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

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Created page with "On this page, I explore some unnamed rank-3 temperaments that catched my interest. == 31 & 53 & 227 == Subgroup: 2.3.5.7 Comma list: 65625/65536 Mapping: <br> {| class="ri..."
 
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On this page, I explore some unnamed rank-3 temperaments that catched my interest.
On this page, I explore some unnamed rank-3 temperaments that catched my interest.


== 31 & 53 & 227 ==
== 31 & 233 & 317 ==
 
Subgroup: 2.5.7.11
 
Comma list: 537109375/536870912
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 29 || ],
|-
| ⟨ || 0 || 1 || 0 || -11 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || ]
|}
 
CTE generators: ~2 = 1200.000, ~5/4 = 386.245, ~7/4 = 968.826
 
{{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 & 311 & 431 ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 4096/4095, 2401/2400, 190512/190333
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 5 || 4 || 4 || 1 || ],
|-
| ⟨ || 0 || 2 || 5 || 3 || 7 || -12 || ],
|-
| ⟨ || 0 || 0 || 8 || 4 || 5 || -12 || ]
|}
 
CTE generators: ~2 = 1199.9603, ~49/40 = 350.9859, ~63/44 = 621.0427
 
{{Optimal ET sequence|legend=1|31, 58f, 89, 120, 191, 222f, 280, 311, 400, 711, 742, 1053, 1453}}
 
Badness: 2.258
 
=== 17-limit ===
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 4096/4095, 2401/2400, 14400/14399, 11016/11011
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 5 || 4 || 4 || 1 || 6 || ],
|-
| ⟨ || 0 || 2 || 5 || 3 || 7 || -12 || -3 || ],
|-
| ⟨ || 0 || 0 || 8 || 4 || 5 || -12 || 2 || ]
|}
 
CTE generators: ~2 = 1199.9677, ~49/40 = 350.9737, ~63/44 = 621.0347
 
{{Optimal ET sequence|legend=1|31, 58f, 89, 120g, 191g, 222f, 280, 311, 400, 711, 742, 1453, 2195ef}}
 
Badness: 1.410
 
=== 19-limit ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 2926/2925, 4096/4095, 3136/3135, 5985/5984, 11016/11011
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 5 || 4 || 4 || 1 || 6 || 4 || ],
|-
| ⟨ || 0 || 2 || 5 || 3 || 7 || -12 || -3 || -8 || ],
|-
| ⟨ || 0 || 0 || 8 || 4 || 5 || -12 || 2 || -5 || ]
|}
 
CTE generators: ~2 = 1199.9748, ~49/40 = 350.9675, ~63/44 = 621.0343
 
{{Optimal ET sequence|legend=1|31, 58f, 89, 120g, 191g, 222f, 280, 311, 400, 653f, 711, 742, 1453, 1795f, 2195ef}}
 
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 ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 655473/655360, 820125/819896, 3764768/3764475
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 18 || 7 || 11|| 0 || ],
|-
| ⟨ || 0 || 1 || 6 || 2 || 6 || -5 || ],
|-
| ⟨ || 0 || 0 || 65 || 19 || 44 || -30 || ]
|}
 
CTE generators: ~2 = 1200.008, ~3/2 = 701.925, ~78975/60368 = 465.007
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831, 1058c, 1089c, 1427f, 1458, 1489, 1889, 3809, 4209, 6129, 8018}}
 
Badness: 5.755
 
=== 17-limit ===
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 14400/14399, 61965/61952, 31213/31212, 3764768/3764475
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 18 || 7 || 11|| 0 || 13 || ],
|-
| ⟨ || 0 || 1 || 6 || 2 || 6 || -5 || 0 || ],
|-
| ⟨ || 0 || 0 || 65 || 19 || 44 || -30 || 23 || ]
|}
 
CTE generators: ~2 = 1200.008, ~3/2 = 701.925, ~78975/60368 = 465.007
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831, 1058cg, 1089c, 1458g, 1489, 1889, 2320, 3809, 4209, 6129, 8018}}
 
