Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 339875048 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 344088750 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-09 18:37:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>344088750</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], <<1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], <<1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | ||
[[POTE tuning|POTE generator]]: 696.239 | [[POTE tuning|POTE generator]]: ~3/2 = 696.239 | ||
Mapping generator: ~3 | |||
[[Map]]: [<1 0 -4|, <0 1 4|] | [[Map]]: [<1 0 -4|, <0 1 4|] | ||
| Line 28: | Line 29: | ||
[[POTE tuning|POTE generator]]: 696.495 | [[POTE tuning|POTE generator]]: 696.495 | ||
Mapping generator: ~3 | |||
Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly. | Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly. | ||
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[[POTE tuning|POTE generator]]: 696.967 | [[POTE tuning|POTE generator]]: 696.967 | ||
Mapping generator: ~3 | |||
[[Algebraic generator]]: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents. | [[Algebraic generator]]: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents. | ||
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[[POTE tuning|POTE generator]]: ~3/2 = 696.642 | [[POTE tuning|POTE generator]]: ~3/2 = 696.642 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -25 -20|, <0 1 4 10 18 15|] | Map: [<1 0 -4 -13 -25 -20|, <0 1 4 10 18 15|] | ||
| Line 69: | Line 73: | ||
POTE generator: ~3/2 = 697.264 | POTE generator: ~3/2 = 697.264 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -25 29|, <0 1 4 10 18 -16|] | Map: [<1 0 -4 -13 -25 29|, <0 1 4 10 18 -16|] | ||
| Line 78: | Line 83: | ||
POTE generator: ~3/2 = 697.529 | POTE generator: ~3/2 = 697.529 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -25 -39|, <0 1 4 10 18 27|] | Map: [<1 0 -4 -13 -25 -39|, <0 1 4 10 18 27|] | ||
| Line 87: | Line 93: | ||
POTE generator: ~52/45 = 250.304 | POTE generator: ~52/45 = 250.304 | ||
Mapping generator: ~26/15 | |||
Map: [<1 0 -4 -13 -25 -5|, <0 2 8 20 36 11|] | Map: [<1 0 -4 -13 -25 -5|, <0 2 8 20 36 11|] | ||
| Line 101: | Line 108: | ||
[[POTE tuning|POTE generator]]: 696.434 | [[POTE tuning|POTE generator]]: 696.434 | ||
Mapping generator: ~3 | |||
[[Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge. | [[Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge. | ||
| Line 117: | Line 125: | ||
POTE generator: ~3/2 = 696.211 | POTE generator: ~3/2 = 696.211 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 24 -20|, <0 1 4 10 -13 15|] | Map: [<1 0 -4 -13 24 -20|, <0 1 4 10 -13 15|] | ||
| Line 126: | Line 135: | ||
POTE generator: ~3/2 = 696.202 | POTE generator: ~3/2 = 696.202 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 24 10|, <0 1 4 10 -13 -4|] | Map: [<1 0 -4 -13 24 10|, <0 1 4 10 -13 -4|] | ||
| Line 135: | Line 145: | ||
[[POTE tuning|POTE generator]]: ~3/2 = 696.250 | [[POTE tuning|POTE generator]]: ~3/2 = 696.250 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -6|, <0 1 4 10 6|] | Map: [<1 0 -4 -13 -6|, <0 1 4 10 6|] | ||
| Line 144: | Line 155: | ||
[[POTE tuning|POTE generator]]: ~3/2 = 696.146 | [[POTE tuning|POTE generator]]: ~3/2 = 696.146 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -6 -20|, <0 1 4 10 6 15|] | Map: [<1 0 -4 -13 -6 -20|, <0 1 4 10 6 15|] | ||
| Line 153: | Line 165: | ||
POTE generator: ~3/2 | POTE generator: ~3/2 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 ... |, <0 1 4 10 6 -4 -5 -3 -6|] | Map: [<1 0 -4 -13 ... |, <0 1 4 10 6 -4 -5 -3 -6|] | ||
