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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | Below are ranges of generators for various L-s patterns of [[MOS scale]]s, 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 bright 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 boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma. We have normalized to the formula for the step size where the leading term is positive. |
| 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:diagonalia|diagonalia]] and made on <tt>2016-12-31 11:58:31 UTC</tt>.<br>
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| : The original revision id was <tt>602928412</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>
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| <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">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. The fourth column gives the range of propriety. The fifth column gives the range of maximum expressiveness. Finally, the sixth column gives the top of the range of diatonicity.
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| 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 > 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.
| | == 2, 3, and 4-tone == |
| | '''Note 1: These sets are given for the sake of completeness as they are not really scales''' |
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| =2, 3, 4=
| | '''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does not apply to them''' |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ Top
| |
| range of diatonicity ||~ Large step ||~ Small step ||
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| || 1L1s || 1\2 < g < 1 || g = 3\4 || 1\2 < g < 2\3 || 2\3 < g < 3\4 || 3\4 < g < 4\5 || g || 1-g ||
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| || 1L2s || 2\3 < g < 1 || g = 5\6 || 2\3 < g < 3\4 || 3\4 < g < 4\5 || 4\5 < g < 5\6 || 2g-1 || 1-g ||
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| || 2L1s || 1\3 < g < 1\2 || g = 5\12 || 1\3 < g < 2\5 || 2\5 < g < 3\7 || 3\7 < g < 4\9 || g || 1-2g ||
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| || 1L3s || 3\4 < g < 1 || g = 7\8 || 3\4 < g < 4\5 || 4\5 < g < 5\6 || 5\6 < g < 6\7 || 3g-2 || 1-g ||
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| || 2L2s || 1\4 < g < 1\2 || g = 3\8 || 1\4 < g < 2\6 || 2\6 < g < 3\8 || 3\8 < g < 4\10 || g || 1\2-g ||
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| || 3L1s || 1\4 < g < 1\3 || g = 7\24 || 1\4 < g < 2\7 || 2\7 < g < 3\10 || 3\10 < g < 4\13 || g || 1-3g ||
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| =5= | | {| class="wikitable" |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ Top | | |- |
| range of diatonicity ||~ Large step ||~ Small step ||
| | ! | L-s pattern |
| || 1L4s || 4\5 < g < 1 || g = 9\10 || 4\5 < g < 5\6 || 5\6 < g < 6\7 || 6\7 < g < 7\8 || -3+4g || -g+1 || | | ! | Generator range |
| || 2L3s || 2\5 < g < 1\2 || g = 9\20 || 2\5 < g < 3\7 || 3\7 < g < 4\9 || 4\9 < g < 5\11 || -1+3g || -2g+1 || | | ! | Boundaries of best, better, good behavior |
| || 3L2s || 3\5 < g < 2\3 || g = 19\30 || 3\5 < g < 5\8 || 5\8 < g < 7\11 || 7\11 < g < 9\14 || -1+2g || -3g+2 || | | ! | Large step-Small step |
| || 4L1s || 1\5 < g < 1\4 || g = 9\40 || 1\5 < g < 2\9 || 2\9 < g < 3\13 || 3\13 < g < 4\17 || g || -4g+1 || | | |- |
| | | | [[1L 1s|''1L 1s'']] |
| | | | ''1\2 < g < 1'' |
| | | | ''g = 2\3, 3\4, 4\5-5\6'' |
| | | | ''g-(1-g) = 2g-1'' |
| | |- |
| | | | [[1L 2s]] |
| | | | 2\3 < g < 1 |
| | | | g = 3\4, 4\5, 5\6-6\7 |
| | | | 2g-1-(1-g) = 3g-2 |
| | |- |
| | | | [[2L 1s|''2L 1s'']] |
| | | | ''1\3 < g < 1\2'' |
| | | | ''g = 2\5, 3\7, 4\9-5\11'' |
| | | | ''g-(1-2g)= 3g-1'' |
| | |- |
| | | | [[1L 3s]] |
| | | | 3\4 < g < 1 |
| | | | g = 4\5, 5\6, 6\7-7\8 |
| | | | 3g-2-(1-g) = 4g-3 |
| | |- |
| | | | [[2L 2s|''2L 2s'']] ''= 1L 1s (2)'' |
| | | | ''1\4 < g < 1\2'' |
| | | | ''g = 2\6, 3\8, 4\10-5\12'' |
| | | | ''g-(1\2-g) = 2g-1\2'' |
| | |- |
| | | | [[3L 1s|''3L 1s'']] |
| | | | ''1\4 < g < 1\3'' |
| | | | ''g = 2\7, 3\10, 4\13-5\16'' |
| | | | ''g-(1-3g) = 4g-1'' |
| | |} |
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| =6= | | == 5-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ Top | | '''Note: italicized generators from here below generate scales which are weakly tonal''' |
| range of diatonicity ||~ Large step ||~ Small step ||
| | {| class="wikitable" |
| || 1L5s || 5\6 < g < 1 || g = 11\12 || 5\6 < g < 6\7 || 6\7 < g < 7\8 || 7\8 < g < 8\9 || 5g-4 || 1-g || | | |- |
| || 2L4s || 2\6 < g < 1\2 || g = 5\12 || 2\6 g < 3\8 || 3\8 < g < 4\10 || 4\10 < g < 5\12 || 2g-1\2 || 1\2-g ||
| | ! | L-s pattern |
| || 3L3s || 1\6 < g < 1\3 || g = 3\12 || 1\6 < g < 2\9 || 2\9 < g < 3\12 || 3\12 < g < 4\15 || g || 1\3-g || | | ! | Generator range |
| || 4L2s || 1\6 < g < 1\4 || g = 5\24 || 1\6 < g < 2\10 || 2\10 < g < 3\14 || 3\14 < g < 4\18 || g || 1\2-2g ||
| | ! | Boundaries of best, better, good behavior |
| || 5L1s || 1\6 < g < 1\5 || g = 11\60 || 1\6 < g < 2\11 || 2\11 < g < 3\16 || 3\16 < g < 4\21 || g || 1-5g || | | ! | Large step-Small step |
| | |- |
| | | | [[1L 4s]] |
| | | | 4\5 < g < 1 |
| | | | g = 5\6, 6\7, 7\8-8\9 |
| | | | 4g-3-(1-g) = 5g-4 |
| | |- |
| | | | [[2L 3s]] |
| | | | 2\5 < g < 1\2 |
| | | | g = 3\7, 4\9, 5\11-6\13 |
| | | | 3g-1-(1-2g) = 5g-2 |
| | |- |
| | | | [[3L 2s]] |
| | | | 3\5 < g < 2\3 |
| | | | g = 5\8, 7\11, 9\14-11\17 |
| | | | 2g-1-(2-3g) = 5g-3 |
| | |- |
| | | | [[4L 1s|''4L 1s'']] |
| | | | ''1\5 < g < 1\4'' |
| | | | ''g = 2\9, 3\13, 4\17-5\21'' |
| | | | ''g-(1-4g) = 5g-1'' |
| | |} |
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| =7= | | == 6-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L6s || 6\7 < g < 1 || g = 13\14 || 6\7 < g < 7\8 || 7\8 < g < 8\9 || 8\9 < g < 9\10 || 6g-5 || 1-g || | | |- |
| || 2L5s || 3\7 < g < 1\2 || g = 13\28 || 3\7 < g < 4\9 || 4\9 < g < 5\11 || 5\11 < g < 6\13 || 5g-2 || 1-2g || | | ! | L-s pattern |
| || 3L4s || 2\7 < g < 1\3 || g = 13\42 || 2\7 < g < 3\10 || 3\10 < g < 4\13 || 4\13 < g < 5\16 || 4g-1 || 1-3g || | | ! | Generator range |
| || 4L3s || 5\7 < g < 3\4 || g = 41\56 || 5\7 < g < 8\11 || 8\11 < g < 11\15 || 11\15 < g < 14\19 || 3g-2 || 3-4g ||
| | ! | Boundaries of best, better, good behavior |
| || 5L2s || 4\7 < g < 3\5 || g = 41\70 || 4\7 < g < 7\12 || 7\12 < g < 10\17 || 10\17 < g < 13\22 || 2g-1 || 3-5g || | | ! | Large step-Small step |
| || 6L1s || 1\7 < g < 1\6 || g = 13\84 || 1\7 < g < 2\13 || 2\13 < g < 3\19 || 3\19 < g < 4\25 || g || 1-6g || | | |- |
| | | | [[1L 5s]] |
| | | | 5\6 < g < 1 |
| | | | g = ''6\7'', 7\8, 8\9-9\10 |
| | | | 5g-4-(1-g) = 6g-5 |
| | |- |
| | | | [[2L 4s]] |
| | | | 2\6 < g < 1\2 |
| | | | g = 3\8, 4\10, 5\12-6\14 |
| | | | 2g-1\2-(1\2-g) = 3g-1 |
| | |- |
| | | | [[3L 3s|''3L 3s'']] ''= 1L 1s (3)'' |
| | | | ''1\6 < g < 1\3'' |
| | | | ''g = 2\9, 3\12, 4\15-5\18'' |
| | | | ''g-(1\3-g) = 2g-1\3'' |
| | |- |
| | | | [[4L 2s|''4L 2s'']] ''= 2L 1s (2)'' |
| | | | ''1\6 < g < 1\4'' |
| | | | ''g = 2\10, 3\14, 4\18-5\22'' |
| | | | ''g-(1\2-2g) = 3g-1\2'' |
| | |- |
| | | | [[5L 1s|''5L 1s'']] |
| | | | ''1\6 < g < 1\5'' |
| | | | ''g = 2\11, 3\16, 4\21-5\26'' |
| | | | ''g-(1-5g) = 6g-1'' |
| | |} |
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| =8= | | == 7-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L7s || 7\8 < g < 1 || g = 15\16 || 7\8 < g < 8\9 || 8\9 < g < 9\10 || 9\10 < g < 10\11 || 7g-6 || 1-g || | | |- |
| || 2L6s || 3\8 < g < 1\2 || g = 7\16 || 3\8 < g < 4\10 || 4\10 < g < 5\12 || 5\12 < g < 6\14 || 3g-1 || 1\2-g ||
| | ! | L-s pattern |
| || 3L5s || 5\8 < g < 2\3 || g = 31\48 || 5\8 < g < 7\11 || 7\11 < g < 9\14 || 9\14 < g < 11\17 || 5g-3 || 2-3g || | | ! | Generator range |
| || 4L4s || 1\8 < g < 1\4 || g = 3\16 || 1\8 < g < 2\12 || 2\12 < g < 3\16 || 3\16 < g < 4\20 || g || 1\4-g || | | ! | Boundaries of best, better, good behavior |
| || 5L3s || 3\8 < g < 2\5 || g = 31\80 || 3\8 < g < 5\13 || 5\13 < g < 7\18 || 7\18 < g < 9\23 || 3g-1 || 2-5g || | | ! | Large step-Small step |
| || 6L2s || 1\8 < g < 1\6 || g = 7\48 || 1\8 < g < 2\14 || 2\14 < g < 3\20 || 3\20 < g < 4\26 || g || 1\2-3g || | | |- |
| || 7L1s || 1\8 < g < 1\7 || g = 15\112 || 1\8 < g < 2\15 || 2\15 < g < 3\22 || 3\22 < g < 4\29 || g || 1-7g || | | | | [[1L 6s]] |
| | | | 6\7 < g < 1 |
| | | | g = ''7\8'', 8\9, 9\10-10\11 |
| | | | 6g-5-(1-g) = 7g-6 |
| | |- |
| | | | [[2L 5s]] |
| | | | 3\7 < g < 1\2 |
| | | | g = 4\9, 5\11, 6\13-7\15 |
| | | | 5g-2-(1-2g) = 7g-3 |
| | |- |
| | | | [[3L 4s]] |
| | | | 2\7 < g < 1\3 |
| | | | g = 3\10, 4\13, 5\16-6\19 |
| | | | 4g-1-(1-3g) = 7g-2 |
| | |- |
| | | | [[4L 3s]] |
| | | | 5\7 < g < 3\4 |
| | | | g = 8\11, 11\15, 14\19-17\23 |
| | | | 3g-2-(3-4g) = 7g-5 |
| | |- |
| | | | [[5L 2s]] |
| | | | 4\7 < g < 3\5 |
| | | | g = 7\12, 10\17, 13\22-16\27 |
| | | | 2g-1-(3-5g) = 7g-4 |
| | |- |
| | | | [[6L 1s|''6L 1s'']] |
| | | | ''1\7 < g < 1\6'' |
| | | | ''g = 2\13, 3\19, 4\25-5\31'' |
| | | | ''g-(1-6g) = 7g-1'' |
| | |} |
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| =9= | | == 8-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L8s || 8\9 < g < 1 || g = 17\18 || 8\9 < g < 9\10 || 9\10 < g < 10\11 || 9\10 < g < 10\11 || 8g-7 || 1-g || | | |- |
| || 2L7s || 4\9 < g < 1\2 || g = 17\36 || 4\9 < g < 5\11 || 5\11 < g < 6\13 || 6\13 < g < 7\15 || 7g-3 || 1-2g || | | ! | L-s pattern |
| || 3L6s || 2\9 < g < 1\3 || g = 5\18 || 2\9 < g < 3\12 || 3\12 < g < 4\15 || 4\15 < g < 5\18 || 2g-1\3 || 1\3-g || | | ! | Generator range |
| ||< 4L5s ||< 2\9 < g < 1\4 ||< g = 17\72 ||< 2\9 < g < 3\13 || 3\13 < g < 4\17 ||< 4\17 < g < 5\21 ||< 5g-1 ||< 1-4g || | | ! | Boundaries of best, better, good behavior |
| || 5L4s || 7\9 < g < 4\5 || g = 71\90 || 7\9 < g < 11\1 || 11\14 < g < 15\19 || 15\19 < g <18\23 || 4g-3 || 4-5g || | | ! | Large step-Small step |
| || 6L3s || 1\9 < g < 1\6 || g = 5\36 || 1\9 < g < 2\15 || 2\15 < g < 3\21 || 3\21 < g < 4\27 || g || 1\3-2g || | | |- |
| || 7L2s || 5\9 < g < 4\7 || g = 71\126 || 5\9 < g < 9\16 || 9\16 < g < 10\23 || 10\23 < g < 17\30 || 2g-1 || 4-7g ||
| | | | [[1L 7s]] |
| || 8L1s || 1\9 < g < 1\8 || g = 17\144 || 1\9 < g < 2\17 || 2\17 < g < 3\25 || 3\25 < g < 4\33 || g || 1-8g || | | | | 7\8 < g < 1 |
| | | | g = ''8\9, 9\10'', 10\11-11\12 |
| | | | 7g-6-(1-g) = 8g-7 |
| | |- |
| | | | [[2L 6s|''2L 6s'']] ''= 1L 3s (2)'' |
| | | | 3\8 < g < 1\2 |
| | | | g = ''4\10'', 5\12, 6\14-7\16 |
| | | | 3g-1-(1\2-g) = 4g-3\2 |
| | |- |
| | | | [[3L 5s]] |
| | | | 5\8 < g < 2\3 |
| | | | g = 7\11, 9\14, 11\17-13\20 |
| | | | 5g-3-(2-3g) = 8g-5 |
| | |- |
| | | | [[4L 4s|''4L 4s'']] ''= 1L 1s (4)'' |
| | | | ''1\8 < g < 1\4'' |
| | | | ''g = 2\12, 3\16, 4\20-5\24'' |
| | | | ''g-(1\4-g) = 2g-1\4'' |
| | |- |
| | | | [[5L 3s]] |
| | | | 3\8 < g < 2\5 |
| | | | g = 5\13, 7\18, 9\23-11\28 |
| | | | 3g-1-(2-5g) = 8g-3 |
| | |- |
| | | | [[6L 2s|''6L 2s'']] ''= 3L 1s (2)'' |
| | | | ''1\8 < g < 1\6'' |
| | | | ''g = 2\14, 3\20, 4\26-5\32'' |
| | | | ''g-(1\2-3g) = 4g-1\2'' |
| | |- |
| | | | [[7L 1s|''7L 1s'']] |
| | | | ''1\8 < g < 1\7'' |
| | | | ''g = 2\15, 3\22, 4\29-5\36'' |
| | | | ''g-(1-7g) = 8g-1'' |
| | |} |
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| =10= | | == 9-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L9s || 9\10 < g < 1 || g = 19\20 || 9\10 < g < 10\11 || 10\11 < g < 11\12 || 11\12 < g < 12\13 || -8+9g || -g+1 || | | |- |
| || 2L8s || 4\10 < g < 1\2 || g = 9\20 || 4\10 < g < 5\12 || 5\12 < g < 6\14 || 6\14 < g < 7\19 || -3\2+4g || -g+1\2 ||
| | ! | L-s pattern |
| || 3L7s || 3\10 < g < 1\3 || g = 19\60 || 3\10 < g < 4\13 || 4\13 < g < 5\16 || 5\16 < g < 6\19 || -2+7g || 1-3g || | | ! | Generator range |
| || 4L6s || 2\10 < g < 1\4 || g = 9\40 || 2\10 < g < 3\14 || 3\14 < g < 4\18 || 4\19 < g < 5\22 || 3g-1\2 || -2g+1\2 || | | ! | Boundaries of best, better, good behavior |
| || 5L5s || 1\10 < g < 1\5 || g = 3\20 || 1\10 < g < 2\15 || 2\15 < g < 3\20 || 3\20 < g < 4\25 || g || -g+1\5 || | | ! | Large step-Small step |
| || 6L4s || 3\10 < g < 2\6 || g = 19\60 || 3\10 < g < 5\16 || 5\16 < g < 7\22 || 7\22 < g < 9\28 || -1\2+2g || 1-3g || | | |- |
| || 7L3s || 7\10 < g < 5\7 || g = 99\140 || 7\10 < g < 12\17 || 12\17 < g < 17\24 || 17\24 < g <22\31 || -2+3g || -7g+5 || | | | | [[1L 8s]] |
| || 8L2s || 1\10 < g < 1\8 || g = 9\80 || 1\10 < g < 2\18 || 2\18 < g < 3\26 || 3\26 < g < 4\34 || g || -4g+1\2 || | | | | 8\9 < g < 1 |
| || 9L1s || 1\10 < g < 1\9 || g = 19\180 || 1\10 < g < 2\19 || 2\19 < g < 3\28 || 3\28 < g < 4\37 || g || -9g+1 || | | | | g = ''9\10'', ''10\11'', 11\12-12\13 |
| | | | 8g-7-(1-g) = 9g-8 |
| | |- |
| | | | [[2L 7s]] |
| | | | 4\9 < g < 1\2 |
| | | | g = ''5\11'', 6\13, 7\15-8\17 |
| | | | 7g-3-(1-2g) = 9g-4 |
| | |- |
| | | | [[3L 6s]] |
| | | | 2\9 < g < 1\3 |
| | | | g = 3\12, 4\15, 5\18-6\21 |
| | | | 2g-1\3-(1\3-g) = 3g-2\3 |
| | |- |
| | | | [[4L 5s]] |
| | | | 2\9 < g < 1\4 |
| | | | g = 3\13, 4\17, 5\21-6\25 |
| | | | 5g-1-(1-4g) = 9g-2 |
| | |- |
| | | | [[5L 4s]] |
| | | | 7\9 < g < 4\5 |
| | | | g = 11\14, 15\19, 19\24-23\29 |
| | | | 4g-3-(4-5g) = 9g-7 |
| | |- |
| | | | [[6L 3s|''6L 3s'']] ''= 2L 1s (3)'' |
| | | | ''1\9 < g < 1\6'' |
| | | | ''g = 2\15, 3\21, 4\27-5\33'' |
| | | | ''g-(1\3-2g) = 3g-1\3'' |
| | |- |
| | | | [[7L 2s]] |
| | | | 5\9 < g < 4\7 |
| | | | g = 9\16, 13\23, 17\30-21\37 |
| | | | 2g-1-(4-7g) = 9g-5 |
| | |- |
| | | | [[8L 1s|''8L 1s'']] |
| | | | ''1\9 < g < 1\8'' |
| | | | ''g = 2\17, 3\25, 4\33-5\41'' |
| | | | ''g-(1-8g) = 9g-1'' |
| | |} |
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| =11= | | == 10-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L10s || 10\11 < g < 1 || g = 21\22 || 10\11 < g < 11\12 || 11\12 < g < 12\13 || 12/13 < g < 13\14 || -9+10g || -g+1 || | | |- |
| || 2L9s || 5\11 < g < 1\2 || g = 21\44 || 5\11 < g < 6\13 || 6\13 < g < 7\15 || 7\15 < g < 8\17 || -4+9g || -2g+1 || | | ! | L-s pattern |
| || 3L8s || 7\11 < g < 2\3 || g = 43\66 || 7\11 < g < 9\14 || 9\14 < g < 11\17 || 11\17 < g < 13\20 || -5+8g || -3g+2 ||
| | ! | Generator range |
| || 4L7s || 8\11 < g < 3\4 || g = 65\88 || 8\11 < g < 11\15 || 11\15 < g < 14\19 || 14\19 < g < 17\23 || -5+7g || -4g+3 || | | ! | Boundaries of best, better, good behavior |
| || 5L6s || 2\11 < g < 1\5 || g = 21\110 || 2\11 < g < 3\16 || 3\16 < g < 4\21 || 4\21 < g < 5\26 || -1+6g || -5g+1 || | | ! | Large step-Small step |
| || 6L5s || 9\11 < g < 5\6 || g = 109\132 || 9\11 < g < 14\17 || 14\17 < g < 19\23 || 19\23 < g < 24\29 || -4+5g || -6g+5 || | | |- |
| || 7L4s || 3\11 < g < 2\7 || g = 43\154 || 3\11 < g < 5\18 || 5\18 < g < 7\25 || 7\25 < g < 9\32 || -1+4g || -7g+2 || | | | | [[1L 9s]] |
| || 8L3s || 4\11 < g < 3\8 || g = 65\176 || 4\11 < g < 7\19 || 7\19 < g < 10\27 || 10\27 < g < 13\35 || -1+3g || -8g+3 || | | | | 9\10 < g < 1 |
| || 9L2s || 6\11 < g < 5\9 || g = 109\198 || 6\11 < g < 11\20 || 11\20 < g < 16\29 || 16\29 < g < 21\38 || -1+2g || -9g+5 || | | | | g = ''10\11'', ''11\12'', 12\13-13\14 |
| || 10L1s || 1\11 < g < 1\10 || g = 21\220 || 1\11 < g < 2\21 || 2\21 < g < 3\31 || 3\31 < g < 4\41 || g || -10g+1 || | | | | 9g-8-(1-g) = 10g-9 |
| | |- |
| | | | [[2L 8s]] |
| | | | 4\10 < g < 1\2 |
| | | | g = ''5\12'', 6\14, 7\16-8\18 |
| | | | 4g-3\2-(1\2-g) = 5g-2 |
| | |- |
| | | | [[3L 7s]] |
| | | | 3\10 < g < 1\3 |
| | | | g = 4\13, 5\16, 6\19-7\22 |
| | | | 7g-2-(1-3g) = 10g-3 |
| | |- |
| | | | [[4L 6s]] |
| | | | 2\10 < g < 1\4 |
| | | | g = 3\14, 4\18, 5\22-6\26 |
| | | | 3g-1\2-(1\2-2g) = 5g-1 |
| | |- |
| | | | [[5L 5s|''5L 5s'']] ''= 1L 1s (5)'' |
| | | | ''1\10 < g < 1\5'' |
| | | | ''g = 2\15, 3\20, 4\25-5\30'' |
| | | | ''g-(1\5-g) = 2g-1\5'' |
| | |- |
| | | | [[6L 4s]] |
| | | | 3\10 < g < 2\6 |
| | | | g = 5\16, 7\22, 9\28-11\34 |
| | | | 2g-1\2-(1-3g) = 5g-3\2 |
| | |- |
| | | | [[7L 3s]] |
| | | | 7\10 < g < 5\7 |
| | | | g = 12\17, 17\24, 22\31-27\38 |
| | | | 3g-2-(5-7g) = 10g-7 |
| | |- |
| | | | [[8L 2s|''8L 2s'']] ''= 4L 1s (2)'' |
| | | | ''1\10 < g < 1\8'' |
| | | | ''g = 2\18, 3\26, 4\34-5\42'' |
| | | | ''g-(1\2-4g) = 5g-1\2'' |
| | |- |
| | | | [[9L 1s|''9L 1s'']] |
| | | | ''1\10 < g < 1\9'' |
| | | | ''g = 2\19, 3\28, 4\37-5\46'' |
| | | | ''g-(1-9g) = 10g-1'' |
| | |} |
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| =12= | | == 11-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L11s || 11\12 < g < 1 || g = 23\24 || 11\12 < g < 12\13 || 12\13 < g < 13\14 || 13\14 < g < 14\15 || 11g-10 || 1-g || | | |- |
| || 2L10s || 5\12 < g < 1\2 || g = 11\24 || 5\12 < g < 6\14 || 6\14 < g < 7\16 || 7\16 < g < 8\18 || 5g-2 || 1\2-g ||
| | ! | L-s pattern |
| || 3L9s || 3\12 < g < 1\3 || g = 7\24 || 3\12 < g < 4\15 || 4\15 < g < 5\18 || 5\18 < g < 6\21 || 3g-2\3 || 1\3-g || | | ! | Generator range |
| || 4L8s || 2\12 < g < 1\4 || g = 5\24 || 2/12 < g < 3\16 || 3\16 < g < 4\20 || 4\20 < g < 5\24 || 2g-1\4 || 1\4-g || | | ! | Boundaries of best, better, good behavior |
| || 5L7s || 7\12 < g < 3\5 || g = 71\120 || 7\12 < g < 10\17 || 10\17 < g < 13\22 || 13\22 < g < 16\27 || 7g-4 || 3-5g || | | ! | Large step-Small step |
| || 6L6s || 1\12 < g < 1\6 || g = 3\24 || 1\12 < g < 2\18 || 2\18 < g < 3\24 || 3/24 < g < 4\30 || g || 1\6-g || | | |- |
| || 7L5s || 5\12 < g < 3\7 || g = 71\168 || 5\12 < g < 8\19 || 8\19 < g < 11\26 || 11\26 < g < 14\33 || 5g-2 || 3-7g || | | | | [[1L 10s]] |
| || 8L4s || 1\12 < g < 1\8 || g = 5\48 || 1\12 < g < 2\20 || 2\20 < g < 3\28 || 3\28 < g < 4\36 || g || 1\4-2g || | | | | 10\11 < g < 1 |
| || 9L3s || 1\12 < g < 1\9 || g = 7\72 || 1\12 < g < 2\21 || 2\21 < g < 3\30 || 3\30 < g < 4\39 || g || 1\3-3g || | | | | g = ''11\12'', ''12\13'', 13\14-14\15 |
| || 10L2s || 1\12 < g < 1\10 || g = 11\120 || 1\12 < g < 2\22 || 2\22 < g < 3\32 || 3\32 < g < 4\42 || g || 1\2-5g || | | | | 10g-9-(1-g) = 11g-10 |
| || 11L1s || 1\12 < g < 1\11 || g = 23\264 || 1\12 < g < 2\23 || 2\23 < g < 3\34 || 3\34 < g < 4\45 || g || 1-11g || | | |- |
| | | | [[2L 9s]] |
| | | | 5\11 < g < 1\2 |
| | | | g = ''6\13'', 7\15, 8\17-9\19 |
| | | | 9g-4-(1-2g) = 11g-5 |
| | |- |
| | | | [[3L 8s]] |
| | | | 7\11 < g < 2\3 |
| | | | g = 9\14, 11\17, 13\20-15\23 |
| | | | 8g-5-(2-3g) = 11g-7 |
| | |- |
| | | | [[4L 7s]] |
| | | | 8\11 < g < 3\4 |
| | | | g = 11\15, 14\19, 17\23-20\27 |
| | | | 7g-5-(3-4g) = 11g-8 |
| | |- |
| | | | [[5L 6s]] |
| | | | 2\11 < g < 1\5 |
| | | | g = 3\16, 4\21, 5\26-6\31 |
| | | | 6g-1-(1-5g) = 11g-2 |
| | |- |
| | | | [[6L 5s]] |
| | | | 9\11 < g < 5\6 |
| | | | g = 14\17, 19\23, 24\29-29\35 |
| | | | 5g-4-(5-6g) = 11g-9 |
| | |- |
| | | | [[7L 4s]] |
| | | | 3\11 < g < 2\7 |
| | | | g = 5\18, 7\25, 9\32-11\39 |
| | | | 4g-1-(2-7g) = 11g-3 |
| | |- |
| | | | [[8L 3s]] |
| | | | 4\11 < g < 3\8 |
| | | | g = 7\19, 10\27, 13\35-16\43 |
| | | | 3g-1-(3-8g) = 11g-4 |
| | |- |
| | | | [[9L 2s]] |
| | | | 6\11 < g < 5\9 |
| | | | g = 11\20, 16\29, 21\38-26\47 |
| | | | 2g-1-(5-9g) = 11g-6 |
| | |- |
| | | | [[10L 1s|''10L 1s'']] |
| | | | ''1\11 < g < 1\10'' |
| | | | ''g = 2\21, 3\31, 4\41-5\51'' |
| | | | ''g+1-10g = 11g-1'' |
| | |} |
|
| |
|
| =13= | | == 12-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L12s || 12\13 < g < 1 || g = 25\26 || 12\13 < g < 13\14 || 13\14 < g < 14\15 || 14\15 < g < 15\16 || 12g-11 || 1-g || | | |- |
| || 2L11s || 6\13 < g < 1\2 || g = 25\52 || 6\13 < g < 7\15 || 7\15 < g < 8\17 || 8\17 < g < 9\18 || 11g-5 || 1-2g || | | ! | L-s pattern |
| || 3L10s || 4\13 < g < 1\3 || g = 25\78 || 4\13 < g < 5\16 || 5\16 < g < 6\19 || 6\19 < g < 7/22 || 10g-3 || 1-3g || | | ! | Generator range |
| || 4L9s || 3\13 < g < 1\4 || g = 25\104 || 3\13 < g < 4\17 || 4\17 < g < 5\21 || 5\21 < g < 6\25 || 9g-2 || 1-4g || | | ! | Boundaries of best, better, good behavior |
| || 5L8s || 5\13 < g < 2\5 || g = 51\130 || 5\13 < g < 7\18 || 7\18 < g < 9\23 || 9\23 < g < 11\28 || 8g-3 || 2-5g || | | ! | Large step-Small step |
| || 6L7s || 2\13 < g < 1\6 || g = 25\156 || 2\13 < g < 3\19 || 3\19 < g < 4\25 || 4\25 < g < 5\31 || 7g-1 || 1-6g || | | |- |
| || 7L6s || 11\13 < g < 6\7 || g = 155\182 || 11\13 < g < 17\20 || 17\20 < g < 23\27 || 23\27 < g < 29\34 || 6g-5 || 6-7g || | | | | [[1L 11s]] |
| || 8L5s || 8\13 < g < 5\8 || g = 129\208 || 8\13 < g < 13\21 || 13\21 < g < 18\29 || 18\29 < g < 23\37 || 5g-3 || 5-8g || | | | | 11\12 < g < 1 |
| || 9L4s || 10\13 < g < 7\9 || g = 181\234 || 10\13 < g < 17\22 || 17\22 < g < 24\31 || 24\31 < g < 31\40 || 4g-3 || 7-9g || | | | | g = ''12\13,'' ''13\14, 14\15''-15\16 |
| || 10L3s || 9\13 < g < 7\10 || g = 181\260 || 9\13 < g < 16\23 || 16\23 < g < 23\33 || 23\33 < g < 30\43 || 3g-2 || 7-10g || | | | | 11g-10-(1-g) = 12g-11 |
| || 11L2s || 7\13 < g < 6\11 || g = 155\286 || 7\13 < g < 13\24 || 13\24 < g < 19\35 || 19\35 < g < 25\46 || 2g-1 || 6-11g ||
| | |- |
| || 12L1s || 1\13 < g < 1\12 || g = 25\312 || 1\13 < g < 2\25 || 2\25 < g < 3\37 || 3\37 < g < 4\49 || g || 1-12g || | | | | [[2L 10s]] |
| | | | 5\12 < g < 1\2 |
| | | | g = ''6\14'', 7\16, 8\18-9\20 |
| | | | 5g-2-(1\2-g) = 6g-5\2 |
| | |- |
| | | | [[3L 9s]] |
| | | | 3\12 < g < 1\3 |
| | | | g = ''4\15'', 5\18, 6\21-7\24 |
| | | | 3g-2\3-(1\3-g) = 4g-1 |
| | |- |
| | | | [[4L 8s]] |
| | | | 2\12 < g < 1\4 |
| | | | g = 3\16, 4\20, 5\24-6\28 |
| | | | 2g-1\4-(1\4-g) = 3g-1\2 |
| | |- |
| | | | [[5L 7s]] |
| | | | 7\12 < g < 3\5 |
| | | | g = 10\17, 13\22, 16\27-19\32 |
| | | | 7g-4-(3-5g) = 12g-7 |
| | |- |
| | | | [[6L 6s|''6L 6s'']] ''= 1L 1s (6)'' |
| | | | ''1\12 < g < 1\6'' |
| | | | ''g = 2\18, 3\24, 4\30-5\36'' |
| | | | ''g-(1\6-g) = 2g-1\6'' |
| | |- |
| | | | [[7L 5s]] |
| | | | 5\12 < g < 3\7 |
| | | | g = 8\19, 11\26, 14\33-17\40 |
| | | | 5g-2-(3-7g) = 12g-5 |
| | |- |
| | | | [[8L 4s|''8L 4s'']] ''= 2L 1s (4)'' |
| | | | ''1\12 < g < 1\8'' |
| | | | ''g = 2\20, 3\28, 4\36-5\44'' |
| | | | ''g-(1\4-2g) = 3g-1\4'' |
| | |- |
| | | | [[9L 3s|''9L 3s'']] ''= 3L 1s (3)'' |
| | | | ''1\12 < g < 1\9'' |
| | | | ''g = 2\21, 3\30, 4\39-5\48'' |
| | | | ''g-(1\3-3g) = 4g-1\3'' |
| | |- |
