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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =3L 4s - "mosh"= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 12:15:19 UTC</tt>.<br>
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| : The original revision id was <tt>565160127</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=3L 4s - "mosh"=
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| MOS scales of this form are built from a generator that falls between 1\3 (one degree of [[3edo]] - 400 cents) and 2\7 (two degrees of [[7edo]] - 343 cents. | | MOS scales of this form are built from a generator that falls between 1\3 (one degree of [[3edo|3edo]] - 400 cents) and 2\7 (two degrees of [[7edo|7edo]] - 343 cents. |
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| It has the form s L s L s L s and its various "modes" (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are: | | It has the form s L s L s L s and its various "modes" (with [[Modal_UDP_Notation|Modal UDP Notation]] and nicknames coined by [[Andrew_Heathwaite|Andrew Heathwaite]]) are: |
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| |
|
| ||= **Mode** ||= **UDP** ||= **Nickname** || | | {| class="wikitable" |
| || s L s L s L s ||= 3|3 || bish ||
| | |- |
| || L s L s L s s ||= 6|0 || dril ||
| | | style="text-align:center;" | '''Mode''' |
| || s L s L s s L ||= 2|4 || fish ||
| | | style="text-align:center;" | '''UDP''' |
| || L s L s s L s ||= 5|1 || gil ||
| | | style="text-align:center;" | '''Nickname''' |
| || s L s s L s L ||= 1|5 || jwl ||
| | |- |
| || L s s L s L s ||= 4|2 || kleeth ||
| | | | s L s L s L s |
| || s s L s L s L ||= 0|6 || led ||
| | | style="text-align:center;" | 3|3 |
| The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic family|magic]], where the generator is a 5/4 but five of them make a 3/1.
| | | | bish |
| ||~ ||~ ||~ ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments || | | |- |
| || 1\3 || || || 400.000 || 800.000 || 1200.000 || 400.000 ||= ||
| | | | L s L s L s s |
| || || 15\46 || || 391.304 || 782.609 || 1173.913 || 365.217 ||= ||
| | | style="text-align:center;" | 6|0 |
| || || 14\43 || || 390.698 || 781.395 || 1172.093 || 362.791 ||= ||
| | | | dril |
| || || 13\40 || || 390.000 || 780.000 || 1170.000 || 360.000 ||= ||
| | |- |
| || || 12\37 || || 389.189 || 778.378 || 1167.568 || 356.757 ||= ||
| | | | s L s L s s L |
| || || 11\34 || || 388.235 || 776.471 || 1164.706 || 352.941 ||= ||
| | | style="text-align:center;" | 2|4 |
| || || 10\31 || || 387.097 || 774.194 || 1161.290 || 348.387 ||= <span style="display: block; text-align: center;">[[xenharmonic/Würschmidt family|Würschmidt]] is around here</span> || | | | | fish |
| || || || 19\59 || 386.441 || 772.881 || 1159.322 || 345.763 ||= || | | |- |
| || || 9\28 || || 385.714 || 771.429 || 1157.143 || 342.857 ||= ||
| | | | L s L s s L s |
| || || 8\25 || || 384.000 || 768.000 || 1152.000 || 336.000 ||= ||
| | | style="text-align:center;" | 5|1 |
| || || || 23\72 || 383.333 || 766.667 || 1150.000 || 333.333 ||= ||
| | | | gil |
| || || || 15\47 || 382.988 || 765.957 || 1148.936 || 331.915 ||= ||
| | |- |
| || || 7\22 || || 381.818 || 763.636 || 1145.455 || 327.273 ||= ||
| | | | s L s s L s L |
| || || || 13\41 || 380.488 || 760.976 || 1141.463 || 321.951 ||= <span style="display: block; text-align: center;">Magic is around here</span> ||
| | | style="text-align:center;" | 1|5 |
| || || || 19\60 || 380.000 || 760.000 || 1140.000 || 320.000 ||= ||
| | | | jwl |
| || || || 25\79 || 379.747 || 759.494 || 1139.2405 || 318.987 ||= ||
| | |- |
| || || 6\19 || || 378.947 || 757.895 || 1136.842 || 315.789 ||= || | | | | L s s L s L s |
| || || || 11\35 || 377.143 || 754.286 || 1131.429 || 308.571 ||= ||
| | | style="text-align:center;" | 4|2 |
| || || || 16\51 || 376.471 || 752.941 || 1129.412 || 305.882 ||= ||
| | | | kleeth |
| || || 5\16 || || 375.000 || 750.000 || 1125.000 || 300.000 ||= <span style="display: block; text-align: center;">L/s = 4</span> ||
| | |- |
| || || || 24\77 || 374.026 || 748.052 || 1122.078 || 296.104 ||= || | | | | s s L s L s L |
| || || || 19\61 || 373.7705 || 747.541 || 1121.3115 || 295.082 ||= || | | | style="text-align:center;" | 0|6 |
| || || || 14\45 || 373.333 || 746.667 || 1120.000 || 293.333 ||= || | | | | led |