| Line 162: | Line 175: | ||
POTE generator: ~3/2 = 694.689 | POTE generator: ~3/2 = 694.689 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -13 -6 5|, <0 1 4 10 6 -|] | Map: [<1 0 -4 -13 -6 5|, <0 1 4 10 6 -|] | ||
| Line 183: | Line 197: | ||
[[POTE tuning|POTE generator]]: 693.779 | [[POTE tuning|POTE generator]]: 693.779 | ||
Mapping generator: ~3 | |||
Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4. | Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4. | ||
| Line 196: | Line 211: | ||
POTE generator: ~3/2 = 693.126 | POTE generator: ~3/2 = 693.126 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 17 -6|, <0 1 4 -9 6|] | Map: [<1 0 -4 17 -6|, <0 1 4 -9 6|] | ||
| Line 205: | Line 221: | ||
POTE generator: ~3/2 = 693.058 | POTE generator: ~3/2 = 693.058 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 17 -6 10|, <0 1 4 -9 6 -4|] | Map: [<1 0 -4 17 -6 10|, <0 1 4 -9 6 -4|] | ||
| Line 216: | Line 233: | ||
[[POTE tuning|POTE generator]]: 701.573 | [[POTE tuning|POTE generator]]: 701.573 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6|, <0 1 4 -2|] | Map: [<1 0 -4 6|, <0 1 4 -2|] | ||
| Line 226: | Line 244: | ||
POTE generator: ~3/2 = 703.254 | POTE generator: ~3/2 = 703.254 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 13|, <0 1 4 -2 -6|] | Map: [<1 0 -4 6 13|, <0 1 4 -2 -6|] | ||
| Line 235: | Line 254: | ||
POTE generator: ~3/2 = 698.776 | POTE generator: ~3/2 = 698.776 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 -6|, <0 1 4 -2 6|] | Map: [<1 0 -4 6 -6|, <0 1 4 -2 6|] | ||
| Line 244: | Line 264: | ||
POTE generator: ~3/2 = 705.004 | POTE generator: ~3/2 = 705.004 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 -14|, <0 1 4 -2 11|] | Map: [<1 0 -4 6 -14|, <0 1 4 -2 11|] | ||
| Line 253: | Line 274: | ||
POTE generator: ~3/2 = 705.496 | POTE generator: ~3/2 = 705.496 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 -14 -9|, <0 1 4 -2 11 8|] | Map: [<1 0 -4 6 -14 -9|, <0 1 4 -2 11 8|] | ||
| Line 261: | Line 283: | ||
Commas: 81/80 64/63 45/44 65/64 256/255 153/152 | Commas: 81/80 64/63 45/44 65/64 256/255 153/152 | ||
POTE generator | POTE generator: ~3/2 = 696.217 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 -6 | Map: [<1 0 -4 6 -6 10 12 9|, <0 1 4 -2 6 -4 -5 -3|] | ||
EDOs: 12 | EDOs: 7, 12, 19d, 31def | ||
Badness: | Badness: 0.0204 | ||
==Arnold== | ==Arnold== | ||
Commas: 22/21, 33/32, 36/35 | Commas: 22/21, 33/32, 36/35 | ||
POTE generator: ~3/2 | POTE generator: ~3/2 = 698.491 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 5|, <0 1 4 -2 -1|] | Map: [<1 0 -4 6 5|, <0 1 4 -2 -1|] | ||
| Line 277: | Line 301: | ||
==13-limit== | ==13-limit== | ||
Commas: 22/21, 27/26, 33/32, 40/39 | |||
POTE generator: ~3/2 = 696.743 | |||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 5 -1|, <0 1 4 -2 -1 3|] | Map: [<1 0 -4 6 5 -1|, <0 1 4 -2 -1 3|] | ||
| Line 286: | Line 314: | ||
POTE generator: ~3/2 = 698.544 | POTE generator: ~3/2 = 698.544 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 6 -6 -1|, <0 1 4 -2 6 3|] | Map: [<1 0 -4 6 -6 -1|, <0 1 4 -2 6 3|] | ||
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[[POTE tuning|POTE generator]]: 700.140 | [[POTE tuning|POTE generator]]: 700.140 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -2|, <0 1 4 3|] | Map: [<1 0 -4 -2|, <0 1 4 3|] | ||
| Line 308: | Line 338: | ||
POTE generator: ~3/2 = 682.895 | POTE generator: ~3/2 = 682.895 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -5|, <0 1 4 5|] | Map: [<1 0 -4 -5|, <0 1 4 5|] | ||