| | | | [[10L 2s|''10L 2s'']] ''= 5L 1s (2)'' |
| | | | ''1\12 < g < 1\10'' |
| | | | ''g = 2\22, 3\32, 4\42-5\52'' |
| | | | ''g-(1\2-5g) = 6g-1\2'' |
| | |- |
| | | | [[11L 1s|''11L 1s'']] |
| | | | ''1\12 < g < 1\11'' |
| | | | ''g = 2\23, 3\34, 4\45-5\56'' |
| | | | ''g-(1-11g) = 12g-1'' |
| | |} |
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| =14= | | == 13-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L13s || 13\14 < g < 1 || g = 27\28 || 13\14 < g < 14\15 || 14\15 < g < 15\16 || 15\16 < g < 16\17 || \-12+13g || -g+1 || | | |- |
| || 2L12s || 6\14 < g < 1\2 || g = 13\28 || 6\14 < g < 7\16 || 7\16 < g < 8\18 || 8\18 < g < 9\20 || -5\2+6g || -g+1\2 ||
| | ! | L-s pattern |
| || 3L11s || 9\14 < g < 2\3 || g = 55\84 || 9\14 < g < 11\17 || 11\17 < g < 13\20 || 13\20 < g < 15\23 || -7+11g || -3g+2 || | | ! | Generator range |
| || 4L10s || 3\14 < g < 1\4 || g = 13\56 || 3\14 < g < 4\18 || 4\18 < g < 5\22 || 5\22 < g < 6\26 || -1+5g || -2g+1\2 || | | ! | Boundaries of best, better, good behavior |
| || 5L9s || 11\14 < g < 4\5 || g = 111\140 || 11\14 < g < 15\19 || 15\19 < g < 19\24 || 19\24 < g < 23\29 || -7+9g || -5g+4 || | | ! | Large step-Small step |
| || 6L8s || 2\14 < g < 1\6 || g = 13\84 || 2\14 < g < 3\20 || 3\20 < g < 4\26 || 4\26 < g < 5\32 || 4g-1\2 || -3g+1\2 || | | |- |
| || 7L7s || 1\14 < g < 1\7 || g = 3\28 || 1\14 < g < 2\21 || 2\21 < g < 3\28 || 3\28 < g < 4\35 || g || -g+1\7 || | | | | [[1L 12s]] |
| || 8L6s || 5\14 < g < 3\8 || g = 41\112 || 5\14 < g < 8\22 || 8\22 < g < 11\30 || 11\30 < g < 14\38 || -1+3g || -4g+3\2 || | | | | 12\13 < g < 1 |
| || 9L5s || 3\14 < g < 2\9 || g = 55\252 || 3\14 < g < 5\23 || 5\23 < g < 7\32 || 7\32 < g < 9\41 || -1+5g || -9g+2 || | | | | g = ''13\14, 14\15, 15\16''-16\17 |
| || 10L4s || 4\14 < g < 3\10 || g = 41\140 || 4\14 < g < 7\24 || 7\24 < g < 10\34 || 10\34 < g < 13\44 || -1\2+2g || -5g+3\2 || | | | | 12g-11-(1-g) = 13g-12 |
| || 11L3s || 5\14 < g < 4\11 || g = 111\308 || 5\14 < g < 9\25 || 9\25 < g < 13\36 || 13\36 < g < 17\47 || -1+3g || -11g+4 || | | |- |
| || 12L2s || 1\14 < g < 1\12 || g = 13\168 || 1\14 < g < 2\26 || 2\26 < g < 3\38 || 3\38 < g < 4\50 || g || -6g+1\2 || | | | | [[2L 11s]] |
| || 13L1s || 1\14 < g < 1\13 || g = 27\364 || 1\14 < g < 2\27 || 2\27 < g < 3\40 || 3\40 < g < 4\53 || g || -13g+1 || | | | | 6\13 < g < 1\2 |
| | | | g = ''7\15'', 8\17, 9\19-10\21 |
| | | | 11g-5-(1-2g) = 13g-6 |
| | |- |
| | | | [[3L 10s]] |
| | | | 4\13 < g < 1\3 |
| | | | g = ''5\16'', 6\19, 7\22-8\25 |
| | | | 10g-3-(1-3g) = 13g-4 |
| | |- |
| | | | [[4L 9s]] |
| | | | 3\13 < g < 1\4 |
| | | | g = 4\17, 5\21, 6\25-7\29 |
| | | | 9g-2-(1-4g) = 13g-3 |
| | |- |
| | | | [[5L 8s]] |
| | | | 5\13 < g < 2\5 |
| | | | g = 7\18, 9\23, 11\28-13\33 |
| | | | 8g-3-(2-5g) = 13g-5 |
| | |- |
| | | | [[6L 7s]] |
| | | | 2\13 < g < 1\6 |
| | | | g = 3\19, 4\25, 5\31-6\37 |
| | | | 7g-1-(1-6g) = 13g-2 |
| | |- |
| | | | [[7L 6s]] |
| | | | 11\13 < g < 6\7 |
| | | | g = 17\20, 23\27, 29\34-35\41 |
| | | | 6g-5-(6-7g) = 13g-11 |
| | |- |
| | | | [[8L 5s]] |
| | | | 8\13 < g < 5\8 |
| | | | g = 13\21, 18\29, 23\37-28\45 |
| | | | 5g-3-(5-8g) = 13g-8 |
| | |- |
| | | | [[9L 4s]] |
| | | | 10\13 < g < 7\9 |
| | | | g = 17\22, 24\31, 31\40-38\49 |
| | | | 4g-3-(7-9g) = 13g-10 |
| | |- |
| | | | [[10L 3s]] |
| | | | 9\13 < g < 7\10 |
| | | | g = 16\23, 23\33, 30\43-37\53 |
| | | | 3g-2-(7-10g) = 13g-9 |
| | |- |
| | | | [[11L 2s]] |
| | | | 7\13 < g < 6\11 |
| | | | g = 13\24, 19\35, 25\46-31\57 |
| | | | 2g-1-(6-11g) = 13g-7 |
| | |- |
| | | | [[12L 1s|''12L 1s'']] |
| | | | ''1\13 < g < 1\12'' |
| | | | ''g = 2\25, 3\37, 4\49-5\61'' |
| | | | ''g-(1-12g) = 13g-1'' |
| | |} |
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| =15= | | == 14-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L14s || 14\15 < g < 1 || g = 29\30 || 14\15 < g < 15\16 || 15\16 < g < 16\17 || 16\17 < g < 17\18 || -13+14g || -g+1 || | | |- |
| || 2L13s || 7\15 < g < 1\2 || g = 29\60 || 7\15 < g < 8\17 || 8\17 < g < 9\19 || 9\19 < g < 10\21 || -6+13g || -2g+1 || | | ! | L-s pattern |
| || 3L12s || 4\15 < g < 1\3 || g = 9\30 || 4\15 < g < 5\18 || 5\18 < g < 6\21 || 6\21 < g < 7\24 || -1+4g || -g+1\3 || | | ! | Generator range |
| || 4L11s || 11\15 < g < 3\4 || g = 89\120 || 11\15 < g < 14\19 || 14\19 < g < 17\23 || 17\23 < g < 20\27 || -8+11g || -4g+3 || | | ! | Boundaries of best, better, good behavior |
| || 5L10s || 2\15 < g < 1\5 || g = 5\30 || 2\15 < g < 3\20 || 3\20 < g < 4\25 || 4\25 < g < 5\30 || -1\5+2g || -g+1\5 ||
| | ! | Large step-Small step |
| || 6L9s || 2\15 < g < 1\6 || g = 9\60 || 2\15 < g < 3\21 || 3\21 < g < 4\27 || 4\27 < g < 5\33 || -1\3+3g || -2g+1\3 ||
| | |- |
| || 7L8s || 2\15 < g < 1\7 || g = 29\210 || 2\15 < g < 3\22 || 3\22 < g < 4\29 || 4\29 < g < 5\36 || -1+8g || -7g+1 || | | | | [[1L 13s]] |
| || 8L7s || 13\15 < g < 7\8 || g = 209\240 || 13\15 < g < 20\23 || 20\23 < g < 27\31 || 27\31 < g < 34\39 || -6+7g || -8g+7 || | | | | 13\14 < g < 1 |
| || 9L6s || 3\15 < g < 2\9 || g = 19\90 || 3\15 < g < 5\24 || 5\24 < g < 7\33 || 7\33 < g < 9\42 || -1\3+2g || -3g+2\3 ||
| | | | g = ''14\15, 15\16, 16\17''-17\18 |
| || 10L5s || 1\15 < g < 1\10 || g = 5\60 || 1\15 < g < 2\25 || 2\25 < g < 3\35 || 3\35 < g < 4\45 || g || -2g+1\5 || | | | | 13g-12-(1-g) = 14g-13 |
| || 11L4s || 4\15 < g < 3\11 || g = 89\330 || 4\15 < g < 7\26 || 7\26 < g < 10\37 || 10\37 < g < 13\48 || -1+4g || -11g+3 || | | |- |
| || 12L3s || 1\15 < g < 1\12 || g = 9\120 || 1\15 < g < 2\27 || 2\27 < g < 3\39 || 3\39 < g < 4\51 || g || -4g+1\3 || | | | | [[2L 12s]] |
| || 13L2s || 8\15 < g < 7\13 || g = 209\390 || 8\15 < g < 15\28 || 15\28 < g < 22\41 || 22\41 < g < 29\54 || -1+2g || -13g+7 || | | | | 6\14 < g < 1\2 |
| || 14L1s || 1\15 < g < 1\14 || g = 29\420 || 1\15 < g < 2\29 || 2\29 < g < 3\43 || 3\43 < g < 4\57 || g || -14g+1 || | | | | g = ''7\16'', 8\18, 9\20-10\22 |
| | | | 6g-5\2-(1\2-g) = 7g-3 |
| | |- |
| | | | [[3L 11s]] |
| | | | 9\14 < g < 2\3 |
| | | | g = ''11\17'', 13\20, 15\23-17\26 |
| | | | 11g-7-(2-3g) = 14g-9 |
| | |- |
| | | | [[4L 10s]] |
| | | | 3\14 < g < 1\4 |
| | | | g = 4\18, 5\22, 6\26-7\30 |
| | | | 5g-1-(1\2-2g) = 7g-3\2 |
| | |- |
| | | | [[5L 9s]] |
| | | | 11\14 < g < 4\5 |
| | | | g = 15\19, 19\24, 23\29-27\34 |
| | | | 9g-7-(4-5g) = 14g-11 |
| | |- |
| | | | [[6L 8s]] |
| | | | 2\14 < g < 1\6 |
| | | | g = 3\20, 4\26, 5\32-6\38 |
| | | | 4g-1\2-(1\2-3g) = 7g-1 |
| | |- |
| | | | [[7L 7s|''7L 7s'']] ''= 1L 1s (7)'' |
| | | | ''1\14 < g < 1\7'' |
| | | | ''g = 2\21, 3\28, 4\35-5\42'' |
| | | | ''g-(1\7-g) = 2g-1\7'' |
| | |- |
| | | | [[8L 6s]] |
| | | | 5\14 < g < 3\8 |
| | | | g = 8\22, 11\30, 14\38-17\46 |
| | | | 3g-1-(3\2-4g) = 7g-5\2 |
| | |- |
| | | | [[9L 5s]] |
| | | | 3\14 < g < 2\9 |
| | | | g = 5\23, 7\32, 9\41-11\50 |
| | | | 5g-1-(2-9g) = 14g-3 |
| | |- |
| | | | [[10L 4s]] |
| | | | 4\14 < g < 3\10 |
| | | | g = 7\24, 10\34, 13\44-16\54 |
| | | | 2g-1\2-(3\2-5g) = 7g-2 |
| | |- |
| | | | [[11L 3s]] |
| | | | 5\14 < g < 4\11 |
| | | | g = 9\25, 13\36, 17\47-21\58 |
| | | | 3g-1-(4-11g) = 14g-5 |
| | |- |
| | | | [[12L 2s|''12L 2s'']] ''= 6L 1s (2)'' |
| | | | ''1\14 < g < 1\12'' |
| | | | ''g = 2\26, 3\38, 4\50-5\62'' |
| | | | ''g-(1\2-6g) = 7g-1\2'' |
| | |- |
| | | | [[13L 1s|''13L 1s'']] |
| | | | ''1\14 < g < 1\13'' |
| | | | ''g = 2\27, 3\40, 4\53-5\66'' |
| | | | ''g+1-13g = 14g-1'' |
| | |} |
|
| |
|
| =16= | | == 15-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L15s || 15\16 < g < 1 || g = 31\32 || 15\16 < g < 16\17 || 16\17 < g < 17\18 || 17\18 < g < 18\19 || -14+15g || -g+1 || | | |- |
| || 2L14s || 7\16 < g < 1\2 || g = 15\32 || 7\16 < g < 8\18 || 8\18 < g < 9\20 || 9\20 < g < 10\22 || -3+7g || -g+1\2 ||
| | ! | L-s pattern |
| || 3L13s || 5\16 < g < 1\3 || g = 31\96 || 5\16 < g < 6\19 || 6\19 < g < 7\22 || 7\22 < g < 8\25 || -4+13g || 1-3g || | | ! | Generator range |
| || 4L12s || 3\16 < g < 1\4 || g = 7\32 || 3\16 < g < 4\20 || 4\20 < g < 5\24 || 5\24 < g < 6\28 || 3g-1\2 || -g+1\4 || | | ! | Boundaries of best, better, good behavior |
| || 5L11s || 3\16 < g < 1\5 || g = 31\160 || 3\16 < g < 4\21 || 4\21 < g < 5\26 || 5\26 < g < 6\31 || -2+11g || -5g+1 || | | ! | Large step-Small step |
| || 6L10s || 5\16 < g < 2\6 || g = 31\96 || 5\16 < g < 7\22 || 7\22 < g < 9\28 || 9\28 < g < 11\34 || -3\2+5g || 1-3g || | | |- |
| || 7L9s || 9\16 < g < 4\7 || g = 127\224 || 9\16 < g < 13\23 || 13\23 < g < 17\30 || 17\30 < g < 21\37 || -5+9g || -7g+4 || | | | | [[1L 14s]] |
| || 8L8s || 1\16 < g < 1\8 || g = 3\32 || 1\16 < g < 2\24 || 2\24 < g < 3\32 || 3\32 < g < 4\40 || g || -g+1\8 || | | | | 14\15 < g < 1 |
| || 9L7s || 7\16 < g < 4\9 || g = 127\286 || 7\16 < g < 11\25 || 11\25 < g < 15\34 || 15\34 < g < 19\43 || -3+7g || -9g+4 || | | | | g = ''15\16, 16\17, 17\18-''18\19 |
| || 10L6s || 3\16 < g < 2\10 || g = 31\160 || 3\16 < g < 5\26 || 5\26 < g < 7\36 || 7\36 < g < 8\46 || 3g-1\2 || -5g+1 || | | | | 14g-13-(1-g) = 15g-14 |
| || 11L5s || 13\16 < g < 9\11 || g = 287\352 || 13\16 < g < 22\27 || 22\27 < g < 31\38 || 31\38 < g < 40\49 || -4+5g || -11g+9 || | | |- |
| || 12L4s || 1\16 < g < 1\12 || g = 7\48 || 1\16 < g < 2\28 || 2\28 < g < 3\40 || 3\40 < g < 4\52 || g || -3g+1\4 || | | | | [[2L 13s]] |
| || 13L3s || 11\16 < g < 9\13 || g = 287\416 || 11\16 < g < 20\29 || 20\29 < g < 29\42 || 29\42 < g < 38\55 || -2+3g || -13g+9 || | | | | 7\15 < g < 1\2 |
| || 14L2s || 1\16 < g < 1\14 || g = 15\224 || 1\16 < g < 2\30 || 2\30 < g < 3\44 || 3\44 < g < 4\58 || g || -7g+1\2 || | | | | g = ''8\17'', 9\19, 10\21-11\23 |
| || 15L1s || 1\16 < g < 1\15 || g = 31\480 || 1\16 < g < 2\31 || 2\31 < g < 3\46 || 3\46 < g < 4\61 || g || -15g+1 || | | | | 13g-6-(1-2g) = 15g-7 |
| | |- |
| | | | [[3L 12s]] |
| | | | 4\15 < g < 1\3 |
| | | | g = ''5\18'', 6\21, 7\24-8\27 |
| | | | 4g-1-(1\3-g) = 5g-4\3 |
| | |- |
| | | | [[4L 11s]] |
| | | | 11\15 < g < 3\4 |
| | | | g = 14\19, 17\23, 20\27-23\31 |
| | | | 11g-8-(3-4g) = 15g-11 |
| | |- |
| | | | [[5L 10s]] |
| | | | 2\15 < g < 1\5 |
| | | | g = 3\20, 4\25, 5\30-6\35 |
| | | | 2g-1\5-(1\5-g) = 3g-2\5 |
| | |- |
| | | | [[6L 9s]] |
| | | | 2\15 < g < 1\6 |
| | | | g = 3\21, 4\27, 5\33-6\39 |
| | | | 3g-1\3-(1\3-2g) = 5g-2\3 |
| | |- |
| | | | [[7L 8s]] |
| | | | 2\15 < g < 1\7 |
| | | | g = 3\22, 4\29, 5\36-6\43 |
| | | | 8g-1-(1-7g) = 15g-2 |
| | |- |
| | | | [[8L 7s]] |
| | | | 13\15 < g < 7\8 |
| | | | g = 20\23, 27\31, 34\39-41\47 |
| | | | 7g-6-(7-8g) = 15g-13 |
| | |- |
| | | | [[9L 6s]] |
| | | | 3\15 < g < 2\9 |
| | | | g = 5\24, 7\33, 9\42-11\51 |
| | | | 2g-1\3-(2\3-3g) = 5g-1 |
| | |- |
| | | | [[10L 5s|''10L 5s'']] ''= 2L 1s (5)'' |
| | | | ''1\15 < g < 1\10'' |
| | | | ''g = 2\25, 3\35, 4\45-5\55'' |
| | | | ''g-(1\5-2g) = 3g-1\5'' |
| | |- |
| | | | [[11L 4s]] |
| | | | 4\15 < g < 3\11 |
| | | | g = 7\26, 10\37, 13\48-16\59 |
| | | | 4g-1-(3-11g) = 15g-4 |
| | |- |
| | | | [[12L 3s|''12L 3s'']] ''= 4L 1s (3)'' |
| | | | ''1\15 < g < 1\12'' |
| | | | ''g = 2\27, 3\39, 4\51-5\63'' |
| | | | ''g-(1\3-4g) = 5g-1\3'' |
| | |- |
| | | | [[13L 2s]] |
| | | | 8\15 < g < 7\13 |
| | | | g = 15\28, 22\41, 29\54-36\67 |
| | | | 2g-1-(7-13g) = 15g-8 |
| | |- |
| | | | [[14L 1s|''14L 1s'']] |
| | | | ''1\15 < g < 1\14'' |
| | | | ''g = 2\29, 3\43, 4\57-5\71'' |
| | | | ''g-(1-14g) = 15g-1'' |
| | |} |
|
| |
|
| =17= | | == 16-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ Midpoint ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L16s || 16\17 < g < 1 || g = 33\34 || 16\17 < g < 17\18 || 17\18 < g < 18\19 || 18\19 < g < 19\20 || -15+16g || -g+1 || | | |- |
| || 2L15s || 8\17 < g < 1\2 || g = 33\68 || 8\17 < g < 9\19 || 9\19 < g < 10\21 || 10\21 < g < 11\23 || -7+15g || -2g+1 || | | ! | L-s pattern |
| || 3L14s || 11\17 < g < 2\3 || g = 67\102 || 11\17 < g < 13\20 || 13\20 < g < 15\23 || 15\23 < g < 17\26 || -9+14g || -3g+2 || | | ! | Generator range |
| || 4L13s || 4\17 < g < 1\4 || g = 33\136 || 4\17 < g < 5\21 || 5\21 < g < 6\25 || 6\25 < g < 7\29 || -3+13g || -4g+1 || | | ! | Boundaries of best, better, good behavior |
| || 5L12s || 10\17 < g < 3\5 || g = 101\170 || 10\17 < g < 13\22 || 13\22 < g < 16\27 || 16\27 < g < 19\32 || -7+12g || -5g+3 || | | ! | Large step-Small step |
| || 6L11s || 14\17 < g < 5\6 || g = 169\204 || 14\17 < g < 19\23 || 19\23 < g < 24\29 || 24\29 < g < 29\35 || -9+11g || -6g+5 || | | |- |
| || 7L10s || 12\17 < g < 5\7 || g = 169\238 || 12\17 < g < 17\24 || 17\24 < g < 22\31 || 22\31 < g < 27\38 || -7+10g || -7g+5 || | | | | [[1L 15s]] |
| || 8L9s || 2\17 < g < 1\8 || g = 33\272 || 2\17 < g < 3\25 || 3\25 < g < 4\33 || 4\33 < g < 5\41 || -1+9g || -8g+1 || | | | | 15\16 < g < 1 |
| || 9L8s || 15\17 < g < 8\9 || g = 271\306 || 15\17 < g < 23\26 || 23\26 < g < 31\35 || 31\35 < g < 39\44 || -7+8g || -9g+8 || | | | | g = ''16\17, 17\18, 18\19-19\20'' |
| || 10L7s || 5\17 < g < 3\10 || g = 101\340 || 5\17 < g < 8\27 || 8\27 < g < 11\37 || 11\37 < g < 14\47 || -2+7g || -10g+3 || | | | | 15g-14-(1-g) = 16g-15 |
| || 11L6s || 3\17 < g < 2\11 || g = 67\374 || 3\17 < g < 5\28 || 5\28 < g < 7\39 || 7\39 < g < 9\50 || -1+6g || -11g+2 || | | |- |
| || 12L5s || 7\17 < g < 5\12 || g = 169\408 || 7\17 < g < 12\29 || 12\29 < g < 17\41 || 17\41 < g < 22\53 || -2+5g || -12g+5 || | | | | [[2L 14s]] |
| || 13L4s || 13\17 < g < 10\13 || g = 339\442 || 13\17 < g < 23\30 || 23\30 < g < 33\43 || 33\43 < g < 43\56 || -3+4g || -13g+10 || | | | | 7\16 < g < 1\2 |
| || 14L3s || 6\17 < g < 5\14 || g = 169\476 || 6\17 < g < 11\31 || 11\31 < g < 16\45 || 16\45 < g < 21\59 || -1+3g || -14g+5 || | | | | g = ''8\18, 9\20'', 10\22-11\24 |
| || 15L2s || 9\17 < g < 8\15 || g = 271\510 || 9\17 < g < 17\32 || 17\32 < g < 25\47 || 25\47 < g < 33\62 || -1+2g || -15g+8 ||
| | | | 7g-3-(1\2-g) = 8g-7\2 |
| || 16L1s || 1\17 < g < 1\16 || g = 33\544 || 1\17 < g < 2\33 || 2\33 < g < 3\49 || 3\49 < g < 4\65 || g || -16g+1 || | | |- |
| | | | [[3L 13s]] |
| | | | 5\16 < g < 1\3 |
| | | | g = ''6\19'', 7\22, 8\25-9\28 |
| | | | 13g-4-(1-3g) = 16g-5 |
| | |- |
| | | | [[4L 12s]] |
| | | | 3\16 < g < 1\4 |
| | | | g = ''4\20'', 5\24, 6\28-7\32 |
| | | | 3g-1\2-(1\4-g) = 4g-3\4 |
| | |- |
| | | | [[5L 11s]] |
| | | | 3\16 < g < 1\5 |
| | | | g = 4\21, 5\26, 6\31-7\36 |
| | | | 11g-2-(1-5g) = 16g-3 |
| | |- |
| | | | [[6L 10s]] |
| | | | 5\16 < g < 2\6 |
| | | | g = 7\22, 9\28, 11\34-13\40 |
| | | | 5g-3\2-(1-3g) = 8g-5\2 |
| | |- |
| | | | [[7L 9s]] |
| | | | 9\16 < g < 4\7 |
| | | | g = 13\23, 17\30, 21\37-25\44 |
| | | | 9g-5-(4-7g) = 16g-9 |
| | |- |
| | | | [[8L 8s|''8L 8s'']] = ''1L 1s (8)'' |
| | | | ''1\16 < g < 1\8'' |
| | | | ''g = 2\24, 3\32, 4\40-5\48'' |
| | | | ''g-(1\8-g) = 2g-1\8'' |
| | |- |
| | | | [[9L 7s]] |
| | | | 7\16 < g < 4\9 |
| | | | g = 11\25, 15\34, 19\43-23\52 |
| | | | 7g-3-(4-9g) = 16g-7 |
| | |- |
| | | | [[10L 6s]] |
| | | | 3\16 < g < 2\10 |
| | | | g = 5\26, 7\36, 9\46-11\56 |
| | | | 3g-1\2-(1-5g) = 8g-3\2 |
| | |- |
| | | | [[11L 5s]] |
| | | | 13\16 < g < 9\11 |
| | | | g = 22\27, 31\38, 40\49-49\60 |
| | | | 5g-4-(9-11g) = 16g-13 |
| | |- |
| | | | [[12L 4s|''12L 4s'']] ''= 3L 1s (4)'' |
| | | | ''1\16 < g < 1\12'' |
| | | | ''g = 2\28, 3\40, 4\52-5\64'' |
| | | | ''g-(1\4-3g) = 4g-1\4'' |
| | |- |
| | | | [[13L 3s]] |
| | | | 11\16 < g < 9\13 |
| | | | g = 20\29, 29\42, 38\55-47\68 |
| | | | 3g-2-(9-13g) = 16g-11 |
| | |- |
| | | | [[14L 2s|''14L 2s'']] ''= 7L 1s (2)'' |
| | | | ''1\16 < g < 1\14'' |
| | | | ''g = 2\30, 3\44, 4\58-5\72'' |
| | | | ''g-(1\2-7g) = 8g-1\2'' |
| | |- |
| | | | [[15L 1s|''15L 1s'']] |
| | | | ''1\16 < g < 1\15'' |
| | | | ''g = 2\31, 3\46, 4\61-5\76'' |
| | | | ''g-(1-15g) = 16g-1'' |
| | |} |
|
| |
|
| =18= | | == 17-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L17s || 17\18 < g < 1 || g = 35\36 || 17\18 < g < 18\19 || 18\19 < g < 19\20 || 19\20 < g < 20\21 || -16+17g || -g+1 || | | |- |
| || 2L16s || 8\18 < g < 1\2 || g = 17\36 || 8\18 < g < 9\20 || 9\20 < g < 10\22 || 10\22 < g < 11\24 || -7\2+8g || -g+1\2 ||
| | ! | L-s pattern |
| || 3L15s || 5\18 < g < 1\3 || g = 11\36 || 5\18 < g < 6\21 || 6\21 < g < 7\24 || 7\24 < g < 8\27 || -4\3+5g || -g+1\3 || | | ! | Generator range |
| || 4L14s || <span style="line-height: 15.6000003814697px;">4\18 < g < 1\4</span> || g = 17\72 || <span style="line-height: 15.6000003814697px;">4\18 < g < 5\22</span> || <span style="line-height: 15.6000003814697px;">5\22 < g < 6\26</span> || 6\26 < g < 7\30 || -3\2+7g || -2g+1\2 || | | ! | Boundaries of best, better, good behavior |
| || 5L13s || 7\18 < g < 2\5 || g = 71\180 || 7\18 < g < 9\23 || 9\23 < g < 11\28 || 11\28 < g < 13\33 || -5+13g || -5g+2 || | | ! | Large step-Small step |
| || 6L12s || 2\18 < g < 1\6 || g = 5\36 || 2\18 < g < 3\24 || 3\24 < g < 4\30 || 4\30 < g < 5\36 || -1\6+2g || -g+1\6 || | | |- |
| || 7L11s || 5\18 < g < 2\7 || g = 71\252 || 5\18 < g < 7\25 || 7\25 < g < 9\32 || 9\32 < g < 11\39 || -3+11g || -7g+2 || | | | | [[1L 16s]] |
| || 8L10s || 2\18 < g < 1\8 || g = 17\144 || 2\18 < g < 3\26 || 3\26 < g < 4\34 || 4\34 < g < 5\42 || -1\2+5g || -4g+1\2 || | | | | 16\17 < g < 1 |
| || 9L9s || 1\18 < g < 1\9 || g = 3\36 || 1\18 < g < 2\27 || 2\27 < g < 3\36 || 3\36 < g < 4\45 || g || -g+1\9 || | | | | g = ''17\18, 18\19, 19\20-20\21'' |
| || 10L8s || 7\18 < g < 4\10 || g = 71\180 || 7\18 < g < 11\28 || 11\28 < g < 15\38 || 15\38 < g < 19\43 || -3\2+4g || -5g+2 || | | | | 16g-15-(1-g) = 17g-16 |
| || 11L7s || 13\18 < g < 8\11 || g = 287\396 || 13\18 < g < 21\29 || 21\29 < g < 29\40 || 29\40 < g < 37\51 || -5+7g || -11g+8 || | | |- |
| || 12L6s || 1\18 < g < 1\12 || g = 5\72 || 1\18 < g < 2\30 || 2\30 < g < 3\42 || 3\42 < g < 4\54 || g || -2g+1\6 || | | | | [[2L 15s]] |
| || 13L5s || 11\18 < g < 8\13 || g = 287\468 || 11\18 < g < 19\31 || 19\31 < g < 27\44 || 27\44 < g < 35\57 || -3+5g || -13g+8 || | | | | 8\17 < g < 1\2 |
| || 14L4s || 5\18 < g < 4\14 || g = 71\252 || 5\18 < g < 9\32 || 9\32 < g < 13\46 || 13\46 < g < 17\60 || -1\2+2g || -7g+2 || | | | | g = ''9\19'', ''10\21'', 11\23-13\25 |
| || 15L3s || 1\18 < g < 1\15 || g = 11\180 || 1\18 < g < 2\33 || 2\33 < g < 3\48 || 3\48 < g < 4\63 || g || -5g+1\3 || | | | | 15g-7-(1-2g) = 17g-8 |
| || 16L2s || 1\18 < g < 1\16 || g = 17\288 || 1\18 < g < 2\34 || 2\34 < g < 3\50 || 3\50 < g < 4\66 || g || -8g+1\2 || | | |- |
| || 17L1s || 1\18 < g < 1\17 || g = 35\618 || 1\18 < g < 2\35 || 2\35 < g < 3\52 || 3\52 < g < 4\69 || g || -17g+1 || | | | | [[3L 14s]] |
| | | | 11\17 < g < 2\3 |
| | | | g = ''13\20'', 15\23, 17\26-19\29 |
| | | | 14g-9-(2-3g) = 17g-11 |
| | |- |
| | | | [[4L 13s]] |
| | | | 4\17 < g < 1\4 |
| | | | g = ''5\21'', 6\25, 7\29-8\33 |
| | | | 13g-3-(1-4g) = 17g-4 |
| | |- |
| | | | [[5L 12s]] |
| | | | 10\17 < g < 3\5 |
| | | | g = 13\22, 16\27, 19\32-22\37 |
| | | | 12g-7-(3-5g) = 17g-10 |
| | |- |
| | | | [[6L 11s]] |
| | | | 14\17 < g < 5\6 |
| | | | g = 19\23, 24\29, 29\35-34\41 |
| | | | 11g-9-(5-6g) = 17g-14 |
| | |- |
| | | | [[7L 10s]] |
| | | | 12\17 < g < 5\7 |
| | | | g = 17\24, 22\31, 27\38-32\45 |
| | | | 10g-7-(5-7g) = 17g-12 |
| | |- |
| | | | [[8L 9s]] |
| | | | 2\17 < g < 1\8 |
| | | | g = 3\25, 4\33, 5\41-6\49 |
| | | | 9g-1-(1-8g) = 17g-2 |
| | |- |
| | | | [[9L 8s]] |
| | | | 15\17 < g < 8\9 |
| | | | g = 23\26, 31\35, 39\44-47\53 |
| | | | 8g-7-(8-9g) = 17g-15 |
| | |- |
| | | | [[10L 7s]] |
| | | | 5\17 < g < 3\10 |
| | | | g = 8\27, 11\37, 14\47-17\57 |
| | | | 7g-2-(3-10g) = 17g-5 |
| | |- |
| | | | [[11L 6s]] |
| | | | 3\17 < g < 2\11 |
| | | | g = 5\28, 7\39, 9\50-11\61 |
| | | | 6g-1-(2-11g) = 17g-3 |
| | |- |
| | | | [[12L 5s]] |
| | | | 7\17 < g < 5\12 |
| | | | g = 12\29, 17\41, 22\53-27\65 |
| | | | 5g-2-(5-12g) = 17g-7 |
| | |- |
| | | | [[13L 4s]] |
| | | | 13\17 < g < 10\13 |
| | | | g = 23\30, 33\43, 43\56-53\69 |
| | | | 4g-3-(10-13g) = 17g-13 |
| | |- |
| | | | [[14L 3s]] |
| | | | 6\17 < g < 5\14 |
| | | | g = 11\31, 16\45, 21\59-26\73 |
| | | | 3g-1-(5-14g) = 17g-6 |
| | |- |
| | | | [[15L 2s]] |
| | | | 9\17 < g < 8\15 |
| | | | g = 17\32, 25\47, 33\62-41\77 |
| | | | 2g-1-(8-15g) = 17g-9 |
| | |- |
| | | | [[16L 1s|''16L 1s'']] |
| | | | ''1\17 < g < 1\16'' |
| | | | ''g = 2\33, 3\49, 4\65-5\81'' |
| | | | ''g-(1-16g) = 17g-1'' |
| | |} |
|
| |
|
| =19= | | == 18-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L18s || 18\19 < g < 1 || g = 37\38 || 18\19 < g < 19\20 || 19\20 < g < 20\21 || 20\21 < g < 21\22 || -17+18g || -g+1 || | | |- |
| || 2L17s || 9\19 < g < 1\2 || g = 37\76 || 9\19 < g < 10\21 || 10\21 < g < 11\23 || 11\23 < g < 12\25 || -8+17g || -2g+1 || | | ! | L-s pattern |
| || 3L16s || 6\19 < g < 1\3 || g = 37\114 || 6\19 < g < 7\22 || 7\22 < g < 8\25 || 9\28 < g < 10\31 || -5+16g || 1-3g || | | ! | Generator range |
| || 4L15s || 14\19 < g < 3\4 || g = 113\152 || 14\19 < g < 17\23 || 17\23 < g < 20\27 || 20\27 < g < 23\31 || -11+15g || -4g+3 || | | ! | Boundaries of best, better, good behavior |
| || 5L14s || 15\19 < g < 4\5 || g = 151\190 || 15\19 < g < 19\24 || 19\24 < g < 23\29 || 23\29 < g < 27\34 || -11+14g || -5g+4 || | | ! | Large step-Small step |
| || 6L13s || 3\19 < g < 1\6 || g = 37\228 || 3\19 < g < 4\25 || 4\25 < g < 5\31 || 5\31 < g < 6/37 || -2+13g || -6g+1 || | | |- |
| || 7L12s || 8\19 < g < 3\7 || g = 113\266 || 8\19 < g < 11\26 || 11\26 < g < 14\33 || 14\33 < g < 17\40 || -5+12g || -7g+3 || | | | | [[1L 17s]] |
| || 8L11s || 7\19 < g < 3\8 || g = 113\304 || 7\19 < g < 10\27 || 10\27 < g < 13\35 || 13\35 < g < 16\43 || -4+11g || -8g+3 || | | | | 17\18 < g < 1 |
| || 9L10s || 2\19 < g < 1\9 || g = 37\342 || 2\19 < g < 3\28 || 3\28 < g < 4\37 || 4\37 < g < 5\46 || -1+10g || -9g+1 || | | | | g = ''18\19, 19\20, 20\21-21\22'' |
| || 10L9s || 17\19 < g < 9\10 || g = 341\380 || 17\19 < g < 26\29 || 26\29 < g < 35\39 || 35\39 < g < 44\49 || -8+9g || -10g+9 || | | | | 17g-16-(1-g) = 18g-17 |
| || 11L8s || 12\19 < g < 7\11 || g = 265\418 || 12\19 < g < 19\30 || 19\30 < g < 26\41 || 26\41 < g < 33\52 || -5+8g || -11g+7 || | | |- |
| || 12L7s || 11\19 < g < 7\12 || g = 265\456 || 11\19 < g < 18\31 || 18\31 < g < 25\43 || 25\43 < g < 32\55 || -4+7g || -12g+7 || | | | | [[2L 16s]] |
