5L 3s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601299116 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601299192 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-03 16: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-03 16:28:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601299192</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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|| 11\28 || || || || ||= <span style="display: block; text-align: center;">5 1 5</span> ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||= || | || 11\28 || || || || ||= <span style="display: block; text-align: center;">5 1 5</span> ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||= || | ||
|| 9\23 || || || || ||= <span style="display: block; text-align: center;">4 1 4</span> ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= <span style="display: block; text-align: center;">L/s = 4</span> || | || 9\23 || || || || ||= <span style="display: block; text-align: center;">4 1 4</span> ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= <span style="display: block; text-align: center;">L/s = 4</span> || | ||
|| || || || || ||= pi 1 pi ||= 467.171 ||= [[tel | || || || || || ||= pi 1 pi ||= 467.171 ||= [[tel/934.3425|934.3425]] ||= 201.514 ||= 668.685 ||= <span style="display: block; text-align: center;">L/s = pi</span> || | ||
|| 7\18 || || || || ||= <span style="display: block; text-align: center;">3 1 3</span> ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= <span style="display: block; text-align: center;">L/s = 3</span> || | || 7\18 || || || || ||= <span style="display: block; text-align: center;">3 1 3</span> ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= <span style="display: block; text-align: center;">L/s = 3</span> || | ||
|| || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= <span style="display: block; text-align: center;">L/s = e</span> || | || || || || || ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= <span style="display: block; text-align: center;">L/s = e</span> || | ||
|| || 19\49 || || || ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= [[tel | || || 19\49 || || || ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= [[tel/661.2245|661.2245]] || || | ||
|| || || 50\129 || || ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 || || | || || || 50\129 || || ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 || || | ||
|| || || || 131\338 || ||= 55 21 55 ||= 465.089 ||= [[tel | || || || || 131\338 || ||= 55 21 55 ||= 465.089 ||= [[tel/930.1775|930.1775]] ||= 195.266 ||= 660.335 || || | ||
|| || || || || 212\547 ||= 89 34 89 ||= 465.082 ||= [[tel | || || || || || 212\547 ||= 89 34 89 ||= 465.082 ||= [[tel/930.1645|930.1645]] ||= 195.247 ||= 660.329 || || | ||
|| || || || 81\209 || ||= 34 13 34 ||= 465.072 ||= [[tel | || || || || 81\209 || ||= 34 13 34 ||= 465.072 ||= [[tel/930.1435|930.1435]] ||= 195.215 ||= 660.287 || || | ||
|| || || 31\80 || || ||= 13 5 13 ||= 465 ||= 930 ||= 195 ||= 660 || || | || || || 31\80 || || ||= 13 5 13 ||= 465 ||= 930 ||= 195 ||= 660 || || | ||
