User:Dummy index
- 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 spectrum
| Fifthspan | -8 | -6 | 4 | 6 | Remarks | Mapping development |
|---|---|---|---|---|---|---|
| Flattone | 21/16 | 16/11 | 5/4 | 11/8 | [⟨1 0 ...], ⟨0 1 4 -9]] | |
| Septimal meantone | 9/7 | 10/7 | 5/4 | 7/5 | Good 4:5:7 in 10 fifthspanp-p | [⟨1 0 ...], ⟨0 1 4 10]] +19 |
| Mohajira | 14/11 | 5/4 | 7/5 is at -9.5 fifthspan | [⟨1 0 ...], ⟨0 2 8 -11]] *2-31 | ||
| Undecimal meantone | 14/11 | 10/7 | 5/4 | 7/5 | Good 4:5:7 in 10 fifthspanp-p | [⟨1 0 ...], ⟨0 1 4 10 18]] |
| Dominant | 32/25 | 7/5 | 5/4 | 10/7 | inaccurate | [⟨1 0 ...], ⟨0 1 4 -2]] -12 |
| Schism | 5/4 | 10/7 | 81/64 | 7/5 | inaccurate | [⟨1 0 ...], ⟨0 1 -8 -2]] -12 |
| Grackle | 5/4 | 81/64 | 7/5 is at -18 fifthspan | [⟨1 0 ...], ⟨0 1 -8 -26]] -24 | ||
| Garibaldi | 5/4 | 7/5 | 81/64 | 10/7 | Good 4:5:6:7 in 15 fifthspanp-p Good 4:6 & 5:7 in 6 fifthspanp-p |
[⟨1 0 ...], ⟨0 1 -8 -14]] +12 |
| Andromeda | 5/4 | 7/5 | 14/11 | 10/7 | 11/9 is at -20 fifthspan -> 41edo | [⟨1 0 ...], ⟨0 1 -8 -14 -18]] |
| Hemififths | 7/5 | 14/11 | 10/7 | 5/4 is at 12.5 fifthspan | [⟨1 0 ...], ⟨0 2 25 13 5]] *2+41 | |
| Edson | 7/5 | 14/11 | 10/7 | -> 29edo | [⟨1 0 ...], ⟨0 1 no-five -14-(-8) -18-(-8) -21-(-8)]] | |
| Gentle region Leapfrog |
27/22 | 14/11 | [⟨1 0 ...], ⟨0 1 no-five 15 11 8]] +29 | |||
| Supra | 11/9 | 9/7 14/11 |
[⟨1 0 ...], ⟨0 1 no-five -2 -6]] -17 |
pan-5L2s tuning spectrum
| Eigenmonzo (unchanged interval) |
at (fifthspan) |
Generator (cents) |
in this temperament |
|---|---|---|---|
| 11/8 | +6(A4) | 691.886 | Flattone |
| 6/5 | -3(m3) | 694.786 | Meantone (1/3 comma) |
| 9/7 | -8(d4) | 695.614 | Septimal meantone |
| 5/4 | +4(M3) | 696.578 | Meantone (1/4 comma) |
| 7/5 | +6(A4) | 697.085 | Septimal meantone |
| 14/11 | -8(d4) | 697.812 | Undecimal meantone |
| 7/5 | -18(dd6) | 700.972 | Grackle |
| 5/4 | -8(d4) | 701.711 | Schismatic |
| 6/5 | +9(A2) | 701.738 | Schismatic |
| 3/2 | +1(P5) | 701.955 | Pythagorean |
| 11/8 | -18(dd6) | 702.705 | Andromeda |
| 7/5 | -6(d5) | 702.915 | Garibaldi |
| 13/11 | -3(m3) | 703.597 | Leapfrog |
| 14/11 | +4(M3) | 704.377 | Leapfrog |
| 27/22 | -8(d4) | 705.682 | Leapfrog |
| 11/9 | -8(d4) | 706.574 | Supra |
| 11/8 | -6(d5) | 708.114 | Supra |
| 9/7 | +4(M3) | 708.771 | Archy (1/4 comma) |
| 5/4 | +9(A2) | 709.590 | Superpyth |
| 6/5 | -8(d4) | 710.545 | Superpyth |
| 7/6 | -3(m3) | 711.043 | Archy (1/3 comma) |