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User:Francium/Miscellaneous rank-3 temperaments: Difference between revisions

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Badness: 1.069
Badness: 1.069
== 31 & 317 & 1193 ==
Subgroup: 2.5.7.11
Comma list: {{monzo|-29 11 0 1}}
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 29 || ],
|-
| ⟨ || 0 || 2 || 0 || -22 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || ]
|}
CTE generators: ~2 = 1200.015, ~5/4 = 386.254, ~7/4 = 968.796
{{Optimal ET sequence|legend=1|22e, 25e, 28, 31, 56, 84, 87, 115, 146, 202, 233, 348, 379, 581, 727, 960, 2647, 3607}}
Badness: 0.830


== 31 & 431 & 1889 ==
== 31 & 431 & 1889 ==
Line 336: Line 357:


Badness: 2.413
Badness: 2.413
== 311 & 373 & 1193 ==
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 2401/2400, 142884/142805
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 3 || 2 || 3 || 6 || 6 || ],
|-
| ⟨ || 0 || 8 || 0 || 2 || 13 || 13 || ],
|-
| ⟨ || 0 || 0 || 4 || 2 || -3 || 0 || ]
|}
CTE generators: ~2 = 1200.048, ~147/130 = 212.272, ~55/52 = 96.548
{{Optimal ET sequence|legend=1|23bcf, 39bceff, 51e, 62, 85c, 113, 175f, 198, 311, 373, 571, 684, 1566}}
Badness: 1.605


== 311 & 593 & 1063 ==
== 311 & 593 & 1063 ==
Line 349: Line 391:
| ⟨ || 0 || 3 || 1 || 10 || ],
| ⟨ || 0 || 3 || 1 || 10 || ],
|-
|-
| ⟨ || 0 || 0 || 2 || 3 || ]
| ⟨ || 0 || 0 || 2 || 3 || ]]
|}
|}


CTE generators: ~2 = 1199.963, ~100352/91125 = 165.973, ~224/135 = 876.191
Optimal tuning (CTE): ~2 = 1\1, ~100352/91125 = 165.981, ~224/135 = 876.211


{{Optimal ET sequence|legend=1|7d, 15d, 22, 51, 73c, 79c, 86, 101, 108, 130, 152, 282, 289, 311, 441, 1475, 1916, 2357, 2487, 2928, 3962c, 4403c, 4844c, 9247bcc}}
{{Optimal ET sequence|legend=1|7d, 15d, 22, 51, 73c, 79c, 86, 101, 108, 130, 152, 282, 289, 311, 441, 1475, 1916, 2357, 2487, 2928, 3962c, 4403c, 4844c, 9247bcc}}


Badness: 13.801
Badness: 13.801
== 311 & 653 & 1759 ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 3025/3024, 2500/2499, 56595/56576, 4100625/4100096
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 12 || 15 || -1 || 30 || 19 || ],
|-
| ⟨ || 0 || 1 || 2 || 3 || 1 || 12 || 1 || ],
|-
| ⟨ || 0 || 0 || -14 || -8 || 5 || -43 || 20 || ]]
|}
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.984, ~77/45 = 929.843
{{Optimal ET sequence|legend=1|142fg, 311, 653, 1106, 1448, 1759, 2865}}
Badness: 2.321
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 1549184/1549125
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 12 || 15 || -1 || 30 || 19 || -6 || ],
|-
| ⟨ || 0 || 1 || 2 || 3 || 1 || 12 || 1 || -5 || ],
|-
| ⟨ || 0 || 0 || -14 || -8 || 5 || -43 || 20 || 17 || ]]
|}
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.982, ~77/45 = 929.843
{{Optimal ET sequence|legend=1|142fg, 311, 653, 795, 1106, 1448, 1759}}
Badness: 1.798
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 76545/76544
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 12 || 15 || -1 || 30 || 19 || -6 || -4 || ],
|-
| ⟨ || 0 || 1 || 2 || 3 || 1 || 12 || 1 || -5 || 0 || ],
|-
| ⟨ || 0 || 0 || -14 || -8 || 5 || -43 || 20 || 17 || 11 || ]]
|}
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.980, ~77/45 = 929.843
{{Optimal ET sequence|legend=1|142fg, 311, 653, 795, 1106, 1448, 1759}}
Badness: 1.428
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 7425/7424, 76545/76544
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 12 || 15 || -1 || 30 || 19 || -6 || -4 || 18 || ],
|-
| ⟨ || 0 || 1 || 2 || 3 || 1 || 12 || 1 || -5 || 0 || 8 || ],
|-
| ⟨ || 0 || 0 || -14 || -8 || 5 || -43 || 20 || 17 || 11 || -23 || ]]
|}
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.983, ~77/45 = 929.843
{{Optimal ET sequence|legend=1|142fg, 311, 653, 795, 1106, 1448, 1759, 2865}}
Badness: 1.223
=== 31-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 3025/3024, 2500/2499, 5985/5984, 6175/6174, 3520/3519, 5104/5103, 12397/12393, 6076/6075
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 12 || 15 || -1 || 30 || 19 || -6 || -4 || 18 || -3 || ],
|-
| ⟨ || 0 || 1 || 2 || 3 || 1 || 12 || 1 || -5 || 0 || 8 || 3 || ],
|-
| ⟨ || 0 || 0 || -14 || -8 || 5 || -43 || 20 || 17 || 11 || -23 || 8 || ]]
|}
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.995, ~77/45 = 929.846
{{Optimal ET sequence|legend=1|311, 653, 1106, 1417, 1448k, 1759}}
Badness: 1.368
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