|| || 12\31 || || || ||= <span style="display: block; text-align: center;">5 2 5</span> ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= || | || || 12\31 || || || ||= <span style="display: block; text-align: center;">5 2 5</span> ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||= || | ||
|| 5\13 || || || || ||= <span style="display: block; text-align: center;">2 1 2</span> ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= || | || 5\13 || || || || ||= <span style="display: block; text-align: center;">2 1 2</span> ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||= || | ||
|| || || || || ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 459.417 ||= [[tel | || || || || || ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 459.417 ||= [[tel/918.8345|918.8345]] ||= 178.252 ||= 637.669 || || | ||
|| || 13\34 || || || ||= <span style="display: block; text-align: center;">5 3 5</span> ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= || | || || 13\34 || || || ||= <span style="display: block; text-align: center;">5 3 5</span> ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||= || | ||
|| || || 34\89 || || ||= <span style="display: block; text-align: center;">13 8 13</span> ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= || | || || || 34\89 || || ||= <span style="display: block; text-align: center;">13 8 13</span> ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||= || | ||
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The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes. | The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes. | ||
By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and | By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has [[Bohlen-Pierce]] as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio. | ||
||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || | ||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || | ||
||= 2\5 ||= ||= ||= ||= ||= 1 0 1 ||= 760.782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||= || | ||= 2\5 ||= ||= ||= ||= ||= 1 0 1 ||= 760.782 ||= 1521.564 ||= 380.391 ||= 1141.173 ||= || | ||
||= 27\68 ||= ||= ||= ||= ||= 13 1 13 ||= 755.188 ||= 1510.376 ||= 363.609 ||= 1118.797 ||= || | ||= 27\68 ||= ||= ||= ||= ||= 13 1 13 ||= 755.188 ||= 1510.376 ||= 363.609 ||= 1118.797 ||= || | ||
||= ||= ||= ||= ||= ||= ~6626 [[tel | ||= ||= ||= ||= ||= ||= ~6626 [[tel/515 6626|515 6626]] ||= 755.132 ||= 1510.265 ||= 363.442 ||= 1118.574 ||= <span style="display: block; text-align: center;">2g=12/5 minus quarter comma</span> || | ||
||= 25\63 ||= ||= ||= ||= ||= 12 1 12 ||= 754.744 ||= 1509.488 ||= 362.277 ||= 1117.021 ||= || | ||= 25\63 ||= ||= ||= ||= ||= 12 1 12 ||= 754.744 ||= 1509.488 ||= 362.277 ||= 1117.021 ||= || | ||
||= 23\58 ||= ||= ||= ||= ||= 11 1 11 ||= [[tel | ||= 23\58 ||= ||= ||= ||= ||= 11 1 11 ||= [[tel/754.2235|754.2235]] ||= 1508.447 ||= 360.716 ||= 1114.939 ||= || | ||
||= 21\53 ||= ||= ||= ||= ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||= || | ||= 21\53 ||= ||= ||= ||= ||= 10 1 10 ||= 753.605 ||= 1507.21 ||= 358.859 ||= 1112.464 ||= || | ||
||= 19\48 ||= ||= ||= ||= ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||= || | ||= 19\48 ||= ||= ||= ||= ||= 9 1 9 ||= 752.857 ||= 1505.714 ||= 356.617 ||= 1109.474 ||= || | ||