| Line 318: | Line 349: | ||
POTE generator: ~3/2 = 685.234 | POTE generator: ~3/2 = 685.234 | ||
Mapping generator: ~3 | |||
Map: [<1 0 -4 -5 -6|, <0 1 4 5 6|] | Map: [<1 0 -4 -5 -6|, <0 1 4 5 6|] | ||
| Line 331: | Line 363: | ||
[[POTE tuning|POTE generator]]: 694.375 | [[POTE tuning|POTE generator]]: 694.375 | ||
Mapping generator: ~3 | |||
Map: [<2 0 -8 -7|, <0 1 4 4|] | Map: [<2 0 -8 -7|, <0 1 4 4|] | ||
| Line 344: | Line 377: | ||
POTE generator: ~3/2 = 692.840 | POTE generator: ~3/2 = 692.840 | ||
Mapping generator: ~3 | |||
Map: [<2 0 -8 -7 -12|, <0 1 4 4 6|] | Map: [<2 0 -8 -7 -12|, <0 1 4 4 6|] | ||
| Line 353: | Line 387: | ||
POTE generator: ~3/2 = 692.673 | POTE generator: ~3/2 = 692.673 | ||
Mapping generator: ~3 | |||
Map: [<2 0 -8 -7 -12 -21|, <0 1 4 4 6 9|] | Map: [<2 0 -8 -7 -12 -21|, <0 1 4 4 6 9|] | ||
| Line 371: | Line 406: | ||
POTE generator: ~3/2 = 690.548 | POTE generator: ~3/2 = 690.548 | ||
Mapping generator: ~3 | |||
Map: [<2 0 -8 -7 10|, <0 1 4 4 -1|] | Map: [<2 0 -8 -7 10|, <0 1 4 4 -1|] | ||
| Line 380: | Line 416: | ||
POTE generator: ~3/2 = 699.001 | POTE generator: ~3/2 = 699.001 | ||
Mapping generator: ~3 | |||
Map: [<2 0 -8 -7 7|, <0 1 4 4 0|] | Map: [<2 0 -8 -7 7|, <0 1 4 4 0|] | ||
| Line 392: | Line 429: | ||
[[POTE tuning|POTE generator]]: ~8/7 = 252.635 | [[POTE tuning|POTE generator]]: ~8/7 = 252.635 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2|, <0 2 8 1|] | Map: [<1 0 -4 2|, <0 2 8 1|] | ||
| Line 402: | Line 440: | ||
POTE generator: ~8/7 = 254.027 | POTE generator: ~8/7 = 254.027 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 -6|, <0 2 8 1 12|] | Map: [<1 0 -4 2 -6|, <0 2 8 1 12|] | ||
| Line 411: | Line 450: | ||
POTE generator: ~8/7 = 253.603 | POTE generator: ~8/7 = 253.603 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 -6 -5|, <0 2 8 1 12 11|] | Map: [<1 0 -4 2 -6 -5|, <0 2 8 1 12 11|] | ||
| Line 420: | Line 460: | ||
POTE generator: ~8/7 = 254.042 | POTE generator: ~8/7 = 254.042 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 5|, <0 2 8 1 -2|] | Map: [<1 0 -4 2 5|, <0 2 8 1 -2|] | ||
| Line 429: | Line 470: | ||
POTE generator: ~8/7 = 251.079 | POTE generator: ~8/7 = 251.079 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 -10|, <0 2 8 1 17|] | Map: [<1 0 -4 2 -10|, <0 2 8 1 17|] | ||
| Line 438: | Line 480: | ||
POTE generator: ~8/7 = 251.165 | POTE generator: ~8/7 = 251.165 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 -10 -5|, <0 2 8 1 17 11|] | Map: [<1 0 -4 2 -10 -5|, <0 2 8 1 17 11|] | ||
| Line 447: | Line 490: | ||
POTE generator: ~8/7 = 251.173 | POTE generator: ~8/7 = 251.173 | ||
Mapping generator: ~7/4 | |||
Map: [<1 0 -4 2 9|, <0 2 8 1 -7|] | Map: [<1 0 -4 2 9|, <0 2 8 1 -7|] | ||
| Line 467: | Line 511: | ||
[[Eigenmonzo]]s: 2, 5 | [[Eigenmonzo]]s: 2, 5 | ||
[[POTE tuning|POTE generator]]: 348.415 | [[POTE tuning|POTE generator]]: ~128/105 = 348.415 | ||
Mapping generator: ~128/105 | |||
Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly. | Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly. | ||
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[[POTE tuning|POTE generator]]: ~11/9 = 348.477 | [[POTE tuning|POTE generator]]: ~11/9 = 348.477 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 6 2|, <0 2 8 -11 5|] | Map: [<1 1 0 6 2|, <0 2 8 -11 5|] | ||
| Line 496: | Line 542: | ||
POTE generator: ~11/9 = 348.558 | POTE generator: ~11/9 = 348.558 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 6 2 4|, <0 2 8 -11 5 -1|] | Map: [<1 1 0 6 2 4|, <0 2 8 -11 5 -1|] | ||
