User:Dummy index: Difference between revisions
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===memo=== | ===memo=== | ||
12EDO-complementary comma pairs (e.g. syntonic-schismatic relation) | 12EDO-complementary comma pairs (e.g. syntonic-schismatic relation) | ||
{| class="wikitable" | {| class="wikitable" | ||
! M3 | |||
! A: 4*P5=M3+2*P8 | |||
! B: 8*P5+M3=5*P8 | |||
! | ! | ||
|- | |- | ||
! | ! 6/5 | ||
| [[135/128]]={{monzo| -7 3 1 }} | |||
| (64/63)^2*([[245/243]])={{monzo| 12 -9 1 }} | |||
| A/B={{monzo| -19 12 }}, A: [[Mavila]], B: [[Superpyth]] | |||
|- | |||
! 11/9 | |||
| [[729/704]]={{monzo| -6 6 0 0 -1 }} | |||
| [[8192/8019]]={{monzo| 13 -6 0 0 -1 }} | |||
| A/B={{monzo| -19 12 }}, A: ???, B: [[Archytas clan #Supra]] | |||
|- | |||
! 8192/6561 | |||
| [[531441/524288]]={{monzo| -19 12 }} | |||
| 1/1 | |||
| | |||
|- | |||
! 5/4 | |||
| [[81/80]]={{monzo| -4 4 -1 }} | | [[81/80]]={{monzo| -4 4 -1 }} | ||
| [[32805/32768]]={{monzo| -15 8 1 }} | | [[32805/32768]]={{monzo| -15 8 1 }} | ||
| A*B={{monzo| -19 12 }}, A:[[Meantone]], B:[[Schismatic]] | | A*B={{monzo| -19 12 }}, A: [[Meantone]], B: [[Schismatic]] | ||
|- | |||
! 81/64 | |||
| 1/1 | |||
| [[531441/524288]]={{monzo| -19 12 }} | |||
| | |||
|- | |- | ||
! | ! 9/7 | ||
| [[64/63]]={{monzo| 6 -2 0 -1 }} | | [[64/63]]={{monzo| 6 -2 0 -1 }} | ||
| [[59049/57344]]={{monzo| -13 10 0 -1 }} | | [[59049/57344]]={{monzo| -13 10 0 -1 }} | ||
| B/A={{monzo| -19 12 }}, A:[[Archytas clan]], B:[[Septimal meantone]] | | B/A={{monzo| -19 12 }}, A: [[Archytas clan]], B: [[Septimal meantone]] | ||
|- | |- | ||
! | ! 4/3 | ||
| [[ | | [[256/243]]={{monzo| 8 -5 }} | ||
| [[ | | [[2187/2048]]={{monzo| -11 7 }} | ||
| A | | B/A={{monzo| -19 12 }}, A: (5edo), B: (7edo) | ||
|} | |} | ||
31EDO-complementary comma pairs (e.g. 11-limit meantone-meanpop relation) | 31EDO-complementary comma pairs (e.g. 11-limit meantone-meanpop relation) | ||
Revision as of 06:00, 23 October 2021
- 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
12EDO-complementary comma pairs (e.g. syntonic-schismatic relation)
| M3 | A: 4*P5=M3+2*P8 | B: 8*P5+M3=5*P8 | |
|---|---|---|---|
| 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⟩ | 8192/8019=[13 -6 0 0 -1⟩ | A/B=[-19 12⟩, A: ???, B: Archytas clan #Supra |
| 8192/6561 | 531441/524288=[-19 12⟩ | 1/1 | |
| 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⟩ | |
| 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) |
31EDO-complementary comma pairs (e.g. 11-limit meantone-meanpop relation)