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||= 15\38 ||= ||= ||= ||= ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||= || | ||= 15\38 ||= ||= ||= ||= ||= 7 1 7 ||= 750.771 ||= 1501.543 ||= 350.36 ||= 1101.132 ||= || | ||
||= ||= 28/71 ||= ||= ||= ||= 13 2 13 ||= 750.067 ||= 1500.1335 ||= 348.245 ||= 1098.312 ||= || | ||= ||= 28/71 ||= ||= ||= ||= 13 2 13 ||= 750.067 ||= 1500.1335 ||= 348.245 ||= 1098.312 ||= || | ||
||= ||= 41\104 ||= ||= ||= ||= 19 3 19 ||= 749.809 ||= 1466.618 ||= [[tel | ||= ||= 41\104 ||= ||= ||= ||= 19 3 19 ||= 749.809 ||= 1466.618 ||= [[tel/347.4725|347.4725]] ||= 1097.282 ||= 3g=11/3 near here || | ||
||= 13\33 ||= ||= ||= ||= ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||= || | ||= 13\33 ||= ||= ||= ||= ||= 6 1 6 ||= 749.255 ||= 1498.51 ||= 345.81 ||= 1095.065 ||= || | ||
||= ||= 24\61 ||= ||= ||= ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||= || | ||= ||= 24\61 ||= ||= ||= ||= 11 2 11 ||= 748.31 ||= 1496.62 ||= 342.976 ||= 1091.286 ||= || | ||
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||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= || | ||= ||= 47\120 ||= ||= ||= ||= 21 5 21 ||= 744.932 ||= 1489.865 ||= 332.842 ||= 1077.7745 ||= || | ||
||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 || | ||= 9\23 ||= ||= ||= ||= ||= 4 1 4 ||= 744.243 ||= 1488.487 ||= 330.775 ||= 1075.018 ||= L/s = 4 || | ||
||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= [[tel | ||= ||= 43\110 ||= ||= ||= ||= 19 5 19 ||= [[tel/743.4915|743.4915]] ||= 1486.983 ||= [[tel/328.5195|328.5195]] ||= 1072.011 ||= || | ||
||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here || | ||= ||= ||= 77\197 ||= ||= ||= 34 9 34 ||= 743.404 ||= 1486.807 ||= 328.256 ||= 1071.66 ||= 4g=39/7 near here || | ||
||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= || | ||= ||= 34\87 ||= ||= ||= ||= 15 4 15 ||= 743.293 ||= 1486.586 ||= 327.923 ||= 1071.216 ||= || | ||
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||= ||= ||= 31\80 ||= ||= ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||= || | ||= ||= ||= 31\80 ||= ||= ||= 13 5 13 ||= 737.008 ||= 1474.015 ||= 309.068 ||= 1046.075 ||= || | ||
||= ||= 12\31 ||= ||= ||= ||= 5 2 5 ||= 736.241 ||= 1472.481 ||= 306.767 ||= 1043.007 ||= || | ||= ||= 12\31 ||= ||= ||= ||= 5 2 5 ||= 736.241 ||= 1472.481 ||= 306.767 ||= 1043.007 ||= || | ||
||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">1+√2 1 1+√2</span> ||= 735.542 ||= 1471.084 ||= [[tel | ||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">1+√2 1 1+√2</span> ||= 735.542 ||= 1471.084 ||= [[tel/304.6715|304.6715]] ||= 1040.214 ||= Silver false father || | ||
||= ||= 17\44 ||= ||= ||= ||= 7 3 7 ||= 734.846 ||= 1469.693 ||= 302.584 ||= 1037.41 ||= || | ||= ||= 17\44 ||= ||= ||= ||= 7 3 7 ||= 734.846 ||= 1469.693 ||= 302.584 ||= 1037.41 ||= || | ||
||= ||= 22\57 ||= ||= ||= ||= 9 4 9 ||= 734.088 ||= 1468.176 ||= 300.309 ||= 1034.397 ||= || | ||= ||= 22\57 ||= ||= ||= ||= 9 4 9 ||= 734.088 ||= 1468.176 ||= 300.309 ||= 1034.397 ||= || | ||