| || 13L6s || 16\19 < g < 11\13 || g = 417\494 || 16\19 < g < 27\32 || 27\32 < g < 38\45 || 38\45 < g < 49\58 || -5+6g || -13g+11 || | | | | 8\18 < g < 1\2 |
| || 14L5s || 4\19 < g < 3\14 || g = 113\532 || 4\19 < g < 7\33 || 7\33 < g < 10\47 || 10\47 < g < 13\61 || -1+5g || -14g+3 || | | | | g = ''9\20'', ''10\22'', 11\24-12\26 |
| || 15L4s || 5\19 < g < 4\15 || g = 151\570 || 5\19 < g < 9\34 || 9\34 < g < 13\49 || 13\49 < g < 17\64 || -1+4g || -15g+4 || | | | | 8g-7\2-(1\2-g) = 9g-4 |
| || 16L3s || 13\19 < g < 11\16 || g = 417\608 || 13\19 < g < 24\35 || 24\35 < g < 35\51 || 35\51 < g < 46\67 || -2+3g || -16g+11 || | | |- |
| || 17L2s || 10\19 < g < 9\17 || g = 341\646 || 10\19 < g < 19\36 || 19\36 < g < 28\53 || 28\53 < g < 37\70 || -1+2g || -17g+9 ||
| | | | [[3L 15s]] |
| || 18L1s || 1\19 < g < 1\18 || g = 37\684 || 1\19 < g < 2\37 || 2\37 < g < 3\55 || 3\55 < g < || g || -18g+1 || | | | | 5\18 < g < 1\3 |
| | | | g = ''6\21'', 7\24, 8\27-9\30 |
| | | | 5g-4\3-(1\3-g) = 6g-5\3 |
| | |- |
| | | | [[4L 14s]] |
| | | | 4\18 < g < 1\4 |
| | | | g = ''5\22'', 6\26, 7\30-8\34 |
| | | | 7g-3\2-(1\2-2g) = 9g-2 |
| | |- |
| | | | [[5L 13s]] |
| | | | 7\18 < g < 2\5 |
| | | | g = 9\23, 11\28, 13\33-15\38 |
| | | | 13g-5-(2-5g) = 18g-7 |
| | |- |
| | | | [[6L 12s]] |
| | | | 2\18 < g < 1\6 |
| | | | g = 3\24, 4\30, 5\36-6\42 |
| | | | 2g-1\6-(1\6-g) = 3g-1\3 |
| | |- |
| | | | [[7L 11s]] |
| | | | 5\18 < g < 2\7 |
| | | | g = 7\25, 9\32, 11\39-13\46 |
| | | | 11g-3-(2-7g) = 18g-5 |
| | |- |
| | | | [[8L 10s]] |
| | | | 2\18 < g < 1\8 |
| | | | g = 3\26, 4\34, 5\42-6\50 |
| | | | 5g-1\2-(1\2-4g) = 9g-1 |
| | |- |
| | | | [[9L 9s|''9L 9s'']] ''= 1L 1s (9)'' |
| | | | ''1\18 < g < 1\9'' |
| | | | ''g = 2\27, 3\36, 4\45-5\54'' |
| | | | ''g-(1\9-g) = 2g-1\9'' |
| | |- |
| | | | [[10L 8s]] |
| | | | 7\18 < g < 4\10 |
| | | | g = 11\28, 15\38, 19\48-23\58 |
| | | | 4g-3\2-(2-5g) = 9g-7\2 |
| | |- |
| | | | [[11L 7s]] |
| | | | 13\18 < g < 8\11 |
| | | | g = 21\29, 29\40, 37\51-45\62 |
| | | | 7g-5-(8-11g) = 18g-13 |
| | |- |
| | | | [[12L 6s|''12L 6s'']] ''= 2L 1s (6)'' |
| | | | ''1\18 < g < 1\12'' |
| | | | ''g = 2\30, 3\42, 4\54-5\66'' |
| | | | ''g-(1\6-2g) = 3g-1\6'' |
| | |- |
| | | | [[13L 5s]] |
| | | | 11\18 < g < 8\13 |
| | | | g = 19\31, 27\44, 35\57-43\70 |
| | | | 5g-3-(8-13g) = 18g-11 |
| | |- |
| | | | [[14L 4s]] |
| | | | 5\18 < g < 4\14 |
| | | | g = 9\32, 13\46, 17\60-21\74 |
| | | | 2g-1\2-(2-7g) = 9g-5\2 |
| | |- |
| | | | [[15L 3s|''15L 3s'']] ''= 5L 1s (3)'' |
| | | | ''1\18 < g < 1\15'' |
| | | | ''g = 2\33, 3\48, 4\63-5\78'' |
| | | | ''g-(1\3-5g) = 6g-1\3'' |
| | |- |
| | | | [[16L 2s|''16L 2s'']] ''= 8L 1s (2)'' |
| | | | ''1\18 < g < 1\16'' |
| | | | ''g = 2\34, 3\50, 4\66-5\82'' |
| | | | ''g-(1\2-8g) = 9g-1\2'' |
| | |- |
| | | | [[17L 1s|''17L 1s'']] |
| | | | ''1\18 < g < 1\17'' |
| | | | ''g = 2\35, 3\52, 4\69-5\86'' |
| | | | ''g-(1-17g) = 18g-1'' |
| | |} |
|
| |
|
| =20= | | == 19-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L19s || 19\20 < g < 1 || g = 39\40 || 19\20 < g < 20\21 || 20\21 < g < 21\22 || 21\22 < g < 22\23 || -18+19g || -g+1 || | | |- |
| || 2L18s || 9\20 < g < 1\2 || g = 19\40 || 9\20 < g < 10\22 || 10\22 < g < 11\24 || 11\24 < g < 12\26 || -4+9g || -g+1\2 ||
| | ! | L-s pattern |
| || 3L17s || 13\20 < g < 2\3 || g = 79\120 || 13\20 < g < 15\23 || 15\23 < g < 17\26 || 17\26 < g < 20\29 || -11+17g || -3g+2 || | | ! | Generator range |
| || 4L16s || 4\20 < g < 1\4 || g = 9\40 || 4\20 < g < 5\24 || 5\24 < g < 6\28 || 6\28 < g < 7\32 || -3\4+4g || -g+1\4 || | | ! | Boundaries of best, better, good behavior |
| || 5L15s || 3\20 < g < 1\5 || g = 7\40 || 3\20 < g < 4\25 || 4\25 < g < 5\30 || 5\30 < g < 6\35 || -2\5+3g || -g+1\5 || | | ! | Large step-Small step |
| || 6L14s || 3\20 < g < 1\6 || g = 19\120 || 3\20 < g < 4\26 || 4\26 < g < 5\32 || 5\32 < g < 6\38 || -1+7g || -3g+1\2 ||
| | |- |
| || 7L13s || 17\20 < g < 6\7 || g = 239\280 || 17\20 < g < 23\27 || 23\27 < g < 29\34 || 29\34 < g < 35\41 || -11+13g || -7g+6 || | | | | [[1L 18s]] |
| || 8L12s || 2\20 < g < 1\8 || g = 9\80 || 2\20 < g < 3\28 || 3\28 < g < 4\36 || 4\36 < g < 5\44 || -1\4+3g || -2g+1\4 || | | | | 18\19 < g < 1 |
| || 9L11s || 11\20 < g < 5\9 || g = 199\360 || 11\20 < g < 16\29 || 16\29 < g < 21\38 || 21\38 < g < 26\47 || -6+11g || -9g+5 || | | | | g = ''19\20, 20\21, 21\22-22\23'' |
| || 10L10s || 1\20 < g < 1\10 || g = 3\40 || 1\20 < g < 2\30 || 2\30 < g < 3\40 || 3\40 < g < 4\50 || g || -g+1\10 || | | | | 18g-17-(1-g) = 19g-18 |
| || 11L9s || 9\20 < g < 5\11 || g = 199\440 || 9\20 < g < 14\31 || 14\31 < g < 19\42 || 19\42 < g < 24\53 || -4+9g || -11g+5 || | | |- |
| || 12L8s || 3\20 < g < 2\12 || g = 19\120 || 3\20 < g < 5\32 || 5\32 < g < 7\44 || 7\44 < g < 9\56 || -1\4+2g || -3g+1\2 || | | | | [[2L 17s]] |
| || 13L7s || 3\20 < g < 2\13 || g = 79\520 || 3\20 < g < 5\33 || 5\33 < g < 7\46 || 7\46 < g < 9\59 || -1+7g || -13g+2 || | | | | 9\19 < g < 1\2 |
| || 14L6s || 7\20 < g < 5\14 || g = 99\280 || 7\20 < g < 12\34 || 12\34 < g < 17\48 || 17\48 < g < 22\62 || -1+3g || -7g+5\2 || | | | | g = ''10\21'', ''11\23'', 12\25-13\27 |
| || 15L5s || 1\20 < g < 1\15 || g = 7\120 || 1\20 < g < 2\35 || 2\35 < g < 3\50 || 3\50 < g < 4\65 || g || -3g+1\5 || | | | | 17g-8-(1-2g) = 19g-9 |
| || 16L4s || 1\20 < g < 1\16 || g = 9\160 || 1\20 < g < 2\36 || 2\36 < g < 3\52 || 3\52 < g < 4\68 || g || -4g+1\4 || | | |- |
| || 17L3s || 7\20 < g < 6\17 || g = 239\680 || 7\20 < g < 13\37 || 13\37 < g < 19\54 || 19\54 < g < 25\71 || -1+3g || -17g+6 || | | | | [[3L 16s]] |
| || 18L2s || 1\20 < g < 1\18 || g = 19\360 || 1\20 < g < 2\38 || 2\38 < g < 3\56 || 3\56 < g < 4\74 || g || -9g+1\2 || | | | | 6\19 < g < 1\3 |
| || 19L1s || 1\20 < g < 1\19 || g = 39\760 || 1\20 < g < 2\39 || 2\39 < g < 3\58 || 3\58 < g < 4\77 || g || -19g+1 || | | | | g = ''7\22'', 8\25, 9\28-10\31 |
| | | | 16g-5-(1-3g) = 19g-6 |
| | |- |
| | | | [[4L 15s]] |
| | | | 14\19 < g < 3\4 |
| | | | g = ''17\23'', 20\27, 23\31-27\35 |
| | | | 15g-11-(3-4g) = 19g-14 |
| | |- |
| | | | [[5L 14s]] |
| | | | 15\19 < g < 4\5 |
| | | | g = 19\24, 23\29, 27\34-31\39 |
| | | | 14g-11-(4-5g) = 19g-15 |
| | |- |
| | | | [[6L 13s]] |
| | | | 3\19 < g < 1\6 |
| | | | g = 4\25, 5\31, 6\37-7\43 |
| | | | 13g-2-(1-6g) = 19g-3 |
| | |- |
| | | | [[7L 12s]] |
| | | | 8\19 < g < 3\7 |
| | | | g = 11\26, 14\33, 17\40-20\47 |
| | | | 12g-5-(3-7g) = 19g-8 |
| | |- |
| | | | [[8L 11s]] |
| | | | 7\19 < g < 3\8 |
| | | | g = 10\27, 13\35, 16\43-19\51 |
| | | | 11g-4-(3-8g) = 19g-7 |
| | |- |
| | | | [[9L 10s]] |
| | | | 2\19 < g < 1\9 |
| | | | g = 3\28, 4\37, 5\46-6\55 |
| | | | 10g-1-(1-9g) = 19g-2 |
| | |- |
| | | | [[10L 9s]] |
| | | | 17\19 < g < 9\10 |
| | | | g = 26\29, 35\39, 44\49-53\59 |
| | | | 9g-8-(9-10g) = 19g-17 |
| | |- |
| | | | [[11L 8s]] |
| | | | 12\19 < g < 7\11 |
| | | | g = 19\30, 26\41, 33\52-40\63 |
| | | | 8g-5-(7-11g) = 19g-12 |
| | |- |
| | | | [[12L 7s]] |
| | | | 11\19 < g < 7\12 |
| | | | g = 18\31, 25\43, 32\55-39\67 |
| | | | 7g-4-(7-12g) = 19g-11 |
| | |- |
| | | | [[13L 6s]] |
| | | | 16\19 < g < 11\13 |
| | | | g = 27\32, 38\45, 49\58-60\71 |
| | | | 6g-5-(11-13g) = 19g-16 |
| | |- |
| | | | [[14L 5s]] |
| | | | 4\19 < g < 3\14 |
| | | | g = 7\33, 10\47, 13\61-16\75 |
| | | | 5g-1-(3-14g) = 19g-4 |
| | |- |
| | | | [[15L 4s]] |
| | | | 5\19 < g < 4\15 |
| | | | g = 9\34, 13\49, 17\64-21\79 |
| | | | 4g-1-(4-15g) = 19g-5 |
| | |- |
| | | | [[16L 3s]] |
| | | | 13\19 < g < 11\16 |
| | | | g = 24\35, 35\51, 46\67-57\83 |
| | | | 3g-2-(11-16g) = 19g-13 |
| | |- |
| | | | [[17L 2s]] |
| | | | 10\19 < g < 9\17 |
| | | | g = 19\36, 28\53, 37\70-46\87 |
| | | | 2g-1-(9-17g) = 19g-10 |
| | |- |
| | | | [[18L 1s|''18L 1s'']] |
| | | | ''1\19 < g < 1\18'' |
| | | | ''g = 2\37, 3\55, 4\73-5\91'' |
| | | | ''g-(1-18g) = 19g-1'' |
| | |} |
|
| |
|
| =21= | | == 20-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L20s || 20\21 < g < 1 || g = 41\42 || 20\21 < g < 21\22 || 21\22 < g < 22\23 || 22\23 < g < 23\24 || -19+20g || -g+1 || | | |- |
| || 2L19s || 10\21 < g < 1\2 || g = 41\84 || 10\21 < g < 11\23 || 11\23 < g < 12\25 || 12\25 < g < 13\27 || -9+19g || -2g+1 || | | ! | L-s pattern |
| || 3L18s || 6\21 < g < 1\3 || g = 13\42 || 6\21 < g < 7\24 || 7\24 < g < 8\27 || 8\27 < g < 9\30 || -5\3+6g || -g+1\3 || | | ! | Generator range |
| || 4L17s || 5\21 < g < 1\4 || g = 41\168 || 5\21 < g < 6\25 || 6\25 < g < 7\29 || 7\29 < g < 8\33 || -4+17g || -4g+1 || | | ! | Boundaries of best, better, good behavior |
| || 5L16s || 4\21 < g < 1\5 || g = 41\210 || 4\21 < g < 5\26 || 5\26 < g < 6\31 || 6\31 < g < 7\37 || -3+16g || -5g+1 || | | ! | Large step-Small step |
| || 6L15s || 3\21 < g < 1\6 || g = 13\84 || 3\21 < g < 4\27 || 4\27 < g < 5\33 || 5\33 < g < 6\39 || -2\3+5g || -2g+1\3 ||
| | |- |
| || 7L14s || 2\21 < g < 1\7 || g = 5\42 || 2\21 < g < 3\28 || 3\28 < g < 4\35 || 4\35 < g < 5\42 || -1\7+2g || -g+1\7 || | | | | [[1L 19s]] |
| || 8L13s || 13\21 < g < 5\8 || g = 209\336 || 13\21 < g < 18\29 || 18\29 < g < 23\37 || 23\37 < g < 28\45 || -8+13g || -8g+5 || | | | | 19\20 < g < 1 |
| || 9L12s || 2\21 < g < 1\9 || g = 13\126 || 2\21 < g < 3\30 || 3\30 < g < 4\39 || 4\39 < g < 5\48 || -1\3+4g || -3g+1\3 || | | | | g = ''20\21, 21\22, 22\23-23\24'' |
| || 10L11s || 2\21 < g < 1\10 || g = 41\420 || 2\21 < g < 3\31 || 3\31 < g < 4\41 || 4\41 < g < 5\51 || -1+11g || -10g+1 || | | | | 19g-18-(1-g) = 20g-19 |
| || 11L10s || 19\21 < g < 10\11 || g = 419\462 || 19\21 < g < 29\32 || 29\32 < g < 39\43 || 39\43 < g < 49\54 || -9+10g || -11g+10 || | | |- |
| || 12L9s || 5\21 < g < 3\12 || g = 41\168 || 5\21 < g < 8\33 || 8\33 < g < 11\45 || 11\45 < g < 14\57 || -2\3+3g || -4g+1 || | | | | [[2L 18s]] |
| || 13L8s || 8\21 < g < 5\13 || g = 209\546 || 8\21 < g < 13\34 || 13\34 < g < 18\47 || 18\47 < g < 23\70 || -3+8g || -13g+5 || | | | | 9\20 < g < 1\2 |
| || 14L7s || 1\21 < g < 1\14 || g = 5\84 || 1\21 < g < 2\35 || 2\35 < g < 3\49 || 3\49 < g < 4\63 || g || -2g+1\7 || | | | | g = ''10\22'', ''11\24'', 12\26-13\28 |
| || 15L6s || 4\21 < g < 3\15 || g = 41\210 || 4\21 < g < 7\36 || 7\36 < g < 10\51 || 10\51 < g < 13\66 || -1\3+2g || -5g+1 || | | | | 9g-4-(1\2-g) = 10g-9\2 |
| || 16L5s || 17\21 < g < 13\16 || g = 545\672 || 17\21 < g < 30\37 || 30\37 < g < 43\53 || 43\53 < g < 56\69 || -4+5g || -16g+13 || | | |- |
| || 17L4s || 16\21 < g < 13\17 || g = 545\714 || 16\21 < g < 29\38 || 29\38 < g < 42\55 || 42\55 < g < 55\72 || -3+4g || -17g+13 || | | | | [[3L 17s]] |
| || 18L3s || 1\21 < g < 1\18 || g = 13\252 || 1\21 < g < 2\39 || 2\39 < g < 3\57 || 3\57 < g < 4\75 || g || -6g+1\3 || | | | | 13\20 < g < 2\3 |
| || 19L2s || 11\21 < g < 10\19 || g = 419\798 || 11\21 < g < 21\40 || 21\40 < g < 31\59 || 31\59 < g < 41\78 || -1+2g || -19g+10 || | | | | g = ''15\23'', 17\26, 19\29-21\32 |
| || 20L1s || 1\21 < g < 1\20 || g = 41\840 || 1\21 < g < 2\41 || 2\41 < g < 3\61 || 3\61 < g < 4/81 || g || -20g+1 || | | | | 17g-11-(2-3g) = 20g-13 |
| | |- |
| | | | [[4L 16s]] |
| | | | 4\20 < g < 1\4 |
| | | | g = ''5\24'', 6\28, 7\32-8\36 |
| | | | 4g-3\4-(1\4-g) = 5g-1 |
| | |- |
| | | | [[5L 15s]] |
| | | | 3\20 < g < 1\5 |
| | | | g = ''4\25'', 5\30, 6\35-7\40 |
| | | | 3g-2\5-(1\5-g) = 4g-3\5 |
| | |- |
| | | | [[6L 14s]] |
| | | | 3\20 < g < 1\6 |
| | | | g = 4\26, 5\32, 6\38-7\44 |
| | | | 7g-1-(1\2-3g) = 10g-3\2 |
| | |- |
| | | | [[7L 13s]] |
| | | | 17\20 < g < 6\7 |
| | | | g = 23\27, 29\34, 35\41-41\48 |
| | | | 13g-11-(6-7g) = 20g-17 |
| | |- |
| | | | [[8L 12s]] |
| | | | 2\20 < g < 1\8 |
| | | | g = 3\28, 4\36, 5\44-6\52 |
| | | | 3g-1\4-(1\4-2g) = 5g-1\2 |
| | |- |
| | | | [[9L 11s]] |
| | | | 11\20 < g < 5\9 |
| | | | g = 16\29, 21\38, 26\47-31\56 |
| | | | 11g-6-(5-9g) = 20g-11 |
| | |- |
| | | | [[10L 10s|''10L 10s'']] ''= 1L 1s (10)'' |
| | | | ''1\20 < g < 1\10'' |
| | | | ''g = 2\30, 3\40, 4\50-5\60'' |
| | | | ''g-(1\10-g) = 2g-1\10'' |
| | |- |
| | | | [[11L 9s]] |
| | | | 9\20 < g < 5\11 |
| | | | g = 14\31, 19\42, 24\53-29\64 |
| | | | 9g-4-(5-11g) = 20g-9 |
| | |- |
| | | | [[12L 8s]] |
| | | | 3\20 < g < 2\12 |
| | | | g = 5\32, 7\44, 9\56-11\68 |
| | | | 2g-1\4-(1\2-3g) = 5g-3\4 |
| | |- |
| | | | [[13L 7s]] |
| | | | 3\20 < g < 2\13 |
| | | | g = 5\33, 7\46, 9\59-11\72 |
| | | | 7g-1-(2-13g) = 20g-3 |
| | |- |
| | | | [[14L 6s]] |
| | | | 7\20 < g < 5\14 |
| | | | g = 12\34, 17\48, 22\62-27\76 |
| | | | 3g-1-(5\2-7g) = 10g-7\2 |
| | |- |
| | | | [[15L 5s|''15L 5s'']] ''= 3L 1s (5)'' |
| | | | ''1\20 < g < 1\15'' |
| | | | ''g = 2\35, 3\50, 4\65-5\80'' |
| | | | ''g-(1\5-3g) = 4g-1\5'' |
| | |- |
| | | | [[16L 4s|''16L 4s'']] ''= 4L 1s (4)'' |
| | | | ''1\20 < g < 1\16'' |
| | | | ''g = 2\36, 3\52, 4\68-5\84'' |
| | | | ''g-(1\4-4g) = 5g-1\4'' |
| | |- |
| | | | [[17L 3s]] |
| | | | 7\20 < g < 6\17 |
| | | | g = 13\37, 19\54, 25\71-31\88 |
| | | | 3g-1-(6-17g) = 5-14g |
| | |- |
| | | | [[18L 2s|''18L 2s'']] ''= 9L 1s (2)'' |
| | | | ''1\20 < g < 1\18'' |
| | | | ''g = 2\38, 3\56, 4\74-5\92'' |
| | | | ''g-(1\2-9g) = 10g-1\2'' |
| | |- |
| | | | [[19L 1s|''19L 1s'']] |
| | | | ''1\20 < g < 1\19'' |
| | | | ''g = 2\39, 3\58, 4\77-5\96'' |
| | | | ''g-(1-19g) = 20g-1'' |
| | |} |
|
| |
|
| =22= | | == 21-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | '''Note: bolded generators from here below generate scales which are well temperaments''' |
| || 1L21s || 21\22 < g < 1 || g = 43\44 || 21\22 < g < 22\23 || 22\23 < g < 23\24 || 23\24 < g < 24/25 || -20+21g || -g+1 || | | {| class="wikitable" |
| || 2L20s || 10\22 < g < 1\2 || g = 21\44 || 10\22 < g < 11\24 || 11\24 < g < 12\26 || 12\26 < g < 13\28 || -9\2+10g || -g+1\2 ||
| | |- |
| || 3L19s || 7\22 < g < 1\3 || g = 43\132 || 7\22 < g < 8\25 || 8\25 < g < 9\28 || 9\28 < g < 10\31 || -6+19g || 1-3g || | | ! | L-s pattern |
| || 4L18s || 5\22 < g < 1\4 || g = 21\88 || 5\22 < g < 6\26 || 6\26 < g < 7\30 || 7\30 < g < 8\34 || -2+9g || -2g+1\2 || | | ! | Generator range |
| || 5L17s || 13\22 < g < 3\5 || g = 131\220 || 13\22 < g < 16\27 || 16\27 < g < 19\32 || 19\32 < g < 22\37 || -10+17g || -5g+3 || | | ! | Boundaries of best, better, good behavior |
| || 6L16s || 7\22 < g < 2\6 || g = 43\132 || 7\22 < g < 9\28 || 9\28 < g < 11\34 || 11\34 < g < 13\40 || -5\2+8g || 1-3g || | | ! | Large step-Small step |
| || 7L15s || 3\22 < g < 1\7 || g = 43\308 || 3\22 < g < 4\29 || 4\29 < g < 5\36 || 5\36 < g < 6\43 || -2+15g || -7g+1 || | | |- |
| || 8L14s || 8\22 < g < 3\8 || g = 65\176 || 8\22 < g < 11\30 || 11\30 < g < 14\38 || 14\38 < g < 17\46 || -5\2+7g || -4g+3\2 || | | | | [[1L 20s]] |
| || 9L13s || 17\22 < g < 7\9 || g = 307\396 || 17\22 < g < 24\31 || 24\31 < g < 31\40 || 31\40 < g < 38\49 || -10+13g || -9g+7 || | | | | 20\21 < g < 1 |
| || 10L12s || 2\22 < g < 1\10 || g = 21\220 || 2\22 < g < 3\32 || 3\32 < g < 4\42 || 4\42 < g < 5\52 || -1\2+6g || -5g+1\2 ||
| | | | g = ''21\22, 22\23, 23\24-24\25'' |
| || 11L11s || 1\22 < g < 1\11 || g = 3\44 || 1\22 < g < 2\33 || 2\33 < g < 3\44 || 3\44 < g < 4\55 || g || -g+1\11 || | | | | 20g-19-(1-g) = 21g-20 |
| || 12L10s || 9\22 < g < 5\12 || g = 109\264 || 9\22 < g < 14\34 || 14\34 < g < 19\46 || 19\46 < g < 24\58 || -2+5g || -6g+5\2 || | | |- |
| || 13L9s || 5\22 < g < 3\13 || g = 131\572 || 5\22 < g < 8\35 || 8\35 < g < 11\48 || 11\48 < g < 14\61 || -2+9g || -13g+3 || | | | | [[2L 19s]] |
| || 14L8s || 3\22 < g < 2\14 || g = 43\308 || 3\22 < g < 5\36 || 5\36 < g < 7\50 || 7\50 < g < 9\64 || 4g-1\2 || -7g+1 || | | | | 10\21 < g < 1\2 |
| || 15L7s || 19\22 < g < 13\15 || g = 571\660 || 19\22 < g < 32\37 || 32\37 < g < 45\52 || 45\52 < g < 58\67 || -6+7g || -15g+13 || | | | | g = ''11\23, 12\25'', 13\27-13\29 |
| || 16L6s || 4\22 < g < 3\16 || g = 65\352 || 4\22 < g < 7\38 || 7\38 < g < 10\54 || 10\54 < g < 13\70 || 3g-1\2 || -8g+3\2 || | | | | 19g-9-(1-2g) = 21g-10 |
| || 17L5s || 9\22 < g < 7\17 || g = 207\748 || 9\22 < g < 16\39 || 16\39 < g < 23\56 || 23\56 < g < 30\73 || -2+5g || -17g+7 || | | |- |
| || 18L4s || 6\22 < g < 5\18 || g = 109\396 || 6\22 < g < 11\40 || 11\40 < g < 16\58 || 16\58 < g < 21\76 || -1\2+2g || -9g+5\2 || | | | | [[3L 18s]] |
| || 19L3s || 15\22 < g < 13\19 || g = 571\836 || 15\22 < g < 28\41 || 28\41 < g < 41\60 || 41\60 < g < 54\79 || -2+3g || -19g+13 || | | | | 6\21 < g < 1\3 |
| || 20L2s || 1\22 < g < 1\20 || g = 21\440 || 1\22 < g < 2\42 || 2\42 < g < 3\62 || 3\62 < g < 4\72 || g || -10g+1\2 || | | | | g = ''7\24'', 8\27, 9\30-10\33 |
| || 21L1s || 1\22 < g < 1\21 || g = 43\924 || 1\22 < g < 2\43 || 2\43 < g < 3\64 || 3\64 < g < 4\85 || g || -21g+1 || | | | | 6g-5\3-(1\3-g) = 7g-2 |
| | |- |
| | | | [[4L 17s]] |
| | | | 5\21 < g < 1\4 |
| | | | g = ''6\25'', 7\29, 8\33-9\37 |
| | | | 17g-4-(1-4g) = 21g-5 |
| | |- |
| | | | [[5L 16s]] |
| | | | 4\21 < g < 1\5 |
| | | | g = ''5\26'', 6\31, 7\36-8\41 |
| | | | 16g-3-(1-5g) = 21g-4 |
| | |- |
| | | | [[6L 15s]] |
| | | | 3\21 < g < 1\6 |
| | | | g = 4\27, 5\33, 6\39-7\45 |
| | | | 5g-2\3-(1\3-2g) = 7g-1 |
| | |- |
| | | | [[7L 14s]] |
| | | | 2\21 < g < 1\7 |
| | | | g = 3\28, 4\35, 5\42-6\49 |
| | | | 2g-1\7-(1\7-g) = 3g-2\7 |
| | |- |
| | | | [[8L 13s]] |
| | | | 13\21 < g < 5\8 |
| | | | g = 18\29, 23\37, 28\45-33\53 |
| | | | 13g-8-(5-8g) = 21g-13 |
| | |- |
| | | | [[9L 12s]] |
| | | | 2\21 < g < 1\9 |
| | | | g = 3\30, 4\39, 5\48-6\57 |
| | | | 4g-1\3-(1\3-3g) = 7g-2\3 |
| | |- |
| | | | [[10L 11s]] |
| | | | 2\21 < g < 1\10 |
| | | | g = 3\31, 4\41, 5\51-6\61 |
| | | | 11g-1-(1-10g) = 21g-2 |
| | |- |
| | | | [[11L 10s]] |
| | | | 19\21 < g < 10\11 |
| | | | g = 29\32, 39\43, 49\54-59\65 |
| | | | 10g-9-(10-11g) = 21g-19 |
| | |- |
| | | | [[12L 9s]] |
| | | | 5\21 < g < 3\12 |
| | | | g = 8\33, 11\45, 14\57-17\69 |
| | | | 3g-2\3-(1-4g) = 7g-1\3 |
| | |- |
| | | | [[13L 8s]] |
| | | | 8\21 < g < 5\13 |
| | | | g = 13\34, 18\47, 23\60-28\73 |
| | | | 8g-3-(5-13g) = 21g-8 |
| | |- |
| | | | [[14L 7s|''14L 7s'']] ''= 2L 1s (7)'' |
| | | | ''1\21 < g < 1\14'' |
| | | | ''g = 2\35, 3\49, 4\63-5\77'' |
| | | | ''g-(1\7-2g) = 3g-1\7'' |
| | |- |
| | | | [[15L 6s]] |
| | | | 4\21 < g < 3\15 |
| | | | g = 7\36, 10\51, 13\66-16\81 |
| | | | 2g-1\3-(1-5g) = 7g-4\3 |
| | |- |
| | | | [[16L 5s]] |
| | | | 17\21 < g < 13\16 |
| | | | g = 30\37, 43\53, 56\69-69\85 |
| | | | 5g-4-(13-16g) = 21g-17 |
| | |- |
| | | | [[17L 4s]] |
| | | | 16\21 < g < 13\17 |
| | | | g = 29\38, 42\55, 55\72-68\89 |
| | | | 4g-3-(13-17g) = 21g-16 |
| | |- |
| | | | [[18L 3s|''18L 3s'']] ''= 6L 1s (3)'' |
| | | | ''1\21 < g < 1\18'' |
| | | | ''g = 2\39, 3\57, 4\75-5\93'' |
| | | | ''g-(1\3-6g) = 7g-1\3'' |
| | |- |
| | | | [[19L 2s]] |
| | | | 11\21 < g < 10\19 |
| | | | g = '''21\40''', 31\59, 41\78-51\97 |
| | | | 2g-1-(10-19g) = 21g-11 |
| | |- |
| | | | [[20L 1s|''20L 1s'']] |
| | | | ''1\21 < g < 1\20'' |
| | | | ''g = '''2\41''', 3\61, 4\81-5\101'' |
| | | | ''g-(1-20g) = 21g-1'' |
| | |} |
|
| |
|
| =23= | | == 22-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L22s || <span style="line-height: 15.6000003814697px;">22\23 < g < 1</span> || g = 45\46 || <span style="line-height: 15.6000003814697px;">22\23 </span>< g < 23\24 || <span style="line-height: 15.6000003814697px;">23\24 </span>< g < 24\25 || 24\25 < g < 25\26 || -21+22g || -g+1 || | | |- |
| || 2L21s || 11\23 < g < 1\2 || g = 45\92 || <span style="line-height: 15.6000003814697px;">11\23 </span>< g < 12\25 || 12\25 < g < 13\27 || 13\27 < g < 14\29 || -10+21g || -2g+1 || | | ! | L-s pattern |
| || 3L20s || 15\23 < g < 2\3 || g = 91\138 || 15\23 < g < 17\26 || <span style="line-height: 15.6000003814697px;">17\26 </span>< g < 19\29 || 19\29 < g < 21\32 || -13+20g || 1-3g || | | ! | Generator range |
| || 4L19s || 17\23 < g < 3\4 || g = 137\184 || <span style="line-height: 15.6000003814697px;">17\23 </span>< g < 20\27 || 20\27 < g < 23\31 || 23\31 < g < 26\35 || -14+19g || -4g+3 || | | ! | Boundaries of best, better, good behavior |
| || 5L18s || 9\23 < g < 2\5 || g = 91\230 || 9\23 < g < 11\28 || 11\28 < g < 13\33 || 13\33 < g < 15\38 || -7+18g || -5g+2 || | | ! | Large step-Small step |
| || 6L17s || 19\23 < g < 5\6 || g = 229\276 || 19\23 < g < 24\29 || 24\29 < g < 29\35 || 29\35 < g < 34\41 || -15+17g || 1-6g || | | |- |
| || 7L16s || 13\23 < g < 4\7 || g = 183\322 || 13\23 < g < 17\30 || <span style="line-height: 15.6000003814697px;">17\30 < g < 21\37</span> || 21\37 < g < 25\44 || -9+16g || -7g+4 || | | | | [[1L 21s]] |
| || 8L15s || 20\23 < g < 7\8 || g = 321\368 || 20\23 < g < 27\31 || 27\31 < g < 34\39 || 34\39 < g < 41\47 || -13+15g || -8g+7 || | | | | 21\22 < g < 1 |
| || 9L14s || 5\23 < g < 2\9 || g = 91\414 || 5\23 < g < 7\32 || 7\32 < g < 9\41 || 9\41 < g < 11\50 || 9g-7 || <span style="line-height: 15.6000003814697px;">11-14g</span> || | | | | g = ''22\23, 23\24, 24/25-25\26'' |
| || 10L13s || 16\23 < g < 7\10 || g = 321\460 || 16\23 < g < 23\33 || 23\33 < g < 30\43 || 30\43 < g < 37\53 || -9+13g || -10g+7 || | | | | 21g-20-(1-g) = 22g-21 |
| || 11L12s || 2\23 < g < 1\11 || g = 45\506 || 2\23 < g < 3\34 || 3\34 < g < 4\45 || 4\45 < g < 5\56 || -11g+1 || 12g-1 ||
| | |- |
| || 12L11s || 21\23 < g < 11\12 || g = 505\552 || 21\23 < g < 32\35 || 32\35 < g < 43\47 || 43\47 < g < 54\59 || <span style="line-height: 15.6000003814697px;">11g-10</span> || 11-12g ||
| | | | [[2L 20s]] |
| || 13L10s || 7\23 < g < 4\13 || g = 183\598 || 7\23 < g < 11\36 || 11\36 < g < 15\49 || 15\49 < g < 19\62 || 4-13g || 10g-3 ||
| | | | 10\22 < g < 1\2 |
| || 14L9s || 18\23 < g < 11\14 || g = 505\644 || 18\23 < g < 29\37 || 29\37 < g < 40\51 || 40\51 < g < 51\65 || 14g-3 || -9g+2 ||
| | | | g = ''11\24,'' ''12\26'', 13\28-14\30 |
| || 15L8s || 3\23 < g < 2\15 || g = 91\690 || 3\23 < g < 5\38 || 5\38 < g < 7\53 || 7\53 < g < 9\68 || 2-15g || 8g-1 ||
| | | | 10g-9\2-(1\2-g) = 11g-5 |
| || 16L7s || 10\23 < g < 7\16 || g = 321\736 || 10\23 < g < 17\39 || 17\39 < g < 24\55 || 24\55 < g < 31\71 || 7g-3 || <span style="line-height: 15.6000003814697px;">-16g+7</span> ||
| | |- |
| || 17L6s || 4\23 < g < 3\17 || g = 137\782 || 4\23 < g < 7\40 || 7\40 < g < 10\57 || 10\57 < g < 13\74 || -1+6g || -17g+3 ||
