Generator ranges of MOS: Difference between revisions

: This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2016-12-31 23:00:49 UTC</tt>.<br>

: The original revision id was <tt>602933636</tt>.<br>

<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">Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.

If the number of the [[@Interval class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g &gt; C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[@Modal UDP Notation|chroma-positive]] generator. We have normalized to the formula fir the step size where the leading term is positive.

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L1s || 1\2 &lt; g &lt; 1 || g = 3\4 || g = 2\3, 3\4, 4\5 || g || 1-g ||

|| 1L2s || 2\3 &lt; g &lt; 1 || g = 5\6 || g = 3\4, 4\5, 5\6 || 2g-1 || 1-g ||

|| 2L1s || 1\3 &lt; g &lt; 1\2 || g = 5\12 || g = 2\5, 3\7, 4\9 || g || 1-2g ||

|| 1L3s || 3\4 &lt; g &lt; 1 || g = 7\8 || g = 4\5, 5\6, 6\7 || 3g-2 || 1-g ||

|| 2L2s || 1\4 &lt; g &lt; 1\2 || g = 3\8 || g = 2\6, 3\8, 4\10 || g || 1\2-g ||

|| 3L1s || 1\4 &lt; g &lt; 1\3 || g = 7\24 || g = 2\7, 3\10, 4\13 || g || 1-3g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L4s || 4\5 &lt; g &lt; 1 || g = 9\10 || g = 5\6, 6\7, 7\8 || 4g-3 || 1-g ||

|| 2L3s || 2\5 &lt; g &lt; 1\2 || g = 9\20 || g = 3\7, 4\9, 5\11 || 3g-1 || 1-2g ||

|| 3L2s || 3\5 &lt; g &lt; 2\3 || g = 19\30 || g = 5\8, 7\11, 9\14 || 2g-1 || 2-3g ||

|| 4L1s || 1\5 &lt; g &lt; 1\4 || g = 9\40 || g = 2\9, 3\13, 4\17 || g || 1-4g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L5s || 5\6 &lt; g &lt; 1 || g = 11\12 || g = 6\7, 7\8, 8\9 || 5g-4 || 1-g ||

|| 2L4s || 2\6 &lt; g &lt; 1\2 || g = 5\12 || g = 3\8, 4\10, 5\12 || 2g-1\2 || 1\2-g ||

|| 3L3s || 1\6 &lt; g &lt; 1\3 || g = 3\12 || g = 2\9, 3\12, 4\15 || g || 1\3-g ||

|| 4L2s || 1\6 &lt; g &lt; 1\4 || g = 5\24 || g = 2\10, 3\14, 4\18 || g || 1\2-2g ||

|| 5L1s || 1\6 &lt; g &lt; 1\5 || g = 11\60 || g = 2\11, 3\16, 4\21 || g || 1-5g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L6s || 6\7 &lt; g &lt; 1 || g = 13\14 || g = 7\8, 8\9, 9\10 || 6g-5 || 1-g ||

|| 2L5s || 3\7 &lt; g &lt; 1\2 || g = 13\28 || g = 4\9, 5\11, 6\13 || 5g-2 || 1-2g ||

|| 3L4s || 2\7 &lt; g &lt; 1\3 || g = 13\42 || g = 3\10, 4\13, 5\16 || 4g-1 || 1-3g ||

|| 4L3s || 5\7 &lt; g &lt; 3\4 || g = 41\56 || g = 8\11, 11\15, 14\19 || 3g-2 || 3-4g ||

|| 5L2s || 4\7 &lt; g &lt; 3\5 || g = 41\70 || g = 7\12, 10\17, 13\22 || 2g-1 || 3-5g ||

|| 6L1s || 1\7 &lt; g &lt; 1\6 || g = 13\84 || g = 2\13, 3\19, 4\25 || g || 1-6g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L7s || 7\8 &lt; g &lt; 1 || g = 15\16 || g = //8\9//, 9\10, 10\11 || 7g-6 || 1-g ||

|| 2L6s || 3\8 &lt; g &lt; 1\2 || g = 7\16 || g = 4\10, 5\12, 6\14 || 3g-1 || 1\2-g ||

|| 3L5s || 5\8 &lt; g &lt; 2\3 || g = 31\48 || g = 7\11, 9\14, 11\17 || 5g-3 || 2-3g ||

|| 4L4s || 1\8 &lt; g &lt; 1\4 || g = 3\16 || g = 2\12, 3\16, 4\20 || g || 1\4-g ||

|| 5L3s || 3\8 &lt; g &lt; 2\5 || g = 31\80 || g = 5\13, 7\18, 9\23 || 3g-1 || 2-5g ||

|| 6L2s || 1\8 &lt; g &lt; 1\6 || g = 7\48 || g = 2\14, 3\20, 4\26 || g || 1\2-3g ||

|| 7L1s || 1\8 &lt; g &lt; 1\7 || g = 15\112 || g = 2\15, 3\22, 4\29 || g || 1-7g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L8s || 8\9 &lt; g &lt; 1 || g = 17\18 || g = //9\10//, 10\11, 11\12 || 8g-7 || 1-g ||

|| 2L7s || 4\9 &lt; g &lt; 1\2 || g = 17\36 || g = 5\11, 6\13, 7\15 || 7g-3 || 1-2g ||

|| 3L6s || 2\9 &lt; g &lt; 1\3 || g = 5\18 || g = 3\12, 4\15, 5\18 || 2g-1\3 || 1\3-g ||

||&lt; 4L5s ||&lt; 2\9 &lt; g &lt; 1\4 ||&lt; g = 17\72 ||&lt; g = 3\13, 4\17, 5\21 ||&lt; 5g-1 ||&lt; 1-4g ||

|| 5L4s || 7\9 &lt; g &lt; 4\5 || g = 71\90 || g = 11\14, 15\19, 18\23 || 4g-3 || 4-5g ||

|| 6L3s || 1\9 &lt; g &lt; 1\6 || g = 5\36 || g = 2\15, 3\21, 4\27 || g || 1\3-2g ||

|| 7L2s || 5\9 &lt; g &lt; 4\7 || g = 71\126 || g = 9\16, 10\23, 17\30 || 2g-1 || 4-7g ||

|| 8L1s || 1\9 &lt; g &lt; 1\8 || g = 17\144 || g = 2\17, 3\25, 4\33 || g || 1-8g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L9s || 9\10 &lt; g &lt; 1 || g = 19\20 || g = //10\11//, 11\12, 12\13 || 9g-8 || 1-g ||

|| 2L8s || 4\10 &lt; g &lt; 1\2 || g = 9\20 || g = 5\12, 6\14, 7\16 || 4g-3\2 || 1\2-g ||

|| 3L7s || 3\10 &lt; g &lt; 1\3 || g = 19\60 || g = 4\13, 5\16, 6\19 || 7g-2 || 1-3g ||