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||= ||= 43\112 ||= ||= ||= ||= 17 9 17 ||= 730.215 ||= 1460.43 ||= 288.69 ||= 1018.905 ||= || | ||= ||= 43\112 ||= ||= ||= ||= 17 9 17 ||= 730.215 ||= 1460.43 ||= 288.69 ||= 1018.905 ||= || | ||
||= ||= 38\99 ||= ||= ||= ||= 15 8 15 ||= 730.043 ||= 1460.087 ||= 288.175 ||= 1018.218 ||= || | ||= ||= 38\99 ||= ||= ||= ||= 15 8 15 ||= 730.043 ||= 1460.087 ||= 288.175 ||= 1018.218 ||= || | ||
||= ||= ||= 71\185 ||= ||= ||= 28 15 28 ||= [[tel | ||= ||= ||= 71\185 ||= ||= ||= 28 15 28 ||= [[tel/729.9395|729.9395]] ||= 1459.879 ||= [[tel/287.8635|287.8635]] ||= 1017.803 ||= || | ||
||= ||= ||= 104\271 ||= ||= ||= 41 22 41 ||= 729.902 ||= 1459.803 ||= 287.75 ||= 1017.651 ||= 4g=27/5 near here || | ||= ||= ||= 104\271 ||= ||= ||= 41 22 41 ||= 729.902 ||= 1459.803 ||= 287.75 ||= 1017.651 ||= 4g=27/5 near here || | ||
||= ||= 33\86 ||= ||= ||= ||= 13 7 13 ||= 729.82 ||= 1459.64 ||= 287.505 ||= 1017.325 ||= || | ||= ||= 33\86 ||= ||= ||= ||= 13 7 13 ||= 729.82 ||= 1459.64 ||= 287.505 ||= 1017.325 ||= || | ||
||= ||= 28\73 ||= ||= ||= ||= 11 6 11 ||= 729.547 ||= 1459.034 ||= 286.596 ||= 1016.113 ||= || | ||= ||= 28\73 ||= ||= ||= ||= 11 6 11 ||= 729.547 ||= 1459.034 ||= 286.596 ||= 1016.113 ||= || | ||
||= ||= 23\60 ||= ||= ||= ||= 9 5 9 ||= 729.083 ||= 1458.1655 ||= 285.293 ||= 1014.376 ||= || | ||= ||= 23\60 ||= ||= ||= ||= 9 5 9 ||= 729.083 ||= 1458.1655 ||= 285.293 ||= 1014.376 ||= || | ||
||= ||= ||= 41\107 ||= ||= ||= 16 9 16 ||= [[tel | ||= ||= ||= 41\107 ||= ||= ||= 16 9 16 ||= [[tel/728.7865|728.7865]] ||= 1457.573 ||= [[tel/284.4045|284.4045]] ||= 1013.191 ||= 3g=99/28 near here || | ||
||= ||= ||= 59\154 ||= ||= ||= 23 13 23 ||= 728.671 ||= 1457.342 ||= 284.058 ||= 1012.729 ||= || | ||= ||= ||= 59\154 ||= ||= ||= 23 13 23 ||= 728.671 ||= 1457.342 ||= 284.058 ||= 1012.729 ||= || | ||
||= ||= ||= 77\201 ||= ||= ||= 30 17 30 ||= 728.61 ||= 1457.219 ||= 283.874 ||= 1012.483 ||= || | ||= ||= ||= 77\201 ||= ||= ||= 30 17 30 ||= 728.61 ||= 1457.219 ||= 283.874 ||= 1012.483 ||= || | ||
||= ||= ||= 95\248 ||= ||= ||= 37 21 37 ||= [[tel | ||= ||= ||= 95\248 ||= ||= ||= 37 21 37 ||= [[tel/728.5715|728.5715]] ||= 1457.143 ||= [[tel/283.7595|283.7595]] ||= 1012.331 ||= Golden BP is index-2 near here || | ||
||= ||= 18\47 ||= ||= ||= ||= 7 4 7 ||= 728.408 ||= 1456.817 ||= 283.27 ||= 1011.678 ||= || | ||= ||= 18\47 ||= ||= ||= ||= 7 4 7 ||= 728.408 ||= 1456.817 ||= 283.27 ||= 1011.678 ||= || | ||
||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||= || | ||= ||= ||= ||= ||= ||= <span style="background-color: #ffffff;">√3 1 √3</span> ||= 728.159 ||= 1456.318 ||= 282.522 ||= 1010.6815 ||= || | ||
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||= ||= ||= 34\89 ||= ||= ||= 13 8 13 ||= 726.59 ||= 1453.179 ||= 277.814 ||= 1004.403 ||= || | ||= ||= ||= 34\89 ||= ||= ||= 13 8 13 ||= 726.59 ||= 1453.179 ||= 277.814 ||= 1004.403 ||= || | ||
||= ||= ||= ||= 89\233 ||= ||= 34 21 34 ||= 726.498 ||= 1452.996 ||= 277.538 ||= 1004.036 ||= || | ||= ||= ||= ||= 89\233 ||= ||= 34 21 34 ||= 726.498 ||= 1452.996 ||= 277.538 ||= 1004.036 ||= || | ||
||= ||= ||= ||= ||= 233\610 ||= 89 55 89 ||= [[tel | ||= ||= ||= ||= ||= 233\610 ||= 89 55 89 ||= [[tel/726.4845|726.4845]] ||= 1452.969 ||= [[tel/277.4985|277.4985]] ||= 1003.983 ||= Golden false father || | ||