| | | | [[3L 19s]] |
| || 18L5s || 14\23 < g < 11\18 || g = 505\828 || 14\23 < g < 25\41 || 25\41 < g < 36\59 || 36\59 < g < 47\77 || 11-18g || 5g-4 ||
| | | | 7\22 < g < 1\3 |
| || 19L4s || 6\23 < g < 5\19 || g = 229\874 || 6\23 < g < 11\42 || 11\42 < g < 16\61 || 16\61 < g < 21\80 || -1+4g || -19g+5 ||
| | | | g = ''8\25'', 9\28, 10\31-11\34 |
| || 20L3s || 8\23 < g < 7\20 || g = 321\920 || 8\23 < g < 15\43 || 15\43 < g < 22\63 || 22\63 < g < 29\83 || -1+3g || -20g+13 ||
| | | | 19g-6-(1-3g) = 22g-7 |
| || 21L2s || 12\23 < g < 11\21 || g = 505\966 || 12\23 < g < 23\44 || 23\44 < g < 34\65 || 34\65 < g < 45\86 || -1+2g || -21g+1 ||
| | |- |
| || 22L1s || 1\23 < g < 1\22 || g = 45\1012 || 1\23 < g < 2\45 || 2\45 < g < 3\67 || 3\67 < g < 4\89 || g || -22g+1 ||
| | | | [[4L 18s]] |
| | | | 5\22 < g < 1\4 |
| | | | g = ''6\26'', 7\30, 8\34-9\38 |
| | | | 9g-2-(1\2-2g) = 11g-5\2 |
| | |- |
| | | | [[5L 17s]] |
| | | | 13\22 < g < 3\5 |
| | | | g = ''16\27'', 19\32, 22\37-25\42 |
| | | | 17g-10-(3-5g) = 22g-13 |
| | |- |
| | | | [[6L 16s]] |
| | | | 7\22 < g < 2\6 |
| | | | g = 9\28, 11\34, 13\40-15\46 |
| | | | 8g-5\2-(1-3g) = 11g-7\2 |
| | |- |
| | | | [[7L 15s]] |
| | | | 3\22 < g < 1\7 |
| | | | g = 4\29, 5\36, 6\43-7\50 |
| | | | 15g-2-(1-7g) = 22g-3 |
| | |- |
| | | | [[8L 14s]] |
| | | | 8\22 < g < 3\8 |
| | | | g = 11\30, 14\38, 17\46-20\54 |
| | | | 7g-5\2-(3\2-4g) = 11g-4 |
| | |- |
| | | | [[9L 13s]] |
| | | | 17\22 < g < 7\9 |
| | | | g = 24\31, 31\40, 38\49-45\58 |
| | | | 13g-10-(7-9g) = 22g-17 |
| | |- |
| | | | [[10L 12s]] |
| | | | 2\22 < g < 1\10 |
| | | | g = 3\32, 4\42, 5\52-6\62 |
| | | | 6g-1\2-(1\2-5g) = 11g-1 |
| | |- |
| | | | ''[[11L 11s]] = 1L 1s (11)'' |
| | | | ''1\22 < g < 1\11'' |
| | | | ''g = 2\33, 3\44, 4\55-5\66'' |
| | | | ''g-(1\11-g) = 2g-1\11'' |
| | |- |
| | | | [[12L 10s]] |
| | | | 9\22 < g < 5\12 |
| | | | g = 14\34, 19\46, 24\58-29\70 |
| | | | 5g-2-(5\2-6g) = 11g-7\2 |
| | |- |
| | | | [[13L 9s]] |
| | | | 5\22 < g < 3\13 |
| | | | g = 8\35, 11\48, 14\61-17\74 |
| | | | 9g-2-(3-13g) = 22g-5 |
| | |- |
| | | | [[14L 8s]] |
| | | | 3\22 < g < 2\14 |
| | | | g = 5\36, 7\50, 9\64-11\78 |
| | | | 4g-1\2-(1-7g) = 11g-3\2 |
| | |- |
| | | | [[15L 7s]] |
| | | | 19\22 < g < 13\15 |
| | | | g = 32\37, 45\52, 58\67-71\82 |
| | | | 7g-6-(13-15g) = 22g-13 |
| | |- |
| | | | [[16L 6s]] |
| | | | 4\22 < g < 3\16 |
| | | | g = 7\38, 10\54, 13\70-16\86 |
| | | | 3g-1\2-(3\2-8g) = 11g-2 |
| | |- |
| | | | [[17L 5s]] |
| | | | 9\22 < g < 7\17 |
| | | | g = 16\39, 23\56, 30\73-37\90 |
| | | | 5g-2-(7-17g) = 22g-9 |
| | |- |
| | | | [[18L 4s]] |
| | | | 6\22 < g < 5\18 |
| | | | g = '''11\40''', 16\58, 21\76-26\94 |
| | | | 2g-1\2-(5\2-9g) = 11g-3 |
| | |- |
| | | | [[19L 3s]] |
| | | | 15\22 < g < 13\19 |
| | | | g = '''28\41''', 41\60, 54\79-67\98 |
| | | | 3g-2-(13-19g) = 22g-15 |
| | |- |
| | | | ''[[20L 2s]] = 10L 1s (2)'' |
| | | | ''1\22 < g < 1\20'' |
| | | | ''g = '''2\42''', 3\62, 4\82-5\102'' |
| | | | ''g-(1\2-10g) = 11g-1\2'' |
| | |- |
| | | | [[21L 1s|''21L 1s'']] |
| | | | ''1\22 < g < 1\21'' |
| | | | ''g = '''2\43''', 3\64, 4\85-5\106'' |
| | | | ''g-(1-21g) = 22g-1'' |
| | |} |
|
| |
|
| =24= | | == 23-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L23s || 23\24 < g < 1 || g = 47\48 || 23\24 < g < 24\25 || 24\25 < g < 25\26 || 25\26 < g < 26\27 || -22+23g || -g+1 || | | |- |
| || 2L22s || 11\24 < g < 1\2 || g = 23\48 || 11\24 < g < 12\26 || 12\26 < g < 13\28 || 13\28 < g < 14\30 || -g+1/2 || -5+11g || | | ! | L-s pattern |
| || 3L21s || 7\24 < g < 1\3 || g = 15\48 || 7\24 < g < 8\27 || 8\27 < g < 9\30 || 9\30 < g < 10\33 || 2/3-2g || -1/3+g || | | ! | Generator range |
| || 4L20s || 5\24 < g < 1\4 || g = 11\48 || 5\24 < g < 6\28 || 6\28 < g < 7\32 || 7\32 < g < 8\36 || -1+5g || -g+1/4 || | | ! | Boundaries of best, better, good behavior |
| || 5L19s || 19\24 < g < 4\5 || g = 191\240 || 19\24 < g < 23\29 || 23\29 < g < 27\34 || 27\34 < g < 31\39 || -15+19g || -5g+4 || | | ! | Large step-Small step |
| || 6L18s || 3\24 < g < 1\6 || g = 7\48 || 3\24 < g < 4\30 || 4\30 < g < 5\36 || 5\36 < g < 6\42 || -1\3+3g || 1\6-g || | | |- |
| || 7L17s || 17\24 < g < 5\7 || g = 239\336 || 17\24 < g < 22\31 || 22\31 < g < 27\38 || 27\38 < g < 32\455 || 5-17g || 7g-2 || | | | | [[1L 22s]] |
| || 8L16s || 2\24 < g < 1\8 || g = 5\48 || 2\24 < g < 3\32 || 3\32 < g < 4\40 || 4\40 < g < 5\48 || -1\8+2g || -g+1\8 || | | | | 22\23 < g < 1 |
| || 9L15s || 5\24 < g < 2\9 || g = 31\144 || 5\24 < g < 7\33 || 7\33 < g < 9\42 || 9\42 < g < 11\51 || 5g-1 || 2\3-3g || | | | | g = ''23\24, 24\25, 25\26-26\27'' |
| || 10L14s || 7\24 < g < 3\10 || g = 71\240 || 7\24 < g < 10\34 || 10\34 < g < 13\44 || 13\44 < g < 16\54 || -4+7g || -3\2+5g || | | | | 22g-21-(1-g) = 23g-22 |
| || 11L13s || 13\24 < g < 6\11 || g = 287\528 || 13\24 < g < 19\35 || 19\35 < g < 25\46 || 25|46 < g < 31\57 || 13g-7 || -11g+6 || | | |- |
| || 12L12s || 1\24 < g < 1\12 || g = 3\48 || 1\24 < g < 2\36 || 2\36 < g < 3\48 || 3\48 < g < 4\60 || g || 1\12-g ||
| | | | [[2L 21s]] |
| || 13L11s || 11\24 < g < 6\13 || g = 287\624 || 11\24 < g < 17\37 || 17\37 < g < 23\50 || 23\50 < g < 29\63 || 11g-5 || 6-13g ||
| | | | 11\23 < g < 1\2 |
| || 14L10s || 17\24 < g < 10\14 || g = 239\336 || 17\24 < g < 27\38 || 27\38 < g < 37\52 || 37\52 < g < 47\66 || 3\2-5g || 7g-2 ||
| | | | g = ''12\25, 13\27'', 14\29-15\31 |
| || 15L9s || 3\24 < g < 2\15 || g = 31\240 || 3\24 < g < 5\39 || 5\39 < g < 7\54 || 7\54 < g < 9\69 || 3g-1\3 || -5g+2\3 ||
| | | | 21g-10-(1-2g) = 23g-11 |
| || 16L8s || 1\24 < g < 1\16 || g = 5\96 || 1\24 < g < 2\40 || 2\40 < g < 3\56 || 3\56 < g < 4\72 || g || 1\8-2g ||
| | |- |
| || 17L7s || 7\24 < g < 5\17 || g = 239\816 || 7\24 < g < 12\41 || 12\41 < g < 17\58 || 17\58 < g < 22\75 || -7g+4 || 17g-12 ||
| | | | [[3L 20s]] |
| || 18L6s || 1\24 < g < 1\18 || g = 7\144 || 1\24 < g < 2\42 || 2\42 < g < 3\60 || 3\60 < g < 4\78 || g || 1\6-3g ||
| | | | 15\23 < g < 2\3 |
| || 19L5s || 5\24 < g < 4\19 || g = 191\912 || 5\24 < g < 9\43 || 9\43 < g < 13\62 || 13\62 < g < 17\81 || -5g+4 || -15+19g ||
| | | | g = ''17\26'', 19\29, 21\32-23\35 |
| || 20L4s || 1\24 < g < 1\20 || g = 11\240 || 1\24 < g < 2\44 || 2\44 < g < 3\64 || 3\64 < g < 4\84 || g || -5g+1\4 ||
| | | | 20g-13-(1-3g) = 23g-14 |
| || 21L3s || 1\24 < g < 1\21 || g = 15\336 || 1\24 < g < 2\45 || 2\45 < g < 3\66 || 3\66 < g < 4\87 || g || -7g+1\3 ||
| | |- |
| || 22L2s || 1\24 < g < 1\22 || g = 23\264 || 1\24 < g < 2\46 || 2\46 < g < 3\68 || 3\68 < g < 4\90 || g || -11g+1\2 ||
| | | | [[4L 19s]] |
| || 23L1s || 1\24 < g < 1\23 || g = 47\1104 || 1\24 < g < 2\47 || 2\47 < g < 3\70 || 3\70 < g < 4\93 || g || -23g+1 ||
| | | | 17\23 < g < 3\4 |
| | | | g = ''20\27'', 23\31, 26\35-29\39 |
| | | | 19g-14-(3-4g) = 23g-17 |
| | |- |
| | | | [[5L 18s]] |
| | | | 9\23 < g < 2\5 |
| | | | g = ''11\28'', 13\33, 15\38-17\43 |
| | | | 18g-7-(2-5g) = 13g-9 |
| | |- |
| | | | [[6L 17s]] |
| | | | 19\23 < g < 5\6 |
| | | | g = 24\29, 29\35, 34\41-39\47 |
| | | | 17g-15-(1-6g) = 23g-16 |
| | |- |
| | | | [[7L 16s]] |
| | | | 13\23 < g < 4\7 |
| | | | g = 17\30, 21\37, 25\44-29\51 |
| | | | 16g-9-(4-7g) = 23g-13 |
| | |- |
| | | | [[8L 15s]] |
| | | | 20\23 < g < 7\8 |
| | | | g = 27\31, 34\39, 41\47-48\55 |
| | | | 15g-13-(7-8g) = 23g-20 |
| | |- |
| | | | [[9L 14s]] |
| | | | 5\23 < g < 2\9 |
| | | | g = 7\32, 9\41, 11\50-13\59 |
| | | | 14g-3-(2-9g) = 23g-5 |
| | |- |
| | | | [[10L 13s]] |
| | | | 16\23 < g < 7\10 |
| | | | g = 23\33, 30\43, 37\53-44\63 |
| | | | 13g-9-(7-10g) = 23g-16 |
| | |- |
| | | | [[11L 12s]] |
| | | | 2\23 < g < 1\11 |
| | | | g = 3\34, 4\45, 5\56-6\67 |
| | | | 12g-1-(1-11g) = 23g-2 |
| | |- |
| | | | [[12L 11s]] |
| | | | 21\23 < g < 11\12 |
| | | | g = 32\35, 43\47, 54\59-65\71 |
| | | | 11g-10-(11-12g) = 23g-21 |
| | |- |
| | | | [[13L 10s]] |
| | | | 7\23 < g < 4\13 |
| | | | g = 11\36, 15\49, 19\62-23\75 |
| | | | 10g-3-(4-13g) = 23g-7 |
| | |- |
| | | | [[14L 9s]] |
| | | | 18\23 < g < 11\14 |
| | | | g = 29\37, 40\51, 51\65-62\79 |
| | | | 9g-7-(11-14g) = 23g-18 |
| | |- |
| | | | [[15L 8s]] |
| | | | 3\23 < g < 2\15 |
| | | | g = 5\38, 7\53, 9\68-11\83 |
| | | | 8g-1-(2-15g) = 23g-3 |
| | |- |
| | | | [[16L 7s]] |
| | | | 10\23 < g < 7\16 |
| | | | g = 17\39, 24\55, 31\71-38\87 |
| | | | 7g-3-(7-16g) = 23g-10 |
| | |- |
| | | | [[17L 6s]] |
| | | | 4\23 < g < 3\17 |
| | | | g = '''7\40''', 10\57, 13\74-16\91 |
| | | | 6g-1-(3-17g) = 23g-4 |
| | |- |
| | | | [[18L 5s]] |
| | | | 14\23 < g < 11\18 |
| | | | g = '''25\41''', 36\59, 47\77-58\95 |
| | | | 5g-4-(11-18g) = 23g-15 |
| | |- |
| | | | [[19L 4s]] |
| | | | 6\23 < g < 5\19 |
| | | | g = '''11\42''', 16\61, 21\80-26\99 |
| | | | 4g-1-(5-19g) = 23g-6 |
| | |- |
| | | | [[20L 3s]] |
| | | | 8\23 < g < 7\20 |
| | | | g = '''15\43''', 22\63, 29\83-36\103 |
| | | | 3g-1-(13-20g) = 23g-14 |
| | |- |
| | | | [[21L 2s]] |
| | | | 12\23 < g < 11\21 |
| | | | g = '''23\44''', 34\65, 45\86-56\107 |
| | | | 2g-1-(11-21g) = 23g-12 |
| | |- |
| | | | [[22L 1s|''22L 1s'']] |
| | | | ''1\23 < g < 1\22'' |
| | | | ''g = '''2\45''', 3\67, 4\89-5\111'' |
| | | | ''g-(1-22g) = 23g-1'' |
| | |} |
|
| |
|
| =25= | | == 24-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L24s || 24\25 < g < 1 || g = 49\50 || 24\25 < g < 25\26 || 25\26 < g < 26\27 || 26\27 < g < 27\28 || -23+24g || -g+1 || | | |- |
| || 2L23s || 12\25 < g < 1\2 || g = 49\100 || 12\25 < g < 13\27 || 13\27 < g < 14\29 || 14\29 < g < 15\31 || 2g-11 || 1-2g || | | ! | L-s pattern |
| || 3L22s || 8\25 < g < 1\3 || g = 49\150 || 8\25 < g < 9\28 || 9\28 < g < 10\31 || 10\31 < g < 11\34 || -7+22g || 1-3g || | | ! | Generator range |
| || 4L21s || 6\25 < g < 1\4 || g = 49\200 || 6\25 < g < 7\29 || 7\29 < g < 8\33 || 8\33 < g < 9\37 || -5+21g || -4g+1 || | | ! | Boundaries of best, better, good behavior |
| || 5L20s || 4\25 < g < 1\5 || g = 9\50 || 4\25 < g < 5\30 || 5\30 < g < 6\35 || 6\35 < g < 7\40 || -3\5+4g || 1\5-g || | | ! | Large step-Small step |
| || 6L19s || 4\25 < g < 1\6 || g = 49\300 || 4\25 < g < 5\31 || 5\31 < g < 6\37 || 6\37 < g < 7\43 || -3+19g || -6g+1 || | | |- |
| || 7L18s || 7\25 < g < 2\7 || g = 99\350 || 7\25 < g < 9\32 || 9\32 < g < 11\39 || 11\39 < g < 13\46 || -5+18g || -7g+2 || | | | | [[1L 23s]] |
| || 8L17s || 3\25 < g < 1\8 || g = 49\400 || 3\25 < g < 4\33 || 4\33 < g < 5\41 || 5\41 < g < 6\47 || <span style="line-height: 15.6000003814697px;">17g-2</span> || 1-8g ||
| | | | 23\24 < g < 1 |
| || 9L16s || 11\25 < g < 4\9 || g = 199\450 || 11\25 < g < 15\34 || 15\34 < g < 19\43 || 19\43 < g < 23\52 || -7+16g || <span style="line-height: 15.6000003814697px;">-9g+4</span> || | | | | g = ''24\25, 25\26, 26\27-27\28'' |
| || 10L15s || 2\25 < g < 1\10 || g = 9\100 || 2\25 < g < 3\35 || 3\35 < g < 4\45 || 4\45 < g < 5\55 || -1\5+3g || 1\5-2g || | | | | 23g-22-(1-g) = 24g-23 |
| || 11L14s || 9\25 < g < 4\11 || g = 199\550 || 9\25 < g < 13\36 || 13\36 < g < 17\47 || 17\47 < g < 21\58 || 14g-5 || -11g+4 ||
| | |- |
| || 12L13s || 2\25 < g < 1\12 || g = 49\600 || 2\25 < g < 3\37 || 3\37 < g < 4\49 || 4\49 < g < 5\61 || 13g-1 || 1-12g ||
| | | | [[2L 22s]] |
| || 13L12s || 23\25 < g < 12\13 || g = 599\650 || 23\25 < g < 35\38 || 35\38 < g < 47\51 || 47\51 < g < 59\64 || 12g-11 || 12-13g ||
| | | | 11\24 < g < 1\2 |
| || 14L11s || 16\25 < g < 9\14 || g = 449\700 || 16\25 < g < 25\39 || 25\39 < g < 34\53 || 34\53 < g < 43\67 || -7+11g || -14g+9 ||
| | | | g = ''12\26, 13\28, 14\30''-15\32 |
| || 15L10s || 3\25 < g < 2\15 || g = 19\150 || 3\25 < g < 5\40 || <span style="line-height: 15.6000003814697px;">5\40 </span>< g < 7\55 || 7\55 < g < 9\70 || -2g+1\5 || 3g-2\5 ||
| | | | 11g-5-(1/2-g) = 12g-11/2 |
| || 16L9s || 14\25 < g < 9\16 || g = 449\800 || 14\25 < g < 23\41 || 23\41 < g < 32\57 || 32\57 < g < 41\73 || 9g-5 || 9-16g ||
| | |- |
| || 17L8s || 22\25 < g < 15\17 || g = 749\850 || 22\25 < g < 37\42 || 37\42 < g < 52\59 || 52\59 < g < 67\76 || 8g-7 || -17g+15 ||
| | | | [[3L 21s]] |
| || 18L7s || 18\25 < g < 13\18 || g = 649\900 || 18\25 < g < 31\43 || 31\43 < g < 44\61 || 44\61 < g < 57\79 || g || 1\6-3g ||
| | | | 7\24 < g < 1\3 |
| || 19L6s || 21\25 < g < 16\19 || g = 799\950 || 21\25 < g < 37\44 || 37\44 < g < 53\63 || 53\63 < g < 69\82 || -19g+16 || -5+6g ||
| | | | g = ''8\27, 9\30'', 10\33-11\36 |
| || 20L5s || 1\25 < g < 1\20 || g = 9\200 || 1\25 < g < 2\45 || 2\45 < g < 3\65 || 3\65 < g < 4\85 || g || -4g+1\5 ||
| | | | 7g-2-(1/3-g) = 8g-7/3 |
| || 21L4s || 16\21 < g < 19\25 || g = 799\1050 || 19\25 < g < 35\46 || 35\46 < g < 51\67 || 51\67 < g < 71\88 || 4g-3 || -21g+16 ||
| | |- |
| || 22L3s || 17\25 < g < 15\22 || g = 749\1100 || 17\25 < g < 32\47 || 32\47 < g < 47\69 || 47\69 < g < 62\91 || 3g-2 || -22g+15 ||
| | | | [[4L 20s]] |
| || 23L2s || 13\25 < g < 12\23 || g = 599\1150 || 13\25 < g < 25\48 || 25\48 < g < 37\71 || 37\71 < g < 49\94 || -2g+1 || 23g-11 ||
| | | | 5\24 < g < 1\4 |
| || 24L1s || 1\25 < g < 1\24 || g = 49\1200 || 1\25 < g < 2\49 || 2\49 < g < 3\73 || 3\73 < g < 4\97 || g || -24g+1 ||
| | | | g = ''6\28'', 7\32, 8\36-9\40 |
| | | | 5g-1-(1/4-g) = 6g-5/4 |
| | |- |
| | | | [[5L 19s]] |
| | | | 19\24 < g < 4\5 |
| | | | g = ''23\29'', 27\34, 31\39-35\44 |
| | | | 19g-15-(4-5g) = 24g-19 |
| | |- |
| | | | [[6L 18s]] |
| | | | 3\24 < g < 1\6 |
| | | | g = ''4\30'', 5\36, 6\42-7\48 |
| | | | 3g-1\3-(1\6-g) = 4g-1\2 |
| | |- |
| | | | [[7L 17s]] |
| | | | 17\24 < g < 5\7 |
| | | | g = 22\31, 27\38, 32\45-37\52 |
| | | | 17g-12-(5-7g) = 24g-17 |
| | |- |
| | | | [[8L 16s]] |
| | | | 2\24 < g < 1\8 |
| | | | g = 3\32, 4\40, 5\48-6\56 |
| | | | 2g-1\8-(1\8-g) = 3g-1\4 |
| | |- |
| | | | [[9L 15s]] |
| | | | 5\24 < g < 2\9 |
| | | | g = 7\33, 9\42, 11\51-13\60 |
| | | | 5g-1-(2\3-3g) = 8g-5\3 |
| | |- |
| | | | [[10L 14s]] |
| | | | 7\24 < g < 3\10 |
| | | | g = 10\34, 13\44, 16\54-19\64 |
| | | | 7g-2-(3\2-5g) = 12g-7\2 |
| | |- |
| | | | [[11L 13s]] |
| | | | 13\24 < g < 6\11 |
| | | | g = 19\35, 25\46, 31\57-37\68 |
| | | | 13g-7-(6-11g) = 24g-12 |
| | |- |
| | | | ''[[12L 12s]] = 1L 1s (12)'' |
| | | | ''1\24 < g < 1\12'' |
| | | | ''g = 2\36, 3\48, 4\60-5\72'' |
| | | | ''g-(1\12-g) = 2g-1\12'' |
| | |- |
| | | | [[13L 11s]] |
| | | | 11\24 < g < 6\13 |
| | | | g = 17\37, 23\50, 29\63-35\76 |
| | | | 11g-5-(6-13g) = 24g-11 |
| | |- |
| | | | [[14L 10s]] |
| | | | 17\24 < g < 10\14 |
| | | | g = 27\38, 37\52, 47\66-57\80 |
| | | | 5g-7\2-(5-7g) = 12g-17\2 |
| | |- |
| | | | [[15L 9s]] |
| | | | 3\24 < g < 2\15 |
| | | | g = 5\39, 7\54, 9\69-11\84 |
| | | | 3g-1\3-(2\3-5g) = 8g-1 |
| | |- |
| | | | ''[[16L 8s]] = 2L 1s (8)'' |
| | | | ''1\24 < g < 1\16'' |
| | | | ''g = '''2\40''', 3\56, 4\72-5\88'' |
| | | | ''g-(1\8-2g) = 3g-1\8'' |
| | |- |
| | | | [[17L 7s]] |
| | | | 7\24 < g < 5\17 |
| | | | g = '''12\41''', 17\58, 22\75-27\92 |
| | | | 7g-2-(5-17g) = 24g-7 |
| | |- |
| | | | ''[[18L 6s]] = 3L 1s (6)'' |
| | | | ''1\24 < g < 1\18'' |
| | | | ''g = '''2\42''', 3\60, 4\78-5\96'' |
| | | | ''g-(1\6-3g) = 4g-1\6'' |
| | |- |
| | | | [[19L 5s]] |
| | | | 5\24 < g < 4\19 |
| | | | g = '''9\43''', 13\62, 17\81-21\100 |
| | | | 5g-1-(4-19g) = 24g-5 |
| | |- |
| | | | ''[[20L 4s]] = 5L 1s (4)'' |
| | | | ''1\24 < g < 1\20'' |
| | | | ''g = '''2\44''', 3\64, 4\84-5\104'' |
| | | | ''g-(1\4-5g) = 6g-1\4'' |
| | |- |
| | | | ''[[21L 3s]] = 7L 1s (3)'' |
| | | | ''1\24 < g < 1\21'' |
| | | | ''g = '''2\45''', 3\66, 4\87-5\108'' |
| | | | ''g-(1\3-7g) = 8g-1\3'' |
| | |- |
| | | | ''[[22L 2s]] = 11L 1s (2)'' |
| | | | ''1\24 < g < 1\22'' |
| | | | ''g = '''2\46''', 3\68, 4\90-5\112'' |
| | | | ''g-(1\2-11g) = 12g-1\2'' |
| | |- |
| | | | [[23L 1s|''23L 1s'']] |
| | | | ''1\24 < g < 1\23'' |
| | | | ''g = '''2\47''', 3\70, 4\93-5\116'' |
| | | | ''g+1-23g = 24g-1'' |
| | |} |
|
| |
|
| =26= | | == 25-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L25s || 25\26 < g < 1 || g = 51\52 || 25\26 < g < 26\27 || 26\27 < g < 27\28 || 27\28 < g < 28\29 || -24+25g || -g+1 || | | |- |
| || 2L24s || 12\26 < g < 1\2 || g = 25\52 || <span style="line-height: 15.6000003814697px;">12\26</span> < g < 13\28 || 13\28 < g < 14\30 || 14\30 < g < 15\32 || 12g-11\2 || 1\2-g || | | ! | L-s pattern |
| || 3L23s || 17\26 < g < 2\3 || g = 103\156 || 17\26 < g < 19\29 || 19\29 < g < 21\32 || 21\32 < g < 23\35 || -15+23g || 2-3g || | | ! | Generator range |
| || 4L22s || 6\26 < g < 1\4 || g = 25\104 || 6\26 < g < 7\30 || 7\30 < g < 8\34 || 8\34 < g < 9\38 || 11g-5\2 || <span style="line-height: 15.6000003814697px;">-2g+1\2</span> || | | ! | Boundaries of best, better, good behavior |
| || 5L21s || 5\26 < g < 1\5 || g = 51\260 || 5\26 < g < 6\31 || 6\31 < g < 7\36 || 7\36 < g < 8\41 || -4+21g || 1-5g || | | ! | Large step-Small step |
| || 6L20s || 4\26 < g < 1\6 || g = 25\156 || 4\26 < g < 5\32 || 5\32 < g < 6\38 || 6\38 < g < 7\44 || -3\2+10g || -3g+1\2 || | | |- |
| || 7L19s || 11\26 < g < 3\7 || g = 155\364 || 11\26 < g < 14\33 || 14\33 < g < 17\40 || 17\40 < g < 20\47 || -8+19g || -7g+3 || | | | | [[1L 24s]] |
| || 8L18s || 3\26 < g < 1\8 || g = 25\208 || 3\26 < g < 4\34 || 4\34 < g < 5\42 || 5\42 < g < 6\50 || 9g-1 || 1\2-4g || | | | | 24\25 < g < 1 |
| || 9L17s || 23\26 < g < 8\9 || g = 415\468 || 23\26 < g < 31\35 || 31\35 < g < 39\44 || 39\44 < g < 47\53 || -15+17g || -9g+8 ||
| | | | g = ''25\26, 26\27, 27\28-28\29'' |
| || 10L16s || 5\26 < g < 2\10 || g = 51\260 || 5\26 < g < 7\36 || 7\36 < g < 9\46 || 9\46 < g < 11\56 || -3\2+8g || 1-5g || | | | | 24g-23-(1-g) = 25g-24 |
| || 11L15s || 7\26 < g < 3\11 || g = 155\572 || 7\26 < g < 10\37 || 10\37 < g < 13\48 || 13\48 < g < 16\59 || 15g-4 || -11g+3 || | | |- |
| || 12L14s || 2\26 < g < 1\12 || g = 25\312 || 2\26 < g < 3\38 || 3\38 < g < 4\50 || 4\50 < g < 5\62 || 7g-1\2 || 1\2-6g ||
| | | | [[2L 23s]] |
| || 13L13s || 1\26 < g < 1\13 || g = 3\52 || 1\26 < g < 2\39 || 2\39 < g < 3\52 || 3\52 < g < 4\65 || g || -g+1\13 ||
| | | | 12\25 < g < 1\2 |
| || <span style="line-height: 15.6000003814697px;">14L12s</span> || 11\26 < g < 6\14 || g = 155\364 || 11\26 < g < 17\40 || 17\40 < g < 23\54 || 23\54 < g < 29\68 || 6g-5\2 || 3-7g ||
| | | | g = ''13\27, 14\29, 15\31''-16\33 |
| || <span style="line-height: 15.6000003814697px;">15L11s</span> || 19\26 < g < 11\15 || g = 571\780 || 19\26 < g < 30\41 || 30\41 < g < 41\56 || 41\56 < g < 52\71 || -8+11g || -15g+11 ||
| | | | 23g-11-(1-2g) = 25g-13 |
| || <span style="line-height: 15.6000003814697px;">16L10s</span> || 8\26 < g < 5\16 || g = 129\416 || 8\26 < g < 13\42 || 13\42 < g < 18\58 || 18\58 < g < 23\74 || -8g+13\2 || 5g-4 ||
| | |- |
| || <span style="line-height: 15.6000003814697px;">17L9s</span> || 3\26 < g < 2\17 || g = 103\884 || 3\26 < g < 5\43 || 5\43 < g < 7\60 || 7\60 < g < 9\77 || 9g-1 || 2-17g ||
| | | | [[3L 22s]] |
| || <span style="line-height: 15.6000003814697px;">18L</span>8s || 10\26 < g < 7\18 || g = 181\468 || 10\26 < g < 17\44 || 17\44 < g < 24\62 || 24\62 < g < 31\80 || 8g-7 || -9g+7\2 ||
| | | | 8\25 < g < 1\3 |
| || <span style="line-height: 15.6000003814697px;">19L</span>7s || 15\26 < g < 11\19 || g = 571\988 || 15\26 < g < 26\45 || 26\45 < g < 37\64 || 37\64 < g < 48\83 || 11-19g || -4+7g ||
| | | | g = ''9\28'', ''10\31'', 11\34-12\37 |
| || <span style="line-height: 15.6000003814697px;">20L</span>6s || 9\26 < g < 7\20 || g = 181\520 || 9\26 < g < 16\46 || 16\46 < g < 23\66 || 23\66 < g < 30\86 || -1+3g || 7\2-10g ||
| | | | 22g-7-(1-3g) = 25g-8 |
| || <span style="line-height: 15.6000003814697px;">21L</span>5s || 21\26 < g < 17\21 || g = 883\1092 || 21\26 < g < 38\47 || 38\47 < g < 55\68 || 55\68 < g < 72\89 || 5g-4 || -21g+16 ||
| | |- |
| || <span style="line-height: 15.6000003814697px;">22L</span>4s || 7\26 < g < 6\22 || g = 155\572 || 7\26 < g < 13\48 || 13\48 < g < 19\70 || 19\70 < g < 25\92 || 2g-1\2 || -11g+3 ||
| | | | [[4L 21s]] |
| || <span style="line-height: 15.6000003814697px;">23L</span>3s || 9\26 < g < 8\23 || g = 415\1196 || 9\26 < g < 17\49 || 17\49 < g < 25\72 || 25\72 < g < 33/95 || 3g-1 || -23g+8 ||
| | | | 6\25 < g < 1\4 |
| || <span style="line-height: 15.6000003814697px;">24L</span>2s || 1\26 < g < 1\24 || g = 25\312 || 1\26 < g < 2\50 || 2\50 < g < 3\74 || 3\74 < g < 4\98 || g || -12g+1\2 ||
| | | | g = ''7\29'', 8\33, 9\37-10\41 |
| || 25L1s || 1\26 < g < 1\25 || g = 51\1300 || 1\26 < g < 2\51 || 2\51< g < 3\76 || 3\76 < g < 4\101 || g || -25g+1 ||
| | | | 21g-5-(1-4g) = 25g-6 |
| | |- |
| | | | [[5L 20s]] |
| | | | 4\25 < g < 1\5 |
| | | | g = ''5\30'', 6\35, 7\40-8\45 |
| | | | 4g-3\5-(1\5-g) = 5g-4\5 |
| | |- |
| | | | [[6L 19s]] |
| | | | 4\25 < g < 1\6 |
| | | | g = ''5\31'', 6\37, 7\43-8\49 |
| | | | 19g-3-(1-6g) = 25g-4 |
| | |- |
| | | | [[7L 18s]] |
| | | | 7\25 < g < 2\7 |
| | | | g = 9\32, 11\39, 13\46-15\53 |
| | | | 18g-5-(2-7g) = 25g-7 |
| | |- |
| | | | [[8L 17s]] |
| | | | 3\25 < g < 1\8 |
| | | | g = 4\33, 5\41, 6\49-7\57 |
| | | | 17g-2-(1-8g) = 25g-3 |
| | |- |
| | | | [[9L 16s]] |
| | | | 11\25 < g < 4\9 |
| | | | g = 15\34, 19\43, 23\52-27\61 |
| | | | 16g-7-(4-9g) = 25g-11 |
| | |- |
| | | | [[10L 15s]] |
| | | | 2\25 < g < 1\10 |
| | | | g = 3\35, 4\45, 5\55-6\65 |
| | | | 3g-1\5-(1\5-2g) = 5g-2\5 |
| | |- |
| | | | [[11L 14s]] |
| | | | 9\25 < g < 4\11 |
| | | | g = 13\36, 17\47, 21\58-25\69 |
| | | | 14g-5-(4-11g) = 25g-9 |
| | |- |
| | | | [[12L 13s]] |
| | | | 2\25 < g < 1\12 |
| | | | g = 3\37, 4\49, 5\61-6\73 |
| | | | 13g-1-(1-12g) = 25g-2 |
| | |- |
| | | | [[13L 12s]] |
| | | | 23\25 < g < 12\13 |
| | | | g = 35\38, 47\51, 59\64-71\77 |
| | | | 12g-11-(12-13g) = 25g-23 |
| | |- |
| | | | [[14L 11s]] |
| | | | 16\25 < g < 9\14 |
| | | | g = 25\39, 34\53, 43\67-52\81 |
| | | | 11g-7-(9-14g) = 25g-16 |
| | |- |
| | | | [[15L 10s]] |
| | | | 3\25 < g < 2\15 |
| | | | g = '''5\40''', 7\55, 9\70-11\85 |
| | | | 2g-1\5-(2\5-3g) = 5g-1\5 |
| | |- |
| | | | [[16L 9s]] |
| | | | 14\25 < g < 9\16 |
| | | | g = '''23\41''', 32\57, 41\73-50\89 |
| | | | 9g-5-(9-16g) = 25g-14 |
| | |- |
| | | | [[17L 8s]] |
| | | | 22\25 < g < 15\17 |