| || || || 9\29 || 372.414 || 744.828 || 1117.241 || 289.655 ||= ||
| | |} |
| || || || 13\42 || 371.429 || 742.857 || 1114.286 || 285.714 ||= ||
| | The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic_family|magic]], where the generator is a 5/4 but five of them make a 3/1. |
| || || || 17\55 || 370.909 || 741.818 || 1112.727 || 283.636 ||= ||
| |
| || || || || 370.204 || 740.409 || 1110.613 || 280.817 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
| |
| || || 4\13 || || 369.231 || 738.462 || 1107.692 || 276.923 ||= <span style="display: block; text-align: center;">L/s = 3</span> || | |
| || || || 23\75 || 368.000 || 736.000 || 1104.000 || 272.000 ||= <span style="display: block; text-align: center;"> | |
| </span> ||
| |
| || || || 19\62 || 367.742 || 735.484 || 1103.226 || 270.968 || || | |
| || || || 15\49 || 367.347 || 734.694 || 1102.041 || 269.388 ||= || | |
| || || || || 367.091 || 734.183 || 1101.274 || 268.365 ||= L/s = e || | |
| || || || 11\36 || 366.667 || 733.333 || 1100.000 || 266.667 ||= ||
| |
| || || || || 366.256 || 732.513 || 1198.77 || 265.026 || ||
| |
| || || || 7\23 || 365.217 || 730.435 || 1095.652 || 260.870 ||= <span style="display: block; text-align: center;">Modi Sephiratorum (Kosmorsky)</span> || | |
| || || || 17\56 || 364.286 || 728.571 || 1092.857 || 257.143 ||= || | |
| || || || 10\33 || 363.636 || 727.272 || 1090.909 || 254.545 ||= || | |
| || || || 13\43 || 362.791 || 725.581 || 1088.372 || 251.163 ||= || | |
| || || || 16\53 || 362.264 || 724.528 || 1086.7925 || 249.057 ||= ||
| |
| || || || 19\63 || 361.905 || 723.8095 || 1085.714 || 247.619 ||= ||
| |
| || || 3\10 || || 360.000 || 720.000 || 1080.000 || 240.000 ||= <span style="display: block; text-align: center;">Boundary of propriety</span><span style="display: block; text-align: center;">(generators smaller than this are proper)</span> || | |
| || || || 38\127 || 359.055 || 718.110 || 1077.165 || 236.2205 ||= || | |
| || || || 35\117 || 358.974 || 717.949 || 1076.923 || 235.898 ||= || | |
| || || || 32\107 || 358.8785 || 717.757 || 1076.6355 || 235.514 ||= || | |
| || || || 29\97 || 358.763 || 717.526 || 1076.289 || 235.0515 ||= || | |
| || || || 26\87 || 358.621 || 717.241 || 1075.862 || 234.483 ||= ||
| |
| || || || 23\77 || 358.442 || 716.883 || 1075.325 || 233.767 ||= ||
| |
| || || || 20\67 || 358.209 || 716.418 || 1074.627 || 232.836 ||= ||
| |
| || || || 17\57 || 357.895 || 715.7895 || 1073.684 || 231.579 ||= ||
| |
| || || || 14\47 || 357.447 || 714.894 || 1072.340 || 229.787 ||= ||
| |
| || || || 11\37 || 356.757 || 713.514 || 1070.270 || 227.027 ||= ||
| |
| || || || || 356.5035 || 713.007 || 1069.511 || 226.014 || ||
| |
| || || || 8\27 || 355.556 || 711.111 || 1066.667 || 222.222 ||= <span style="display: block; text-align: center;">Beatles is around here</span> ||
| |
| || || || || 354.930 || 709.859 || 1064.789 || 219.718 ||= <span style="display: block; text-align: center;">Golden neutral thirds scale</span> || | |
| || || || 21\71 || 354.783 || 709.565 || 1064.348 || 219.13 ||= || | |
| || || || 13\44 || 354.5455 || 709.091 || 1063.636 || 218.182 ||= || | |
| || || || || 354.088 || 708.177 || 1062.266 || 216.354 || || | |
| || || 5\17 || || 352.941 || 705.882 || 1058.824 || 211.765 ||= <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2)</span> ||
| |
| || || || 12\41 || 351.220 || 702.439 || 1053.659 || 204.878 ||= <span style="display: block; text-align: center;">2.3.11 neutral thirds scale is around here</span> || | |
| || || 7\24 || || 350.000 || 700.000 || 1050.000 || 200.000 ||= || | |
| || || || 16\55 || 349.091 || 698.182 || 1047.273 || 196.364 || || | |
| || || 9\31 || || 348.387 || 696.774 || 1045.161 || 193.548 ||= <span style="display: block; text-align: center;">Mohajira/dicot is around here</span> ||
| |
| || || 11\38 || || 347.368 || 694.737 || 1042.105 || 189.474 || ||
| |
| || 2\7 || || || 342.857 || 685.714 || 1028.571 || 171.429 ||= ||
| |
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| |
|
| 3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh"). | | {| class="wikitable" |
| | |- |
| | ! | |
| | ! | |
| | ! | |
| | ! | g |
| | ! | 2g |
| | ! | 3g |
| | ! | 4g (-1200) |
| | ! | comments |
| | |- |
| | | | 1\3 |
| | | | |
| | | | |
| | | | 400.000 |