| Line 507: | Line 554: | ||
Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation. | Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation. | ||
[[POTE tuning|POTE generator]]: 350.934 | [[POTE tuning|POTE generator]]: ~11/9 = 350.934 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 4 2|, <0 2 8 -4 5|] | Map: [<1 1 0 4 2|, <0 2 8 -4 5|] | ||
| Line 516: | Line 564: | ||
[[Comma]]s: 81/80, 36/35, 121/120, 144/143 | [[Comma]]s: 81/80, 36/35, 121/120, 144/143 | ||
[[POTE tuning|POTE generator]]: 350.816 | [[POTE tuning|POTE generator]]: ~11/9 = 350.816 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 4 2 4|, <0 2 8 -4 5 -1|] | Map: [<1 1 0 4 2 4|, <0 2 8 -4 5 -1|] | ||
| Line 526: | Line 575: | ||
POTE generator: ~11/9 = 348.182 | POTE generator: ~11/9 = 348.182 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 -3 2|, <0 2 8 20 5|] | Map: [<1 1 0 -3 2|, <0 2 8 20 5|] | ||
| Line 535: | Line 585: | ||
POTE generator: ~25/21 = 350.586 | POTE generator: ~25/21 = 350.586 | ||
Mapping generator: ~25/21 | |||
Map: [<1 1 0 -1|, <0 2 8 13|] | Map: [<1 1 0 -1|, <0 2 8 13|] | ||
| Line 544: | Line 595: | ||
POTE generator: ~11/9 = 350.565 | POTE generator: ~11/9 = 350.565 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 -1 2|, <0 2 8 13 5|] | Map: [<1 1 0 -1 2|, <0 2 8 13 5|] | ||
| Line 553: | Line 605: | ||
POTE generator: ~11/9 = 350.745 | POTE generator: ~11/9 = 350.745 | ||
Mapping generator: ~11/9 | |||
Map: [<1 1 0 -1 2 4|, <0 2 8 13 5 -1|] | Map: [<1 1 0 -1 2 4|, <0 2 8 13 5 -1|] | ||
| Line 562: | Line 615: | ||
POTE generator: ~7/6 = 275.794 | POTE generator: ~7/6 = 275.794 | ||
Mapping generator: ~343/288 | |||
Map: [<2 1 -4 4|, <0 4 16 3|] | Map: [<2 1 -4 4|, <0 4 16 3|] | ||
| Line 581: | Line 635: | ||
POTE generator: ~7/6 = 275.774 | POTE generator: ~7/6 = 275.774 | ||
Mapping generator: ~77/64 | |||
Map: [<2 1 -4 4 8 2|, <0 4 16 3 -2 10|] | Map: [<2 1 -4 4 8 2|, <0 4 16 3 -2 10|] | ||
| Line 924: | Line 979: | ||
<!-- ws:end:WikiTextTocRule:241 -->The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | <!-- ws:end:WikiTextTocRule:241 -->The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.239<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 -4|, &lt;0 1 4|]<br /> | <a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 -4|, &lt;0 1 4|]<br /> | ||
| Line 943: | Line 999: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.495<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.495<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.<br /> | Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.<br /> | ||
| Line 961: | Line 1,018: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.967<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.967<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.<br /> | <a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.<br /> | ||
| Line 975: | Line 1,033: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.642<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.642<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]<br /> | Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]<br /> | ||
| Line 984: | Line 1,043: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 697.264<br /> | POTE generator: ~3/2 = 697.264<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -25 29|, &lt;0 1 4 10 18 -16|]<br /> | Map: [&lt;1 0 -4 -13 -25 29|, &lt;0 1 4 10 18 -16|]<br /> | ||