|| 4L6s || 2\10 &lt; g &lt; 1\4 || g = 9\40 || g = 3\14, 4\18, 5\22 || 3g-1\2 || 1\2-2g ||

|| 5L5s || 1\10 &lt; g &lt; 1\5 || g = 3\20 || g = 2\15, 3\20, 4\25 || g || 1\5-g ||

|| 6L4s || 3\10 &lt; g &lt; 2\6 || g = 19\60 || g = 5\16, 7\22, 9\28 || 2g-1\2 || 1-3g ||

|| 7L3s || 7\10 &lt; g &lt; 5\7 || g = 99\140 || g = 12\17, 17\24, 22\31 || 3g-2 || 5-7g ||

|| 8L2s || 1\10 &lt; g &lt; 1\8 || g = 9\80 || g = 2\18, 3\26, 4\34 || g || 1\2-4g ||

|| 9L1s || 1\10 &lt; g &lt; 1\9 || g = 19\180 || g = 2\19, 3\28, 4\37 || g || 1-9g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L10s || 10\11 &lt; g &lt; 1 || g = 21\22 || g = //11\12//, 12\13, 13\14 || 10g-9 || 1-g ||

|| 2L9s || 5\11 &lt; g &lt; 1\2 || g = 21\44 || g = 6\13, 7\15, 8\17 || 9g-4 || 1-2g ||

|| 3L8s || 7\11 &lt; g &lt; 2\3 || g = 43\66 || g = 9\14, 11\17, 13\20 || 8g-5 || 2-3g ||

|| 4L7s || 8\11 &lt; g &lt; 3\4 || g = 65\88 || g = 11\15, 14\19, 17\23 || 7g-5 || 3-4g ||

|| 5L6s || 2\11 &lt; g &lt; 1\5 || g = 21\110 || g = 3\16, 4\21, 5\26 || 6g-1 || 1-5g ||

|| 6L5s || 9\11 &lt; g &lt; 5\6 || g = 109\132 || g = 14\17, 19\23, 24\29 || 5g-4 || 5-6g ||

|| 7L4s || 3\11 &lt; g &lt; 2\7 || g = 43\154 || g = 5\18, 7\25, 9\32 || 4g-1 || 2-7g ||

|| 8L3s || 4\11 &lt; g &lt; 3\8 || g = 65\176 || g = 7\19, 10\27, 13\35 || 3g-1 || 3-8g ||

|| 9L2s || 6\11 &lt; g &lt; 5\9 || g = 109\198 || g = 11\20, 16\29, 21\38 || 2g-1 || 5-9g ||

|| 10L1s || 1\11 &lt; g &lt; 1\10 || g = 21\220 || g = 2\21, 3\31, 4\41 || g || 1-10g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L11s || 11\12 &lt; g &lt; 1 || g = 23\24 || g = //12\13,// //13\14//, 14\15 || 11g-10 || 1-g ||

|| 2L10s || 5\12 &lt; g &lt; 1\2 || g = 11\24 || g = //6\14//, 7\16, 8\18 || 5g-2 || 1\2-g ||

|| 3L9s || 3\12 &lt; g &lt; 1\3 || g = 7\24 || g = 4\15, 5\18, 6\21 || 3g-2\3 || 1\3-g ||

|| 4L8s || 2\12 &lt; g &lt; 1\4 || g = 5\24 || g = 3\16, 4\20, 5\24 || 2g-1\4 || 1\4-g ||

|| 5L7s || 7\12 &lt; g &lt; 3\5 || g = 71\120 || g = 10\17, 13\22, 16\27 || 7g-4 || 3-5g ||

|| 6L6s || 1\12 &lt; g &lt; 1\6 || g = 3\24 || g = 2\18, 3\24, 4\30 || g || 1\6-g ||

|| 7L5s || 5\12 &lt; g &lt; 3\7 || g = 71\168 || g = 8\19, 11\26, 14\33 || 5g-2 || 3-7g ||

|| 8L4s || 1\12 &lt; g &lt; 1\8 || g = 5\48 || g = 2\20, 3\28, 4\36 || g || 1\4-2g ||

|| 9L3s || 1\12 &lt; g &lt; 1\9 || g = 7\72 || g = 2\21, 3\30, 4\39 || g || 1\3-3g ||

|| 10L2s || 1\12 &lt; g &lt; 1\10 || g = 11\120 || g = 2\22, 3\32, 4\42 || g || 1\2-5g ||

|| 11L1s || 1\12 &lt; g &lt; 1\11 || g = 23\264 || g = 2\23, 3\34, 4\45 || g || 1-11g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L12s || 12\13 &lt; g &lt; 1 || g = 25\26 || g = //13\14,// //14\15//, 15\16 || 12g-11 || 1-g ||

|| 2L11s || 6\13 &lt; g &lt; 1\2 || g = 25\52 || g = //7\15//, 8\17, 9\19 || 11g-5 || 1-2g ||

|| 3L10s || 4\13 &lt; g &lt; 1\3 || g = 25\78 || g = 5\16, 6\19, 7/22 || 10g-3 || 1-3g ||

|| 4L9s || 3\13 &lt; g &lt; 1\4 || g = 25\104 || g = 4\17, 5\21, 6\25 || 9g-2 || 1-4g ||

|| 5L8s || 5\13 &lt; g &lt; 2\5 || g = 51\130 || g = 7\18, 9\23, 11\28 || 8g-3 || 2-5g ||

|| 6L7s || 2\13 &lt; g &lt; 1\6 || g = 25\156 || g = 3\19, 4\25, 5\31 || 7g-1 || 1-6g ||

|| 7L6s || 11\13 &lt; g &lt; 6\7 || g = 155\182 || g = 17\20, 23\27, 29\34 || 6g-5 || 6-7g ||

|| 8L5s || 8\13 &lt; g &lt; 5\8 || g = 129\208 || g = 13\21, 18\29, 23\37 || 5g-3 || 5-8g ||

|| 9L4s || 10\13 &lt; g &lt; 7\9 || g = 181\234 || g = 17\22, 24\31, 31\40 || 4g-3 || 7-9g ||

|| 10L3s || 9\13 &lt; g &lt; 7\10 || g = 181\260 || g = 16\23, 23\33, 30\43 || 3g-2 || 7-10g ||

|| 11L2s || 7\13 &lt; g &lt; 6\11 || g = 155\286 || g = 13\24, 19\35, 25\46 || 2g-1 || 6-11g ||

|| 12L1s || 1\13 &lt; g &lt; 1\12 || g = 25\312 || g = 2\25, 3\37, 4\49 || g || 1-12g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L13s || 13\14 &lt; g &lt; 1 || g = 27\28 || g = //14\15,// //15\16//, 16\17 || 13g-12 || 1-g ||

|| 2L12s || 6\14 &lt; g &lt; 1\2 || g = 13\28 || g = //7\16//, 8\18, 9\20 || 6g-5\2 || 1\2-g ||

|| 3L11s || 9\14 &lt; g &lt; 2\3 || g = 55\84 || g = 11\17, 13\20, 15\23 || 11g-7 || 2-3g ||