Badness: 2.373
 
=== 19-limit ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 5985/5984, 14400/14399, 13377/13376, 61965/61952, 3764768/3764475
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 18 || 7 || 11|| 0 || 13 || 4 || ],
|-
| ⟨ || 0 || 1 || 6 || 2 || 6 || -5 || 0 || -4 || ],
|-
| ⟨ || 0 || 0 || 65 || 19 || 44 || -30 || 23 || -17 || ]
|}
 
CTE generators: ~2 = 1200.011, ~3/2 = 701.921, ~22880/17493 = 465.008
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831, 1058cg, 1089c, 1458g, 1489, 1889, 2320, 3809, 6129h, 9938h}}
 
Badness: 1.706
 
== 37 & 109 & 577 ==
 
Subgroup: 2.5.7.11
 
Comma list: 102487/102400
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 4 || 2 || ],
|-
| ⟨ || 0 || 1 || 6 || -1 || ],
|-
| ⟨ || 0 || 0 || 8 || -2 || ]
|}
 
CTE generators: ~2 = 1200.048, ~5/4 = 386.260, ~11/8 = 550.980
 
{{Optimal ET sequence|legend=1|7, 11cd, 13, 15, 22, 35, 37, 72, 109, 233, 270, 342, 379, 612, 1333, 1603, 1945e, 2557e, 2936e, 3548ee}}
 
Badness: 0.189
 
=== 13-limit ===
 
Subgroup: 2.5.7.11.13
 
Comma list:  1001/1000, 6656/6655
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 4 || 2 || -3 || ],
|-
| ⟨ || 0 || 1 || 6 || -1 || -2 || ],
|-
| ⟨ || 0 || 0 || 8 || -2 || -6 || ]
|}
 
CTE generators: ~2 = 1200.021, ~5/4 = 386.630, ~11/8 = 551.170
 
{{Optimal ET sequence|legend=1|11cdf, 13, 15, 22, 35f, 37, 87, 109, 124, 161, 196, 233, 270, 503, 627, 664, 897, 1167}}
 
Badness: 0.177
 
== 37 & 307 & 457 ==
 
Subgroup: 2.5.7.11.13.17
 
Comma list: 6656/6655, 140800/140777, 10985/10976
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 2 || 1 || 3 || 2 || 10 || ],
|-
| ⟨ || 0 || 3 || 1 || -1 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 3 || 1 || 3 || -11 || ]
|}
 
CTE generators: ~2 = 1199.992, ~14/13 = 128.753, ~77/52 = 680.105
 
{{Optimal ET sequence|legend=1|30cg, 37, 113, 150, 187, 270, 307, 457, 764, 1221, 1715, 2479d}}
 
Badness: 1.001
 
=== 19-limit ===
 
Subgroup: 2.5.7.11.13.17.19
 
Comma list: 2432/2431, 10241/10240, 12103/12100, 64220/64141
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 2 || 1 || 3 || 2 || 10 || 8 || ],
|-
| ⟨ || 0 || 3 || 1 || -1 || 0 || 3 || 2 || ],
|-
| ⟨ || 0 || 0 || 3 || 1 || 3 || -11 || -7 || ]
|}
 
CTE generators: ~2 = 1200.016, ~14/13 = 128.743, ~77/52 = 680.094
 
{{Optimal ET sequence|legend=1|30cg, 37, 83g, 113, 120g, 150, 187, 270, 307, 420, 457, 764, 1184h, 1221h}}
 
Badness: 0.899
 
== 41 & 53 & 167 ==
 
Subgroup: 2.3.5.7
 
Comma list: 20480000/20253807
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 5 || ],
|-
| ⟨ || 0 || 1 || 1 || -2 || ],
|-
| ⟨ || 0 || 0 || 3 || 4 || ]
|}
 
