Quince clan

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This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The quince clan tempers out the quince comma, [-15 0 -2 7⟩ = 823543/819200. Quince temperaments include:

Mercy

Mercy is the no-3 version of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of 31edo. Two generators make an 8/7; five generators make a 7/5.

Subgroup: 2.5.7

Comma list: 823543/819200

Sval mapping: [⟨1 3 3], ⟨0 -7 -2]]

mapping generators: ~2, ~343/320

Gencom mapping: [⟨1 0 3 3], ⟨0 0 -7 -2]]

gencom: [2 343/320; 823543/819200]

Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 116.291

Optimal ET sequence: 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd

2.5.7.13 subgroup

Subgroup: 2.5.7.13

Comma list: 343/338, 640/637

Sval mapping: [⟨1 3 3 4], ⟨0 -7 -2 -3]]

Gencom mapping: [⟨1 0 3 3 0 4], ⟨0 0 -7 -2 0 -3]]

gencom: [2 14/13; 343/338 640/637]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094

Optimal ET sequence: 10, 21, 31

2.5.7.13.17 subgroup

Subgroup: 2.5.7.13.17

Comma list: 170/169, 224/221, 640/637

Sval mapping: [⟨1 3 3 4 4], ⟨0 -7 -2 -3 1]]

Gencom mapping: [⟨1 0 3 3 0 4 4], ⟨0 0 -7 -2 0 -3 1]]

gencom: [2 14/13; 170/169 224/221 640/637]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769

Optimal ET sequence: 10, 21, 31

2.5.7.13.17.19 subgroup

Subgroup: 2.5.7.13.17.19

Comma list: 170/169, 343/338, 640/637, 16384/16055

Sval mapping: [⟨1 3 3 4 4 3], ⟨0 -7 -2 -3 1 13]]

Gencom mapping: [⟨1 0 3 3 0 4 4 3], ⟨0 0 -7 -2 0 -3 1 13]]

gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]

Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716

Optimal ET sequence: 10, 21, 31, 52f

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