|| 4L10s || 3\14 &lt; g &lt; 1\4 || g = 13\56 || g = 4\18, 5\22, 6\26 || 5g-1 || 1\2-2g ||

|| 5L9s || 11\14 &lt; g &lt; 4\5 || g = 111\140 || g = 15\19, 19\24, 23\29 || 9g-7 || 4-5g ||

|| 6L8s || 2\14 &lt; g &lt; 1\6 || g = 13\84 || g = 3\20, 4\26, 5\32 || 4g-1\2 || 1\2-3g ||

|| 7L7s || 1\14 &lt; g &lt; 1\7 || g = 3\28 || g = 2\21, 3\28, 4\35 || g || 1\7-g ||

|| 8L6s || 5\14 &lt; g &lt; 3\8 || g = 41\112 || g = 8\22, 11\30, 14\38 || 3g-1 || 3\2-4g ||

|| 9L5s || 3\14 &lt; g &lt; 2\9 || g = 55\252 || g = 5\23, 7\32, 9\41 || 5g-1 || 2-9g ||

|| 10L4s || 4\14 &lt; g &lt; 3\10 || g = 41\140 || g = 7\24, 10\34, 13\44 || 2g-1\2 || 3\2-5g ||

|| 11L3s || 5\14 &lt; g &lt; 4\11 || g = 111\308 || g = 9\25, 13\36, 17\47 || 3g-1 || 4-11g ||

|| 12L2s || 1\14 &lt; g &lt; 1\12 || g = 13\168 || g = 2\26, 3\38, 4\50 || g || 1\2-6g ||

|| 13L1s || 1\14 &lt; g &lt; 1\13 || g = 27\364 || g = 2\27, 3\40, 4\53 || g || 1-13g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L14s || 14\15 &lt; g &lt; 1 || g = 29\30 || g = //15\16,// //16\17//, 17\18 || 14g-13 || 1-g ||

|| 2L13s || 7\15 &lt; g &lt; 1\2 || g = 29\60 || g = //8\17//, 9\19, 10\21 || 13g-6 || 1-2g ||

|| 3L12s || 4\15 &lt; g &lt; 1\3 || g = 9\30 || g = 5\18, 6\21, 7\24 || 4g-1 || 1\3-g ||

|| 4L11s || 11\15 &lt; g &lt; 3\4 || g = 89\120 || g = 14\19, 17\23, 20\27 || 11g-8 || 3-4g ||

|| 5L10s || 2\15 &lt; g &lt; 1\5 || g = 5\30 || g = 3\20, 4\25, 5\30 || 2g-1\5 || 1\5-g ||

|| 6L9s || 2\15 &lt; g &lt; 1\6 || g = 9\60 || g = 3\21, 4\27, 5\33 || 3g-1\3 || 1\3-2g ||

|| 7L8s || 2\15 &lt; g &lt; 1\7 || g = 29\210 || g = 3\22, 4\29, 5\36 || 8g-1 || 1-7g ||

|| 8L7s || 13\15 &lt; g &lt; 7\8 || g = 209\240 || g = 20\23, 27\31, 34\39 || 7g-6 || 7-8g ||

|| 9L6s || 3\15 &lt; g &lt; 2\9 || g = 19\90 || g = 5\24, 7\33, 9\42 || 2g-1\3 || 2\3-3g ||

|| 10L5s || 1\15 &lt; g &lt; 1\10 || g = 5\60 || g = 2\25, 3\35, 4\45 || g || 1\5-2g ||

|| 11L4s || 4\15 &lt; g &lt; 3\11 || g = 89\330 || g = 7\26, 10\37, 13\48 || 4g-1 || 3-11g ||

|| 12L3s || 1\15 &lt; g &lt; 1\12 || g = 9\120 || g = 2\27, 3\39, 4\51 || g || 1\3-4g ||

|| 13L2s || 8\15 &lt; g &lt; 7\13 || g = 209\390 || g = 15\28, 22\41, 29\54 || 2g-1 || 7-13g ||

|| 14L1s || 1\15 &lt; g &lt; 1\14 || g = 29\420 || g = 2\29, 3\43, 4\57 || g || 1-14g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L15s || 15\16 &lt; g &lt; 1 || g = 31\32 || g = //16\17,// //17\18,// //18\19// || 15g-14 || 1-g ||

|| 2L14s || 7\16 &lt; g &lt; 1\2 || g = 15\32 || g = //8\18//, 9\20, 10\22 || 7g-3 || 1\2-g ||

|| 3L13s || 5\16 &lt; g &lt; 1\3 || g = 31\96 || g = //6\19//, 7\22, 8\25 || 13g-4 || 1-3g ||

|| 4L12s || 3\16 &lt; g &lt; 1\4 || g = 7\32 || g = 4\20, 5\24, 6\28 || 3g-1\2 || 1\4-g ||

|| 5L11s || 3\16 &lt; g &lt; 1\5 || g = 31\160 || g = 4\21, 5\26, 6\31 || 11g-2 || 1-5g ||

|| 6L10s || 5\16 &lt; g &lt; 2\6 || g = 31\96 || g = 7\22, 9\28, 11\34 || 5g-3\2 || 1-3g ||

|| 7L9s || 9\16 &lt; g &lt; 4\7 || g = 127\224 || g = 13\23, 17\30, 21\37 || 9g-5 || 4-7g ||

|| 8L8s || 1\16 &lt; g &lt; 1\8 || g = 3\32 || g = 2\24, 3\32, 4\40 || g || 1\8-g ||

|| 9L7s || 7\16 &lt; g &lt; 4\9 || g = 127\286 || g = 11\25, 15\34, 19\43 || 7g-3 || 4-9g ||

|| 10L6s || 3\16 &lt; g &lt; 2\10 || g = 31\160 || g = 5\26, 7\36, 8\46 || 3g-1\2 || 1-5g ||

|| 11L5s || 13\16 &lt; g &lt; 9\11 || g = 287\352 || g = 22\27, 31\38, 40\49 || 5g-4 || 9-11g ||

|| 12L4s || 1\16 &lt; g &lt; 1\12 || g = 7\48 || g = 2\28, 3\40, 4\52 || g || 1\4-3g ||

|| 13L3s || 11\16 &lt; g &lt; 9\13 || g = 287\416 || g = 20\29, 29\42, 38\55 || 3g-2 || 9-13g ||

|| 14L2s || 1\16 &lt; g &lt; 1\14 || g = 15\224 || g = 2\30, 3\44, 4\58 || g || 1\2-7g ||

|| 15L1s || 1\16 &lt; g &lt; 1\15 || g = 31\480 || g = 2\31, 3\46, 4\61 || g || 1-15g ||

||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L16s || 16\17 &lt; g &lt; 1 || g = 33\34 || g = //17\18,// //18\19,// //19\20// || 16g-15 || 1-g ||