CTE generators: ~2 = 1199.544, ~3/2 = 703.173, ~189/160 = 294.314
 
{{Optimal ET sequence|legend=1|9c, 12, 29, 41, 53, 94, 167, 179, 208, 220, 481bd, 493bd, 534bd, 754bdd}}
 
Badness: 12.361
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 2200/2187, 102400/101871
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 5 || -3 || ],
|-
| ⟨ || 0 || 1 || 1 || -2 || 5 || ],
|-
| ⟨ || 0 || 0 || 3 || 4 || -6 || ]
|}
 
CTE generators: ~2 = 1199.676, ~3/2 = 703.329, ~189/160 = 294.194
 
{{Optimal ET sequence|legend=1|9c, 12e, 20ce, 32c, 41, 53, 94, 167, 208, 220, 261}}
 
Badness: 4.132
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 41600/41503
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 5 || -3 || 2 || ],
|-
| ⟨ || 0 || 1 || 1 || -2 || 5 || 2 || ],
|-
| ⟨ || 0 || 0 || 3 || 4 || -6 || -6|| ]
|}
 
CTE generators: ~2 = 1199.700, ~3/2 = 703.310, ~189/160 = 294.172
 
{{Optimal ET sequence|legend=1|12e, 20ce, 41, 53, 94, 167, 208, 261}}
 
Badness: 2.413
 
== 41 & 53 & 509 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 65625/65536
Comma list: {{monzo|45 -26 2 -3}}
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 15 || ],
|-
| ⟨ || 0 || 1 || 1 || -8 || ],
|-
| ⟨ || 0 || 0 || 3 || 2 || ]
|}
 
CTE generators: ~2 = 1200.000, ~3/2 = 702.507, ~163840/137781 = 294.678
 
{{Optimal ET sequence|legend=1|12, 29, 41, 53, 94, 280c, 292c, 321c, 333c, 362, 374c, 415, 427c, 456, 468, 509, 521, 562, 1030, 1083d, 1592bd, 2113bcdd, 2675bbcdd}}
 
Badness: 145.624
 
== 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 = 1200.000, ~147/130 = 212.258, ~55/52 = 96.555
 
{{Optimal ET sequence|legend=1|23bcf, 39bceff, 51e, 62, 85c, 113, 175f, 198, 311, 373, 571, 684, 1566}}
 
Badness: 1.605
 
== 311 & 593 & 1063 ==
 
Subgroup: 2.3.5.7
 
Comma list: {{monzo|31 -17 -9 6}}
 
Mapping: <br>
{| class="right-all"
| [⟨ || 1 || 2 || 1 || 2 || ],
|-
| ⟨ || 0 || 3 || 1 || 10 || ],
|-
| ⟨ || 0 || 0 || 2 || 3 || ]]
|}
 
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}}
 
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
 
== 311 & 1063 & 5113 ==
 
Subgroup: 2.3.5.7.11
 
Comma list: {{monzo|0 2 15 -16 2}}, {{monzo|74 -21 -10 -5 -1}}


Mapping: <br>
Mapping: <br>
{| class="right-all"
{| class="right-all"
| [⟨ || 1 || 0 || 1 || 11 || ],
| [⟨ || 1 || 1 || 6 || 3 || -22 || ],
|-
|-
| ⟨ || 0 || 1 || 1 || -6 || ],
| ⟨ || 0 || 1 || 18 || -5 || -176 || ],
|-
|-
| ⟨ || 0 || 0 || 2 || -10 || ],
| ⟨ || 0 || 0 || -26 || 5 || 235 || ]]
|}
|}


CTE generators: ~2 = 1200.0937, ~3 = 1901.9403, ~175/192 = -157.9391
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.964, ~268435456/183784545 = 655.732


{{Optimal ET sequence|legend=1|9, 19d, 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd}}
{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063, 2676cde, 2987e, 3298e, 3428, 3609e, 3739, 4050, 4361, 4802, 5113, 9163, 9474}}


Badness: 0.761
Badness: 75.622
Retrieved from "https://en.xen.wiki/w/User:Francium/Miscellaneous_rank-3_temperaments"