| | | | g = '''37\42''', 52\59, 67\76-82\93 |
| | | | 8g-7-(15-17g) = 25g-22 |
| | |- |
| | | | [[18L 7s]] |
| | | | 18\25 < g < 13\18 |
| | | | g = '''31\43''', 44\61, 57\79-80\97 |
| | | | 7g-5-(13-18g) = 25g-18 |
| | |- |
| | | | [[19L 6s]] |
| | | | 21\25 < g < 16\19 |
| | | | g = '''37\44''', 53\63, 69\82-85\101 |
| | | | 6g-5+16-19g = 25g-21 |
| | |- |
| | | | ''[[20L 5s]] = 4L 1s (5)'' |
| | | | ''1\25 < g < 1\20'' |
| | | | ''g = '''2\45''', 3\65, 4\85-5\105'' |
| | | | ''g-(1\5-4g) = 5g-1\5'' |
| | |- |
| | | | [[21L 4s]] |
| | | | 19\25 < g < 16\21 |
| | | | g = '''35\46''', 51\67, 67\88-83\109 |
| | | | 4g-3-(16-21g) = 25g-19 |
| | |- |
| | | | [[22L 3s]] |
| | | | 17\25 < g < 15\22 |
| | | | g = '''32\47''', 47\69, 62\91-77\113 |
| | | | 3g-2-(15-22g) = 25g-17 |
| | |- |
| | | | [[23L 2s]] |
| | | | 13\25 < g < 12\23 |
| | | | g = '''25\48''', 37\71, 49\94-61\117 |
| | | | 2g-1-(11-23g) = 25g-13 |
| | |- |
| | | | [[24L 1s|''24L 1s'']] |
| | | | ''1\25 < g < 1\24'' |
| | | | ''g = '''2\49''', 3\73, 4\97-5\121'' |
| | | | ''g-(1-24g) = 25g-1'' |
| | |} |
|
| |
|
| =27= | | == 26-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L26s || 26\27 < g < 1 || g = 53\54 || <span style="line-height: 15.6000003814697px;">26\27 < g < 27\28</span> || 27\28 < g < 28\29 || 28\29 < g < 29\30 || -25+26g || -g+1 || | | |- |
| || 2L25s || 13\27 < g < 1\2 || g = 53\108 || <span style="line-height: 15.6000003814697px;">13</span>\27 < g < 14\29 || 14\29 < g < 15\31 || 15\31 < g < 16\33 || 25g-12 || -2g+1 || | | ! | L-s pattern |
| || 3L24s || 8\27 < g < 1\3 || g = 17\54 || 8\27 < g < 9\30 || 9\30 < g < 10\33 || 10\33 < g < 11\36 || -7\3+8g || 1-3-g || | | ! | Generator range |
| || 4L23s || 20\27 < g < 3\4 || g = 161\216 || 20\27 < g < 23\31 || 23\31 < g < 26\35 || 26\35 < g < 29\39 || 23g-17 || -4g+3 || | | ! | Boundaries of best, better, good behavior |
| || 5L22s || 16\27 < g < 3\5 || g = 161\270 || 16\27 < g < 19\32 || 19\32 < g < 22\37 || 22\37 < g < 25\42 || -13+22g || 3-5g || | | ! | Large step-Small step |
| || 6L21s || 4\27 < g < 1\6 || g = 17\108 || 4\27 < g < 5\33 || 5\33 < g < 6\39 || 6\39 < g < 7\45 || -1+7g || -2g+1\3 || | | |- |
| || 7L20s || 23\27 < g < 6\7 || g = 323\378 || 23\27 < g < 29\34 || 29\34 < g < 35\41 || 35\41 < g < 41\48 || -17+20g || -7g+6 || | | | | [[1L 25s]] |
| || 8L19s || 10\27 < g < 3\8 || g = 161\432 || 10\27 < g < 13\35 || 13\35 < g < 16\43 || 16\43 < g < 19\51 || 19g-7 || 3-8g || | | | | 25\26 < g < 1 |
| || 9L18s || 2\27 < g < 1\9 || g = 5\54 || 2\27 < g < 3\36 || 3\36 < g < 4\45 || 4\45 < g < 5\54 || -1\9+2g || -g+1\9 ||
| | | | g = ''26\27, 27\28, 28\29-29\30'' |
| || 10L17s || 8\27 < g < 3\10 || g = 161\540 || 8\27 < g < 11\37 || 11\37 < g < 14\47 || 14\47 < g < 17\57 || -5+17g || 3-10g || | | | | 25g-24-(1-g) = 25g-24 |
| || 11L16s || 22\27 < g < 9\11 || g = 485\594 || 22\27 < g < 31\38 || 31\38 < g < 40\49 || 40\49 < g < 49\60 || 16g-13 || -11g+9 || | | |- |
| || 12L15s || 2\27 < g < 1\12 || g = 17\216 || 2\27 < g < 3\39 || 3\39 < g < 4\51 || 4\51 < g < 5\63 || 5g-1\3 || 1\3-4g ||
| | | | [[2L 24s]] |
| || 13L14s || 2\27 < g < 1\13 || g = 53\702 || 2\27 < g < 3\40 || 3\40 < g < 4\53 || 4\53 < g < 5\66 || 14g-1 || -13g+1 ||
| | | | 12\26 < g < 1\2 |
| || 14L13s || 25\27 < g < 13\14 || g = 701\756 || 25\27 < g < 38\41 || 38\41 < g < 51\55 || 51\55 < g < 64\69 || 13g-12 || 13-14g ||
| | | | g = ''13\28, 14\30, 15\32''-16\34 |
| || 15L12s || 7\27 < g < 4\15 || g = 71\270 || 7\27 < g < 11\42 || 11\42 < g < 15\57 || 15\57 < g < 19\72 || -4+4g || -5g+14\3 ||
| | | | 12g-11\2-(1\2-g) = 13g-6 |
| || 16L11s || 5\27 < g < 3\16 || g = 161\864 || 5\27 < g < 8\43 || 8\43 < g < 11\59 || 11\59 < g < 14\75 || 11g-2 || -16g+3 ||
| | |- |
| || 17L10s || 19\27 < g < 12\17 || g = 647\918 || 19\27 < g < 31\44 || 31\44 < g < 43\61 || 43\61 < g < 55\78 || 10g-7 || 12-17g ||
| | | | [[3L 23s]] |
| || 18L9s || 1\27 < g < 1\18 || g = 5\108 || 1\27 < g < 2\45 || 2\45 < g < 3\63 || 3\63 < g < 4\81 || g || -2g+1\9 ||
| | | | 17\26 < g < 2\3 |
| || 19L8s || 17\27 < g < 12\19 || g = 647\1026 || 17\27 < g < 29\46 || 29\46 < g < 41\65 || 41\65 < g < 53\84 || -5+8g || 12-19g ||
| | | | g = ''19\29'', ''21\32'', 23\35-25\38 |
| || 20L7s || 4\27 < g < 3\20 || g = 161\1080 || 4\27 < g < 7\47 || 7\47 < g < 10\67 || 10\67 < g < 13\87 || -1+7g || 3-20g ||
| | | | 23g-15-(2-3g) = 26g-17 |
| || 21L6s || 5\27 < g < 4\21 || g = 71\378 || 5\27 < g < 9\48 || 9\48 < g < 13\69 || 13\69 < g < 17\90 || 2g-1\3 || -7g+4 ||
| | |- |
| || 22L5s || <span style="line-height: 15.6000003814697px;">11</span>\27 < g < 9\22 || g = 485\1188 || 11\27 < g < 20\49 || 20\49 < g < 29\71 || 29\71 < g < 38\93 || 5g-2 || -22g+9 ||
| | | | [[4L 22s]] |
| || 23L4s || 7\27 < g < 6\23 || g = 323\1242 || 7\27 < g < 13\50 || 13\50 < g < 19\73 || 19\73 < g < 25\96 || 4g-1 || -23g+6 ||
| | | | 6\26 < g < 1\4 |
| || 24L3s || 1\27 < g < 1\24 || g = 17\432 || 1\27 < g < 2\51 || 2/51 < g < 3\75 || 3\75 < g < 4\99 || g || -8g+1\3 ||
| | | | g = ''7\30'', 8\34, 9\38-10\42 |
| || 25L2s || 14\27 < g < 13\25 || g = 701\1350 || 14\27 < g < 27\52 || 27\52 < g < 40\77 || 40\77 < g < 53\102 || 2g-1 || -25g+13 ||
| | | | 11g-5\2-(1\2-2g) = 13g-3 |
| || 26L1s || 1\27 < g < 1\26 || g = 53\1404 || 1\27 < g < 2\53 || 2\53 < g < 3\79 || 3\79 < g < 4\105 || g || -26g+1 ||
| | |- |
| | | | [[5L 21s]] |
| | | | 5\26 < g < 1\5 |
| | | | g = ''6\31'', 7\36, 8\41-9\46 |
| | | | 21g-4-(1-5g) = 26g-5 |
| | |- |
| | | | [[6L 20s]] |
| | | | 4\26 < g < 1\6 |
| | | | g = ''5\32'', 6\38, 7\44-8\50 |
| | | | 10g-3\2-(1\2-3g) = 13g-2 |
| | |- |
| | | | [[7L 19s]] |
| | | | 11\26 < g < 3\7 |
| | | | g = 14\33, 17\40, 20\47-23\54 |
| | | | 19g-8-(3-7g) = 26g-11 |
| | |- |
| | | | [[8L 18s]] |
| | | | 3\26 < g < 1\8 |
| | | | g = 4\34, 5\42, 6\50-7\58 |
| | | | 9g-1-(1\2-4g) = 13g-3\2 |
| | |- |
| | | | [[9L 17s]] |
| | | | 23\26 < g < 8\9 |
| | | | g = 31\35, 39\44, 47\53-55\62 |
| | | | 17g-15-(8-9g) = 26g-23 |
| | |- |
| | | | [[10L 16s]] |
| | | | 5\26 < g < 2\10 |
| | | | g = 7\36, 9\46, 11\56-13\66 |
| | | | 8g-3\2-(1-5g) = 13g-5\2 |
| | |- |
| | | | [[11L 15s]] |
| | | | 7\26 < g < 3\11 |
| | | | g = 10\37, 13\48, 16\59-19\70 |
| | | | 15g-4-(3-11g) = 26g-7 |
| | |- |
| | | | [[12L 14s]] |
| | | | 2\26 < g < 1\12 |
| | | | g = 3\38, 4\50, 5\62-6\74 |
| | | | 7g-1\2-(1\2-6g) = 13g-1 |
| | |- |
| | | | ''[[13L 13s]] = 1L 1s (13)'' |
| | | | ''1\26 < g < 1\13'' |
| | | | ''g = 2\39, 3\52, 4\65-5\78'' |
| | | | ''g-(1\13-g) = 2g-1\13'' |
| | |- |
| | | | [[14L 12s]] |
| | | | 11\26 < g < 6\14 |
| | | | g = '''17\40''', 23\54, 29\68-35\82 |
| | | | 6g-5\2-(3-7g) = 13g-11\2 |
| | |- |
| | | | [[15L 11s]] |
| | | | 19\26 < g < 11\15 |
| | | | g = '''30\41''', 41\56, 52\71-63\86 |
| | | | 11g-8-(11-15g) = 26g-19 |
| | |- |
| | | | [[16L 10s]] |
| | | | 8\26 < g < 5\16 |
| | | | g = '''13\42''', 18\58, 23\74-28\90 |
| | | | 5g-3\2-(5\2-8g) = 13g-4 |
| | |- |
| | | | [[17L 9s]] |
| | | | 3\26 < g < 2\17 |
| | | | g = '''5\43''', 7\60, 9\77-11\94 |
| | | | 9g-1-(2-17g) = 26g-3 |
| | |- |
| | | | [[18L 8s]] |
| | | | 10\26 < g < 7\18 |
| | | | g = '''17\44''', 24\62, 31\80-38\98 |
| | | | 4g-3\2-(7\2-9g) = 13g-5 |
| | |- |
| | | | [[19L 7s]] |
| | | | 15\26 < g < 11\19 |
| | | | g = '''26\45''', 37\64, 48\83-59\102 |
| | | | 7g-4-(11-19g) = 26g-15 |
| | |- |
| | | | [[20L 6s]] |
| | | | 9\26 < g < 7\20 |
| | | | g = '''16\46''', 23\66, 30\86-37\106 |
| | | | 3g-1-(7\2-10g) = 13g-9\2 |
| | |- |
| | | | [[21L 5s]] |
| | | | 21\26 < g < 17\21 |
| | | | g = '''38\47''', 55\68, 72\89-89\110 |
| | | | 5g-4-(17-21g) = 26g-21 |
| | |- |
| | | | [[22L 4s]] |
| | | | 7\26 < g < 6\22 |
| | | | g = '''13\48''', 19\70, 25\92-31\114 |
| | | | 2g-1\2-(3-11g) = 13g-7\2 |
| | |- |
| | | | [[23L 3s]] |
| | | | 9\26 < g < 8\23 |
| | | | g = '''17\49''', 25\72, 33\95-41\118 |
| | | | 3g-1-(8-23g) = 26g-9 |
| | |- |
| | | | ''[[24L 2s]] = 12L 1s (2)'' |
| | | | ''1\26 < g < 1\24'' |
| | | | ''g = '''2\50''', 3\74, 4\98-5\122'' |
| | | | ''g-(1\2-12g) = 13g-1\2'' |
| | |- |
| | | | [[25L 1s|''25L 1s'']] |
| | | | ''1\26 < g < 1\25'' |
| | | | ''g = '''2\51''', 3\76, 4\101-5\126'' |
| | | | ''g-(1-25g) = 26g-1'' |
| | |} |
|
| |
|
| =28= | | == 27-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L27s || 27\28 < g < 1 || g = 55\56 || 27\28 < g < 28\29 || 28\29 < g < 29\30 || 29\30 < g < 30\31 || -26+27g || -g+1 || | | |- |
| || 2L26s || 13\28 < g < 1\2 || g = 27\56 || 13\28 < g < 14\30 || 14\30 < g < 15\32 || 15\32 < g < 16\34 || 13g-6 || -2g+1\2 || | | ! | L-s pattern |
| || 3L25s || 9\28 < g < 1\3 || g = 55\168 || 9\28 < g < 10\31 || <span style="line-height: 15.6000003814697px;">10\31 < g < 11\34</span> || 11\34 < g < 12\37 || -8+25g || 1-3g || | | ! | Generator range |
| || 4L24s || 6\28 < g < 1\4 || g = 13\56 || 6\28 < g < 7\32 || 7\32 < g < 8\36 || 8\36 < g < 9\40 || 6g-5\4 || -g+1\4 || | | ! | Boundaries of best, better, good behavior |
| || 5L23s || 11\28 < g < 2\5 || g = 111\280 || 11\28 < g < 13\33 || 13\33 < g < 15\38 || 15\38 < g < 17\43 || -9+23g || 2-5g || | | ! | Large step-Small step |
| || 6L22s || 9\28 < g < 2\6 || g = 55\168 || 9\28 < g < 11\34 || 11\34 < g < 13\40 || 13\40 < g < 15\46 || -7\2+11g || -3g+1 || | | |- |
| || 7L21s || 3\28 < g < 1\7 || g = 7\56 || 3\28 < g < 4\35 || 4\35 < g < 5\42 || 5\42 < g < 6\49 || -2\7+3g || -g+1\7 || | | | | [[1L 26s]] |
| || 8L20s || 3\28 < g < 1\8 || g = 13\112 || 3\28 < g < 4\36 || 4\36 < g < 5\44 || 5\44 < g < 6\52 || 5g-1\2 || 1\4-2g || | | | | 26\27 < g < 1 |
| || 9L19s || 3\28 < g < 1\9 || g = 55\504 || 3\28 < g < 4\37 || 4\37 < g < 5\46 || 5\46 < g < 6\55 || -2+19g || -9g+1 || | | | | g = ''27\28, 28\29, 29\30-30\31'' |
| || 10L18s || 11\28 < g < 4\10 || g = 111\280 || 11\28 < g < 15\38 || 15\38 < g < 19\48 || 19\48 < g < 23\58 || -7\2+4g || 2-5g || | | | | 26g-25-(1-g) = 27g-26 |
| || 11L17s || 5\28 < g < 2\11 || g = 111\616 || 5\28 < g < 7\39 || 7\39 < g < 9\50 || 9\50 < g < 11\61 || 17g-3 || -11g+2 || | | |- |
| || 12L16s || 2\28 < g < 1\12 || g = 13\168 || 2\28 < g < 3\40 || 3\40 < g < 4\52 || 4\52 < g < 5\64 || 4g-1\4 || 1\4-3g || | | | | [[2L 25s]] |
| || 13L15s || 15\28 < g < 7\13 || g = 391\728 || 15\28 < g < 22\41 || 22\41 < g < 29\54 || 29\54 < g < 36\67 || 15g-8 || -13g+7 ||
| | | | 13\27 < g < 1\2 |
| || 14L14s || 1\28 < g < 1\14 || g = 3\56 || 1\28 < g < 2\42 || 2\42 < g < 3\56 || 3\56 < g < 4\70 || g || -g+1\14 ||
| | | | g = ''14\29, 15\31, 16\33''-17\35 |
| || <span style="line-height: 15.6000003814697px;">15L13s</span> || 13\28 < g < 7\15 || g = 391\840 || 13\28 < g < 20\43 || 20\43 < g < 27\58 || 27\58 < g < 34\73 || 13g-6 || 7-15g ||
| | | | 25g-12-(1-2g) = 27g-12 |
| || <span style="line-height: 15.6000003814697px;">16L12s</span> || 5\28 < g < 3\16 || g = 41\224 || 5\28 < g < 8\44 || 8\44 < g < 11\60 || 11\60 < g < 14\76 || -1\2+3g || -4g+3\4 ||
| | |- |
| || <span style="line-height: 15.6000003814697px;">17L11s</span> || 23\28 < g < 14\17 || g = 783\952 || 23\28 < g < 37\45 || 37\45 < g < 51\62 || 51\62 < g < 65\79 || 11g-9 || -17g+13 ||
| | | | [[3L 24s]] |
| || <span style="line-height: 15.6000003814697px;">18L10s</span> || 3\28 < g < 2\18 || g = 55\504 || 3\28 < g < 5\46 || 5\46 < g < 7\64 || 7\64 < g < 9\82 || 5g-1\2 || 1-9g ||
| | | | 8\27 < g < 1\3 |
| || <span style="line-height: 15.6000003814697px;">19L9s</span> || 25\28 < g < 17\19 || g = 951\1064 || 25\28 < g < 42\47 || 42\47 < g < 59\66 || 59\66 < g < 76\85 || 9g-8 || -19g+17 ||
| | | | g = ''9\30'', ''10\33'', 11\36-12\39 |
| || <span style="line-height: 15.6000003814697px;">20L</span>8s || 4\28 < g < 3\20 || g = 41\280 || 4\28 < g < 7\48 || 7\48 < g < 10\68 || 10\68 < g < 13\88 || -1\4+2g || 3\4-5g ||
| | | | 8g-7\3-(1\3-3g) = 9g-8\3 |
| || <span style="line-height: 15.6000003814697px;">21L7s</span> || 1\28 < g < 1\21 || g = 7\168 || 1\28 < g < 2\49 || 2\49 < g < 3\70 || 3\70 < g < 4\91 || g || <span style="line-height: 15.6000003814697px;">-1\7+3g</span> ||
| | |- |
| || <span style="line-height: 15.6000003814697px;">22L</span>6s || 5\28 < g < 4\22 || g = 111\616 || 5\28 < g < 9\50 || 9\50 < g < 13\72 || 13\72 < g < 17\94 || 3g-1\2 || -11g+2 ||
| | | | [[4L 23s]] |
| || <span style="line-height: 15.6000003814697px;">23L</span>5s || 17\28 < g < 14\23 || g = 783\1288 || 17\28 < g < 31\51 || 31\51 < g < 45\74 || 45\74 < g < 59\97 || 5g-3 || -23g+14 ||
| | | | 20\27 < g < 3\4 |
| || <span style="line-height: 15.6000003814697px;">24L</span>4s || 1\28 < g < 1\24 || g = 13\336 || 1\28 < g < 2\52 || 2\52 < g < 3\76 || 3\76 < g < 4\100 || g || -6g+1\4 ||
| | | | g = ''23\31'', 26\35, 29\39-32\43 |
| || <span style="line-height: 15.6000003814697px;">25L</span>3s || 19\28 < g < 17\25 || g = 951\1400 || 19\28 < g < 36\53 || 36\53 < g < 53\78 || 53\76 < g < 70\103 || 3g-2 || -25g+17 ||
| | | | 23g-17-(3-4g) = 19g-14 |
| || <span style="line-height: 15.6000003814697px;">26L</span>2s || 13\28 < g < 12\26 || g = 391\728 || 13\28 < g < 25\54 || 25\54 < g < 37\80 || 37\80 < g < 49\106 || g-1\2 || -13g+19\2 ||
| | |- |
| || 27L1s || 1\28 < g < 1\27 || g = 55\1512 || 1\28 < g < 2\55 || 2\55 < g < 3\82 || 3\82 < g < 4\109 || g || -27g+1 ||
| | | | [[5L 22s]] |
| | | | 16\27 < g < 3\5 |
| | | | g = ''19\32'', 22\37, 25\42-28\47 |
| | | | 22g-13-(3-5g) = 27g-16 |
| | |- |
| | | | [[6L 21s]] |
| | | | 4\27 < g < 1\6 |
| | | | g = ''5\33'', 6\39, 7\45-8\51 |
| | | | 7g-1-(1\3-2g) = 9g-4\3 |
| | |- |
| | | | [[7L 20s]] |
| | | | 23\27 < g < 6\7 |
| | | | g = 29\34, 35\41, 41\48-47\55 |
| | | | 20g-17-(6-7g) = 27g-23 |
| | |- |
| | | | [[8L 19s]] |
| | | | 10\27 < g < 3\8 |
| | | | g = 13\35, 16\43, 19\51-22\59 |
| | | | 19g-7-(3-8g) = 27g-10 |
| | |- |
| | | | [[9L 18s]] |
| | | | 2\27 < g < 1\9 |
| | | | g = 3\36, 4\45, 5\54-6\63 |
| | | | 2g-1\9-(1\9-g) = 3g-1\9 |
| | |- |
| | | | [[10L 17s]] |
| | | | 8\27 < g < 3\10 |
| | | | g = 11\37, 14\47, 17\57–20\67 |
| | | | 17g-5-(3-10g) = 27g-8 |
| | |- |
| | | | [[11L 16s]] |
| | | | 22\27 < g < 9\11 |
| | | | g = 31\38, 40\49, 49\60-58\71 |
| | | | 16g-13-(9-11g) = 27g-22 |
| | |- |
| | | | [[12L 15s]] |
| | | | 2\27 < g < 1\12 |
| | | | g = 3\39, 4\51, 5\63-6\75 |
| | | | 5g-1\3-(1\3-4g) = 9g-2\3 |
| | |- |
| | | | [[13L 14s]] |
| | | | 2\27 < g < 1\13 |
| | | | g = '''3\40''', 4\53, 5\66-6\79 |
| | | | 14g-1-(1-13g) = 27g-2 |
| | |- |
| | | | [[14L 13s]] |
| | | | 25\27 < g < 13\14 |
| | | | g = '''38\41''', 51\55, 64\69-77\83 |
| | | | 13g-12-(13-14g) = 27g-25 |
| | |- |
| | | | [[15L 12s]] |
| | | | 7\27 < g < 4\15 |
| | | | g = '''11\42''', 15\57, 19\72-23\87 |
| | | | 4g-1-(4\3-5g) = 9g-4\3 |
| | |- |
| | | | [[16L 11s]] |
| | | | 5\27 < g < 3\16 |
| | | | g = '''8\43''', 11\59, 14\75-17\91 |
| | | | 11g-2-(3-16g) = 27g-5 |
| | |- |
| | | | [[17L 10s]] |
| | | | 19\27 < g < 12\17 |
| | | | g = '''31\44''', 43\61, 55\78-67\95 |
| | | | 10g-7-(12-17g) = 27g-19 |
| | |- |
| | | | ''[[18L 9s]] = 2L 1s (9)'' |
| | | | ''1\27 < g < 1\18'' |
| | | | ''g = '''2\45''', 3\63, 4\81-5\99'' |
| | | | ''g-(1\9-2g) = 3g-1\9'' |
| | |- |
| | | | [[19L 8s]] |
| | | | 17\27 < g < 12\19 |
| | | | g = '''29\46''', 41\65, 53\84-65\103 |
| | | | 8g-5-(12-19g) = 27g-17 |
| | |- |
| | | | [[20L 7s]] |
| | | | 4\27 < g < 3\20 |
| | | | g = '''7\47''', 10\67, 13\87-16\107 |
| | | | 7g-1-(3-20g) = 27g-4 |
| | |- |
| | | | [[21L 6s]] |
| | | | 5\27 < g < 4\21 |
| | | | g = '''9\48''', 13\69, 17\90-17\111 |
| | | | 2g-1\3-(4\3-7g) = 9g-5\3 |
| | |- |
| | | | [[22L 5s]] |
| | | | 11\27 < g < 9\22 |
| | | | g = '''20\49''', 29\71, 38\93-47\115 |
| | | | 5g-2-(9-22g) = 27g-11 |
| | |- |
| | | | [[23L 4s]] |
| | | | 7\27 < g < 6\23 |
| | | | g = '''13\50''', 19\73, 25\96-31\119 |
| | | | 4g-1-(6-23g) = 27g-7 |
| | |- |
| | | | ''[[24L 3s]] = 8L 1s (3)'' |
| | | | ''1\27 < g < 1\24'' |
| | | | ''g = '''2\51''', 3\75, 4\99-5\123'' |
| | | | ''g-(1\3-8g) = 9g-1\3'' |
| | |- |
| | | | [[25L 2s]] |
| | | | 14\27 < g < 13\25 |
| | | | g = '''27\52''', 40\77, 53\102-66\127 |
| | | | 2g-1-(13-25g) = 24g-14 |
| | |- |
| | | | [[26L 1s|''26L 1s'']] |
| | | | ''1\27 < g < 1\26'' |
| | | | ''g = '''2\53''', 3\79, 4\105-5\131'' |
| | | | ''g-(1-26g) = 27g-1'' |
| | |} |
|
| |
|
| =29= | | == 28-tone == |
| ||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff;">Midpoint</span> ||~ Range of propriety ||~ Range of maximum expressiveness ||~ <span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span> ||~ Large step ||~ Small step || | | {| class="wikitable" |
| || 1L28s || 28\29 < g < 1 || g = 57\58 || 28\29 < g < 29\30 || 29\30 < g < 30\31 || 30\31 < g < 31\32 || -27+28g || -g+1 || | | |- |
| || 2L27s || 14\29 < g < 1\2 || g = 57\116 || 14\29 < g < 15\31 || 15\31 < g < 16\33 || 16\33 < g < 17\35 || 27g-13 || -2g+1 || | | ! | L-s pattern |
| || 3L26s || 19\29 < g < 2\3 || g = 115\174 || 19\29 < g < 21\32 || 21\32 < g < 23\35 || 23\35 < g < 25\38 || -17+23g || 2-3g || | | ! | Generator range |
| || 4L25s || 7\29 < g < 1\4 || g = 57\232 || 7\29 < g < 8\33 || 8\33 < g < 9\37 || 9\37 < g < 10\41 || 25g-6 || -4g+1 || | | ! | Boundaries of best, better, good behavior |
| || 5L24s || 23\29 < g < 4\5 || g = 231\290 || 23\29 < g < 27\34 || 27\34 < g < 31\39 || 31\39 < g < 35\44 || -19+24g || 4-5g || | | ! | Large step-Small step |
| || 6L23s || 24\29 < g < 5\6 || g = 289\348 || 24\29 < g < 29\35 || 29\35 < g < 34\41 || 34\41 < g < 39\47 || -19+23g || -6g+5 || | | |- |
| || 7L22s || 4\29 < g < 1\7 || g = 57\406 || 4\29 < g < 5\36 || 5\36 < g < 6\43 || 6\43 < g < 7\50 || -3+22g || -7g+1 || | | | | [[1L 27s]] |
| || 8L21s || 18\29 < g < 5\8 || g = 289\464 || 18\29 < g < 23\37 || 23\37 < g < 28\45 || 28\45 < g < 33\53 || <span style="line-height: 15.6000003814697px;">-13+21g</span> || <span style="line-height: 15.6000003814697px;">-8g+5</span> || | | | | 27\28 < g < 1 |
| || 9L20s || 16\29 < g < 5\9 || g = 289\522 || 16\29 < g < 21\38 || 21\38 < g < 26\47 || 26\47 < g < 31\56 || -11+20g || -9g+5 ||
| | | | g = ''28\29, 29\30, 30\31-30\32'' |
| || 10L19s || 26\29 < g < 9\10 || g = 521\580 || 26\29 < g < 35\39 || 35\39 < g < 44\49 || 44\49 < g < 53\59 || -17+19g || 9-10g || | | | | 27g-26-(1-g) = 28g-27 |
| || 11L18s || 21\29 < g < 8\11 || g = 463\638 || 21\29 < g < 29\40 || 29\40 < g < 37\51 || 37\51 < g < 45\62 || 18g-13 || -11g+8 ||
| | |- |
| || 12L17s || 12\29 < g < 5\12 || g = 289\696 || 12\29 < g < 17\41 || 17\41 < g < 22\53 || 22\53 < g < 27\65 || 17g-7 || 5-12g || | | | | [[2L 26s]] |
| || 13L16s || 20\29 < g < 9\13 || g = 521\754 || 20\29 < g < 29\42 || 29\42 < g < 38\55 || 38\55 < g < 47\68 || 16g+11 || -13g+9 || | | | | 13\28 < g < 1\2 |
| || 14L15s || 2\29 < g < 1\14 || g = 57\812 || 2\29 < g < 3\43 || 3\43 < g < 4\57 || 4\57 < g < 5\71 || 15g-1 || -14g+1 || | | | | g = ''14\30, 15\32, 16\34''-17\36 |
| || 15L14s || 27\29 < g < 14\15 || g = 811\870 || 27\29 < g < 41\44 || 41\44 < g < 55\59 || 55\59 < g < 69\74 || 14g-13 || 14-15g ||
| | | | 13g-6-(1\2-g) = 14g-13\2 |
| || 16L13s || 9\29 < g < 5\16 || g = 289\928 || 9\29 < g < 14\45 || 14\45 < g < 19\61 || 19\61 < g < 24\77 || -4+13g || -16g+5 ||
| | |- |
| || 17L12s || 17\29 < g < 10\17 || g = 579\986 || 17\29 < g < 27\46 || 27\46 < g < 37\63 || 37\63 < g < 47\80 || 17g-7 || -12g+5 ||
| | | | [[3L 25s]] |
| || 18L11s || 8\29 < g < 5\18 || g = 289\1044 || 8\29 < g < 13\47 || 13\47 < g < 18\65 || 18\65 < g < 23\83 || 11g-3 || 5-18g ||
| | | | 9\28 < g < 1\3 |
| || 19L10s || 3\29 < g < 2\19 || g = 115\1102 || 3\29 < g < 5\48 || 5\48 < g < 7\67 || 7\67 < g < 9\86 || 10g-1 || -19g+2 ||
| | | | g = ''10\31'', ''11\34'', 12\37-13\40 |
| || 20L9s || 13\29 < g < 9\20 || g = 521\1160 || 13\29 < g < 22\49 || 22\49 < g < 31\69 || 31\69 < g < 40\89 || 9-20g || -5+11g ||
| | | | 25g-8-(1-3g) = 28g-9 |
| || 21L8s || 11\29 < g < 8\21 || g = 463\1216 || 11\29 < g < 19\50 || 19\50 < g < 27\71 || 27\71 < g < 35\92 || 8g-3 || 8-21g ||
| | |- |
| || 22L7s || 25\29 < g < 19\22 || g = 1001\1274 || 25\29 < g < 44\51 || 44\51 < g < 63\73 || 63\73 < g < 82\95 || 7g-6 || -22g+9 ||
| | | | [[4L 24s]] |
| || 23L6s || 5\29 < g < 4\23 || g = 231\1332 || 5\28 < g < 9\52 || 9\52 < g < 13\75 || 13\75 < g < 17\98 || 6g-1 || -23g+4 ||
| | | | 6\28 < g < 1\4 |
| || 24L5s || 6\29 < g < 5\24 || g = 289\1392 || 6\29 < g < 11\53 || 11\53 < g < 16\77 || 16\77 < g < 21\101 || 5g-9 || -24g+5 ||
| | | | g = ''7\32'', 8\36, 9\40-10\44 |
| || 25L4s || 22\29 < g < 19\25 || g = 1001\1450 || 22\29 < g < 41\54 || 41\54 < g < 60\79 || 60\79 < g < 79\104 || 4g-3 || -25g+19 ||
| | | | 6g-5\4-(1\4-g) = 7g-3\2 |
| || 26L3s || 10\29 < g < 9\26 || g = 521\1508 || 10\29 < g < 19\55 || 19\55 < g < 28\81 || 28\81 < g < 37\107 || 3g-1 || -26g+19\2 ||
| | |- |
| || 27L2s || 15\29 < g < 14\27 || g = 811\1564 || 15\29 < g < 29\56 || 29\56 < g < 43\83 || 43\83 < g < 57\110 || 2g-1 || -27g+17 ||
| | | | [[5L 23s]] |
| || 28L1s || 1\29 < g < 1\28 || g = 57\1622 || 1\29 < g < 2\57 || <span style="line-height: 15.6000003814697px;">2\57 < g < 3\85</span> || 3\85 < g < 4\113 || g || -28g+1 ||</pre></div>
| | | | 11\28 < g < 2\5 |
| <h4>Original HTML content:</h4>
| | | | g = ''13\33'', 15\38, 17\43-19\48 |
| <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>Generator ranges of MOS</title></head><body>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. The fourth column gives the range of propriety. The fifth column gives the range of maximum expressiveness. Finally, the sixth column gives the top of the range of diatonicity.<br />
| | | | 23g-9-(2-5g) = 28g-11 |
| <br />
| | |- |
| If the number of the <a class="wiki_link" href="/Interval%20class" target="_blank">generic interval</a> 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 <a class="wiki_link" href="/Modal%20UDP%20Notation" target="_blank">chroma-positive</a> generator.<br />
| | | | [[6L 22s]] |
| <br />
| | | | 9\28 < g < 2\6 |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2, 3, 4"></a><!-- ws:end:WikiTextHeadingRule:0 -->2, 3, 4</h1>
| | | | g = ''11\34'', 13\40, 15\46-17\52 |
|
| | | | 11g-7\2-(1-3g) = 14g-9\2 |
| | |- |
| | | | [[7L 21s]] |
| | | | 3\28 < g < 1\7 |
| | | | g = 4\35, 5\42, 6\49-7\56 |