| | | | 800.000 |
| | | | 1200.000 |
| | | | 400.000 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 15\46 |
| | | | |
| | | | 391.304 |
| | | | 782.609 |
| | | | 1173.913 |
| | | | 365.217 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 14\43 |
| | | | |
| | | | 390.698 |
| | | | 781.395 |
| | | | 1172.093 |
| | | | 362.791 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 13\40 |
| | | | |
| | | | 390.000 |
| | | | 780.000 |
| | | | 1170.000 |
| | | | 360.000 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 12\37 |
| | | | |
| | | | 389.189 |
| | | | 778.378 |
| | | | 1167.568 |
| | | | 356.757 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 11\34 |
| | | | |
| | | | 388.235 |
| | | | 776.471 |
| | | | 1164.706 |
| | | | 352.941 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 10\31 |
| | | | |
| | | | 387.097 |
| | | | 774.194 |
| | | | 1161.290 |
| | | | 348.387 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">[[Würschmidt_family|Würschmidt]] is around here</span> |
| | |- |
| | | | |
| | | | |
| | | | 19\59 |
| | | | 386.441 |
| | | | 772.881 |
| | | | 1159.322 |
| | | | 345.763 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 9\28 |
| | | | |
| | | | 385.714 |
| | | | 771.429 |
| | | | 1157.143 |
| | | | 342.857 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 8\25 |
| | | | |
| | | | 384.000 |
| | | | 768.000 |
| | | | 1152.000 |
| | | | 336.000 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 23\72 |
| | | | 383.333 |
| | | | 766.667 |
| | | | 1150.000 |
| | | | 333.333 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 15\47 |
| | | | 382.988 |
| | | | 765.957 |
| | | | 1148.936 |
| | | | 331.915 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 7\22 |
| | | | |
| | | | 381.818 |
| | | | 763.636 |
| | | | 1145.455 |
| | | | 327.273 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 13\41 |
| | | | 380.488 |
| | | | 760.976 |
| | | | 1141.463 |
| | | | 321.951 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Magic is around here</span> |
| | |- |
| | | | |
| | | | |
| | | | 19\60 |
| | | | 380.000 |
| | | | 760.000 |
| | | | 1140.000 |
| | | | 320.000 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 25\79 |
| | | | 379.747 |
| | | | 759.494 |
| | | | 1139.2405 |
| | | | 318.987 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 6\19 |
| | | | |
| | | | 378.947 |
| | | | 757.895 |
| | | | 1136.842 |
| | | | 315.789 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 11\35 |
| | | | 377.143 |
| | | | 754.286 |
| | | | 1131.429 |
| | | | 308.571 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 16\51 |
| | | | 376.471 |
| | | | 752.941 |
| | | | 1129.412 |
| | | | 305.882 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 5\16 |
| | | | |
| | | | 375.000 |
| | | | 750.000 |
| | | | 1125.000 |
| | | | 300.000 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = 4</span> |
| | |- |
| | | | |
| | | | |
| | | | 24\77 |
| | | | 374.026 |
| | | | 748.052 |
| | | | 1122.078 |
| | | | 296.104 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 19\61 |
| | | | 373.7705 |
| | | | 747.541 |
| | | | 1121.3115 |
| | | | 295.082 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 14\45 |
| | | | 373.333 |
| | | | 746.667 |
| | | | 1120.000 |
| | | | 293.333 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 9\29 |
| | | | 372.414 |
| | | | 744.828 |
| | | | 1117.241 |
| | | | 289.655 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 13\42 |
| | | | 371.429 |
| | | | 742.857 |
| | | | 1114.286 |
| | | | 285.714 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 17\55 |
| | | | 370.909 |
| | | | 741.818 |
| | | | 1112.727 |
| | | | 283.636 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 370.204 |
| | | | 740.409 |
| | | | 1110.613 |
| | | | 280.817 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span> |
| | |- |
| | | | |
| | | | 4\13 |
| | | | |
| | | | 369.231 |
| | | | 738.462 |
| | | | 1107.692 |
| | | | 276.923 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = 3</span> |
| | |- |
| | | | |
| | | | |
| | | | 23\75 |
| | | | 368.000 |
| | | | 736.000 |
| | | | 1104.000 |
| | | | 272.000 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;"> |
|
| |
|
| In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".