||= ||= ||= ||= 144\377 ||= ||= 55 34 55 ||= 726.476 ||= 1452.952 ||= 277.473 ||= 1003.95 ||= || | ||= ||= ||= ||= 144\377 ||= ||= 55 34 55 ||= 726.476 ||= 1452.952 ||= 277.473 ||= 1003.95 ||= || | ||
||= ||= ||= 55\144 ||= ||= ||= 21 13 21 ||= 726.441 ||= 1452.882 ||= 277.368 ||= 1003.809 ||= || | ||= ||= ||= 55\144 ||= ||= ||= 21 13 21 ||= 726.441 ||= 1452.882 ||= 277.368 ||= 1003.809 ||= || | ||
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||= ||= 19\50 ||= ||= ||= ||= 7 5 7 ||= 722.743 ||= 1445.486 ||= 266.274 ||= 989.017 ||= || | ||= ||= 19\50 ||= ||= ||= ||= 7 5 7 ||= 722.743 ||= 1445.486 ||= 266.274 ||= 989.017 ||= || | ||
||= 11\29 ||= ||= ||= ||= ||= 4 3 4 ||= 721.431 ||= 1442.862 ||= 262.338 ||= 983.77 ||= || | ||= 11\29 ||= ||= ||= ||= ||= 4 3 4 ||= 721.431 ||= 1442.862 ||= 262.338 ||= 983.77 ||= || | ||
||= ||= 25\66 ||= ||= ||= ||= 9 7 9 ||= [[tel | ||= ||= 25\66 ||= ||= ||= ||= 9 7 9 ||= [[tel/720.4375|720.4375]] ||= 1440.875 ||= [[tel/259.3575|259.3575]] ||= 979.795 ||= || | ||
||= ||= ||= 64\169 ||= ||= ||= 23 18 23 ||= 720.267 ||= 1440.534 ||= 258.848 ||= 979.113 ||= || | ||= ||= ||= 64\169 ||= ||= ||= 23 18 23 ||= 720.267 ||= 1440.534 ||= 258.848 ||= 979.113 ||= || | ||
||= ||= ||= ||= 167\441 ||= ||= 60 47 60 ||= [[tel | ||= ||= ||= ||= 167\441 ||= ||= 60 47 60 ||= [[tel/720.2415|720.2415]] ||= 1440.483 ||= [[tel/258.7965|258.7965]] ||= 979.001 ||= || | ||
||= ||= ||= ||= ||= 437\1154 ||= [[tel | ||= ||= ||= ||= ||= 437\1154 ||= [[tel/157 123 157|157 123 157]] ||= 720.238 ||= 1440.475 ||= 258.758 ||= 978.996 ||= || | ||
||= ||= ||= ||= 270\713 ||= ||= 97 76 97 ||= 720.235 ||= 1440.471 ||= 258.751 ||= 978.987 ||= || | ||= ||= ||= ||= 270\713 ||= ||= 97 76 97 ||= 720.235 ||= 1440.471 ||= 258.751 ||= 978.987 ||= || | ||
||= ||= ||= 103\272 ||= ||= ||= 37 29 37 ||= 720.226 ||= 1440.451 ||= 258.722 ||= 978.947 ||= || | ||= ||= ||= 103\272 ||= ||= ||= 37 29 37 ||= 720.226 ||= 1440.451 ||= 258.722 ||= 978.947 ||= || | ||
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||= ||= ||= 79\209 ||= ||= ||= 28 23 28 ||= 718.921 ||= 1437.842 ||= 254.807 ||= 973.728 ||= || | ||= ||= ||= 79\209 ||= ||= ||= 28 23 28 ||= 718.921 ||= 1437.842 ||= 254.807 ||= 973.728 ||= || | ||
||= ||= ||= ||= 206\545 ||= ||= 73 60 73 ||= 718.904 ||= 1437.808 ||= 254.757 ||= 973.661 ||= || | ||= ||= ||= ||= 206\545 ||= ||= 73 60 73 ||= 718.904 ||= 1437.808 ||= 254.757 ||= 973.661 ||= || | ||
||= ||= ||= ||= ||= 539\1426 ||= [[tel | ||= ||= ||= ||= ||= 539\1426 ||= [[tel/191 117 191|191 117 191]] ||= 718.902 ||= 1437.803 ||= 254.75 ||= 973.652 ||= || | ||
||= ||= ||= ||= 333\881 ||= ||= [[tel | ||= ||= ||= ||= 333\881 ||= ||= [[tel/118 97 118|118 97 118]] ||= 718.90 ||= 1437.80 ||= 254.745 ||= [[tel/973.6455|973.6455]] ||= || | ||
||= ||= ||= 127\336 ||= ||= ||= 45 37 45 ||= 718.893 ||= 1437.787 ||= 254.726 ||= 973.619 ||= || | ||= ||= ||= 127\336 ||= ||= ||= 45 37 45 ||= 718.893 ||= 1437.787 ||= 254.726 ||= 973.619 ||= || | ||
||= ||= 48\127 ||= ||= ||= ||= 17 14 17 ||= 718.849 ||= 1437.698 ||= 254.592 ||= 973.441 ||= || | ||= ||= 48\127 ||= ||= ||= ||= 17 14 17 ||= 718.849 ||= 1437.698 ||= 254.592 ||= 973.441 ||= || | ||