|| 2L15s || 8\17 &lt; g &lt; 1\2 || g = 33\68 || g = //9\19//, 10\21, 11\23 || 15g-7 || 1-2g ||

|| 3L14s || 11\17 &lt; g &lt; 2\3 || g = 67\102 || g = //13\20//, 15\23, 17\26 || 14g-9 || 2-3g ||

|| 4L13s || 4\17 &lt; g &lt; 1\4 || g = 33\136 || g = 5\21, 6\25, 7\29 || 13g-3 || 1-4g ||

|| 5L12s || 10\17 &lt; g &lt; 3\5 || g = 101\170 || g = 13\22, 16\27, 19\32 || 12g-7 || 3-5g ||

|| 6L11s || 14\17 &lt; g &lt; 5\6 || g = 169\204 || g = 19\23, 24\29, 29\35 || 11g-9 || 5-6g ||

|| 7L10s || 12\17 &lt; g &lt; 5\7 || g = 169\238 || g = 17\24, 22\31, 27\38 || 10g-7 || 5-7g ||

|| 8L9s || 2\17 &lt; g &lt; 1\8 || g = 33\272 || g = 3\25, 4\33, 5\41 || 9g-1 || 1-8g ||

|| 9L8s || 15\17 &lt; g &lt; 8\9 || g = 271\306 || g = 23\26, 31\35, 39\44 || 8g-7 || 8-9g ||

|| 10L7s || 5\17 &lt; g &lt; 3\10 || g = 101\340 || g = 8\27, 11\37, 14\47 || 7g-2 || 3-10g ||

|| 11L6s || 3\17 &lt; g &lt; 2\11 || g = 67\374 || g = 5\28, 7\39, 9\50 || 6g-1 || 2-11g ||

|| 12L5s || 7\17 &lt; g &lt; 5\12 || g = 169\408 || g = 12\29, 17\41, 22\53 || 5g-2 || 5-12g ||

|| 13L4s || 13\17 &lt; g &lt; 10\13 || g = 339\442 || g = 23\30, 33\43, 43\56 || 4g-3 || 10-13g ||

|| 14L3s || 6\17 &lt; g &lt; 5\14 || g = 169\476 || g = 11\31, 16\45, 21\59 || 3g-1 || 5-14g ||

|| 15L2s || 9\17 &lt; g &lt; 8\15 || g = 271\510 || g = 17\32, 25\47, 33\62 || 2g-1 || 8-15g ||

|| 16L1s || 1\17 &lt; g &lt; 1\16 || g = 33\544 || g = 2\33, 3\49, 4\65 || g || 1-16g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L17s || 17\18 &lt; g &lt; 1 || g = 35\36 || g = //18\19, 19\20, 20\21// || 17g-16 || 1-g ||

|| 2L16s || 8\18 &lt; g &lt; 1\2 || g = 17\36 || g -= //9\20//, 10\22, 11\24 || 8g-7\2 || 1\2-g ||

|| 3L15s || 5\18 &lt; g &lt; 1\3 || g = 11\36 || g = //6\21//, 7\24, 8\27 || 5g-4\3 || 1\3-g ||

|| 4L14s || &lt;span style="line-height: 15.6000003814697px;"&gt;4\18 &lt; g &lt; 1\4&lt;/span&gt; || g = 17\72 || &lt;span style="line-height: 15.6000003814697px;"&gt;g = 5\22, 6\26,&lt;/span&gt; 7\30 || 7g-3\2 || 1\2-2g ||

|| 5L13s || 7\18 &lt; g &lt; 2\5 || g = 71\180 || g = 9\23, 11\28, 13\33 || 13g-5 || 2-5g ||

|| 6L12s || 2\18 &lt; g &lt; 1\6 || g = 5\36 || g = 3\24, 4\30, 5\36 || 2g-1\6 || 1\6-g ||

|| 7L11s || 5\18 &lt; g &lt; 2\7 || g = 71\252 || g = 7\25, 9\32, 11\39 || 11g-3 || 2-7g ||

|| 8L10s || 2\18 &lt; g &lt; 1\8 || g = 17\144 || g = 3\26, 4\34, 5\42 || 5g-1\2 || 1\2-4g ||

|| 9L9s || 1\18 &lt; g &lt; 1\9 || g = 3\36 || g = 2\27, 3\36, 4\45 || g || 1\9-g ||

|| 10L8s || 7\18 &lt; g &lt; 4\10 || g = 71\180 || g = 11\28, 15\38, 19\48 || 4g-3\2 || 2-5g ||

|| 11L7s || 13\18 &lt; g &lt; 8\11 || g = 287\396 || g = 21\29, 29\40, 37\51 || 7g-5 || 8-11g ||

|| 12L6s || 1\18 &lt; g &lt; 1\12 || g = 5\72 || g = 2\30, 3\42, 4\54 || g || 1\6-2g ||

|| 13L5s || 11\18 &lt; g &lt; 8\13 || g = 287\468 || g = 19\31, 27\44, 35\57 || 5g-3 || 8-13g ||

|| 14L4s || 5\18 &lt; g &lt; 4\14 || g = 71\252 || g = 9\32, 13\46, 17\60 || 2g-1\2 || 2-7g ||

|| 15L3s || 1\18 &lt; g &lt; 1\15 || g = 11\180 || g = 2\33, 3\48, 4\63 || g || 1\3-5g ||

|| 16L2s || 1\18 &lt; g &lt; 1\16 || g = 17\288 || g = 2\34, 3\50, 4\66 || g || 1\2-8g ||

|| 17L1s || 1\18 &lt; g &lt; 1\17 || g = 35\618 || g = 2\35, 3\52, 4\69 || g || 1-17g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L18s || 18\19 &lt; g &lt; 1 || g = 37\38 || g = //19\20, 20\21, 21\22// || 18g-17 || 1-g ||

|| 2L17s || 9\19 &lt; g &lt; 1\2 || g = 37\76 || g = //10\21//, 11\23, 12\25 || 17g-8 || 1-2g ||

|| 3L16s || 6\19 &lt; g &lt; 1\3 || g = 37\114 || g = 7\22, 8\25, 10\31 || 16g-5 || 1-3g ||

|| 4L15s || 14\19 &lt; g &lt; 3\4 || g = 113\152 || g = 17\23, 20\27, 23\31 || 15g-11 || 3-4g ||

|| 5L14s || 15\19 &lt; g &lt; 4\5 || g = 151\190 || g = 19\24, 23\29, 27\34 || 14g-11 || 4-5g ||

|| 6L13s || 3\19 &lt; g &lt; 1\6 || g = 37\228 || g = 4\25, 5\31, 6/37 || 13g-2 || 1-6g ||

|| 7L12s || 8\19 &lt; g &lt; 3\7 || g = 113\266 || g = 11\26, 14\33, 17\40 || 12g-5 || 3-7g ||

|| 8L11s || 7\19 &lt; g &lt; 3\8 || g = 113\304 || g = 10\27, 13\35, 16\43 || 11g-4 || 3-8g ||

