Garischismic temperaments

From Xenharmonic Wiki
Jump to: navigation, search

This family of temperaments tempers out the garischisma, |25 -14 0 -1> = 33554432/33480783, and includes vulture, newt, garibaldi, sextile, and satin.

Satin

Comma: |104 -70 3>

POTE generator: ~|-34 23 -1> = 165.907

Map: [<1 2 12|, <0 -3 -70|]

EDOs: 94, 123, 217, 311, 405, 528, 745

Badness: 2.8530

7-limit

Commas: 2100875/2097152, 4802000/4782969

POTE generator: ~8575/7776 = 165.913

Map: [<1 2 12 -3|, <0 -3 -70 42|]

EDOs: 94, 123, 217, 311, 405, 528

Badness: 0.1972

11-limit

Commas: 4000/3993, 19712/19683, 41503/41472

POTE generator: ~11/10 = 165.915

Map: [<1 2 12 -3 13|, <0 -3 -70 42 -69|]

EDOs: 94, 123, 217, 311, 405, 528

Badness: 0.0580

13-limit

Commas: 1575/1573, 2080/2079, 4096/4095, 13720/13689

POTE generator: ~11/10 = 165.914

Map: [<1 2 12 -3 13 -1|, <0 -3 -70 42 -69 34|]

EDOs: 94, 123, 217, 311, 405, 528

Badness: 0.0303

17-limit

Commas: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095

POTE generator: ~11/10 = 165.913

Map: [<1 2 12 -3 13 -1 11|, <0 -3 -70 42 -69 34 -50|]

EDOs: 94, 123, 217, 311, 405, 528

Badness: 0.0200

19-limit

Commas: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573

POTE generator: ~11/10 = 165.913

Map: [<1 2 12 -3 13 -1 11 16|, <0 -3 -70 42 -69 34 -50 -85|]

EDOs: 94, 123h, 217, 311, 405, 528

Badness: 0.0145

23-limit

Commas: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155

POTE generator: ~11/10 = 165.914

Map: [<1 2 12 -3 13 -1 11 16 16|, <0 -3 -70 42 -69 34 -50 -85 -83|]

EDOs: 94, 217, 311, 405

Badness: 0.0122