:6:7 in 15 fifthspanp-p Good 4:6 & 5:7 in 6 fifthspanp-p |
| Hemififths | 7/5 | 10/7 | 5/4 is at 12.5 fifthspan |