|| 9L10s || 2\19 &lt; g &lt; 1\9 || g = 37\342 || g = 3\28, 4\37, 5\46 || 10g-1 || 1-9g ||

|| 10L9s || 17\19 &lt; g &lt; 9\10 || g = 341\380 || g = 26\29, 35\39, 44\49 || 9g-8 || 9-10g ||

|| 11L8s || 12\19 &lt; g &lt; 7\11 || g = 265\418 || g = 19\30, 26\41, 33\52 || 8g-5 || 7-11g ||

|| 12L7s || 11\19 &lt; g &lt; 7\12 || g = 265\456 || g = 18\31, 25\43, 32\55 || 7g-4 || 7-12g ||

|| 13L6s || 16\19 &lt; g &lt; 11\13 || g = 417\494 || g = 27\32, 38\45, 49\58 || 6g-5 || 11-13g ||

|| 14L5s || 4\19 &lt; g &lt; 3\14 || g = 113\532 || g = 7\33, 10\47, 13\61 || 5g-1 || 3-14g ||

|| 15L4s || 5\19 &lt; g &lt; 4\15 || g = 151\570 || g = 9\34, 13\49, 17\64 || 4g-1 || 4-15g ||

|| 16L3s || 13\19 &lt; g &lt; 11\16 || g = 417\608 || g = 24\35, 35\51, 46\67 || 3g-2 || 11-16g ||

|| 17L2s || 10\19 &lt; g &lt; 9\17 || g = 341\646 || g = 19\36, 28\53, 37\70 || 2g-1 || 9-17g ||

|| 18L1s || 1\19 &lt; g &lt; 1\18 || g = 37\684 || g = 2\37, 3\55, 4\73 || g || 1-18g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L19s || 19\20 &lt; g &lt; 1 || g = 39\40 || g = //20\21, 21\22, 22\23// || 19g-18 || 1-g ||

|| 2L18s || 9\20 &lt; g &lt; 1\2 || g = 19\40 || g = //10\22, 11\24//, 12\26 || 9g-4 || 1\2-g ||

|| 3L17s || 13\20 &lt; g &lt; 2\3 || g = 79\120 || g = //15\23//, 17\26, 20\29 || 17g-11 || 2-3g ||

|| 4L16s || 4\20 &lt; g &lt; 1\4 || g = 9\40 || g = //5\24//, 6\28, 7\32 || 4g-3\4 || 1\4-g ||

|| 5L15s || 3\20 &lt; g &lt; 1\5 || g = 7\40 || g = 4\25, 5\30, 6\35 || 3g-2\5 || 1\5-g ||

|| 6L14s || 3\20 &lt; g &lt; 1\6 || g = 19\120 || g = 4\26, 5\32, 6\38 || 7g-1 || 1\2-3g ||

|| 7L13s || 17\20 &lt; g &lt; 6\7 || g = 239\280 || g = 23\27, 29\34, 35\41 || 13g-11 || 6-7g ||

|| 8L12s || 2\20 &lt; g &lt; 1\8 || g = 9\80 || g = 3\28, 4\36, 5\44 || 3g-1\4 || 1\4-2g ||

|| 9L11s || 11\20 &lt; g &lt; 5\9 || g = 199\360 || g = 16\29, 21\38, 26\47 || 11g-6 || 5-9g ||

|| 10L10s || 1\20 &lt; g &lt; 1\10 || g = 3\40 || g = 2\30, 3\40, 4\50 || g || 1\10-g ||

|| 11L9s || 9\20 &lt; g &lt; 5\11 || g = 199\440 || g = 14\31, 19\42, 24\53 || 9g-4 || 5-11g ||

|| 12L8s || 3\20 &lt; g &lt; 2\12 || g = 19\120 || g = 5\32, 7\44, 9\56 || 2g-1\4 || 1\2-3g ||

|| 13L7s || 3\20 &lt; g &lt; 2\13 || g = 79\520 || g = 5\33, 7\46, 9\59 || 7g-1 || 2-13g ||

|| 14L6s || 7\20 &lt; g &lt; 5\14 || g = 99\280 || g = 12\34, 17\48, 22\62 || 3g-1 || 5\2-7g ||

|| 15L5s || 1\20 &lt; g &lt; 1\15 || g = 7\120 || g = 2\35, 3\50, 4\65 || g || 1\5-3g ||

|| 16L4s || 1\20 &lt; g &lt; 1\16 || g = 9\160 || g = 2\36, 3\52, 4\68 || g || 1\4-4g ||

|| 17L3s || 7\20 &lt; g &lt; 6\17 || g = 239\680 || g = 13\37, 19\54, 25\71 || 3g-1 || 6-17g ||

|| 18L2s || 1\20 &lt; g &lt; 1\18 || g = 19\360 || g = 2\38, 3\56, 4\74 || g || 1\2-9g ||

|| 19L1s || 1\20 &lt; g &lt; 1\19 || g = 39\760 || g = 2\39, 3\58, 4\77 || g || -19g+1 ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L20s || 20\21 &lt; g &lt; 1 || g = 41\42 || g = //21\22, 22\23, 23\24// || 20g-19 || 1-g ||

|| 2L19s || 10\21 &lt; g &lt; 1\2 || g = 41\84 || g = //11\23, 12\25//, 13\27 || 19g-9 || 1-2g ||

|| 3L18s || 6\21 &lt; g &lt; 1\3 || g = 13\42 || g = //7\24//, 8\27, 9\30 || 6g-5\3 || 1\3-g ||

|| 4L17s || 5\21 &lt; g &lt; 1\4 || g = 41\168 || g = //6\25//, 7\29, 8\33 || 17g-2 || 1-4g ||

|| 5L16s || 4\21 &lt; g &lt; 1\5 || g = 41\210 || g = 5\26, 6\31, 7\36 || 16g-3 || 1-5g ||

|| 6L15s || 3\21 &lt; g &lt; 1\6 || g = 13\84 || g = 4\27, 5\33, 6\39 || 5g-2\3 || 1\3-2g ||

|| 7L14s || 2\21 &lt; g &lt; 1\7 || g = 5\42 || g = 3\28, 4\35, 5\42 || 2g-1\7 || 1\7-g ||

|| 8L13s || 13\21 &lt; g &lt; 5\8 || g = 209\336 || g = 18\29, 23\37, 28\45 || 13g-8 || 5-8g ||

|| 9L12s || 2\21 &lt; g &lt; 1\9 || g = 13\126 || g = 3\30, 4\39, 5\48 || 4g-1\3 || 1\3-3g ||

|| 10L11s || 2\21 &lt; g &lt; 1\10 || g = 41\420 || g = 3\31, 4\41, 5\51 || 11g-1 || 1-10g ||

|| 11L10s || 19\21 &lt; g &lt; 10\11 || g = 419\462 || g = 29\32, 39\43, 49\54 || 10g-9 || 10-11g ||

