memo
12ET-complementary comma pairs (e.g. syntonic-schismatic relation)
| M3 or d4
|
A: 4*P5=M3+2*P8
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B: 8*P5+d4=5*P8
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Remarks
|
| 32/27
|
2187/2048=[-11 7⟩
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256/243=[8 -5⟩
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A/B=[-19 12⟩, A: (7edo), B: (5edo)
|
| 6/5
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135/128=[-7 3 1⟩
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(64/63)^2*(245/243)=[12 -9 1⟩
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A/B=[-19 12⟩, A: Mavila, B: Superpyth
|
| 11/9
|
729/704=[-6 6 0 0 -1⟩
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(64/63)^2/(99/98)=[13 -6 0 0 -1⟩
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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⟩
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32805/32768=[-15 8 1⟩
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A*B=[-19 12⟩, A: Meantone, B: Schismatic
|
| 81/64
|
1/1
|
531441/524288=[-19 12⟩
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B: (12edo)
|
| 9/7
|
64/63=[6 -2 0 -1⟩
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59049/57344=[-13 10 0 -1⟩
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B/A=[-19 12⟩, A: Archytas clan, B: Septimal meantone
|
| 4/3
|
256/243=[8 -5⟩
|
2187/2048=[-11 7⟩
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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⟩
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A/B=[-38 24⟩, A: (7edo), B: (17edo)
|
| (3/2)^(4/7)
|
531441/524288=[-19 12⟩
|
531441/524288=[-19 12⟩
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A*B=[-38 24⟩, A: (12edo), B: (12edo)
|
| (3/2)^(2/3)
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256/243=[8 -5⟩
|
[-41 26⟩
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B/A=[-49 31⟩, A: (5edo), B: (26edo)
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temperaments with septimal tritones