||= 17\45 ||= ||= ||= ||= ||= 6 5 6 ||= 718.516 ||= 1437.032 ||= 253.549 ||= 972.11 ||= || | ||= 17\45 ||= ||= ||= ||= ||= 6 5 6 ||= 718.516 ||= 1437.032 ||= 253.549 ||= 972.11 ||= || | ||
||= 20\53 ||= ||= ||= ||= ||= 7 6 7 ||= 717.719 ||= 1435.438 ||= 251.202 ||= [[tel | ||= 20\53 ||= ||= ||= ||= ||= 7 6 7 ||= 717.719 ||= 1435.438 ||= 251.202 ||= [[tel/968.9205|968.9205]] ||= || | ||
||= ||= ||= ||= ||= ||= ~401 344 401 ||= 717.695 ||= 1435.3905 ||= 251.131 ||= 968.826 ||= 4g=21/4 || | ||= ||= ||= ||= ||= ||= ~401 344 401 ||= 717.695 ||= 1435.3905 ||= 251.131 ||= 968.826 ||= 4g=21/4 || | ||
||= 23\61 ||= ||= ||= ||= ||= 8 7 8 ||= 717.131 ||= 1434.261 ||= 249.437 ||= 966.567 ||= || | ||= 23\61 ||= ||= ||= ||= ||= 8 7 8 ||= 717.131 ||= 1434.261 ||= 249.437 ||= 966.567 ||= || | ||
||= ||= ||= ||= ||= ||= ~6682 [[tel | ||= ||= ||= ||= ||= ||= ~6682 [[tel/5875 6682|5875 6682]] ||= [[tel/716.9925|716.9925]] ||= 1433.985 ||= [[tel/249.0225|249.0225]] ||= 966.015 ||= 6g=12 || | ||
||= 26\69 ||= ||= ||= ||= ||= 9 8 9 ||= 716.679 ||= 1433.357 ||= 248.081 ||= 964.76 ||= || | ||= 26\69 ||= ||= ||= ||= ||= 9 8 9 ||= 716.679 ||= 1433.357 ||= 248.081 ||= 964.76 ||= || | ||
||= 29\77 ||= ||= ||= ||= ||= 10 9 10 ||= 716.321 ||= 1432.641 ||= 247.007 ||= 963.328 ||= || | ||= 29\77 ||= ||= ||= ||= ||= 10 9 10 ||= 716.321 ||= 1432.641 ||= 247.007 ||= 963.328 ||= || | ||
||= 32\85 ||= ||= ||= ||= ||= 11 10 11 ||= 716.03 ||= 1432.06 ||= 246.135 ||= [[tel | ||= 32\85 ||= ||= ||= ||= ||= 11 10 11 ||= 716.03 ||= 1432.06 ||= 246.135 ||= [[tel/962.1655|962.1655]] ||= || | ||
||= 35\93 ||= ||= ||= ||= ||= 12 11 12 ||= [[tel | ||= 35\93 ||= ||= ||= ||= ||= 12 11 12 ||= [[tel/715.7895|715.7895]] ||= 1431.759 ||= [[tel/245.4135|245.4135]] ||= 961.203 ||= || | ||
||= 38/101 ||= ||= ||= ||= ||= 13 12 13 ||= 715.587 ||= 1431.174 ||= 244.806 ||= 960.393 ||= 2g=16\7 near here || | ||= 38/101 ||= ||= ||= ||= ||= 13 12 13 ||= 715.587 ||= 1431.174 ||= 244.806 ||= 960.393 ||= 2g=16\7 near here || | ||
||= 3\8 ||= ||= ||= ||= ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= [[tel | ||= 3\8 ||= ||= ||= ||= ||= 1 1 1 ||= 713.233 ||= 1426.466 ||= 237.744 ||= [[tel/950.9775|950.9775]] ||= || | ||
.</pre></div> | .</pre></div> | ||
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The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br /> | The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.<br /> | ||
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By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3 and | By a weird coincidence, the other generator for this MOS will generate the same pattern within a tritave equivalence. By yet another weird coincidence, this MOS belongs to a temperament which has <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> as its index-2 subtemperament. In addition to being harmonious, this tuning of the MOS gives an L/s ratio between 3/1 and 3/2, which is squarely in the middle of the range, being thus neither too exaggerated nor too equalized to be recognizable as such, unlike in octaves, where the only notable harmonic entropy minimum is near a greatly exaggerated 10/1 L/s ratio.<br /> | ||
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