|| 12L9s || 5\21 &lt; g &lt; 3\12 || g = 41\168 || g = 8\33, 11\45, 14\57 || 3g-2\3 || 1-4g ||

|| 13L8s || 8\21 &lt; g &lt; 5\13 || g = 209\546 || g = 13\34, 18\47, 23\70 || 8g-3 || 5-13g ||

|| 14L7s || 1\21 &lt; g &lt; 1\14 || g = 5\84 || g = 2\35, 3\49, 4\63 || g || 1\7-2g ||

|| 15L6s || 4\21 &lt; g &lt; 3\15 || g = 41\210 || g = 7\36, 10\51, 13\66 || 2g-1\3 || 1-5g ||

|| 16L5s || 17\21 &lt; g &lt; 13\16 || g = 545\672 || g = 30\37, 43\53, 56\69 || 5g-4 || 13-16g ||

|| 17L4s || 16\21 &lt; g &lt; 13\17 || g = 545\714 || g = 29\38, 42\55, 55\72 || 4g-3 || 13-17g ||

|| 18L3s || 1\21 &lt; g &lt; 1\18 || g = 13\252 || g = 2\39, 3\57, 4\75 || g || 1\3-6g ||

|| 19L2s || 11\21 &lt; g &lt; 10\19 || g = 419\798 || g = 21\40, 31\59, 41\78 || 2g-1 || 10-19g ||

|| 20L1s || 1\21 &lt; g &lt; 1\20 || g = 41\840 || g = 2\41, 3\61, 4/81 || g || 1-20g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff; color: #000000;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L21s || 21\22 &lt; g &lt; 1 || g = 43\44 || g = //22\23,// //23\24,// //24/25// || 21g-20 || 1-g ||

|| 2L20s || 10\22 &lt; g &lt; 1\2 || g = 21\44 || g = //11\24,// //12\26//, 13\28 || 10g-9\2 || 1\2-g ||

|| 3L19s || 7\22 &lt; g &lt; 1\3 || g = 43\132 || g = //8\25//, 9\28, 10\31 || 19g-6 || 1-3g ||

|| 4L18s || 5\22 &lt; g &lt; 1\4 || g = 21\88 || g = //6\26//, 7\30, 8\34 || 9g-2 || 1\2-2g ||

|| 5L17s || 13\22 &lt; g &lt; 3\5 || g = 131\220 || g = 16\27, 19\32, 22\37 || 17g-10 || 3-5g ||

|| 6L16s || 7\22 &lt; g &lt; 2\6 || g = 43\132 || g = 9\28, 11\34, 13\40 || 8g-5\2 || 1-3g ||

|| 7L15s || 3\22 &lt; g &lt; 1\7 || g = 43\308 || g = 4\29, 5\36, 6\43 || 15g-2 || 1-7g ||

|| 8L14s || 8\22 &lt; g &lt; 3\8 || g = 65\176 || g = 11\30, 14\38, 17\46 || 7g-5\2 || 3\2-4g ||

|| 9L13s || 17\22 &lt; g &lt; 7\9 || g = 307\396 || g = 24\31, 31\40, 38\49 || 13g-10 || 7-9g ||

|| 10L12s || 2\22 &lt; g &lt; 1\10 || g = 21\220 || g = 3\32, 4\42, 5\52 || 6g-1\2 || 1\2-5g ||

|| 11L11s || 1\22 &lt; g &lt; 1\11 || g = 3\44 || g = 2\33, 3\44, 4\55 || g || 1\11-g ||

|| 12L10s || 9\22 &lt; g &lt; 5\12 || g = 109\264 || g = 14\34, 19\46, 24\58 || 5g-2 || 5\2-6g ||

|| 13L9s || 5\22 &lt; g &lt; 3\13 || g = 131\572 || g = 8\35, 11\48, 14\61 || 9g-2 || 3-13g ||

|| 14L8s || 3\22 &lt; g &lt; 2\14 || g = 43\308 || g = 5\36, 7\50, 9\64 || 4g-1\2 || 1-7g ||

|| 15L7s || 19\22 &lt; g &lt; 13\15 || g = 571\660 || g = 32\37, 45\52, 58\67 || 7g-6 || 13-15g ||

|| 16L6s || 4\22 &lt; g &lt; 3\16 || g = 65\352 || g = 7\38, 10\54, 13\70 || 3g-1\2 || 3\2-8g ||

|| 17L5s || 9\22 &lt; g &lt; 7\17 || g = 207\748 || g = 16\39, 23\56, 30\73 || 5g-2 || 7-17g ||

|| 18L4s || 6\22 &lt; g &lt; 5\18 || g = 109\396 || g = 11\40, 16\58, 21\76 || 2g-1\2 || 5\2-9g ||

|| 19L3s || 15\22 &lt; g &lt; 13\19 || g = 571\836 || g = 28\41, 41\60, 54\79 || 3g-2 || 13-19g ||

|| 20L2s || 1\22 &lt; g &lt; 1\20 || g = 21\440 || g = 2\42, 3\62, 4\72 || g || 1\2-10g ||

|| 21L1s || 1\22 &lt; g &lt; 1\21 || g = 43\924 || g = 2\43, 3\64, 4\85 || g || 1-21g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L22s || &lt;span style="line-height: 15.6000003814697px;"&gt;22\23 &lt; g &lt; 1&lt;/span&gt; || g = 45\46 || g = //23\24, 24\25, 25\26// || 22g-21 || 1-g ||

|| 2L21s || 11\23 &lt; g &lt; 1\2 || g = 45\92 || g = //12\25, 13\27//, 14\29 || 21g-10 || 1-2g ||

|| 3L20s || 15\23 &lt; g &lt; 2\3 || g = 91\138 || g = //17\26//, 19\29, 21\32 || 20g-13 || 1-3g ||

|| 4L19s || 17\23 &lt; g &lt; 3\4 || g = 137\184 || g = //20\27//, 23\31, 26\35 || 19g-14 || 3-4g ||

|| 5L18s || 9\23 &lt; g &lt; 2\5 || g = 91\230 || g = 11\28, 13\33, 15\38 || 18g-7 || 2-5g ||

|| 6L17s || 19\23 &lt; g &lt; 5\6 || g = 229\276 || g = 24\29, 29\35, 34\41 || 17g-15 || 1-6g ||

|| 7L16s || 13\23 &lt; g &lt; 4\7 || g = 183\322 || g = 17\30,&lt;span style="line-height: 15.6000003814697px;"&gt; 21\37,&lt;/span&gt; 25\44 || 16g-9 || 4-7g ||

|| 8L15s || 20\23 &lt; g &lt; 7\8 || g = 321\368 || g = 27\31, 34\39, 41\47 || 15g-13 || 7-8g ||

|| 9L14s || 5\23 &lt; g &lt; 2\9 || g = 91\414 || g = 7\32, 9\41, 11\50 || 14g-7 || &lt;span style="line-height: 15.6000003814697px;"&gt;11-9g&lt;/span&gt; ||