| | </span> |
| | |- |
| | | | |
| | | | |
| | | | 19\62 |
| | | | 367.742 |
| | | | 735.484 |
| | | | 1103.226 |
| | | | 270.968 |
| | | | |
| | |- |
| | | | |
| | | | |
| | | | 15\49 |
| | | | 367.347 |
| | | | 734.694 |
| | | | 1102.041 |
| | | | 269.388 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 367.091 |
| | | | 734.183 |
| | | | 1101.274 |
| | | | 268.365 |
| | | style="text-align:center;" | L/s = e |
| | |- |
| | | | |
| | | | |
| | | | 11\36 |
| | | | 366.667 |
| | | | 733.333 |
| | | | 1100.000 |
| | | | 266.667 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 366.256 |
| | | | 732.513 |
| | | | 1198.77 |
| | | | 265.026 |
| | | | |
| | |- |
| | | | |
| | | | |
| | | | 7\23 |
| | | | 365.217 |
| | | | 730.435 |
| | | | 1095.652 |
| | | | 260.870 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Modi Sephiratorum (Kosmorsky)</span> |
| | |- |
| | | | |
| | | | |
| | | | 17\56 |
| | | | 364.286 |
| | | | 728.571 |
| | | | 1092.857 |
| | | | 257.143 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 10\33 |
| | | | 363.636 |
| | | | 727.272 |
| | | | 1090.909 |
| | | | 254.545 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 13\43 |
| | | | 362.791 |
| | | | 725.581 |
| | | | 1088.372 |
| | | | 251.163 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 16\53 |
| | | | 362.264 |
| | | | 724.528 |
| | | | 1086.7925 |
| | | | 249.057 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 19\63 |
| | | | 361.905 |
| | | | 723.8095 |
| | | | 1085.714 |
| | | | 247.619 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | 3\10 |
| | | | |
| | | | 360.000 |
| | | | 720.000 |
| | | | 1080.000 |
| | | | 240.000 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Boundary of propriety</span><span style="display: block; text-align: center;">(generators smaller than this are proper)</span> |
| | |- |
| | | | |
| | | | |
| | | | 38\127 |
| | | | 359.055 |
| | | | 718.110 |
| | | | 1077.165 |
| | | | 236.2205 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 35\117 |
| | | | 358.974 |
| | | | 717.949 |
| | | | 1076.923 |
| | | | 235.898 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 32\107 |
| | | | 358.8785 |
| | | | 717.757 |
| | | | 1076.6355 |
| | | | 235.514 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 29\97 |
| | | | 358.763 |
| | | | 717.526 |
| | | | 1076.289 |
| | | | 235.0515 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 26\87 |
| | | | 358.621 |
| | | | 717.241 |
| | | | 1075.862 |
| | | | 234.483 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 23\77 |
| | | | 358.442 |
| | | | 716.883 |
| | | | 1075.325 |
| | | | 233.767 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 20\67 |
| | | | 358.209 |
| | | | 716.418 |
| | | | 1074.627 |
| | | | 232.836 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 17\57 |
| | | | 357.895 |
| | | | 715.7895 |
| | | | 1073.684 |
| | | | 231.579 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 14\47 |
| | | | 357.447 |
| | | | 714.894 |
| | | | 1072.340 |
| | | | 229.787 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 11\37 |
| | | | 356.757 |
| | | | 713.514 |
| | | | 1070.270 |
| | | | 227.027 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 356.5035 |
| | | | 713.007 |
| | | | 1069.511 |
| | | | 226.014 |
| | | | |
| | |- |
| | | | |
| | | | |
| | | | 8\27 |
| | | | 355.556 |
| | | | 711.111 |
| | | | 1066.667 |
| | | | 222.222 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Beatles is around here</span> |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 354.930 |
| | | | 709.859 |
| | | | 1064.789 |
| | | | 219.718 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Golden neutral thirds scale</span> |
| | |- |
| | | | |
| | | | |
| | | | 21\71 |
| | | | 354.783 |
| | | | 709.565 |
| | | | 1064.348 |
| | | | 219.13 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 13\44 |
| | | | 354.5455 |
| | | | 709.091 |
| | | | 1063.636 |
| | | | 218.182 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | 354.088 |
| | | | 708.177 |
| | | | 1062.266 |
| | | | 216.354 |
| | | | |
| | |- |
| | | | |
| | | | 5\17 |
| | | | |
| | | | 352.941 |
| | | | 705.882 |
| | | | 1058.824 |
| | | | 211.765 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2)</span> |
| | |- |
| | | | |
| | | | |
| | | | 12\41 |
| | | | 351.220 |
| | | | 702.439 |
| | | | 1053.659 |
| | | | 204.878 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">2.3.11 neutral thirds scale is around here</span> |
| | |- |
| | | | |
| | | | 7\24 |
| | | | |
| | | | 350.000 |
| | | | 700.000 |
| | | | 1050.000 |
| | | | 200.000 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | 16\55 |
| | | | 349.091 |
| | | | 698.182 |
| | | | 1047.273 |
| | | | 196.364 |
| | | | |