| Line 993: | Line 1,053: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 697.529<br /> | POTE generator: ~3/2 = 697.529<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -25 -39|, &lt;0 1 4 10 18 27|]<br /> | Map: [&lt;1 0 -4 -13 -25 -39|, &lt;0 1 4 10 18 27|]<br /> | ||
| Line 1,002: | Line 1,063: | ||
<br /> | <br /> | ||
POTE generator: ~52/45 = 250.304<br /> | POTE generator: ~52/45 = 250.304<br /> | ||
Mapping generator: ~26/15<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -25 -5|, &lt;0 2 8 20 36 11|]<br /> | Map: [&lt;1 0 -4 -13 -25 -5|, &lt;0 2 8 20 36 11|]<br /> | ||
| Line 1,016: | Line 1,078: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.434<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.434<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.<br /> | <a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.<br /> | ||
| Line 1,032: | Line 1,095: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 696.211<br /> | POTE generator: ~3/2 = 696.211<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 24 -20|, &lt;0 1 4 10 -13 15|]<br /> | Map: [&lt;1 0 -4 -13 24 -20|, &lt;0 1 4 10 -13 15|]<br /> | ||
| Line 1,041: | Line 1,105: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 696.202<br /> | POTE generator: ~3/2 = 696.202<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 24 10|, &lt;0 1 4 10 -13 -4|]<br /> | Map: [&lt;1 0 -4 -13 24 10|, &lt;0 1 4 10 -13 -4|]<br /> | ||
| Line 1,050: | Line 1,115: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.250<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.250<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 4 10 6|]<br /> | Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 4 10 6|]<br /> | ||
| Line 1,059: | Line 1,125: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.146<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.146<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|]<br /> | Map: [&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|]<br /> | ||
| Line 1,068: | Line 1,135: | ||
<br /> | <br /> | ||
POTE generator: ~3/2<br /> | POTE generator: ~3/2<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 ... |, &lt;0 1 4 10 6 -4 -5 -3 -6|]<br /> | Map: [&lt;1 0 -4 -13 ... |, &lt;0 1 4 10 6 -4 -5 -3 -6|]<br /> | ||
| Line 1,077: | Line 1,145: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 694.689<br /> | POTE generator: ~3/2 = 694.689<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -13 -6 5|, &lt;0 1 4 10 6 -|]<br /> | Map: [&lt;1 0 -4 -13 -6 5|, &lt;0 1 4 10 6 -|]<br /> | ||
| Line 1,098: | Line 1,167: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 693.779<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 693.779<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4.<br /> | Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4.<br /> | ||
| Line 1,111: | Line 1,181: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 693.126<br /> | POTE generator: ~3/2 = 693.126<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 17 -6|, &lt;0 1 4 -9 6|]<br /> | Map: [&lt;1 0 -4 17 -6|, &lt;0 1 4 -9 6|]<br /> | ||
| Line 1,120: | Line 1,191: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 693.058<br /> | POTE generator: ~3/2 = 693.058<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 17 -6 10|, &lt;0 1 4 -9 6 -4|]<br /> | Map: [&lt;1 0 -4 17 -6 10|, &lt;0 1 4 -9 6 -4|]<br /> | ||
| Line 1,131: | Line 1,203: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.573<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.573<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|]<br /> | Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|]<br /> | ||