| | | | 3g-2\7-(1\7-g) = 4g-3\7 |
| | |- |
| | | | [[8L 20s]] |
| | | | 3\28 < g < 1\8 |
| | | | g = 4\36, 5\44, 6\52-7\60 |
| | | | 5g-1\2-(1\4-2g) = 7g-3\4 |
| | |- |
| | | | [[9L 19s]] |
| | | | 3\28 < g < 1\9 |
| | | | g = 4\37, 5\46, 6\55-7\64 |
| | | | 19g-2-(1-9g) = 28g-3 |
| | |- |
| | | | [[10L 18s]] |
| | | | 11\28 < g < 4\10 |
| | | | g = 15\38, 19\48, 23\58-27\68 |
| | | | 9g-7\2-(2-5g) = 14g-11\2 |
| | |- |
| | | | [[11L 17s]] |
| | | | 5\28 < g < 2\11 |
| | | | g = 7\39, 9\50, 11\61-13\72 |
| | | | 17g-3-(2-11g) = 28g-5 |
| | |- |
| | | | [[12L 16s]] |
| | | | 2\28 < g < 1\12 |
| | | | g = '''3\40''', 4\52, 5\64-6\76 |
| | | | 4g-1\4-(1\4-3g) = 7g-1\2 |
| | |- |
| | | | [[13L 15s]] |
| | | | 15\28 < g < 7\13 |
| | | | g = '''22\41''', 29\54, 36\67-43\80 |
| | | | 15g-8-(7-13g) = 28g-15 |
| | |- |
| | | | ''[[14L 14s]] = 1L 1s (14)'' |
| | | | ''1\28 < g < 1\14'' |
| | | | ''g = '''2\42''', 3\56, 4\70-5\84'' |
| | | | ''g-(1\14-g) = 2g-1\14'' |
| | |- |
| | | | [[15L 13s]] |
| | | | 13\28 < g < 7\15 |
| | | | g = '''20\43''', 27\58, 34\73-41\88 |
| | | | 13g-6-(7-15g) = 28g-13 |
| | |- |
| | | | [[16L 12s]] |
| | | | 5\28 < g < 3\16 |
| | | | g = '''8\44''', 11\60, 14\76-17\92 |
| | | | 3g-1\2-(3\4-4g) = 7g-7\4 |
| | |- |
| | | | [[17L 11s]] |
| | | | 23\28 < g < 14\17 |
| | | | g = '''37\45''', 51\62, 65\79-79\96 |
| | | | 11g-9-(14-17g) = 28g-23 |
| | |- |
| | | | [[18L 10s]] |
| | | | 3\28 < g < 2\18 |
| | | | g = '''5\46''', 7\64, 9\82-11\100 |
| | | | 5g-1\2-(1-9g) = 14g-3\2 |
| | |- |
| | | | [[19L 9s]] |
| | | | 25\28 < g < 17\19 |
| | | | g = '''42\47''', 59\66, 76\85-93\104 |
| | | | 9g-8-(17-19g) = 28g-25 |
| | |- |
| | | | [[20L 8s]] |
| | | | 4\28 < g < 3\20 |
| | | | g = '''7\48''', 10\68, 13\88-16\108 |
| | | | 2g-1\4-(3\4-5g) = 7g-1 |
| | |- |
| | | | ''[[21L 7s]] = 3L 1s (7)'' |
| | | | ''1\28 < g < 1\21'' |
| | | | ''g = '''2\49''', 3\70, 4\91-5\112'' |
| | | | ''g-(1\7-3g) = 4g-1\7'' |
| | |- |
| | | | [[22L 6s]] |
| | | | 5\28 < g < 4\22 |
| | | | g = '''9\50''', 13\72, 17\94-21\116 |
| | | | 3g-1\2-(2-11g) = 14g-5\2 |
| | |- |
| | | | [[23L 5s]] |
| | | | 17\28 < g < 14\23 |
| | | | g = '''31\51''', 45\74, 59\97-73\120 |
| | | | 5g-3-(14-23g) = 28g-17 |
| | |- |
| | | | ''[[24L 4s]] = 6L 1s (4)'' |
| | | | ''1\28 < g < 1\24'' |
| | | | ''g = '''2\52''', 3\76, 4\100-5\124'' |
| | | | ''g-(1\4-6g) = 7g-1\4'' |
| | |- |
| | | | [[25L 3s]] |
| | | | 19\28 < g < 17\25 |
| | | | g = '''36\53''', 53\78, 70\103-87\128 |
| | | | 3g-2-(17-25g) = 28g-19 |
| | |- |
| | | | ''[[26L 2s]] = 13L 1s (2)'' |
| | | | ''15\28 < g < 14\26'' |
| | | | ''g = '''29\54''', 43\80, 57\106-71\132'' |
| | | | ''g-1\2-(7-13g) = 14g-15\2'' |
| | |- |
| | | | [[27L 1s|''27L 1s'']] |
| | | | ''1\28 < g < 1\27'' |
| | | | ''g = '''2\55''', 3\82, 4\109-5\136'' |
| | | | ''g-(1-27g) = 28g-1'' |
| | |} |
|
| |
|
| <table class="wiki_table">
| | == 29-tone == |
| <tr>
| | {| class="wikitable" |
| <th>Large-small numbers<br />
| | |- |
| </th>
| | ! | L-s pattern |
| <th>Generator range<br />
| | ! | Generator range |
| </th>
| | ! | Boundaries of best, better, good behavior |
| <th>Midpoint<br />
| | ! | Large step-Small step |
| </th>
| | |- |
| <th>Range of propriety<br />
| | | | [[1L 28s]] |
| </th>
| | | | 28\29 < g < 1 |
| <th>Range of maximum expressiveness<br />
| | | | g = ''29\30, 30\31, 31\32-32\33'' |
| </th>
| | | | 28g-27-(1-g) = 29g-28 |
| <th>Top<br />
| | |- |
| range of diatonicity<br />
| | | | [[2L 27s]] |
| </th>
| | | | 14\29 < g < 1\2 |
| <th>Large step<br />
| | | | g = ''15\31, 16\33, 17\35''-18\37 |
| </th>
| | | | 27g-13-(1-2g) = 29g-15 |
| <th>Small step<br />
| | |- |
| </th>
| | | | [[3L 26s]] |
| </tr>
| | | | 19\29 < g < 2\3 |
| <tr>
| | | | g = ''21\32'', ''23\35'', 25\38-27\41 |
| <td>1L1s<br />
| | | | 26g-17-(2-3g) = 29g-19 |
| </td>
| | |- |
| <td>1\2 &lt; g &lt; 1<br />
| | | | [[4L 25s]] |
| </td>
| | | | 7\29 < g < 1\4 |
| <td>g = 3\4<br />
| | | | g = ''8\33'', 9\37, 10\41-11\45 |
| </td>
| | | | 25g-6-(1-4g) = 29g-7 |
| <td>1\2 &lt; g &lt; 2\3<br />
| | |- |
| </td>
| | | | [[5L 24s]] |
| <td>2\3 &lt; g &lt; 3\4<br />
| | | | 23\29 < g < 4\5 |
| </td>
| | | | g = ''27\34'', 31\39, 35\44-39\49 |
| <td>3\4 &lt; g &lt; 4\5<br />
| | | | 24g-19-(4-5g) = 29g-23 |
| </td>
| | |- |
| <td>g<br />
| | | | [[6L 23s]] |
| </td>
| | | | 24\29 < g < 5\6 |
| <td>1-g<br />
| | | | g = ''29\35'', 34\41, 39\47-44\53 |
| </td>
| | | | 23g-19-(5-6g) = 29g-24 |
| </tr>
| | |- |
| <tr>
| | | | [[7L 22s]] |
| <td>1L2s<br />
| | | | 4\29 < g < 1\7 |
| </td>
| | | | g = ''5\36'', 6\43, 7\50-8\57 |
| <td>2\3 &lt; g &lt; 1<br />
| | | | 22g-3-(1-7g) = 29g-4 |
| </td>
| | |- |
| <td>g = 5\6<br />
| | | | [[8L 21s]] |
| </td>
| | | | 18\29 < g < 5\8 |
| <td>2\3 &lt; g &lt; 3\4<br />
| | | | g = 23\37, 28\45, 33\53-38\61 |
| </td>
| | | | 21g-13-(5-8g) = 29g-18 |
| <td>3\4 &lt; g &lt; 4\5<br />
| | |- |
| </td>
| | | | [[9L 20s]] |
| <td>4\5 &lt; g &lt; 5\6<br />
| | | | 16\29 < g < 5\9 |
| </td>
| | | | g = 21\38, 26\47, 31\56-36\65 |
| <td>2g-1<br />
| | | | 20g-11-(5-9g) = 29g-16 |
| </td>
| | |- |
| <td>1-g<br />
| | | | [[10L 19s]] |
| </td>
| | | | 26\29 < g < 9\10 |
| </tr>
| | | | g = 35\39, 44\49, 53\59-62\69 |
| <tr>
| | | | 19g-17-(9-10g) = 29g-26 |
| <td>2L1s<br />
| | |- |
| </td>
| | | | [[11L 18s]] |
| <td>1\3 &lt; g &lt; 1\2<br />
| | | | 21\29 < g < 8\11 |
| </td>
| | | | g = '''29\40''', 37\51, 45\62-53\73 |
| <td>g = 5\12<br />
| | | | 18g-13-(8-11g) = 29g-21 |
| </td>
| | |- |
| <td>1\3 &lt; g &lt; 2\5<br />
| | | | [[12L 17s]] |
| </td>
| | | | 12\29 < g < 5\12 |
| <td>2\5 &lt; g &lt; 3\7<br />
| | | | g = '''17\41''', 22\53, 27\65-32\77 |
| </td>
| | | | 17g-7-(5-12g) = 29g-12 |
| <td>3\7 &lt; g &lt; 4\9<br />
| | |- |
| </td>
| | | | [[13L 16s]] |
| <td>g<br />
| | | | 20\29 < g < 9\13 |
| </td>
| | | | g = '''29\42''', 38\55, 47\68-56\81 |
| <td>1-2g<br />
| | | | 16g+11-(9-13g) = 29g-20 |
| </td>
| | |- |
| </tr>
| | | | [[14L 15s]] |
| <tr>
| | | | 2\29 < g < 1\14 |
| <td>1L3s<br />
| | | | g = '''3\43''', 4\57, 5\71-6\85 |
| </td>
| | | | 15g-1-(1-14g) = 29g-2 |
| <td>3\4 &lt; g &lt; 1<br />
| | |- |
| </td>
| | | | [[15L 14s]] |
| <td>g = 7\8<br />
| | | | 27\29 < g < 14\15 |
| </td>
| | | | g = '''41\44''', 55\59, 69\74-83\89 |
| <td>3\4 &lt; g &lt; 4\5<br />
| | | | 14g-13-(14-15g) = 29g-27 |
| </td>
| | |- |
| <td>4\5 &lt; g &lt; 5\6<br />
| | | | [[16L 13s]] |
| </td>
| | | | 9\29 < g < 5\16 |
| <td>5\6 &lt; g &lt; 6\7<br />
| | | | g = '''14\45''', 19\61, 24\77-29\93 |
| </td>
| | | | 13g-4-(5-16g) = 29g-9 |
| <td>3g-2<br />
| | |- |
| </td>
| | | | [[17L 12s]] |
| <td>1-g<br />
| | | | 17\29 < g < 10\17 |
| </td>
| | | | g = '''27\46''', 37\63, 47\80-57\97 |
| </tr>
| | | | 12g-5-(7-17g) = 29g-12 |
| <tr>
| | |- |
| <td>2L2s<br />
| | | | [[18L 11s]] |
| </td>
| | | | 8\29 < g < 5\18 |
| <td>1\4 &lt; g &lt; 1\2<br />
| | | | g = '''13\47''', 18\65, 23\83-28\101 |
| </td>
| | | | 11g-3-(5-18g) = 29g-8 |
| <td>g = 3\8<br />
| | |- |
| </td>
| | | | [[19L 10s]] |
| <td>1\4 &lt; g &lt; 2\6<br />
| | | | 3\29 < g < 2\19 |
| </td>
| | | | g = '''5\48''', 7\67, 9\86-11\105 |
| <td>2\6 &lt; g &lt; 3\8<br />
| | | | 10g-1-(2-19g) = 29g-1 |
| </td>
| | |- |
| <td>3\8 &lt; g &lt; 4\10<br />
| | | | [[20L 9s]] |
| </td>
| | | | 13\29 < g < 9\20 |
| <td>g<br />
| | | | g = '''22\49''', 31\69, 40\89-49\109 |
| </td>
| | | | 9g-4-(9-20g) = 29g-13 |
| <td>1\2-g<br />
| | |- |
| </td>
| | | | [[21L 8s]] |
| </tr>
| | | | 11\29 < g < 8\21 |
| <tr>
| | | | g = '''19\50''', 27\71, 35\92-43\113 |
| <td>3L1s<br />
| | | | 8g-3-(8-21g) = 29g-11 |
| </td>
| | |- |
| <td>1\4 &lt; g &lt; 1\3<br />
| | | | [[22L 7s]] |
| </td>
| | | | 25\29 < g < 19\22 |
| <td>g = 7\24<br />
| | | | g = '''44\51''', 63\73, 82\95-101\117 |
| </td>
| | | | 7g-6-(9-22g) = 29g-15 |
| <td>1\4 &lt; g &lt; 2\7<br />
| | |- |
| </td>
| | | | [[23L 6s]] |
| <td>2\7 &lt; g &lt; 3\10<br />
| | | | 5\29 < g < 4\23 |
| </td>
| | | | g = '''9\52''', 13\75, 17\98-21\121 |
| <td>3\10 &lt; g &lt; 4\13<br />
| | | | 6g-1-(4-23g) = 29g-5 |
| </td>
| | |- |
| <td>g<br />
| | | | [[24L 5s]] |
| </td>
| | | | 6\29 < g < 5\24 |
| <td>1-3g<br />
| | | | g = '''11\53''', 16\77, 21\101-26\125 |
| </td>
| | | | 5g-9-(5-24g) = 29g-14 |
| </tr>
| | |- |
| </table>
| | | | [[25L 4s]] |
| | | | 22\29 < g < 19\25 |
| | | | g = '''41\54''', 60\79, 79\104-98\129 |
| | | | 4g-3-(19-25g) = 29g-22 |
| | |- |
| | | | [[26L 3s]] |
| | | | 10\29 < g < 9\26 |
| | | | g = '''19\55''', 28\81, 37\107-46\133 |
| | | | 3g-1-(9-26g) = 29g-10 |
| | |- |
| | | | [[27L 2s]] |
| | | | 15\29 < g < 14\27 |
| | | | g = '''29\56''', 43\83, 57\110-71\137 |
| | | | 2g-1-(17-27g) = 29g-18 |
| | |- |
| | | | [[28L 1s|''28L 1s'']] |
| | | | ''1\29 < g < 1\28'' |
| | | | ''g = '''2\57''', 3\85, 4\113-5\141'' |
| | | | ''g-(1-28g) = 29g-28'' |
| | |} |
|
| |
|
| <br />
| | [[Category:MOS scale]] |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x5"></a><!-- ws:end:WikiTextHeadingRule:2 -->5</h1>
| | [[Category:Lists of scales]] |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th>Top<br />
| |
| range of diatonicity<br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L4s<br />
| |
| </td>
| |
| <td>4\5 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 9\10<br />
| |
| </td>
| |
| <td>4\5 &lt; g &lt; 5\6<br />
| |
| </td>
| |
| <td>5\6 &lt; g &lt; 6\7<br />
| |
| </td>
| |
| <td>6\7 &lt; g &lt; 7\8<br />
| |
| </td>
| |
| <td>-3+4g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L3s<br />
| |
| </td>
| |
| <td>2\5 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 9\20<br />
| |
| </td>
| |
| <td>2\5 &lt; g &lt; 3\7<br />
| |
| </td>
| |
| <td>3\7 &lt; g &lt; 4\9<br />
| |
| </td>
| |
| <td>4\9 &lt; g &lt; 5\11<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L2s<br />
| |
| </td>
| |
| <td>3\5 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 19\30<br />
| |
| </td>
| |
| <td>3\5 &lt; g &lt; 5\8<br />
| |
| </td>
| |
| <td>5\8 &lt; g &lt; 7\11<br />
| |
| </td>
| |
| <td>7\11 &lt; g &lt; 9\14<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-3g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L1s<br />
| |
| </td>
| |
| <td>1\5 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 9\40<br />
| |
| </td>
| |
| <td>1\5 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>2\9 &lt; g &lt; 3\13<br />
| |
| </td>
| |
| <td>3\13 &lt; g &lt; 4\17<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x6"></a><!-- ws:end:WikiTextHeadingRule:4 -->6</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th>Top<br />
| |
| range of diatonicity<br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L5s<br />
| |
| </td>
| |
| <td>5\6 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 11\12<br />
| |
| </td>
| |
| <td>5\6 &lt; g &lt; 6\7<br />
| |
| </td>
| |
| <td>6\7 &lt; g &lt; 7\8<br />
| |
| </td>
| |
| <td>7\8 &lt; g &lt; 8\9<br />
| |
| </td>
| |
| <td>5g-4<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L4s<br />
| |
| </td>
| |
| <td>2\6 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 5\12<br />
| |
| </td>
| |
| <td>2\6 g &lt; 3\8<br />
| |
| </td>
| |
| <td>3\8 &lt; g &lt; 4\10<br />
| |
| </td>
| |
| <td>4\10 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>2g-1\2<br />
| |
| </td>
| |
| <td>1\2-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L3s<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 3\12<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>2\9 &lt; g &lt; 3\12<br />
| |
| </td>
| |
| <td>3\12 &lt; g &lt; 4\15<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\3-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L2s<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 5\24<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 2\10<br />
| |
| </td>
| |
| <td>2\10 &lt; g &lt; 3\14<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 4\18<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\2-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L1s<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 11\60<br />
| |
| </td>
| |
| <td>1\6 &lt; g &lt; 2\11<br />
| |
| </td>
| |
| <td>2\11 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\21<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-5g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x7"></a><!-- ws:end:WikiTextHeadingRule:6 -->7</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L6s<br />
| |
| </td>
| |
| <td>6\7 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 13\14<br />
| |
| </td>
| |
| <td>6\7 &lt; g &lt; 7\8<br />
| |
| </td>
| |
| <td>7\8 &lt; g &lt; 8\9<br />
| |
| </td>
| |
| <td>8\9 &lt; g &lt; 9\10<br />
| |
| </td>
| |
| <td>6g-5<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L5s<br />
| |
| </td>
| |
| <td>3\7 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 13\28<br />
| |
| </td>
| |
| <td>3\7 &lt; g &lt; 4\9<br />
| |
| </td>
| |
| <td>4\9 &lt; g &lt; 5\11<br />
| |
| </td>
| |
| <td>5\11 &lt; g &lt; 6\13<br />
| |
| </td>
| |
| <td>5g-2<br />
| |
| </td>
| |
| <td>1-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L4s<br />
| |
| </td>
| |
| <td>2\7 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 13\42<br />
| |
| </td>
| |
| <td>2\7 &lt; g &lt; 3\10<br />
| |
| </td>
| |
| <td>3\10 &lt; g &lt; 4\13<br />
| |
| </td>
| |
| <td>4\13 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>4g-1<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L3s<br />
| |
| </td>
| |
| <td>5\7 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 41\56<br />
| |
| </td>
| |
| <td>5\7 &lt; g &lt; 8\11<br />
| |
| </td>
| |
| <td>8\11 &lt; g &lt; 11\15<br />
| |
| </td>
| |
| <td>11\15 &lt; g &lt; 14\19<br />
| |
| </td>
| |
| <td>3g-2<br />
| |
| </td>
| |
| <td>3-4g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L2s<br />
| |
| </td>
| |
| <td>4\7 &lt; g &lt; 3\5<br />
| |
| </td>
| |
| <td>g = 41\70<br />
| |
| </td>
| |
| <td>4\7 &lt; g &lt; 7\12<br />
| |
| </td>
| |
| <td>7\12 &lt; g &lt; 10\17<br />
| |
| </td>
| |
| <td>10\17 &lt; g &lt; 13\22<br />
| |
| </td>
| |
| <td>2g-1<br />
| |
| </td>
| |
| <td>3-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L1s<br />
| |
| </td>
| |
| <td>1\7 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 13\84<br />
| |
| </td>
| |
| <td>1\7 &lt; g &lt; 2\13<br />
| |
| </td>
| |
| <td>2\13 &lt; g &lt; 3\19<br />
| |
| </td>
| |
| <td>3\19 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-6g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x8"></a><!-- ws:end:WikiTextHeadingRule:8 -->8</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L7s<br />
| |
| </td>
| |
| <td>7\8 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 15\16<br />
| |
| </td>
| |
| <td>7\8 &lt; g &lt; 8\9<br />
| |
| </td>
| |
| <td>8\9 &lt; g &lt; 9\10<br />
| |
| </td>
| |
| <td>9\10 &lt; g &lt; 10\11<br />
| |
| </td>
| |
| <td>7g-6<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L6s<br />
| |
| </td>
| |
| <td>3\8 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 7\16<br />
| |
| </td>
| |
| <td>3\8 &lt; g &lt; 4\10<br />
| |
| </td>
| |
| <td>4\10 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 6\14<br />
| |
| </td>
| |
| <td>3g-1<br />
| |
| </td>
| |
| <td>1\2-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L5s<br />
| |
| </td>
| |
| <td>5\8 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 31\48<br />
| |
| </td>
| |
| <td>5\8 &lt; g &lt; 7\11<br />
| |
| </td>
| |
| <td>7\11 &lt; g &lt; 9\14<br />
| |
| </td>
| |
| <td>9\14 &lt; g &lt; 11\17<br />
| |
| </td>
| |
| <td>5g-3<br />
| |
| </td>
| |
| <td>2-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L4s<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 3\16<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 2\12<br />
| |
| </td>
| |
| <td>2\12 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\20<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\4-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L3s<br />
| |
| </td>
| |
| <td>3\8 &lt; g &lt; 2\5<br />
| |
| </td>
| |
| <td>g = 31\80<br />
| |
| </td>
| |
| <td>3\8 &lt; g &lt; 5\13<br />
| |
| </td>
| |
| <td>5\13 &lt; g &lt; 7\18<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 9\23<br />
| |
| </td>
| |
| <td>3g-1<br />
| |
| </td>
| |
| <td>2-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L2s<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 7\48<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 2\14<br />
| |
| </td>
| |
| <td>2\14 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\26<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\2-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L1s<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 15\112<br />
| |
| </td>
| |
| <td>1\8 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\22<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 4\29<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-7g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x9"></a><!-- ws:end:WikiTextHeadingRule:10 -->9</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L8s<br />
| |
| </td>
| |
| <td>8\9 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 17\18<br />
| |
| </td>
| |
| <td>8\9 &lt; g &lt; 9\10<br />
| |
| </td>
| |
| <td>9\10 &lt; g &lt; 10\11<br />
| |
| </td>
| |
| <td>9\10 &lt; g &lt; 10\11<br />
| |
| </td>
| |
| <td>8g-7<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L7s<br />
| |
| </td>
| |
| <td>4\9 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 17\36<br />
| |
| </td>
| |
| <td>4\9 &lt; g &lt; 5\11<br />
| |
| </td>
| |
| <td>5\11 &lt; g &lt; 6\13<br />
| |
| </td>
| |
| <td>6\13 &lt; g &lt; 7\15<br />
| |
| </td>
| |
| <td>7g-3<br />
| |
| </td>
| |
| <td>1-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L6s<br />
| |
| </td>
| |
| <td>2\9 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 5\18<br />
| |
| </td>
| |
| <td>2\9 &lt; g &lt; 3\12<br />
| |
| </td>
| |
| <td>3\12 &lt; g &lt; 4\15<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>2g-1\3<br />
| |
| </td>
| |
| <td>1\3-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: left;">4L5s<br />
| |
| </td>
| |
| <td style="text-align: left;">2\9 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td style="text-align: left;">g = 17\72<br />
| |
| </td>
| |
| <td style="text-align: left;">2\9 &lt; g &lt; 3\13<br />
| |
| </td>
| |
| <td>3\13 &lt; g &lt; 4\17<br />
| |
| </td>
| |
| <td style="text-align: left;">4\17 &lt; g &lt; 5\21<br />
| |
| </td>
| |
| <td style="text-align: left;">5g-1<br />
| |
| </td>
| |
| <td style="text-align: left;">1-4g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L4s<br />
| |
| </td>
| |
| <td>7\9 &lt; g &lt; 4\5<br />
| |
| </td>
| |
| <td>g = 71\90<br />
| |
| </td>
| |
| <td>7\9 &lt; g &lt; 11\1<br />
| |
| </td>
| |
| <td>11\14 &lt; g &lt; 15\19<br />
| |
| </td>
| |
| <td>15\19 &lt; g &lt;18\23<br />
| |
| </td>
| |
| <td>4g-3<br />
| |
| </td>
| |
| <td>4-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L3s<br />
| |
| </td>
| |
| <td>1\9 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 5\36<br />
| |
| </td>
| |
| <td>1\9 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\21<br />
| |
| </td>
| |
| <td>3\21 &lt; g &lt; 4\27<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\3-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L2s<br />
| |
| </td>
| |
| <td>5\9 &lt; g &lt; 4\7<br />
| |
| </td>
| |
| <td>g = 71\126<br />
| |
| </td>
| |
| <td>5\9 &lt; g &lt; 9\16<br />
| |
| </td>
| |
| <td>9\16 &lt; g &lt; 10\23<br />
| |
| </td>
| |
| <td>10\23 &lt; g &lt; 17\30<br />
| |
| </td>
| |
| <td>2g-1<br />
| |
| </td>
| |
| <td>4-7g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L1s<br />
| |
| </td>
| |
| <td>1\9 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 17\144<br />
| |
| </td>
| |
| <td>1\9 &lt; g &lt; 2\17<br />
| |
| </td>
| |
| <td>2\17 &lt; g &lt; 3\25<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 4\33<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-8g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x10"></a><!-- ws:end:WikiTextHeadingRule:12 -->10</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L9s<br />
| |
| </td>
| |
| <td>9\10 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 19\20<br />
| |
| </td>
| |
| <td>9\10 &lt; g &lt; 10\11<br />
| |
| </td>
| |
| <td>10\11 &lt; g &lt; 11\12<br />
| |
| </td>
| |
| <td>11\12 &lt; g &lt; 12\13<br />
| |
| </td>
| |
| <td>-8+9g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L8s<br />
| |
| </td>
| |
| <td>4\10 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 9\20<br />
| |
| </td>
| |
| <td>4\10 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 6\14<br />
| |
| </td>
| |
| <td>6\14 &lt; g &lt; 7\19<br />
| |
| </td>
| |
| <td>-3\2+4g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L7s<br />
| |
| </td>
| |
| <td>3\10 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 19\60<br />
| |
| </td>
| |
| <td>3\10 &lt; g &lt; 4\13<br />
| |
| </td>
| |
| <td>4\13 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 6\19<br />
| |
| </td>
| |
| <td>-2+7g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L6s<br />
| |
| </td>
| |
| <td>2\10 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 9\40<br />
| |
| </td>
| |
| <td>2\10 &lt; g &lt; 3\14<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 4\18<br />
| |
| </td>
| |
| <td>4\19 &lt; g &lt; 5\22<br />
| |
| </td>
| |
| <td>3g-1\2<br />
| |
| </td>
| |
| <td>-2g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L5s<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 3\20<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L4s<br />
| |
| </td>
| |
| <td>3\10 &lt; g &lt; 2\6<br />
| |
| </td>
| |
| <td>g = 19\60<br />
| |
| </td>
| |
| <td>3\10 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 7\22<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 9\28<br />
| |
| </td>
| |
| <td>-1\2+2g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L3s<br />
| |
| </td>
| |
| <td>7\10 &lt; g &lt; 5\7<br />
| |
| </td>
| |