| | |- |
| | | | |
| | | | 9\31 |
| | | | |
| | | | 348.387 |
| | | | 696.774 |
| | | | 1045.161 |
| | | | 193.548 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">Mohajira/dicot is around here</span> |
| | |- |
| | | | |
| | | | 11\38 |
| | | | |
| | | | 347.368 |
| | | | 694.737 |
| | | | 1042.105 |
| | | | 189.474 |
| | | | |
| | |- |
| | | | 2\7 |
| | | | |
| | | | |
| | | | 342.857 |
| | | | 685.714 |
| | | | 1028.571 |
| | | | 171.429 |
| | | style="text-align:center;" | |
| | |} |
|
| |
|
| In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.</pre></div>
| | 3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo|10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L_3s|7L 3s]] ("unfair mosh"); the other scales make MOS [[3L_7s|3L 7s]] ("fair mosh"). |
| <h4>Original HTML content:</h4>
| |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>3L 4s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L 4s - &quot;mosh&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L 4s - &quot;mosh&quot;</h1>
| |
| <br />
| |
| MOS scales of this form are built from a generator that falls between 1\3 (one degree of <a class="wiki_link" href="/3edo">3edo</a> - 400 cents) and 2\7 (two degrees of <a class="wiki_link" href="/7edo">7edo</a> - 343 cents.<br /> | |
| <br />
| |
| It has the form s L s L s L s and its various &quot;modes&quot; (with <a class="wiki_link" href="/Modal%20UDP%20Notation">Modal UDP Notation</a> and nicknames coined by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>) are:<br />
| |
| <br />
| |
|
| |
|
| | In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone". |
|
| |
|
| <table class="wiki_table">
| | In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller. |
| <tr>
| | [[Category:mos]] |
| <td style="text-align: center;"><strong>Mode</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>UDP</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Nickname</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>s L s L s L s<br />
| |
| </td>
| |
| <td style="text-align: center;">3|3<br />
| |
| </td>
| |
| <td>bish<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>L s L s L s s<br />
| |
| </td>
| |
| <td style="text-align: center;">6|0<br />
| |
| </td>
| |
| <td>dril<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>s L s L s s L<br />
| |
| </td>
| |
| <td style="text-align: center;">2|4<br />
| |
| </td>
| |
| <td>fish<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>L s L s s L s<br />
| |
| </td>
| |
| <td style="text-align: center;">5|1<br />
| |
| </td>
| |
| <td>gil<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>s L s s L s L<br />
| |
| </td>
| |
| <td style="text-align: center;">1|5<br />
| |
| </td>
| |
| <td>jwl<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>L s s L s L s<br />
| |
| </td>
| |
| <td style="text-align: center;">4|2<br />
| |
| </td>
| |
| <td>kleeth<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>s s L s L s L<br />
| |
| </td>
| |
| <td style="text-align: center;">0|6<br />
| |
| </td>
| |
| <td>led<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| The two notable harmonic entropy minima with this pattern are neutral third scales (&quot;dicot&quot; / &quot;hemififth&quot; / &quot;mohajira&quot;) where two generators make a 3/2, and <a class="wiki_link" href="/Magic%20family">magic</a>, where the generator is a 5/4 but five of them make a 3/1.<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th>g<br />
| |
| </th>
| |
| <th>2g<br />
| |
| </th>
| |
| <th>3g<br />
| |
| </th>
| |
| <th>4g (-1200)<br />
| |
| </th>
| |
| <th>comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1\3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400.000<br />
| |
| </td>
| |
| <td>800.000<br />
| |
| </td>
| |
| <td>1200.000<br />
| |
| </td>
| |
| <td>400.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>15\46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>391.304<br />
| |
| </td>
| |
| <td>782.609<br />
| |
| </td>
| |
| <td>1173.913<br />
| |
| </td>
| |
| <td>365.217<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>14\43<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>390.698<br />
| |
| </td>
| |
| <td>781.395<br />
| |
| </td>
| |
| <td>1172.093<br />
| |
| </td>
| |
| <td>362.791<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>13\40<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>390.000<br />
| |
| </td>
| |
| <td>780.000<br />
| |
| </td>
| |
| <td>1170.000<br />
| |
| </td>
| |
| <td>360.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>12\37<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>389.189<br />
| |
| </td>
| |
| <td>778.378<br />
| |
| </td>
| |
| <td>1167.568<br />
| |
| </td>
| |