| Line 1,141: | Line 1,214: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 703.254<br /> | POTE generator: ~3/2 = 703.254<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 13|, &lt;0 1 4 -2 -6|]<br /> | Map: [&lt;1 0 -4 6 13|, &lt;0 1 4 -2 -6|]<br /> | ||
| Line 1,150: | Line 1,224: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 698.776<br /> | POTE generator: ~3/2 = 698.776<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 -6|, &lt;0 1 4 -2 6|]<br /> | Map: [&lt;1 0 -4 6 -6|, &lt;0 1 4 -2 6|]<br /> | ||
| Line 1,159: | Line 1,234: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 705.004<br /> | POTE generator: ~3/2 = 705.004<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 -14|, &lt;0 1 4 -2 11|]<br /> | Map: [&lt;1 0 -4 6 -14|, &lt;0 1 4 -2 11|]<br /> | ||
| Line 1,168: | Line 1,244: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 705.496<br /> | POTE generator: ~3/2 = 705.496<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 -14 -9|, &lt;0 1 4 -2 11 8|]<br /> | Map: [&lt;1 0 -4 6 -14 -9|, &lt;0 1 4 -2 11 8|]<br /> | ||
| Line 1,176: | Line 1,253: | ||
Commas: 81/80 64/63 45/44 65/64 256/255 153/152<br /> | Commas: 81/80 64/63 45/44 65/64 256/255 153/152<br /> | ||
<br /> | <br /> | ||
POTE generator<br /> | POTE generator: ~3/2 = 696.217<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 -6 | Map: [&lt;1 0 -4 6 -6 10 12 9|, &lt;0 1 4 -2 6 -4 -5 -3|]<br /> | ||
EDOs: 12<br /> | EDOs: 7, 12, 19d, 31def<br /> | ||
Badness:<br /> | Badness: 0.0204<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Dominant-Arnold"></a><!-- ws:end:WikiTextHeadingRule:46 -->Arnold</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Dominant-Arnold"></a><!-- ws:end:WikiTextHeadingRule:46 -->Arnold</h2> | ||
Commas: 22/21, 33/32, 36/35<br /> | Commas: 22/21, 33/32, 36/35<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2<br /> | POTE generator: ~3/2 = 698.491<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|]<br /> | Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|]<br /> | ||
| Line 1,192: | Line 1,271: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Dominant-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | ||
<br /> | Commas: 22/21, 27/26, 33/32, 40/39<br /> | ||
<br /> | |||
POTE generator: ~3/2 = 696.743<br /> | |||
Mapping generator: ~3<br /> | |||
<br /> | |||
Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]<br /> | Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]<br /> | ||
EDOs: 5, 7, 12ef, 19def, 31def<br /> | EDOs: 5, 7, 12ef, 19def, 31def<br /> | ||
| Line 1,201: | Line 1,284: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 698.544<br /> | POTE generator: ~3/2 = 698.544<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]<br /> | Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]<br /> | ||
| Line 1,213: | Line 1,297: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 700.140<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 700.140<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]<br /> | Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]<br /> | ||
| Line 1,223: | Line 1,308: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 682.895<br /> | POTE generator: ~3/2 = 682.895<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -5|, &lt;0 1 4 5|]<br /> | Map: [&lt;1 0 -4 -5|, &lt;0 1 4 5|]<br /> | ||
