Porcupine family: Difference between revisions
m →Nautilus: extend beyond optimal patent val as 44 is considerably closer to ideal tuning. |
Update keys |
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[[Comma list]]: 250/243 | [[Comma list]]: 250/243 | ||
{{Mapping|legend=1| 1 2 3 | 0 -3 -5 }} | |||
: mapping generators: ~2, ~10/9 | : mapping generators: ~2, ~10/9 | ||
Line 46: | Line 46: | ||
Comma list: 55/54, 100/99 | Comma list: 55/54, 100/99 | ||
Sval mapping: | Sval mapping: {{mapping| 1 2 3 4 | 0 -3 -5 -4 }} | ||
Gencom mapping: | Gencom mapping: {{mapping| 1 2 3 0 4 | 0 -3 -5 0 -4 }} | ||
: gencom: [2 10/9; 55/54, 100/99] | |||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.8867 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.8867 | ||
Line 63: | Line 63: | ||
Comma list: 55/54, 100/99, 512/507 | Comma list: 55/54, 100/99, 512/507 | ||
Sval mapping: | Sval mapping: {{mapping| 1 5 8 8 2 | 0 -6 -10 -8 3 }} | ||
: sval mapping generators: ~2, ~65/44 | : sval mapping generators: ~2, ~65/44 | ||
Line 82: | Line 82: | ||
[[Comma list]]: 64/63, 250/243 | [[Comma list]]: 64/63, 250/243 | ||
{{Mapping|legend=1| 1 2 3 2 | 0 -3 -5 6 }} | |||
{{Multival|legend=1| 3 5 -6 1 -18 -28 }} | {{Multival|legend=1| 3 5 -6 1 -18 -28 }} | ||
Line 90: | Line 90: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }} | * [[7-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5 | ||
* [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }} | * [[9-odd-limit]]: ~10/9 = {{monzo| 1/6 -1/6 0 1/12 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7 | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
Line 109: | Line 109: | ||
Comma list: 55/54, 64/63, 100/99 | Comma list: 55/54, 64/63, 100/99 | ||
Mapping: | Mapping: {{mapping| 1 2 3 2 4 | 0 -3 -5 6 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.1055 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.1055 | ||
Line 131: | Line 131: | ||
Comma list: 40/39, 55/54, 64/63, 66/65 | Comma list: 40/39, 55/54, 64/63, 66/65 | ||
Mapping: | Mapping: {{mapping| 1 2 3 2 4 4 | 0 -3 -5 6 -4 -2 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.4425 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.4425 | ||
Line 157: | Line 157: | ||
Comma list: 55/54, 64/63, 91/90, 100/99 | Comma list: 55/54, 64/63, 91/90, 100/99 | ||
Mapping: | Mapping: {{mapping| 1 2 3 2 4 6 | 0 -3 -5 6 -4 -17 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 162.6361 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 162.6361 | ||
Line 181: | Line 181: | ||
Comma list: 55/54, 64/63, 100/99, 196/195 | Comma list: 55/54, 64/63, 100/99, 196/195 | ||
Mapping: | Mapping: {{mapping| 1 2 3 2 4 1 | 0 -3 -5 6 -4 20 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.3781 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.3781 | ||
Line 198: | Line 198: | ||
Comma list: 55/54, 64/63, 65/63, 100/99 | Comma list: 55/54, 64/63, 65/63, 100/99 | ||
Mapping: | Mapping: {{mapping| 1 2 3 2 4 3 | 0 -3 -5 6 -4 5 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.6778 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 163.6778 | ||
Line 217: | Line 217: | ||
[[Comma list]]: 28/27, 126/125 | [[Comma list]]: 28/27, 126/125 | ||
{{Mapping|legend=1| 1 2 3 4 | 0 -3 -5 -9 }} | |||
{{Multival|legend=1| 3 5 9 1 6 7 }} | {{Multival|legend=1| 3 5 9 1 6 7 }} | ||
Line 224: | Line 224: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo | * [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7 | ||
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }} | {{Optimal ET sequence|legend=1| 7d, 8d, 15 }} | ||
Line 235: | Line 235: | ||
Comma list: 28/27, 55/54, 77/75 | Comma list: 28/27, 55/54, 77/75 | ||
Mapping: | Mapping: {{mapping| 1 2 3 4 4 | 0 -3 -5 -9 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.3646 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.3646 | ||
Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit eigenmonzo | * 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7 | ||
{{Optimal ET sequence|legend=1| 7d, 8d, 15 }} | {{Optimal ET sequence|legend=1| 7d, 8d, 15 }} | ||
Line 251: | Line 251: | ||
Comma list: 28/27, 40/39, 55/54, 66/65 | Comma list: 28/27, 40/39, 55/54, 66/65 | ||
Mapping: | Mapping: {{mapping| 1 2 3 4 4 4 | 0 -3 -5 -9 -4 -2 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.6312 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.6312 | ||
Minimax tuning: | Minimax tuning: | ||