| <td>356.757<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>11\34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>388.235<br />
| |
| </td>
| |
| <td>776.471<br />
| |
| </td>
| |
| <td>1164.706<br />
| |
| </td>
| |
| <td>352.941<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>10\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>387.097<br />
| |
| </td>
| |
| <td>774.194<br />
| |
| </td>
| |
| <td>1161.290<br />
| |
| </td>
| |
| <td>348.387<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/W%C3%BCrschmidt%20family">Würschmidt</a> is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>19\59<br />
| |
| </td>
| |
| <td>386.441<br />
| |
| </td>
| |
| <td>772.881<br />
| |
| </td>
| |
| <td>1159.322<br />
| |
| </td>
| |
| <td>345.763<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>9\28<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>385.714<br />
| |
| </td>
| |
| <td>771.429<br />
| |
| </td>
| |
| <td>1157.143<br />
| |
| </td>
| |
| <td>342.857<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>8\25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>384.000<br />
| |
| </td>
| |
| <td>768.000<br />
| |
| </td>
| |
| <td>1152.000<br />
| |
| </td>
| |
| <td>336.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>23\72<br />
| |
| </td>
| |
| <td>383.333<br />
| |
| </td>
| |
| <td>766.667<br />
| |
| </td>
| |
| <td>1150.000<br />
| |
| </td>
| |
| <td>333.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>15\47<br />
| |
| </td>
| |
| <td>382.988<br />
| |
| </td>
| |
| <td>765.957<br />
| |
| </td>
| |
| <td>1148.936<br />
| |
| </td>
| |
| <td>331.915<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>7\22<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>381.818<br />
| |
| </td>
| |
| <td>763.636<br />
| |
| </td>
| |
| <td>1145.455<br />
| |
| </td>
| |
| <td>327.273<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\41<br />
| |
| </td>
| |
| <td>380.488<br />
| |
| </td>
| |
| <td>760.976<br />
| |
| </td>
| |
| <td>1141.463<br />
| |
| </td>
| |
| <td>321.951<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Magic is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>19\60<br />
| |
| </td>
| |
| <td>380.000<br />
| |
| </td>
| |
| <td>760.000<br />
| |
| </td>
| |
| <td>1140.000<br />
| |
| </td>
| |
| <td>320.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>25\79<br />
| |
| </td>
| |
| <td>379.747<br />
| |
| </td>
| |
| <td>759.494<br />
| |
| </td>
| |
| <td>1139.2405<br />
| |
| </td>
| |
| <td>318.987<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>6\19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>378.947<br />
| |
| </td>
| |
| <td>757.895<br />
| |
| </td>
| |
| <td>1136.842<br />
| |
| </td>
| |
| <td>315.789<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11\35<br />
| |
| </td>
| |
| <td>377.143<br />
| |
| </td>
| |
| <td>754.286<br />
| |
| </td>
| |
| <td>1131.429<br />
| |
| </td>
| |
| <td>308.571<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>16\51<br />
| |
| </td>
| |
| <td>376.471<br />
| |
| </td>
| |
| <td>752.941<br />
| |
| </td>
| |
| <td>1129.412<br />
| |
| </td>
| |
| <td>305.882<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5\16<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>375.000<br />
| |
| </td>
| |
| <td>750.000<br />
| |
| </td>
| |
| <td>1125.000<br />
| |
| </td>
| |
| <td>300.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 4</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>24\77<br />
| |
| </td>
| |
| <td>374.026<br />
| |
| </td>
| |
| <td>748.052<br />
| |
| </td>
| |
| <td>1122.078<br />
| |
| </td>
| |
| <td>296.104<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>19\61<br />
| |
| </td>
| |
| <td>373.7705<br />
| |
| </td>
| |
| <td>747.541<br />
| |
| </td>
| |
| <td>1121.3115<br />
| |
| </td>
| |
| <td>295.082<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>14\45<br />
| |
| </td>
| |
| <td>373.333<br />
| |
| </td>
| |
| <td>746.667<br />
| |
| </td>
| |
| <td>1120.000<br />
| |
| </td>
| |
| <td>293.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9\29<br />
| |
| </td>
| |
| <td>372.414<br />
| |
| </td>
| |
| <td>744.828<br />
| |
| </td>
| |
| <td>1117.241<br />
| |
| </td>
| |
| <td>289.655<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\42<br />
| |
| </td>
| |
| <td>371.429<br />
| |
| </td>
| |
| <td>742.857<br />
| |
| </td>
| |
| <td>1114.286<br />
| |
| </td>
| |
| <td>285.714<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>17\55<br />
| |
| </td>
| |
| <td>370.909<br />
| |
| </td>
| |
| <td>741.818<br />
| |
| </td>
| |
| <td>1112.727<br />
| |
| </td>
| |
| <td>283.636<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>370.204<br />
| |
| </td>
| |