| Line 1,233: | Line 1,319: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 685.234<br /> | POTE generator: ~3/2 = 685.234<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -5 -6|, &lt;0 1 4 5 6|]<br /> | Map: [&lt;1 0 -4 -5 -6|, &lt;0 1 4 5 6|]<br /> | ||
| Line 1,246: | Line 1,333: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 694.375<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 694.375<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 0 -8 -7|, &lt;0 1 4 4|]<br /> | Map: [&lt;2 0 -8 -7|, &lt;0 1 4 4|]<br /> | ||
| Line 1,259: | Line 1,347: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 692.840<br /> | POTE generator: ~3/2 = 692.840<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 0 -8 -7 -12|, &lt;0 1 4 4 6|]<br /> | Map: [&lt;2 0 -8 -7 -12|, &lt;0 1 4 4 6|]<br /> | ||
| Line 1,268: | Line 1,357: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 692.673<br /> | POTE generator: ~3/2 = 692.673<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 0 -8 -7 -12 -21|, &lt;0 1 4 4 6 9|]<br /> | Map: [&lt;2 0 -8 -7 -12 -21|, &lt;0 1 4 4 6 9|]<br /> | ||
| Line 1,286: | Line 1,376: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 690.548<br /> | POTE generator: ~3/2 = 690.548<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 0 -8 -7 10|, &lt;0 1 4 4 -1|]<br /> | Map: [&lt;2 0 -8 -7 10|, &lt;0 1 4 4 -1|]<br /> | ||
| Line 1,295: | Line 1,386: | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 699.001<br /> | POTE generator: ~3/2 = 699.001<br /> | ||
Mapping generator: ~3<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 0 -8 -7 7|, &lt;0 1 4 4 0|]<br /> | Map: [&lt;2 0 -8 -7 7|, &lt;0 1 4 4 0|]<br /> | ||
| Line 1,307: | Line 1,399: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 252.635<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 252.635<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2|, &lt;0 2 8 1|]<br /> | Map: [&lt;1 0 -4 2|, &lt;0 2 8 1|]<br /> | ||
| Line 1,317: | Line 1,410: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 254.027<br /> | POTE generator: ~8/7 = 254.027<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 -6|, &lt;0 2 8 1 12|]<br /> | Map: [&lt;1 0 -4 2 -6|, &lt;0 2 8 1 12|]<br /> | ||
| Line 1,326: | Line 1,420: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 253.603<br /> | POTE generator: ~8/7 = 253.603<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 -6 -5|, &lt;0 2 8 1 12 11|]<br /> | Map: [&lt;1 0 -4 2 -6 -5|, &lt;0 2 8 1 12 11|]<br /> | ||
| Line 1,335: | Line 1,430: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 254.042<br /> | POTE generator: ~8/7 = 254.042<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 5|, &lt;0 2 8 1 -2|]<br /> | Map: [&lt;1 0 -4 2 5|, &lt;0 2 8 1 -2|]<br /> | ||
| Line 1,344: | Line 1,440: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 251.079<br /> | POTE generator: ~8/7 = 251.079<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 -10|, &lt;0 2 8 1 17|]<br /> | Map: [&lt;1 0 -4 2 -10|, &lt;0 2 8 1 17|]<br /> | ||
| Line 1,353: | Line 1,450: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 251.165<br /> | POTE generator: ~8/7 = 251.165<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 -10 -5|, &lt;0 2 8 1 17 11|]<br /> | Map: [&lt;1 0 -4 2 -10 -5|, &lt;0 2 8 1 17 11|]<br /> | ||
| Line 1,362: | Line 1,460: | ||
<br /> | <br /> | ||
POTE generator: ~8/7 = 251.173<br /> | POTE generator: ~8/7 = 251.173<br /> | ||
Mapping generator: ~7/4<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 2 9|, &lt;0 2 8 1 -7|]<br /> | Map: [&lt;1 0 -4 2 9|, &lt;0 2 8 1 -7|]<br /> | ||
| Line 1,382: | Line 1,481: | ||