* 13- and 15-odd-limit eigenmonzo | * 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7 | ||
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 38bceff }} | {{Optimal ET sequence|legend=1| 7d, 8d, 15, 38bceff }} | ||
Line 269: | Line 269: | ||
[[Comma list]]: 225/224, 250/243 | [[Comma list]]: 225/224, 250/243 | ||
{{Mapping|legend=1| 1 2 3 5 | 0 -3 -5 -16 }} | |||
{{Multival|legend=1| 3 5 16 1 17 23 }} | {{Multival|legend=1| 3 5 16 1 17 23 }} | ||
Line 277: | Line 277: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/11 0 1/11 -1/11 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5 | ||
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 29, 51, 73c }} | {{Optimal ET sequence|legend=1| 7d, 15d, 22, 29, 51, 73c }} | ||
Line 288: | Line 288: | ||
Comma list: 55/54, 100/99, 225/224 | Comma list: 55/54, 100/99, 225/224 | ||
Mapping: | Mapping: {{mapping| 1 2 3 5 4 | 0 -3 -5 -16 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.3207 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.3207 | ||
Line 294: | Line 294: | ||
Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }} | * 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }} | ||
: | : eigenmonzo basis (unchanged-interval basis): 2.7/5 | ||
{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51 }} | {{Optimal ET sequence|legend=1| 7d, 15d, 22, 51 }} | ||
Line 305: | Line 305: | ||
Comma list: 55/54, 65/64, 91/90, 100/99 | Comma list: 55/54, 65/64, 91/90, 100/99 | ||
Mapping: | Mapping: {{mapping| 1 2 3 5 4 3 | 0 -3 -5 -16 -4 5 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.4782 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.4782 | ||
Line 320: | Line 320: | ||
[[Comma list]]: 250/243, 525/512 | [[Comma list]]: 250/243, 525/512 | ||
{{Mapping|legend=1| 1 2 3 1 | 0 -3 -5 13 }} | |||
{{Multival|legend=1| 3 5 -13 1 -29 -44 }} | {{Multival|legend=1| 3 5 -13 1 -29 -44 }} | ||
Line 328: | Line 328: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 2/3 -1/3 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3 | ||
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65c, 94cd }} | {{Optimal ET sequence|legend=1| 7, 22d, 29, 65c, 94cd }} | ||
Line 339: | Line 339: | ||
Comma list: 55/54, 100/99, 525/512 | Comma list: 55/54, 100/99, 525/512 | ||
Mapping: | Mapping: {{mapping| 1 2 3 1 4 | 0 -3 -5 13 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 165.9246 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 165.9246 | ||
Line 345: | Line 345: | ||
Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }} | * 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }} | ||
: | : eigenmonzo basis (unchanged-interval basis): 2.3 | ||
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65ce }} | {{Optimal ET sequence|legend=1| 7, 22d, 29, 65ce }} | ||
Line 356: | Line 356: | ||
Comma list: 55/54, 65/64, 100/99, 105/104 | Comma list: 55/54, 65/64, 100/99, 105/104 | ||
Mapping: | Mapping: {{mapping| 1 2 3 1 4 3 | 0 -3 -5 13 -4 5 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 166.0459 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 166.0459 | ||
Line 362: | Line 362: | ||
Minimax tuning: | Minimax tuning: | ||
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }} | * 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }} | ||
: | : eigenmonzo basis (unchanged-interval basis): 2.3 | ||
{{Optimal ET sequence|legend=1| 7, 22d, 29, 65cef }} | {{Optimal ET sequence|legend=1| 7, 22d, 29, 65cef }} | ||
Line 375: | Line 375: | ||
[[Comma list]]: 36/35, 160/147 | [[Comma list]]: 36/35, 160/147 | ||
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -1 }} | |||
{{Multival|legend=1| 3 5 1 1 -7 -12 }} | {{Multival|legend=1| 3 5 1 1 -7 -12 }} | ||
Line 383: | Line 383: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }} | * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }} | ||
: [[Eigenmonzo basis | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5 | ||
{{Optimal ET sequence|legend=1| 7, 8d, 15d }} | {{Optimal ET sequence|legend=1| 7, 8d, 15d }} | ||
Line 394: | Line 394: | ||
Comma list: 22/21, 36/35, 80/77 | Comma list: 22/21, 36/35, 80/77 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 | 0 -3 -5 -1 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684 | Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684 | ||
Line 409: | Line 409: | ||
[[Comma list]]: 21/20, 175/162 | [[Comma list]]: 21/20, 175/162 | ||
{{Mapping|legend=1| 1 2 3 3 | 0 -3 -5 -2 }} | |||
{{Multival|legend=1| 3 5 2 1 -5 -9 }} | {{Multival|legend=1| 3 5 2 1 -5 -9 }} | ||