| <td>740.409<br />
| |
| </td>
| |
| <td>1110.613<br />
| |
| </td>
| |
| <td>280.817<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>4\13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>369.231<br />
| |
| </td>
| |
| <td>738.462<br />
| |
| </td>
| |
| <td>1107.692<br />
| |
| </td>
| |
| <td>276.923<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>23\75<br />
| |
| </td>
| |
| <td>368.000<br />
| |
| </td>
| |
| <td>736.000<br />
| |
| </td>
| |
| <td>1104.000<br />
| |
| </td>
| |
| <td>272.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;"><br />
| |
| </span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>19\62<br />
| |
| </td>
| |
| <td>367.742<br />
| |
| </td>
| |
| <td>735.484<br />
| |
| </td>
| |
| <td>1103.226<br />
| |
| </td>
| |
| <td>270.968<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>15\49<br />
| |
| </td>
| |
| <td>367.347<br />
| |
| </td>
| |
| <td>734.694<br />
| |
| </td>
| |
| <td>1102.041<br />
| |
| </td>
| |
| <td>269.388<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>367.091<br />
| |
| </td>
| |
| <td>734.183<br />
| |
| </td>
| |
| <td>1101.274<br />
| |
| </td>
| |
| <td>268.365<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = e<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11\36<br />
| |
| </td>
| |
| <td>366.667<br />
| |
| </td>
| |
| <td>733.333<br />
| |
| </td>
| |
| <td>1100.000<br />
| |
| </td>
| |
| <td>266.667<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>366.256<br />
| |
| </td>
| |
| <td>732.513<br />
| |
| </td>
| |
| <td>1198.77<br />
| |
| </td>
| |
| <td>265.026<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\23<br />
| |
| </td>
| |
| <td>365.217<br />
| |
| </td>
| |
| <td>730.435<br />
| |
| </td>
| |
| <td>1095.652<br />
| |
| </td>
| |
| <td>260.870<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Modi Sephiratorum (Kosmorsky)</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>17\56<br />
| |
| </td>
| |
| <td>364.286<br />
| |
| </td>
| |
| <td>728.571<br />
| |
| </td>
| |
| <td>1092.857<br />
| |
| </td>
| |
| <td>257.143<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>10\33<br />
| |
| </td>
| |
| <td>363.636<br />
| |
| </td>
| |
| <td>727.272<br />
| |
| </td>
| |
| <td>1090.909<br />
| |
| </td>
| |
| <td>254.545<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\43<br />
| |
| </td>
| |
| <td>362.791<br />
| |
| </td>
| |
| <td>725.581<br />
| |
| </td>
| |
| <td>1088.372<br />
| |
| </td>
| |
| <td>251.163<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>16\53<br />
| |
| </td>
| |
| <td>362.264<br />
| |
| </td>
| |
| <td>724.528<br />
| |
| </td>
| |
| <td>1086.7925<br />
| |
| </td>
| |
| <td>249.057<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>19\63<br />
| |
| </td>
| |
| <td>361.905<br />
| |
| </td>
| |
| <td>723.8095<br />
| |
| </td>
| |
| <td>1085.714<br />
| |
| </td>
| |
| <td>247.619<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3\10<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>360.000<br />
| |
| </td>
| |
| <td>720.000<br />
| |
| </td>
| |
| <td>1080.000<br />
| |
| </td>
| |
| <td>240.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Boundary of propriety</span><span style="display: block; text-align: center;">(generators smaller than this are proper)</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>38\127<br />
| |
| </td>
| |
| <td>359.055<br />
| |
| </td>
| |
| <td>718.110<br />
| |
| </td>
| |
| <td>1077.165<br />
| |
| </td>
| |
| <td>236.2205<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>35\117<br />
| |
| </td>
| |
| <td>358.974<br />
| |
| </td>
| |
| <td>717.949<br />
| |
| </td>
| |
| <td>1076.923<br />
| |
| </td>
| |
| <td>235.898<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>32\107<br />
| |
| </td>
| |
| <td>358.8785<br />
| |
| </td>
| |
| <td>717.757<br />
| |
| </td>
| |
| <td>1076.6355<br />
| |
| </td>
| |
| <td>235.514<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>29\97<br />
| |
| </td>
| |
| <td>358.763<br />
| |
| </td>
| |
| <td>717.526<br />
| |
| </td>
| |
| <td>1076.289<br />
| |
| </td>
| |
| <td>235.0515<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>26\87<br />
| |
| </td>
| |
| <td>358.621<br />
| |
| </td>
| |
| <td>717.241<br />
| |
| </td>
| |
| <td>1075.862<br />
| |
| </td>
| |
| <td>234.483<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>23\77<br />
| |
| </td>
| |
| <td>358.442<br />
| |
| </td>
| |
| <td>716.883<br />
| |
| </td>
| |
| <td>1075.325<br />
| |
| </td>
| |
| <td>233.767<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20\67<br />
| |
| </td>
| |
| <td>358.209<br />
| |
| </td>
| |
| <td>716.418<br />
| |
| </td>
| |
| <td>1074.627<br />
| |
| </td>
| |