| <td>g = 99\140<br />
| |
| </td>
| |
| <td>7\10 &lt; g &lt; 12\17<br />
| |
| </td>
| |
| <td>12\17 &lt; g &lt; 17\24<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt;22\31<br />
| |
| </td>
| |
| <td>-2+3g<br />
| |
| </td>
| |
| <td>-7g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L2s<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 9\80<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 2\18<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 3\26<br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 4\34<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-4g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L1s<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 19\180<br />
| |
| </td>
| |
| <td>1\10 &lt; g &lt; 2\19<br />
| |
| </td>
| |
| <td>2\19 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\37<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-9g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x11"></a><!-- ws:end:WikiTextHeadingRule:14 -->11</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L10s<br />
| |
| </td>
| |
| <td>10\11 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 21\22<br />
| |
| </td>
| |
| <td>10\11 &lt; g &lt; 11\12<br />
| |
| </td>
| |
| <td>11\12 &lt; g &lt; 12\13<br />
| |
| </td>
| |
| <td>12/13 &lt; g &lt; 13\14<br />
| |
| </td>
| |
| <td>-9+10g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L9s<br />
| |
| </td>
| |
| <td>5\11 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 21\44<br />
| |
| </td>
| |
| <td>5\11 &lt; g &lt; 6\13<br />
| |
| </td>
| |
| <td>6\13 &lt; g &lt; 7\15<br />
| |
| </td>
| |
| <td>7\15 &lt; g &lt; 8\17<br />
| |
| </td>
| |
| <td>-4+9g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L8s<br />
| |
| </td>
| |
| <td>7\11 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 43\66<br />
| |
| </td>
| |
| <td>7\11 &lt; g &lt; 9\14<br />
| |
| </td>
| |
| <td>9\14 &lt; g &lt; 11\17<br />
| |
| </td>
| |
| <td>11\17 &lt; g &lt; 13\20<br />
| |
| </td>
| |
| <td>-5+8g<br />
| |
| </td>
| |
| <td>-3g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L7s<br />
| |
| </td>
| |
| <td>8\11 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 65\88<br />
| |
| </td>
| |
| <td>8\11 &lt; g &lt; 11\15<br />
| |
| </td>
| |
| <td>11\15 &lt; g &lt; 14\19<br />
| |
| </td>
| |
| <td>14\19 &lt; g &lt; 17\23<br />
| |
| </td>
| |
| <td>-5+7g<br />
| |
| </td>
| |
| <td>-4g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L6s<br />
| |
| </td>
| |
| <td>2\11 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 21\110<br />
| |
| </td>
| |
| <td>2\11 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\21<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 5\26<br />
| |
| </td>
| |
| <td>-1+6g<br />
| |
| </td>
| |
| <td>-5g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L5s<br />
| |
| </td>
| |
| <td>9\11 &lt; g &lt; 5\6<br />
| |
| </td>
| |
| <td>g = 109\132<br />
| |
| </td>
| |
| <td>9\11 &lt; g &lt; 14\17<br />
| |
| </td>
| |
| <td>14\17 &lt; g &lt; 19\23<br />
| |
| </td>
| |
| <td>19\23 &lt; g &lt; 24\29<br />
| |
| </td>
| |
| <td>-4+5g<br />
| |
| </td>
| |
| <td>-6g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L4s<br />
| |
| </td>
| |
| <td>3\11 &lt; g &lt; 2\7<br />
| |
| </td>
| |
| <td>g = 43\154<br />
| |
| </td>
| |
| <td>3\11 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 7\25<br />
| |
| </td>
| |
| <td>7\25 &lt; g &lt; 9\32<br />
| |
| </td>
| |
| <td>-1+4g<br />
| |
| </td>
| |
| <td>-7g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L3s<br />
| |
| </td>
| |
| <td>4\11 &lt; g &lt; 3\8<br />
| |
| </td>
| |
| <td>g = 65\176<br />
| |
| </td>
| |
| <td>4\11 &lt; g &lt; 7\19<br />
| |
| </td>
| |
| <td>7\19 &lt; g &lt; 10\27<br />
| |
| </td>
| |
| <td>10\27 &lt; g &lt; 13\35<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-8g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L2s<br />
| |
| </td>
| |
| <td>6\11 &lt; g &lt; 5\9<br />
| |
| </td>
| |
| <td>g = 109\198<br />
| |
| </td>
| |
| <td>6\11 &lt; g &lt; 11\20<br />
| |
| </td>
| |
| <td>11\20 &lt; g &lt; 16\29<br />
| |
| </td>
| |
| <td>16\29 &lt; g &lt; 21\38<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-9g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L1s<br />
| |
| </td>
| |
| <td>1\11 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 21\220<br />
| |
| </td>
| |
| <td>1\11 &lt; g &lt; 2\21<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\31<br />
| |
| </td>
| |
| <td>3\31 &lt; g &lt; 4\41<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-10g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x12"></a><!-- ws:end:WikiTextHeadingRule:16 -->12</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L11s<br />
| |
| </td>
| |
| <td>11\12 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 23\24<br />
| |
| </td>
| |
| <td>11\12 &lt; g &lt; 12\13<br />
| |
| </td>
| |
| <td>12\13 &lt; g &lt; 13\14<br />
| |
| </td>
| |
| <td>13\14 &lt; g &lt; 14\15<br />
| |
| </td>
| |
| <td>11g-10<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L10s<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 11\24<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 6\14<br />
| |
| </td>
| |
| <td>6\14 &lt; g &lt; 7\16<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 8\18<br />
| |
| </td>
| |
| <td>5g-2<br />
| |
| </td>
| |
| <td>1\2-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L9s<br />
| |
| </td>
| |
| <td>3\12 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 7\24<br />
| |
| </td>
| |
| <td>3\12 &lt; g &lt; 4\15<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 6\21<br />
| |
| </td>
| |
| <td>3g-2\3<br />
| |
| </td>
| |
| <td>1\3-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L8s<br />
| |
| </td>
| |
| <td>2\12 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 5\24<br />
| |
| </td>
| |
| <td>2/12 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\20<br />
| |
| </td>
| |
| <td>4\20 &lt; g &lt; 5\24<br />
| |
| </td>
| |
| <td>2g-1\4<br />
| |
| </td>
| |
| <td>1\4-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L7s<br />
| |
| </td>
| |
| <td>7\12 &lt; g &lt; 3\5<br />
| |
| </td>
| |
| <td>g = 71\120<br />
| |
| </td>
| |
| <td>7\12 &lt; g &lt; 10\17<br />
| |
| </td>
| |
| <td>10\17 &lt; g &lt; 13\22<br />
| |
| </td>
| |
| <td>13\22 &lt; g &lt; 16\27<br />
| |
| </td>
| |
| <td>7g-4<br />
| |
| </td>
| |
| <td>3-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L6s<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 3\24<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 2\18<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 3\24<br />
| |
| </td>
| |
| <td>3/24 &lt; g &lt; 4\30<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\6-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L5s<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 3\7<br />
| |
| </td>
| |
| <td>g = 71\168<br />
| |
| </td>
| |
| <td>5\12 &lt; g &lt; 8\19<br />
| |
| </td>
| |
| <td>8\19 &lt; g &lt; 11\26<br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 14\33<br />
| |
| </td>
| |
| <td>5g-2<br />
| |
| </td>
| |
| <td>3-7g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L4s<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 5\48<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 2\20<br />
| |
| </td>
| |
| <td>2\20 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\36<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\4-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L3s<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 7\72<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 2\21<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\30<br />
| |
| </td>
| |
| <td>3\30 &lt; g &lt; 4\39<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\3-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L2s<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 11\120<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 2\22<br />
| |
| </td>
| |
| <td>2\22 &lt; g &lt; 3\32<br />
| |
| </td>
| |
| <td>3\32 &lt; g &lt; 4\42<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\2-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L1s<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 1\11<br />
| |
| </td>
| |
| <td>g = 23\264<br />
| |
| </td>
| |
| <td>1\12 &lt; g &lt; 2\23<br />
| |
| </td>
| |
| <td>2\23 &lt; g &lt; 3\34<br />
| |
| </td>
| |
| <td>3\34 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-11g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="x13"></a><!-- ws:end:WikiTextHeadingRule:18 -->13</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L12s<br />
| |
| </td>
| |
| <td>12\13 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 25\26<br />
| |
| </td>
| |
| <td>12\13 &lt; g &lt; 13\14<br />
| |
| </td>
| |
| <td>13\14 &lt; g &lt; 14\15<br />
| |
| </td>
| |
| <td>14\15 &lt; g &lt; 15\16<br />
| |
| </td>
| |
| <td>12g-11<br />
| |
| </td>
| |
| <td>1-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L11s<br />
| |
| </td>
| |
| <td>6\13 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 25\52<br />
| |
| </td>
| |
| <td>6\13 &lt; g &lt; 7\15<br />
| |
| </td>
| |
| <td>7\15 &lt; g &lt; 8\17<br />
| |
| </td>
| |
| <td>8\17 &lt; g &lt; 9\18<br />
| |
| </td>
| |
| <td>11g-5<br />
| |
| </td>
| |
| <td>1-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L10s<br />
| |
| </td>
| |
| <td>4\13 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 25\78<br />
| |
| </td>
| |
| <td>4\13 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 6\19<br />
| |
| </td>
| |
| <td>6\19 &lt; g &lt; 7/22<br />
| |
| </td>
| |
| <td>10g-3<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L9s<br />
| |
| </td>
| |
| <td>3\13 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 25\104<br />
| |
| </td>
| |
| <td>3\13 &lt; g &lt; 4\17<br />
| |
| </td>
| |
| <td>4\17 &lt; g &lt; 5\21<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 6\25<br />
| |
| </td>
| |
| <td>9g-2<br />
| |
| </td>
| |
| <td>1-4g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L8s<br />
| |
| </td>
| |
| <td>5\13 &lt; g &lt; 2\5<br />
| |
| </td>
| |
| <td>g = 51\130<br />
| |
| </td>
| |
| <td>5\13 &lt; g &lt; 7\18<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 9\23<br />
| |
| </td>
| |
| <td>9\23 &lt; g &lt; 11\28<br />
| |
| </td>
| |
| <td>8g-3<br />
| |
| </td>
| |
| <td>2-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L7s<br />
| |
| </td>
| |
| <td>2\13 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 25\156<br />
| |
| </td>
| |
| <td>2\13 &lt; g &lt; 3\19<br />
| |
| </td>
| |
| <td>3\19 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\31<br />
| |
| </td>
| |
| <td>7g-1<br />
| |
| </td>
| |
| <td>1-6g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L6s<br />
| |
| </td>
| |
| <td>11\13 &lt; g &lt; 6\7<br />
| |
| </td>
| |
| <td>g = 155\182<br />
| |
| </td>
| |
| <td>11\13 &lt; g &lt; 17\20<br />
| |
| </td>
| |
| <td>17\20 &lt; g &lt; 23\27<br />
| |
| </td>
| |
| <td>23\27 &lt; g &lt; 29\34<br />
| |
| </td>
| |
| <td>6g-5<br />
| |
| </td>
| |
| <td>6-7g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L5s<br />
| |
| </td>
| |
| <td>8\13 &lt; g &lt; 5\8<br />
| |
| </td>
| |
| <td>g = 129\208<br />
| |
| </td>
| |
| <td>8\13 &lt; g &lt; 13\21<br />
| |
| </td>
| |
| <td>13\21 &lt; g &lt; 18\29<br />
| |
| </td>
| |
| <td>18\29 &lt; g &lt; 23\37<br />
| |
| </td>
| |
| <td>5g-3<br />
| |
| </td>
| |
| <td>5-8g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L4s<br />
| |
| </td>
| |
| <td>10\13 &lt; g &lt; 7\9<br />
| |
| </td>
| |
| <td>g = 181\234<br />
| |
| </td>
| |
| <td>10\13 &lt; g &lt; 17\22<br />
| |
| </td>
| |
| <td>17\22 &lt; g &lt; 24\31<br />
| |
| </td>
| |
| <td>24\31 &lt; g &lt; 31\40<br />
| |
| </td>
| |
| <td>4g-3<br />
| |
| </td>
| |
| <td>7-9g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L3s<br />
| |
| </td>
| |
| <td>9\13 &lt; g &lt; 7\10<br />
| |
| </td>
| |
| <td>g = 181\260<br />
| |
| </td>
| |
| <td>9\13 &lt; g &lt; 16\23<br />
| |
| </td>
| |
| <td>16\23 &lt; g &lt; 23\33<br />
| |
| </td>
| |
| <td>23\33 &lt; g &lt; 30\43<br />
| |
| </td>
| |
| <td>3g-2<br />
| |
| </td>
| |
| <td>7-10g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L2s<br />
| |
| </td>
| |
| <td>7\13 &lt; g &lt; 6\11<br />
| |
| </td>
| |
| <td>g = 155\286<br />
| |
| </td>
| |
| <td>7\13 &lt; g &lt; 13\24<br />
| |
| </td>
| |
| <td>13\24 &lt; g &lt; 19\35<br />
| |
| </td>
| |
| <td>19\35 &lt; g &lt; 25\46<br />
| |
| </td>
| |
| <td>2g-1<br />
| |
| </td>
| |
| <td>6-11g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L1s<br />
| |
| </td>
| |
| <td>1\13 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 25\312<br />
| |
| </td>
| |
| <td>1\13 &lt; g &lt; 2\25<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 3\37<br />
| |
| </td>
| |
| <td>3\37 &lt; g &lt; 4\49<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1-12g<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x14"></a><!-- ws:end:WikiTextHeadingRule:20 -->14</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L13s<br />
| |
| </td>
| |
| <td>13\14 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 27\28<br />
| |
| </td>
| |
| <td>13\14 &lt; g &lt; 14\15<br />
| |
| </td>
| |
| <td>14\15 &lt; g &lt; 15\16<br />
| |
| </td>
| |
| <td>15\16 &lt; g &lt; 16\17<br />
| |
| </td>
| |
| <td>\-12+13g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L12s<br />
| |
| </td>
| |
| <td>6\14 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 13\28<br />
| |
| </td>
| |
| <td>6\14 &lt; g &lt; 7\16<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 8\18<br />
| |
| </td>
| |
| <td>8\18 &lt; g &lt; 9\20<br />
| |
| </td>
| |
| <td>-5\2+6g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L11s<br />
| |
| </td>
| |
| <td>9\14 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 55\84<br />
| |
| </td>
| |
| <td>9\14 &lt; g &lt; 11\17<br />
| |
| </td>
| |
| <td>11\17 &lt; g &lt; 13\20<br />
| |
| </td>
| |
| <td>13\20 &lt; g &lt; 15\23<br />
| |
| </td>
| |
| <td>-7+11g<br />
| |
| </td>
| |
| <td>-3g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L10s<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 13\56<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 4\18<br />
| |
| </td>
| |
| <td>4\18 &lt; g &lt; 5\22<br />
| |
| </td>
| |
| <td>5\22 &lt; g &lt; 6\26<br />
| |
| </td>
| |
| <td>-1+5g<br />
| |
| </td>
| |
| <td>-2g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L9s<br />
| |
| </td>
| |
| <td>11\14 &lt; g &lt; 4\5<br />
| |
| </td>
| |
| <td>g = 111\140<br />
| |
| </td>
| |
| <td>11\14 &lt; g &lt; 15\19<br />
| |
| </td>
| |
| <td>15\19 &lt; g &lt; 19\24<br />
| |
| </td>
| |
| <td>19\24 &lt; g &lt; 23\29<br />
| |
| </td>
| |
| <td>-7+9g<br />
| |
| </td>
| |
| <td>-5g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L8s<br />
| |
| </td>
| |
| <td>2\14 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 13\84<br />
| |
| </td>
| |
| <td>2\14 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\26<br />
| |
| </td>
| |
| <td>4\26 &lt; g &lt; 5\32<br />
| |
| </td>
| |
| <td>4g-1\2<br />
| |
| </td>
| |
| <td>-3g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L7s<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 3\28<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 2\21<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\35<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L6s<br />
| |
| </td>
| |
| <td>5\14 &lt; g &lt; 3\8<br />
| |
| </td>
| |
| <td>g = 41\112<br />
| |
| </td>
| |
| <td>5\14 &lt; g &lt; 8\22<br />
| |
| </td>
| |
| <td>8\22 &lt; g &lt; 11\30<br />
| |
| </td>
| |
| <td>11\30 &lt; g &lt; 14\38<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-4g+3\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L5s<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>g = 55\252<br />
| |
| </td>
| |
| <td>3\14 &lt; g &lt; 5\23<br />
| |
| </td>
| |
| <td>5\23 &lt; g &lt; 7\32<br />
| |
| </td>
| |
| <td>7\32 &lt; g &lt; 9\41<br />
| |
| </td>
| |
| <td>-1+5g<br />
| |
| </td>
| |
| <td>-9g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L4s<br />
| |
| </td>
| |
| <td>4\14 &lt; g &lt; 3\10<br />
| |
| </td>
| |
| <td>g = 41\140<br />
| |
| </td>
| |
| <td>4\14 &lt; g &lt; 7\24<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 10\34<br />
| |
| </td>
| |
| <td>10\34 &lt; g &lt; 13\44<br />
| |
| </td>
| |
| <td>-1\2+2g<br />
| |
| </td>
| |
| <td>-5g+3\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L3s<br />
| |
| </td>
| |
| <td>5\14 &lt; g &lt; 4\11<br />
| |
| </td>
| |
| <td>g = 111\308<br />
| |
| </td>
| |
| <td>5\14 &lt; g &lt; 9\25<br />
| |
| </td>
| |
| <td>9\25 &lt; g &lt; 13\36<br />
| |
| </td>
| |
| <td>13\36 &lt; g &lt; 17\47<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-11g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L2s<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 13\168<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 2\26<br />
| |
| </td>
| |
| <td>2\26 &lt; g &lt; 3\38<br />
| |
| </td>
| |
| <td>3\38 &lt; g &lt; 4\50<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-6g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L1s<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 1\13<br />
| |
| </td>
| |
| <td>g = 27\364<br />
| |
| </td>
| |
| <td>1\14 &lt; g &lt; 2\27<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\40<br />
| |
| </td>
| |
| <td>3\40 &lt; g &lt; 4\53<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-13g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="x15"></a><!-- ws:end:WikiTextHeadingRule:22 -->15</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L14s<br />
| |
| </td>
| |
| <td>14\15 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 29\30<br />
| |
| </td>
| |
| <td>14\15 &lt; g &lt; 15\16<br />
| |
| </td>
| |
| <td>15\16 &lt; g &lt; 16\17<br />
| |
| </td>
| |
| <td>16\17 &lt; g &lt; 17\18<br />
| |
| </td>
| |
| <td>-13+14g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L13s<br />
| |
| </td>
| |
| <td>7\15 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 29\60<br />
| |
| </td>
| |
| <td>7\15 &lt; g &lt; 8\17<br />
| |
| </td>
| |
| <td>8\17 &lt; g &lt; 9\19<br />
| |
| </td>
| |
| <td>9\19 &lt; g &lt; 10\21<br />
| |
| </td>
| |
| <td>-6+13g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L12s<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 9\30<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 6\21<br />
| |
| </td>
| |
| <td>6\21 &lt; g &lt; 7\24<br />
| |
| </td>
| |
| <td>-1+4g<br />
| |
| </td>
| |
| <td>-g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L11s<br />
| |
| </td>
| |
| <td>11\15 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 89\120<br />
| |
| </td>
| |
| <td>11\15 &lt; g &lt; 14\19<br />
| |
| </td>
| |
| <td>14\19 &lt; g &lt; 17\23<br />
| |
| </td>
| |
| <td>17\23 &lt; g &lt; 20\27<br />
| |
| </td>
| |
| <td>-8+11g<br />
| |
| </td>
| |
| <td>-4g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L10s<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 5\30<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\30<br />
| |
| </td>
| |
| <td>-1\5+2g<br />
| |
| </td>
| |
| <td>-g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L9s<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 9\60<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\21<br />
| |
| </td>
| |
| <td>3\21 &lt; g &lt; 4\27<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 5\33<br />
| |
| </td>
| |
| <td>-1\3+3g<br />
| |
| </td>
| |
| <td>-2g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L8s<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 29\210<br />
| |
| </td>
| |
| <td>2\15 &lt; g &lt; 3\22<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 4\29<br />
| |
| </td>
| |
| <td>4\29 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>-1+8g<br />
| |
| </td>
| |
| <td>-7g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L7s<br />
| |
| </td>
| |
| <td>13\15 &lt; g &lt; 7\8<br />
| |
| </td>
| |
| <td>g = 209\240<br />
| |
| </td>
| |
| <td>13\15 &lt; g &lt; 20\23<br />
| |
| </td>
| |
| <td>20\23 &lt; g &lt; 27\31<br />
| |
| </td>
| |
| <td>27\31 &lt; g &lt; 34\39<br />
| |
| </td>
| |
| <td>-6+7g<br />
| |
| </td>
| |
| <td>-8g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L6s<br />
| |
| </td>
| |
| <td>3\15 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>g = 19\90<br />
| |
| </td>
| |
| <td>3\15 &lt; g &lt; 5\24<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 7\33<br />
| |
| </td>
| |
| <td>7\33 &lt; g &lt; 9\42<br />
| |
| </td>
| |
| <td>-1\3+2g<br />
| |
| </td>
| |
| <td>-3g+2\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L5s<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 5\60<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 2\25<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 3\35<br />
| |
| </td>
| |
| <td>3\35 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-2g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L4s<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 3\11<br />
| |
| </td>
| |
| <td>g = 89\330<br />
| |
| </td>
| |
| <td>4\15 &lt; g &lt; 7\26<br />
| |
| </td>
| |
| <td>7\26 &lt; g &lt; 10\37<br />
| |
| </td>
| |
| <td>10\37 &lt; g &lt; 13\48<br />
| |
| </td>
| |
| <td>-1+4g<br />
| |
| </td>
| |
| <td>-11g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L3s<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 9\120<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 2\27<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\39<br />
| |
| </td>
| |
| <td>3\39 &lt; g &lt; 4\51<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-4g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L2s<br />
| |
| </td>
| |
| <td>8\15 &lt; g &lt; 7\13<br />
| |
| </td>
| |
| <td>g = 209\390<br />
| |
| </td>
| |
| <td>8\15 &lt; g &lt; 15\28<br />
| |
| </td>
| |
| <td>15\28 &lt; g &lt; 22\41<br />
| |
| </td>
| |