Line 429: | Line 429: | ||
[[Comma list]]: 50/49, 245/243 | [[Comma list]]: 50/49, 245/243 | ||
{{Mapping|legend=1| 2 1 1 2 | 0 3 5 5 }} | |||
: mapping generators: ~7/5, ~9/7 | : mapping generators: ~7/5, ~9/7 | ||
Line 446: | Line 446: | ||
Comma list: 50/49, 55/54, 99/98 | Comma list: 50/49, 55/54, 99/98 | ||
Mapping: | Mapping: {{mapping| 2 1 1 2 4 | 0 3 5 5 4 }} | ||
Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.5281 | Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.5281 | ||
Line 459: | Line 459: | ||
Comma list: 50/49, 55/54, 65/63, 99/98 | Comma list: 50/49, 55/54, 65/63, 99/98 | ||
Mapping: | Mapping: {{mapping| 2 1 1 2 4 3 | 0 3 5 5 4 6 }} | ||
Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 436.3087 | Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 436.3087 | ||
Line 472: | Line 472: | ||
Comma list: 40/39, 50/49, 55/54, 66/65 | Comma list: 40/39, 50/49, 55/54, 66/65 | ||
Mapping: | Mapping: {{mapping| 2 1 1 2 4 6 | 0 3 5 5 4 2 }} | ||
Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.1856 | Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.1856 | ||
Line 485: | Line 485: | ||
Comma list: 50/49, 245/243, 385/384 | Comma list: 50/49, 245/243, 385/384 | ||
Mapping: | Mapping: {{mapping| 2 1 1 2 12 | 0 3 5 5 -7 }} | ||
Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.3289 | Optimal tuning (CTE): ~7/5 = 1\2, ~9/7 = 435.3289 | ||
Line 501: | Line 501: | ||
[[Comma list]]: 49/48, 250/243 | [[Comma list]]: 49/48, 250/243 | ||
{{Mapping|legend=1| 1 2 3 3 | 0 -6 -10 -3 }} | |||
: mapping generators: ~2, ~21/20 | : mapping generators: ~2, ~21/20 | ||
Line 518: | Line 518: | ||
Comma list: 49/48, 55/54, 245/242 | Comma list: 49/48, 55/54, 245/242 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 | 0 -6 -10 -3 -8 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.8017 | Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.8017 | ||
Line 531: | Line 531: | ||
Comma list: 49/48, 55/54, 91/90, 100/99 | Comma list: 49/48, 55/54, 91/90, 100/99 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 5 | 0 -6 -10 -3 -8 -19 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.9123 | Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 81.9123 | ||
Line 544: | Line 544: | ||
Comma list: 40/39, 49/48, 55/54, 66/65 | Comma list: 40/39, 49/48, 55/54, 66/65 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 4 | 0 -6 -10 -3 -8 -4 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 82.0342 | Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 82.0342 | ||
Line 560: | Line 560: | ||
[[Comma list]]: 250/243, 686/675 | [[Comma list]]: 250/243, 686/675 | ||
{{Mapping|legend=1| 1 5 8 10 | 0 -9 -15 -19 }} | |||
: mapping generators: ~2, ~9/7 | : mapping generators: ~2, ~9/7 | ||
Line 577: | Line 577: | ||
Comma list: 55/54, 100/99, 686/675 | Comma list: 55/54, 100/99, 686/675 | ||
Mapping: | Mapping: {{mapping| 1 5 8 10 8 | 0 -9 -15 -19 -12 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 454.5050 | Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 454.5050 | ||
Line 590: | Line 590: | ||
Comma list: 55/54, 91/90, 100/99, 169/168 | Comma list: 55/54, 91/90, 100/99, 169/168 | ||
Mapping: | Mapping: {{mapping| 1 5 8 10 8 9 | 0 -9 -15 -19 -12 -14 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~13/10 = 454.4798 | Optimal tuning (CTE): ~2 = 1\1, ~13/10 = 454.4798 | ||
Line 603: | Line 603: | ||
[[Comma list]]: 250/243, 1728/1715 | [[Comma list]]: 250/243, 1728/1715 | ||
{{Mapping|legend=1| 1 2 3 3 | 0 -9 -15 -4 }} | |||
: mapping generators: ~2, ~36/35 | : mapping generators: ~2, ~36/35 | ||
Line 620: | Line 620: | ||
Comma list: 55/54, 100/99, 352/343 | Comma list: 55/54, 100/99, 352/343 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 | 0 -9 -15 -4 -12 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.7019 | Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.7019 | ||
Line 633: | Line 633: | ||
Comma list: 55/54, 65/63, 100/99, 352/343 | Comma list: 55/54, 65/63, 100/99, 352/343 | ||
Mapping: | Mapping: {{mapping| 1 2 3 3 4 4 | 0 -9 -15 -4 -12 -7 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.5751 | Optimal tuning (CTE): ~2 = 1\1, ~36/35 = 54.5751 | ||
Line 643: | Line 643: | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Porcupine family| ]] <!-- main article --> | [[Category:Porcupine family| ]] <!-- main article --> | ||
[[Category:Porcupine]] | [[Category:Porcupine| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] |