| <td>232.836<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>17\57<br />
| |
| </td>
| |
| <td>357.895<br />
| |
| </td>
| |
| <td>715.7895<br />
| |
| </td>
| |
| <td>1073.684<br />
| |
| </td>
| |
| <td>231.579<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>14\47<br />
| |
| </td>
| |
| <td>357.447<br />
| |
| </td>
| |
| <td>714.894<br />
| |
| </td>
| |
| <td>1072.340<br />
| |
| </td>
| |
| <td>229.787<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11\37<br />
| |
| </td>
| |
| <td>356.757<br />
| |
| </td>
| |
| <td>713.514<br />
| |
| </td>
| |
| <td>1070.270<br />
| |
| </td>
| |
| <td>227.027<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>356.5035<br />
| |
| </td>
| |
| <td>713.007<br />
| |
| </td>
| |
| <td>1069.511<br />
| |
| </td>
| |
| <td>226.014<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\27<br />
| |
| </td>
| |
| <td>355.556<br />
| |
| </td>
| |
| <td>711.111<br />
| |
| </td>
| |
| <td>1066.667<br />
| |
| </td>
| |
| <td>222.222<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Beatles is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>354.930<br />
| |
| </td>
| |
| <td>709.859<br />
| |
| </td>
| |
| <td>1064.789<br />
| |
| </td>
| |
| <td>219.718<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Golden neutral thirds scale</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>21\71<br />
| |
| </td>
| |
| <td>354.783<br />
| |
| </td>
| |
| <td>709.565<br />
| |
| </td>
| |
| <td>1064.348<br />
| |
| </td>
| |
| <td>219.13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\44<br />
| |
| </td>
| |
| <td>354.5455<br />
| |
| </td>
| |
| <td>709.091<br />
| |
| </td>
| |
| <td>1063.636<br />
| |
| </td>
| |
| <td>218.182<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>354.088<br />
| |
| </td>
| |
| <td>708.177<br />
| |
| </td>
| |
| <td>1062.266<br />
| |
| </td>
| |
| <td>216.354<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5\17<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>352.941<br />
| |
| </td>
| |
| <td>705.882<br />
| |
| </td>
| |
| <td>1058.824<br />
| |
| </td>
| |
| <td>211.765<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Optimum rank range (L/s=3/2)</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>12\41<br />
| |
| </td>
| |
| <td>351.220<br />
| |
| </td>
| |
| <td>702.439<br />
| |
| </td>
| |
| <td>1053.659<br />
| |
| </td>
| |
| <td>204.878<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">2.3.11 neutral thirds scale is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>7\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>350.000<br />
| |
| </td>
| |
| <td>700.000<br />
| |
| </td>
| |
| <td>1050.000<br />
| |
| </td>
| |
| <td>200.000<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>16\55<br />
| |
| </td>
| |
| <td>349.091<br />
| |
| </td>
| |
| <td>698.182<br />
| |
| </td>
| |
| <td>1047.273<br />
| |
| </td>
| |
| <td>196.364<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>9\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>348.387<br />
| |
| </td>
| |
| <td>696.774<br />
| |
| </td>
| |
| <td>1045.161<br />
| |
| </td>
| |
| <td>193.548<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">Mohajira/dicot is around here</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>11\38<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>347.368<br />
| |
| </td>
| |
| <td>694.737<br />
| |
| </td>
| |
| <td>1042.105<br />
| |
| </td>
| |
| <td>189.474<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2\7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>342.857<br />
| |
| </td>
| |
| <td>685.714<br />
| |
| </td>
| |
| <td>1028.571<br />
| |
| </td>
| |
| <td>171.429<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| 3\10 on this chart represents a dividing line between &quot;neutral third scales&quot; on the bottom (eg. <a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a>), and something else I don't have a name for yet on the top, with <a class="wiki_link" href="/10edo">10edo</a> standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> (&quot;unfair mosh&quot;); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> (&quot;fair mosh&quot;).<br />
| |
| <br />
| |
| In &quot;neutral third scale territory,&quot; the generators are all &quot;neutral thirds,&quot; and two of them make an approximation of the &quot;perfect fifth.&quot; Additionally, the L of the scale is somewhere around a &quot;whole tone&quot; and the s of the scale is somewhere around a &quot;neutral tone&quot;.<br />
| |
| <br />
| |
| In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &quot;supermajor second&quot; to a &quot;major third&quot; and s is a &quot;semitone&quot; or smaller.</body></html></pre></div> | |