3L 4s
3L 4s - "mosh"[edit]
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.
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:
| Mode | UDP | Nickname |
| s L s L s L s | 3|3 | bish |
| L s L s L s s | 6|0 | dril |
| s L s L s s L | 2|4 | fish |
| L s L s s L s | 5|1 | gil |
| s L s s L s L | 1|5 | jwl |
| L s s L s L s | 4|2 | kleeth |
| s s L s L s L | 0|6 | led |
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, where the generator is a 5/4 but five of them make a 3/1.
| g | 2g | 3g | 4g (-1200) | comments | |||
|---|---|---|---|---|---|---|---|
| 1\3 | 400.000 | 800.000 | 1200.000 | 400.000 | |||
| 15\46 | 391.304 | 782.609 | 1173.913 | 365.217 | |||
| 14\43 | 390.698 | 781.395 | 1172.093 | 362.791 | |||
| 13\40 | 390.000 | 780.000 | 1170.000 | 360.000 | |||
| 12\37 | 389.189 | 778.378 | 1167.568 | 356.757 | |||
| 11\34 | 388.235 | 776.471 | 1164.706 | 352.941 | |||
| 10\31 | 387.097 | 774.194 | 1161.290 | 348.387 | Würschmidt is around here | ||
| 19\59 | 386.441 | 772.881 | 1159.322 | 345.763 | |||
| 9\28 | 385.714 | 771.429 | 1157.143 | 342.857 | |||
| 8\25 | 384.000 | 768.000 | 1152.000 | 336.000 | |||
| 23\72 | 383.333 | 766.667 | 1150.000 | 333.333 | |||
| 15\47 | 382.988 | 765.957 | 1148.936 | 331.915 | |||
| 7\22 | 381.818 | 763.636 | 1145.455 | 327.273 | |||
| 13\41 | 380.488 | 760.976 | 1141.463 | 321.951 | Magic is around here | ||
| 19\60 | 380.000 | 760.000 | 1140.000 | 320.000 | |||
| 25\79 | 379.747 | 759.494 | 1139.2405 | 318.987 | |||
| 6\19 | 378.947 | 757.895 | 1136.842 | 315.789 | |||
| 11\35 | 377.143 | 754.286 | 1131.429 | 308.571 | |||
| 16\51 | 376.471 | 752.941 | 1129.412 | 305.882 | |||
| 5\16 | 375.000 | 750.000 | 1125.000 | 300.000 | L/s = 4 | ||
| 24\77 | 374.026 | 748.052 | 1122.078 | 296.104 | |||
| 19\61 | 373.7705 | 747.541 | 1121.3115 | 295.082 | |||
| 14\45 | 373.333 | 746.667 | 1120.000 | 293.333 | |||
| 9\29 | 372.414 | 744.828 | 1117.241 | 289.655 | |||
| 13\42 | 371.429 | 742.857 | 1114.286 | 285.714 | |||
| 17\55 | 370.909 | 741.818 | 1112.727 | 283.636 | |||
| 370.204 | 740.409 | 1110.613 | 280.817 | L/s = pi | |||
| 4\13 | 369.231 | 738.462 | 1107.692 | 276.923 | L/s = 3 | ||
| 23\75 | 368.000 | 736.000 | 1104.000 | 272.000 |
| ||
| 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 | Modi Sephiratorum (Kosmorsky) | ||
| 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 | Boundary of propriety(generators smaller than this are proper) | ||
| 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 | Beatles is around here | ||
| 354.930 | 709.859 | 1064.789 | 219.718 | Golden neutral thirds scale | |||
| 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 | Optimum rank range (L/s=3/2) | ||
| 12\41 | 351.220 | 702.439 | 1053.659 | 204.878 | 2.3.11 neutral thirds scale is around here | ||
| 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 | Mohajira/dicot is around here | ||
| 11\38 | 347.368 | 694.737 | 1042.105 | 189.474 | |||
| 2\7 | 342.857 | 685.714 | 1028.571 | 171.429 |
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").
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".
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.