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 348.415<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~128/105 = 348.415<br /> | ||
Mapping generator: ~128/105<br /> | |||
<br /> | <br /> | ||
Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly.<br /> | Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly.<br /> | ||
| Line 1,401: | Line 1,501: | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 348.477<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 348.477<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br /> | Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br /> | ||
| Line 1,411: | Line 1,512: | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 348.558<br /> | POTE generator: ~11/9 = 348.558<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 6 2 4|, &lt;0 2 8 -11 5 -1|]<br /> | Map: [&lt;1 1 0 6 2 4|, &lt;0 2 8 -11 5 -1|]<br /> | ||
| Line 1,422: | Line 1,524: | ||
Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered &quot;middle-of-the-road&quot; intonation.<br /> | Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered &quot;middle-of-the-road&quot; intonation.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 350.934<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 350.934<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]<br /> | Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]<br /> | ||
| Line 1,431: | Line 1,534: | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 36/35, 121/120, 144/143<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 36/35, 121/120, 144/143<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 350.816<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 350.816<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]<br /> | Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]<br /> | ||
| Line 1,441: | Line 1,545: | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 348.182<br /> | POTE generator: ~11/9 = 348.182<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]<br /> | Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]<br /> | ||
| Line 1,450: | Line 1,555: | ||
<br /> | <br /> | ||
POTE generator: ~25/21 = 350.586<br /> | POTE generator: ~25/21 = 350.586<br /> | ||
Mapping generator: ~25/21<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 -1|, &lt;0 2 8 13|]<br /> | Map: [&lt;1 1 0 -1|, &lt;0 2 8 13|]<br /> | ||
| Line 1,459: | Line 1,565: | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 350.565<br /> | POTE generator: ~11/9 = 350.565<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 -1 2|, &lt;0 2 8 13 5|]<br /> | Map: [&lt;1 1 0 -1 2|, &lt;0 2 8 13 5|]<br /> | ||
| Line 1,468: | Line 1,575: | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 350.745<br /> | POTE generator: ~11/9 = 350.745<br /> | ||
Mapping generator: ~11/9<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 0 -1 2 4|, &lt;0 2 8 13 5 -1|]<br /> | Map: [&lt;1 1 0 -1 2 4|, &lt;0 2 8 13 5 -1|]<br /> | ||
| Line 1,477: | Line 1,585: | ||
<br /> | <br /> | ||
POTE generator: ~7/6 = 275.794<br /> | POTE generator: ~7/6 = 275.794<br /> | ||
Mapping generator: ~343/288<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 1 -4 4|, &lt;0 4 16 3|]<br /> | Map: [&lt;2 1 -4 4|, &lt;0 4 16 3|]<br /> | ||
| Line 1,496: | Line 1,605: | ||
<br /> | <br /> | ||
POTE generator: ~7/6 = 275.774<br /> | POTE generator: ~7/6 = 275.774<br /> | ||
Mapping generator: ~77/64<br /> | |||
<br /> | <br /> | ||
Map: [&lt;2 1 -4 4 8 2|, &lt;0 4 16 3 -2 10|]<br /> | Map: [&lt;2 1 -4 4 8 2|, &lt;0 4 16 3 -2 10|]<br /> | ||