|| 10L13s || 16\23 &lt; g &lt; 7\10 || g = 321\460 || g = 23\33, 30\43, 37\53 || 13g-9 || 7-10g ||

|| 11L12s || 2\23 &lt; g &lt; 1\11 || g = 45\506 || g = 3\34, 4\45, 5\56 || 12g-1 || 1-11g ||

|| 12L11s || 21\23 &lt; g &lt; 11\12 || g = 505\552 || g = 32\35, 43\47, 54\59 || &lt;span style="line-height: 15.6000003814697px;"&gt;11g-10&lt;/span&gt; || 11-12g ||

|| 13L10s || 7\23 &lt; g &lt; 4\13 || g = 183\598 || g = 11\36, 15\49, 19\62 || 10g-3 || 4-13g ||

|| 14L9s || 18\23 &lt; g &lt; 11\14 || g = 505\644 || g = 29\37, 40\51, 51\65 || 9g-7 || 11-14g ||

|| 15L8s || 3\23 &lt; g &lt; 2\15 || g = 91\690 || g = 5\38, 7\53, 9\68 || 8g-1 || 2-15g ||

|| 16L7s || 10\23 &lt; g &lt; 7\16 || g = 321\736 || g = 17\39, 24\55, 31\71 || 7g-3 || &lt;span style="line-height: 15.6000003814697px;"&gt;7-16g&lt;/span&gt; ||

|| 17L6s || 4\23 &lt; g &lt; 3\17 || g = 137\782 || g = 7\40, 10\57, 13\74 || 6g-1 || 3-17g ||

|| 18L5s || 14\23 &lt; g &lt; 11\18 || g = 505\828 || g = 25\41, 36\59, 47\77 || 5g-4 || 11-18g ||

|| 19L4s || 6\23 &lt; g &lt; 5\19 || g = 229\874 || g = 11\42, 16\61, 21\80 || 4g-1 || 5-19g ||

|| 20L3s || 8\23 &lt; g &lt; 7\20 || g = 321\920 || g = 15\43, 22\63, 29\83 || 3g-1 || 13-20g ||

|| 21L2s || 12\23 &lt; g &lt; 11\21 || g = 505\966 || g = 23\44, 34\65, 45\86 || 2g-1 || 1-21g ||

|| 22L1s || 1\23 &lt; g &lt; 1\22 || g = 45\1012 || g = 2\45, 3\67, 4\89 || g || 1-22g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L23s || 23\24 &lt; g &lt; 1 || g = 47\48 || g = //24\25, 25\26, 26\27// || 23g-22 || 1-g ||

|| 2L22s || 11\24 &lt; g &lt; 1\2 || g = 23\48 || g = //12\26, 13\28//, 14\30 || 1/2-g || 11g-5 ||

|| 3L21s || 7\24 &lt; g &lt; 1\3 || g = 15\48 || g = //8\27//, 9\30, 10\33 || 2/3-2g || g-1/3 ||

|| 4L20s || 5\24 &lt; g &lt; 1\4 || g = 11\48 || g = //6\28//, 7\32, 8\36 || 5g-1 || 1/4-g ||

|| 5L19s || 19\24 &lt; g &lt; 4\5 || g = 191\240 || g = //23\29//, 27\34, 31\39 || 19g-15 || 4-5g ||

|| 6L18s || 3\24 &lt; g &lt; 1\6 || g = 7\48 || g = 4\30, 5\36, 6\42 || 3g-1\3 || 1\6-g ||

|| 7L17s || 17\24 &lt; g &lt; 5\7 || g = 239\336 || g = 22\31, 27\38, 32\45 || 5-17g || 7g-2 ||

|| 8L16s || 2\24 &lt; g &lt; 1\8 || g = 5\48 || g = 3\32, 4\40, 5\48 || 2g-1\8 || 1\8-g ||

|| 9L15s || 5\24 &lt; g &lt; 2\9 || g = 31\144 || g = 7\33, 9\42, 11\51 || 5g-1 || 2\3-3g ||

|| 10L14s || 7\24 &lt; g &lt; 3\10 || g = 71\240 || g = 10\34, 13\44, 16\54 || 7g-2 || 3\2-5g ||

|| 11L13s || 13\24 &lt; g &lt; 6\11 || g = 287\528 || g = 19\35, 25\46, 31\57 || 13g-7 || 6-11g ||

|| 12L12s || 1\24 &lt; g &lt; 1\12 || g = 3\48 || g = 2\36, 3\48, 4\60 || g || 1\12-g ||

|| 13L11s || 11\24 &lt; g &lt; 6\13 || g = 287\624 || g = 17\37, 23\50, 29\63 || 11g-5 || 6-13g ||

|| 14L10s || 17\24 &lt; g &lt; 10\14 || g = 239\336 || g = 27\38, 37\52, 47\66 || 3\2-5g || 7g-2 ||

|| 15L9s || 3\24 &lt; g &lt; 2\15 || g = 31\240 || g = 5\39, 7\54, 9\69 || 3g-1\3 || 2\3-5g ||

|| 16L8s || 1\24 &lt; g &lt; 1\16 || g = 5\96 || g = 2\40, 3\56, 4\72 || g || 1\8-2g ||

|| 17L7s || 7\24 &lt; g &lt; 5\17 || g = 239\816 || g = 12\41, 17\58, 22\75 || 4-7g || 17g-12 ||

|| 18L6s || 1\24 &lt; g &lt; 1\18 || g = 7\144 || g = 2\42, 3\60, 4\78 || g || 1\6-3g ||

|| 19L5s || 5\24 &lt; g &lt; 4\19 || g = 191\912 || g = 9\43, 13\62, 17\81 || 5g-5 || 4-19g ||

|| 20L4s || 1\24 &lt; g &lt; 1\20 || g = 11\240 || g = 2\44, 3\64, 4\84 || g || 1\4-5g ||

|| 21L3s || 1\24 &lt; g &lt; 1\21 || g = 15\336 || g = 2\45, 3\66, 4\87 || g || 1\3-7g ||

|| 22L2s || 1\24 &lt; g &lt; 1\22 || g = 23\264 || g = 2\46, 3\68, 4\90 || g || 1\2-11g ||

|| 23L1s || 1\24 &lt; g &lt; 1\23 || g = 47\1104 || g = 2\47, 3\70, 4\93 || g || 1-23g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||

|| 1L24s || 24\25 &lt; g &lt; 1 || g = 49\50 || g = //25\26, 26\27, 27\28// || 24g-23 || 1-g ||

|| 2L23s || 12\25 &lt; g &lt; 1\2 || g = 49\100 || g = //13\27, 14\29//, 15\31 || 23g-11 || 1-2g ||

|| 3L22s || 8\25 &lt; g &lt; 1\3 || g = 49\150 || g = //9\28//, 10\31, 11\34 || 22g-7 || 1-3g ||

