User:Moremajorthanmajor/Greater whole tone scale
5L 1s(<major seventh>), also known as the greater whole tone scale, refers to MOS scales with 5 large steps and 1 small step. When L=s we have 6edo, the equal-tempered "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach 5edo, with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others — perhaps not a "whole tone" at all.
The only notable low-harmonic-entropy scale with this MOS pattern is slendric, in which the large step is 8/7 and three of them make a 3/2. Other low-harmonic-entropy scales with this MOS pattern tune the seventh (septave) 1050¢ or flatter for making a quarter 3/2 and between 1080¢ and 1100¢ for making a 7/2-equivalent augmented thirteenth scale.
Scales with this pattern are always proper, because there is only one small step.
Scale tree
| Generator | Normalized Cents (septave) | Cents | L | s | L/s | Comments |
|---|---|---|---|---|---|---|
| 1\6 | 171.429 | 200.000 | 1 | 1 | 1.000 | |
| 9\53 | 177.049 | 203.774 | 9 | 8 | 1.125 | |
| 8\47 | 177.778 | 204.255 | 8 | 7 | 1.143 | |
| 7\41 | 178.723 | 204.878 | 7 | 6 | 1.167 | |
| 13\76 | 179.310 | 205.263 | 13 | 11 | 1.273 | |
| 6\35 | 180.000 | 205.714 | 6 | 5 | 1.200 | |
| 5\29 | 181.818 | 206.897 | 5 | 4 | 1.250 | |
| 14\81 | 182.609 | 207.407 | 14 | 11 | 1.273 | |
| 9\52 | 183.051 | 207.692 | 9 | 7 | 1.286 | |
| 4\23 | 184.615 | 208.696 | 4 | 3 | 1.333 | |
| 11\63 | 185.915 | 209.524 | 11 | 8 | 1.375 | |
| 7\40 | 186.667 | 210.000 | 7 | 5 | 1.400 | |
| 10\57 | 187.500 | 210.528 | 10 | 7 | 1.428 | |
| 13\74 | 187.952 | 210.811 | 13 | 9 | 1.444 | |
| 16\91 | 188.235 | 210.989 | 16 | 11 | 1.4545 | |
| 3\17 | 189.474 | 211.765 | 3 | 2 | 1.500 | L/s = 3/2 |
| 14\79 | 190.909 | 212.658 | 14 | 9 | 1.556 | |
| 11\62 | 191.304 | 212.903 | 11 | 7 | 1.571 | |
| 8\45 | 192.000 | 213.333 | 8 | 5 | 1.600 | |
| 13\73 | 192.593 | 213.699 | 13 | 8 | 1.625 | Golden Ionianic-machine |
| 5\28 | 193.548 | 214.286 | 5 | 3 | 1.667 | Ionianic-Machine |
| 12\67 | 194.595 | 214.925 | 12 | 7 | 1.714 | |
| 7\39 | 195.349 | 215.385 | 7 | 4 | 1.750 | |
| 9\50 | 196.364 | 216.000 | 9 | 5 | 1.800 | |
| 11\61 | 197.015 | 216.393 | 11 | 6 | 1.833 | |
| 13\72 | 197.468 | 216.667 | 13 | 7 | 1.857 | |
| 15\83 | 197.802 | 216.867 | 15 | 8 | 1.875 | |
| 17\94 | 198.058 | 217.021 | 17 | 9 | 1.889 | |
| 2\11 | 200.000 | 218.182 | 2 | 1 | 2.000 | Basic Ionianic-machinoid |
| 17\93 | 201.980 | 219.355 | 17 | 8 | 2.125 | |
| 15\82 | 202.247 | 219.512 | 15 | 7 | 2.143 | |
| 13\71 | 202.597 | 219.718 | 13 | 6 | 2.167 | |
| 11\60 | 203.077 | 220.000 | 11 | 5 | 2.200 | |
| 9\49 | 203.774 | 220.408 | 9 | 4 | 2.250 | |
| 7\38 | 204.878 | 221.053 | 7 | 3 | 2.333 | |
| 12\65 | 205.714 | 221.538 | 12 | 5 | 2.400 | |
| 5\27 | 206.897 | 222.222 | 5 | 2 | 2.500 | |
| 18\97 | 207.692 | 222.680 | 18 | 7 | 2.571 | |
| 13\70 | 208.000 | 222.857 | 13 | 5 | 2.600 | Unnamed golden tuning |
| 8\43 | 208.697 | 223.256 | 8 | 3 | 2.667 | |
| 11\59 | 209.524 | 223.729 | 11 | 4 | 2.750 | |
| 14\75 | 210.000 | 224.000 | 14 | 5 | 3.000 | |
| 3\16 | 211.765 | 225.000 | 3 | 1 | 3.000 | L/s = 3/1, Ionianic-clyndro |
| 22\117 | 212.903 | 225.641 | 22 | 7 | 3.143 | |
| 19\101 | 213.084 | 225.743 | 19 | 6 | 3.167 | |
| 16\85 | 213.333 | 225.882 | 16 | 5 | 3.200 | |
| 13\69 | 213.698 | 226.087 | 13 | 4 | 3.250 | |
| 10\53 | 214.857 | 226.415 | 10 | 3 | 3.333 | |
| 7\37 | 215.385 | 227.027 | 7 | 2 | 3.500 | Ionianic-Laconic |
| 11\58 | 216.393 | 227.586 | 11 | 3 | 3.667 | |
| 15\79 | 216.867 | 227.848 | 15 | 4 | 3.750 | |
| 19\100 | 217.143 | 228.000 | 19 | 5 | 3.800 | |
| 4\21 | 218.182 | 228.571 | 4 | 1 | 4.000 | Ionianic-Gorgo |
| 13\68 | 219.718 | 229.412 | 13 | 3 | 4.333 | |
| 9\47 | 220.408 | 229.787 | 9 | 2 | 4.500 | |
| 14\73 | 221.053 | 230.137 | 14 | 3 | 4.667 | |
| 5\26 | 222.222 | 230.769 | 5 | 1 | 5.000 | Ionianic-Gidorah |
| 11\57 | 223.729 | 231.579 | 11 | 2 | 5.500 | |
| 17\88 | 224.179 | 231.818 | 17 | 3 | 5.667 | |
| 6\31 | 225.000 | 232.258 | 6 | 1 | 6.000 | Ionianic-Slendric↓ |
| 13\67 | 226.087 | 232.839 | 13 | 2 | 6.500 | |
| 7\36 | 227.027 | 233.333 | 7 | 1 | 7.000 | |
| 8\41 | 228.571 | 234.146 | 8 | 1 | 8.000 | |
| 9\46 | 229.787 | 234.783 | 9 | 1 | 9.000 | |
| 1\5 | 240.000 | 240.000 | 1 | 0 | → inf |
See also
5L 1s (11/6-equivalent) - simplest tuning
5L 1s (15/8-equivalent) - classical tuning
5L 1s (21\11-equivalent) - Neogothic tuning
5L 1s (27/14-equivalent) - septimal tuning