|| 4L21s || 6\25 &lt; g &lt; 1\4 || g = 49\200 || g = //7\29//, 8\33, 9\37 || 21g-5 || 1-4g ||

|| 5L20s || 4\25 &lt; g &lt; 1\5 || g = 9\50 || g = //5\30//, 6\35, 7\40 || 4g-3\5 || 1\5-g ||

|| 6L19s || 4\25 &lt; g &lt; 1\6 || g = 49\300 || g = 5\31, 6\37, 7\43 || 19g-3 || 1-6g ||

|| 7L18s || 7\25 &lt; g &lt; 2\7 || g = 99\350 || g = 9\32, 11\39, 13\46 || 18g-5 || 2-7g ||

|| 8L17s || 3\25 &lt; g &lt; 1\8 || g = 49\400 || g = 4\33, 5\41, 6\47 || &lt;span style="line-height: 15.6000003814697px;"&gt;17g-2&lt;/span&gt; || 1-8g ||

|| 9L16s || 11\25 &lt; g &lt; 4\9 || g = 199\450 || g = 15\34, 19\43, 23\52 || 16g-7 || &lt;span style="line-height: 15.6000003814697px;"&gt;-9g+4&lt;/span&gt; ||

|| 10L15s || 2\25 &lt; g &lt; 1\10 || g = 9\100 || g = 3\35, 4\45, 5\55 || 3g-1\5 || 1\5-2g ||

|| 11L14s || 9\25 &lt; g &lt; 4\11 || g = 199\550 || g = 13\36, 17\47, 21\58 || 14g-5 || -11g+4 ||

|| 12L13s || 2\25 &lt; g &lt; 1\12 || g = 49\600 || g = 3\37, 4\49, 5\61 || 13g-1 || 1-12g ||

|| 13L12s || 23\25 &lt; g &lt; 12\13 || g = 599\650 || g = 35\38, 47\51, 59\64 || 12g-11 || 12-13g ||

|| 14L11s || 16\25 &lt; g &lt; 9\14 || g = 449\700 || g = 25\39, 34\53, 43\67 || 11g-7 || -14g+9 ||

|| 15L10s || 3\25 &lt; g &lt; 2\15 || g = 19\150 || g = 5\40, 7\55, 9\70 || 2g-1\5 || 2\5-3g ||

|| 16L9s || 14\25 &lt; g &lt; 9\16 || g = 449\800 || g = 23\41, 32\57, 41\73 || 9g-5 || 9-16g ||

|| 17L8s || 22\25 &lt; g &lt; 15\17 || g = 749\850 || g = 37\42, 52\59, 67\76 || 8g-7 || 15-17g ||

|| 18L7s || 18\25 &lt; g &lt; 13\18 || g = 649\900 || g = 31\43, 44\61, 57\79 || 7g-5 || 13-18g ||

|| 19L6s || 21\25 &lt; g &lt; 16\19 || g = 799\950 || g = 37\44, 53\63, 69\82 || 6g-5 || 16-19g ||

|| 20L5s || 1\25 &lt; g &lt; 1\20 || g = 9\200 || g = 2\45, 3\65, 4\85 || g || 1\5-4g ||

|| 21L4s || 16\21 &lt; g &lt; 19\25 || g = 799\1050 || g = 35\46, 51\67, 71\88 || 4g-3 || 16-21g ||

|| 22L3s || 17\25 &lt; g &lt; 15\22 || g = 749\1100 || g = 32\47, 47\69, 62\91 || 3g-2 || 15-22g ||

|| 23L2s || 13\25 &lt; g &lt; 12\23 || g = 599\1150 || g = 25\48, 37\71, 49\94 || 2g-1 || 11-23g ||

|| 24L1s || 1\25 &lt; g &lt; 1\24 || g = 49\1200 || g = 2\49, 3\73, 4\97 || g || 1-24g ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Range of maximum expressiveness ||~ &lt;span style="display: block; text-align: center;"&gt;Top&lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;range of diatonicity&lt;/span&gt; ||~ Large step ||~ Small step ||

||~ Large-small numbers ||~ Generator range ||~ &lt;span style="background-color: #ffffff;"&gt;Midpoint&lt;/span&gt; ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Range of maximum expressiveness ||~ &lt;span style="display: block; text-align: center;"&gt;Top&lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;range of diatonicity&lt;/span&gt; ||~ Large step ||~ Small step ||

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generator ranges of MOS&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.&lt;br /&gt;

If the number of the &lt;a class="wiki_link" href="/Interval%20class" target="_blank"&gt;generic interval&lt;/a&gt; to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g &amp;gt; C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the &lt;a class="wiki_link" href="/Modal%20UDP%20Notation" target="_blank"&gt;chroma-positive&lt;/a&gt; generator. We have normalized to the formula fir the step size where the leading term is positive.&lt;br /&gt;

  &lt;strong&gt;Note: These sets are given for the sake of completeness as they are not really scales&lt;/strong&gt;&lt;br /&gt;

 

         &lt;th&gt;Boundaries of propriety, maximum expressiveness, diatonicity&lt;br /&gt;

         &lt;td&gt;g = 2\3, 3\4, 4\5&lt;br /&gt;

         &lt;td&gt;g = 3\4, 4\5, 5\6&lt;br /&gt;

         &lt;td&gt;g = 2\5, 3\7, 4\9&lt;br /&gt;

         &lt;td&gt;g = 4\5, 5\6, 6\7&lt;br /&gt;

         &lt;td&gt;g = 2\6, 3\8, 4\10&lt;br /&gt;

         &lt;td&gt;g = 2\7, 3\10, 4\13&lt;br /&gt;

         &lt;th&gt;Boundaries of propriety, maximum expressiveness, diatonicity&lt;br /&gt;

         &lt;td&gt;g = 5\6, 6\7, 7\8&lt;br /&gt;

         &lt;td&gt;4g-3&lt;br /&gt;

         &lt;td&gt;1-g&lt;br /&gt;

         &lt;td&gt;g = 3\7, 4\9, 5\11&lt;br /&gt;

         &lt;td&gt;3g-1&lt;br /&gt;

         &lt;td&gt;1-2g&lt;br /&gt;

         &lt;td&gt;g = 5\8, 7\11, 9\14&lt;br /&gt;

         &lt;td&gt;2g-1&lt;br /&gt;

         &lt;td&gt;2-3g&lt;br /&gt;

         &lt;td&gt;g = 2\9, 3\13, 4\17&lt;br /&gt;

         &lt;td&gt;g&lt;br /&gt;

         &lt;td&gt;1-4g&lt;br /&gt;

         &lt;th&gt;Boundaries of propriety, maximum expressiveness, diatonicity&lt;br /&gt;

         &lt;td&gt;g = 6\7, 7\8, 8\9&lt;br /&gt;

         &lt;td&gt;g = 3\8, 4\10, 5\12&lt;br /&gt;

         &lt;td&gt;g = 2\9, 3\12, 4\15&lt;br /&gt;