| <td>22\41 &lt; g &lt; 29\54<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-13g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L1s<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 1\14<br />
| |
| </td>
| |
| <td>g = 29\420<br />
| |
| </td>
| |
| <td>1\15 &lt; g &lt; 2\29<br />
| |
| </td>
| |
| <td>2\29 &lt; g &lt; 3\43<br />
| |
| </td>
| |
| <td>3\43 &lt; g &lt; 4\57<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-14g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="x16"></a><!-- ws:end:WikiTextHeadingRule:24 -->16</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L15s<br />
| |
| </td>
| |
| <td>15\16 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 31\32<br />
| |
| </td>
| |
| <td>15\16 &lt; g &lt; 16\17<br />
| |
| </td>
| |
| <td>16\17 &lt; g &lt; 17\18<br />
| |
| </td>
| |
| <td>17\18 &lt; g &lt; 18\19<br />
| |
| </td>
| |
| <td>-14+15g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L14s<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 15\32<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 8\18<br />
| |
| </td>
| |
| <td>8\18 &lt; g &lt; 9\20<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 10\22<br />
| |
| </td>
| |
| <td>-3+7g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L13s<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 31\96<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 6\19<br />
| |
| </td>
| |
| <td>6\19 &lt; g &lt; 7\22<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 8\25<br />
| |
| </td>
| |
| <td>-4+13g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L12s<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 7\32<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\20<br />
| |
| </td>
| |
| <td>4\20 &lt; g &lt; 5\24<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 6\28<br />
| |
| </td>
| |
| <td>3g-1\2<br />
| |
| </td>
| |
| <td>-g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L11s<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 31\160<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 4\21<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 5\26<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 6\31<br />
| |
| </td>
| |
| <td>-2+11g<br />
| |
| </td>
| |
| <td>-5g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L10s<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 2\6<br />
| |
| </td>
| |
| <td>g = 31\96<br />
| |
| </td>
| |
| <td>5\16 &lt; g &lt; 7\22<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 9\28<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 11\34<br />
| |
| </td>
| |
| <td>-3\2+5g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L9s<br />
| |
| </td>
| |
| <td>9\16 &lt; g &lt; 4\7<br />
| |
| </td>
| |
| <td>g = 127\224<br />
| |
| </td>
| |
| <td>9\16 &lt; g &lt; 13\23<br />
| |
| </td>
| |
| <td>13\23 &lt; g &lt; 17\30<br />
| |
| </td>
| |
| <td>17\30 &lt; g &lt; 21\37<br />
| |
| </td>
| |
| <td>-5+9g<br />
| |
| </td>
| |
| <td>-7g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L8s<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 3\32<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 2\24<br />
| |
| </td>
| |
| <td>2\24 &lt; g &lt; 3\32<br />
| |
| </td>
| |
| <td>3\32 &lt; g &lt; 4\40<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L7s<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 4\9<br />
| |
| </td>
| |
| <td>g = 127\286<br />
| |
| </td>
| |
| <td>7\16 &lt; g &lt; 11\25<br />
| |
| </td>
| |
| <td>11\25 &lt; g &lt; 15\34<br />
| |
| </td>
| |
| <td>15\34 &lt; g &lt; 19\43<br />
| |
| </td>
| |
| <td>-3+7g<br />
| |
| </td>
| |
| <td>-9g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L6s<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 2\10<br />
| |
| </td>
| |
| <td>g = 31\160<br />
| |
| </td>
| |
| <td>3\16 &lt; g &lt; 5\26<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 7\36<br />
| |
| </td>
| |
| <td>7\36 &lt; g &lt; 8\46<br />
| |
| </td>
| |
| <td>3g-1\2<br />
| |
| </td>
| |
| <td>-5g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L5s<br />
| |
| </td>
| |
| <td>13\16 &lt; g &lt; 9\11<br />
| |
| </td>
| |
| <td>g = 287\352<br />
| |
| </td>
| |
| <td>13\16 &lt; g &lt; 22\27<br />
| |
| </td>
| |
| <td>22\27 &lt; g &lt; 31\38<br />
| |
| </td>
| |
| <td>31\38 &lt; g &lt; 40\49<br />
| |
| </td>
| |
| <td>-4+5g<br />
| |
| </td>
| |
| <td>-11g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L4s<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 7\48<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 2\28<br />
| |
| </td>
| |
| <td>2\28 &lt; g &lt; 3\40<br />
| |
| </td>
| |
| <td>3\40 &lt; g &lt; 4\52<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-3g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L3s<br />
| |
| </td>
| |
| <td>11\16 &lt; g &lt; 9\13<br />
| |
| </td>
| |
| <td>g = 287\416<br />
| |
| </td>
| |
| <td>11\16 &lt; g &lt; 20\29<br />
| |
| </td>
| |
| <td>20\29 &lt; g &lt; 29\42<br />
| |
| </td>
| |
| <td>29\42 &lt; g &lt; 38\55<br />
| |
| </td>
| |
| <td>-2+3g<br />
| |
| </td>
| |
| <td>-13g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L2s<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 1\14<br />
| |
| </td>
| |
| <td>g = 15\224<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 2\30<br />
| |
| </td>
| |
| <td>2\30 &lt; g &lt; 3\44<br />
| |
| </td>
| |
| <td>3\44 &lt; g &lt; 4\58<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-7g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L1s<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 1\15<br />
| |
| </td>
| |
| <td>g = 31\480<br />
| |
| </td>
| |
| <td>1\16 &lt; g &lt; 2\31<br />
| |
| </td>
| |
| <td>2\31 &lt; g &lt; 3\46<br />
| |
| </td>
| |
| <td>3\46 &lt; g &lt; 4\61<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-15g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="x17"></a><!-- ws:end:WikiTextHeadingRule:26 -->17</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th>Midpoint<br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L16s<br />
| |
| </td>
| |
| <td>16\17 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 33\34<br />
| |
| </td>
| |
| <td>16\17 &lt; g &lt; 17\18<br />
| |
| </td>
| |
| <td>17\18 &lt; g &lt; 18\19<br />
| |
| </td>
| |
| <td>18\19 &lt; g &lt; 19\20<br />
| |
| </td>
| |
| <td>-15+16g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L15s<br />
| |
| </td>
| |
| <td>8\17 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 33\68<br />
| |
| </td>
| |
| <td>8\17 &lt; g &lt; 9\19<br />
| |
| </td>
| |
| <td>9\19 &lt; g &lt; 10\21<br />
| |
| </td>
| |
| <td>10\21 &lt; g &lt; 11\23<br />
| |
| </td>
| |
| <td>-7+15g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L14s<br />
| |
| </td>
| |
| <td>11\17 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 67\102<br />
| |
| </td>
| |
| <td>11\17 &lt; g &lt; 13\20<br />
| |
| </td>
| |
| <td>13\20 &lt; g &lt; 15\23<br />
| |
| </td>
| |
| <td>15\23 &lt; g &lt; 17\26<br />
| |
| </td>
| |
| <td>-9+14g<br />
| |
| </td>
| |
| <td>-3g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L13s<br />
| |
| </td>
| |
| <td>4\17 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 33\136<br />
| |
| </td>
| |
| <td>4\17 &lt; g &lt; 5\21<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 6\25<br />
| |
| </td>
| |
| <td>6\25 &lt; g &lt; 7\29<br />
| |
| </td>
| |
| <td>-3+13g<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L12s<br />
| |
| </td>
| |
| <td>10\17 &lt; g &lt; 3\5<br />
| |
| </td>
| |
| <td>g = 101\170<br />
| |
| </td>
| |
| <td>10\17 &lt; g &lt; 13\22<br />
| |
| </td>
| |
| <td>13\22 &lt; g &lt; 16\27<br />
| |
| </td>
| |
| <td>16\27 &lt; g &lt; 19\32<br />
| |
| </td>
| |
| <td>-7+12g<br />
| |
| </td>
| |
| <td>-5g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L11s<br />
| |
| </td>
| |
| <td>14\17 &lt; g &lt; 5\6<br />
| |
| </td>
| |
| <td>g = 169\204<br />
| |
| </td>
| |
| <td>14\17 &lt; g &lt; 19\23<br />
| |
| </td>
| |
| <td>19\23 &lt; g &lt; 24\29<br />
| |
| </td>
| |
| <td>24\29 &lt; g &lt; 29\35<br />
| |
| </td>
| |
| <td>-9+11g<br />
| |
| </td>
| |
| <td>-6g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L10s<br />
| |
| </td>
| |
| <td>12\17 &lt; g &lt; 5\7<br />
| |
| </td>
| |
| <td>g = 169\238<br />
| |
| </td>
| |
| <td>12\17 &lt; g &lt; 17\24<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt; 22\31<br />
| |
| </td>
| |
| <td>22\31 &lt; g &lt; 27\38<br />
| |
| </td>
| |
| <td>-7+10g<br />
| |
| </td>
| |
| <td>-7g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L9s<br />
| |
| </td>
| |
| <td>2\17 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 33\272<br />
| |
| </td>
| |
| <td>2\17 &lt; g &lt; 3\25<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 4\33<br />
| |
| </td>
| |
| <td>4\33 &lt; g &lt; 5\41<br />
| |
| </td>
| |
| <td>-1+9g<br />
| |
| </td>
| |
| <td>-8g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L8s<br />
| |
| </td>
| |
| <td>15\17 &lt; g &lt; 8\9<br />
| |
| </td>
| |
| <td>g = 271\306<br />
| |
| </td>
| |
| <td>15\17 &lt; g &lt; 23\26<br />
| |
| </td>
| |
| <td>23\26 &lt; g &lt; 31\35<br />
| |
| </td>
| |
| <td>31\35 &lt; g &lt; 39\44<br />
| |
| </td>
| |
| <td>-7+8g<br />
| |
| </td>
| |
| <td>-9g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L7s<br />
| |
| </td>
| |
| <td>5\17 &lt; g &lt; 3\10<br />
| |
| </td>
| |
| <td>g = 101\340<br />
| |
| </td>
| |
| <td>5\17 &lt; g &lt; 8\27<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 11\37<br />
| |
| </td>
| |
| <td>11\37 &lt; g &lt; 14\47<br />
| |
| </td>
| |
| <td>-2+7g<br />
| |
| </td>
| |
| <td>-10g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L6s<br />
| |
| </td>
| |
| <td>3\17 &lt; g &lt; 2\11<br />
| |
| </td>
| |
| <td>g = 67\374<br />
| |
| </td>
| |
| <td>3\17 &lt; g &lt; 5\28<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 7\39<br />
| |
| </td>
| |
| <td>7\39 &lt; g &lt; 9\50<br />
| |
| </td>
| |
| <td>-1+6g<br />
| |
| </td>
| |
| <td>-11g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L5s<br />
| |
| </td>
| |
| <td>7\17 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>g = 169\408<br />
| |
| </td>
| |
| <td>7\17 &lt; g &lt; 12\29<br />
| |
| </td>
| |
| <td>12\29 &lt; g &lt; 17\41<br />
| |
| </td>
| |
| <td>17\41 &lt; g &lt; 22\53<br />
| |
| </td>
| |
| <td>-2+5g<br />
| |
| </td>
| |
| <td>-12g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L4s<br />
| |
| </td>
| |
| <td>13\17 &lt; g &lt; 10\13<br />
| |
| </td>
| |
| <td>g = 339\442<br />
| |
| </td>
| |
| <td>13\17 &lt; g &lt; 23\30<br />
| |
| </td>
| |
| <td>23\30 &lt; g &lt; 33\43<br />
| |
| </td>
| |
| <td>33\43 &lt; g &lt; 43\56<br />
| |
| </td>
| |
| <td>-3+4g<br />
| |
| </td>
| |
| <td>-13g+10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L3s<br />
| |
| </td>
| |
| <td>6\17 &lt; g &lt; 5\14<br />
| |
| </td>
| |
| <td>g = 169\476<br />
| |
| </td>
| |
| <td>6\17 &lt; g &lt; 11\31<br />
| |
| </td>
| |
| <td>11\31 &lt; g &lt; 16\45<br />
| |
| </td>
| |
| <td>16\45 &lt; g &lt; 21\59<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-14g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L2s<br />
| |
| </td>
| |
| <td>9\17 &lt; g &lt; 8\15<br />
| |
| </td>
| |
| <td>g = 271\510<br />
| |
| </td>
| |
| <td>9\17 &lt; g &lt; 17\32<br />
| |
| </td>
| |
| <td>17\32 &lt; g &lt; 25\47<br />
| |
| </td>
| |
| <td>25\47 &lt; g &lt; 33\62<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-15g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L1s<br />
| |
| </td>
| |
| <td>1\17 &lt; g &lt; 1\16<br />
| |
| </td>
| |
| <td>g = 33\544<br />
| |
| </td>
| |
| <td>1\17 &lt; g &lt; 2\33<br />
| |
| </td>
| |
| <td>2\33 &lt; g &lt; 3\49<br />
| |
| </td>
| |
| <td>3\49 &lt; g &lt; 4\65<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-16g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="x18"></a><!-- ws:end:WikiTextHeadingRule:28 -->18</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L17s<br />
| |
| </td>
| |
| <td>17\18 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 35\36<br />
| |
| </td>
| |
| <td>17\18 &lt; g &lt; 18\19<br />
| |
| </td>
| |
| <td>18\19 &lt; g &lt; 19\20<br />
| |
| </td>
| |
| <td>19\20 &lt; g &lt; 20\21<br />
| |
| </td>
| |
| <td>-16+17g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L16s<br />
| |
| </td>
| |
| <td>8\18 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 17\36<br />
| |
| </td>
| |
| <td>8\18 &lt; g &lt; 9\20<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 10\22<br />
| |
| </td>
| |
| <td>10\22 &lt; g &lt; 11\24<br />
| |
| </td>
| |
| <td>-7\2+8g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L15s<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 11\36<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 6\21<br />
| |
| </td>
| |
| <td>6\21 &lt; g &lt; 7\24<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 8\27<br />
| |
| </td>
| |
| <td>-4\3+5g<br />
| |
| </td>
| |
| <td>-g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L14s<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 1\4</span><br />
| |
| </td>
| |
| <td>g = 17\72<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 5\22</span><br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">5\22 &lt; g &lt; 6\26</span><br />
| |
| </td>
| |
| <td>6\26 &lt; g &lt; 7\30<br />
| |
| </td>
| |
| <td>-3\2+7g<br />
| |
| </td>
| |
| <td>-2g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L13s<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 2\5<br />
| |
| </td>
| |
| <td>g = 71\180<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 9\23<br />
| |
| </td>
| |
| <td>9\23 &lt; g &lt; 11\28<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 13\33<br />
| |
| </td>
| |
| <td>-5+13g<br />
| |
| </td>
| |
| <td>-5g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L12s<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 5\36<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 3\24<br />
| |
| </td>
| |
| <td>3\24 &lt; g &lt; 4\30<br />
| |
| </td>
| |
| <td>4\30 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>-1\6+2g<br />
| |
| </td>
| |
| <td>-g+1\6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L11s<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 2\7<br />
| |
| </td>
| |
| <td>g = 71\252<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 7\25<br />
| |
| </td>
| |
| <td>7\25 &lt; g &lt; 9\32<br />
| |
| </td>
| |
| <td>9\32 &lt; g &lt; 11\39<br />
| |
| </td>
| |
| <td>-3+11g<br />
| |
| </td>
| |
| <td>-7g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L10s<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 17\144<br />
| |
| </td>
| |
| <td>2\18 &lt; g &lt; 3\26<br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 4\34<br />
| |
| </td>
| |
| <td>4\34 &lt; g &lt; 5\42<br />
| |
| </td>
| |
| <td>-1\2+5g<br />
| |
| </td>
| |
| <td>-4g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L9s<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 3\36<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 2\27<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\36<br />
| |
| </td>
| |
| <td>3\36 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L8s<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 4\10<br />
| |
| </td>
| |
| <td>g = 71\180<br />
| |
| </td>
| |
| <td>7\18 &lt; g &lt; 11\28<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 15\38<br />
| |
| </td>
| |
| <td>15\38 &lt; g &lt; 19\43<br />
| |
| </td>
| |
| <td>-3\2+4g<br />
| |
| </td>
| |
| <td>-5g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L7s<br />
| |
| </td>
| |
| <td>13\18 &lt; g &lt; 8\11<br />
| |
| </td>
| |
| <td>g = 287\396<br />
| |
| </td>
| |
| <td>13\18 &lt; g &lt; 21\29<br />
| |
| </td>
| |
| <td>21\29 &lt; g &lt; 29\40<br />
| |
| </td>
| |
| <td>29\40 &lt; g &lt; 37\51<br />
| |
| </td>
| |
| <td>-5+7g<br />
| |
| </td>
| |
| <td>-11g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L6s<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 5\72<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 2\30<br />
| |
| </td>
| |
| <td>2\30 &lt; g &lt; 3\42<br />
| |
| </td>
| |
| <td>3\42 &lt; g &lt; 4\54<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-2g+1\6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L5s<br />
| |
| </td>
| |
| <td>11\18 &lt; g &lt; 8\13<br />
| |
| </td>
| |
| <td>g = 287\468<br />
| |
| </td>
| |
| <td>11\18 &lt; g &lt; 19\31<br />
| |
| </td>
| |
| <td>19\31 &lt; g &lt; 27\44<br />
| |
| </td>
| |
| <td>27\44 &lt; g &lt; 35\57<br />
| |
| </td>
| |
| <td>-3+5g<br />
| |
| </td>
| |
| <td>-13g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L4s<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 4\14<br />
| |
| </td>
| |
| <td>g = 71\252<br />
| |
| </td>
| |
| <td>5\18 &lt; g &lt; 9\32<br />
| |
| </td>
| |
| <td>9\32 &lt; g &lt; 13\46<br />
| |
| </td>
| |
| <td>13\46 &lt; g &lt; 17\60<br />
| |
| </td>
| |
| <td>-1\2+2g<br />
| |
| </td>
| |
| <td>-7g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L3s<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 1\15<br />
| |
| </td>
| |
| <td>g = 11\180<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 2\33<br />
| |
| </td>
| |
| <td>2\33 &lt; g &lt; 3\48<br />
| |
| </td>
| |
| <td>3\48 &lt; g &lt; 4\63<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-5g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L2s<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 1\16<br />
| |
| </td>
| |
| <td>g = 17\288<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 2\34<br />
| |
| </td>
| |
| <td>2\34 &lt; g &lt; 3\50<br />
| |
| </td>
| |
| <td>3\50 &lt; g &lt; 4\66<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-8g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L1s<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 1\17<br />
| |
| </td>
| |
| <td>g = 35\618<br />
| |
| </td>
| |
| <td>1\18 &lt; g &lt; 2\35<br />
| |
| </td>
| |
| <td>2\35 &lt; g &lt; 3\52<br />
| |
| </td>
| |
| <td>3\52 &lt; g &lt; 4\69<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-17g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="x19"></a><!-- ws:end:WikiTextHeadingRule:30 -->19</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L18s<br />
| |
| </td>
| |
| <td>18\19 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 37\38<br />
| |
| </td>
| |
| <td>18\19 &lt; g &lt; 19\20<br />
| |
| </td>
| |
| <td>19\20 &lt; g &lt; 20\21<br />
| |
| </td>
| |
| <td>20\21 &lt; g &lt; 21\22<br />
| |
| </td>
| |
| <td>-17+18g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L17s<br />
| |
| </td>
| |
| <td>9\19 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 37\76<br />
| |
| </td>
| |
| <td>9\19 &lt; g &lt; 10\21<br />
| |
| </td>
| |
| <td>10\21 &lt; g &lt; 11\23<br />
| |
| </td>
| |
| <td>11\23 &lt; g &lt; 12\25<br />
| |
| </td>
| |
| <td>-8+17g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L16s<br />
| |
| </td>
| |
| <td>6\19 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 37\114<br />
| |
| </td>
| |
| <td>6\19 &lt; g &lt; 7\22<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 8\25<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 10\31<br />
| |
| </td>
| |
| <td>-5+16g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L15s<br />
| |
| </td>
| |
| <td>14\19 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 113\152<br />
| |
| </td>
| |
| <td>14\19 &lt; g &lt; 17\23<br />
| |
| </td>
| |
| <td>17\23 &lt; g &lt; 20\27<br />
| |
| </td>
| |
| <td>20\27 &lt; g &lt; 23\31<br />
| |
| </td>
| |
| <td>-11+15g<br />
| |
| </td>
| |
| <td>-4g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L14s<br />
| |
| </td>
| |
| <td>15\19 &lt; g &lt; 4\5<br />
| |
| </td>
| |
| <td>g = 151\190<br />
| |
| </td>
| |
| <td>15\19 &lt; g &lt; 19\24<br />
| |
| </td>
| |
| <td>19\24 &lt; g &lt; 23\29<br />
| |
| </td>
| |
| <td>23\29 &lt; g &lt; 27\34<br />
| |
| </td>
| |
| <td>-11+14g<br />
| |
| </td>
| |
| <td>-5g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L13s<br />
| |
| </td>
| |
| <td>3\19 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 37\228<br />
| |
| </td>
| |
| <td>3\19 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\31<br />
| |
| </td>
| |
| <td>5\31 &lt; g &lt; 6/37<br />
| |
| </td>
| |
| <td>-2+13g<br />
| |
| </td>
| |
| <td>-6g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L12s<br />
| |
| </td>
| |
| <td>8\19 &lt; g &lt; 3\7<br />
| |
| </td>
| |
| <td>g = 113\266<br />
| |
| </td>
| |
| <td>8\19 &lt; g &lt; 11\26<br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 14\33<br />
| |
| </td>
| |
| <td>14\33 &lt; g &lt; 17\40<br />
| |
| </td>
| |
| <td>-5+12g<br />
| |
| </td>
| |
| <td>-7g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L11s<br />
| |
| </td>
| |
| <td>7\19 &lt; g &lt; 3\8<br />
| |
| </td>
| |
| <td>g = 113\304<br />
| |
| </td>
| |
| <td>7\19 &lt; g &lt; 10\27<br />
| |
| </td>
| |
| <td>10\27 &lt; g &lt; 13\35<br />
| |
| </td>
| |
| <td>13\35 &lt; g &lt; 16\43<br />
| |
| </td>
| |
| <td>-4+11g<br />
| |
| </td>
| |
| <td>-8g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L10s<br />
| |
| </td>
| |
| <td>2\19 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 37\342<br />
| |
| </td>
| |
| <td>2\19 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\37<br />
| |
| </td>
| |
| <td>4\37 &lt; g &lt; 5\46<br />
| |
| </td>
| |
| <td>-1+10g<br />
| |
| </td>
| |
| <td>-9g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L9s<br />
| |
| </td>
| |
| <td>17\19 &lt; g &lt; 9\10<br />
| |
| </td>
| |
| <td>g = 341\380<br />
| |
| </td>
| |
| <td>17\19 &lt; g &lt; 26\29<br />
| |
| </td>
| |
| <td>26\29 &lt; g &lt; 35\39<br />
| |
| </td>
| |
| <td>35\39 &lt; g &lt; 44\49<br />
| |
| </td>
| |
| <td>-8+9g<br />
| |
| </td>
| |
| <td>-10g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L8s<br />
| |
| </td>
| |
| <td>12\19 &lt; g &lt; 7\11<br />
| |
| </td>
| |
| <td>g = 265\418<br />
| |
| </td>
| |
| <td>12\19 &lt; g &lt; 19\30<br />
| |
| </td>
| |
| <td>19\30 &lt; g &lt; 26\41<br />
| |
| </td>
| |
| <td>26\41 &lt; g &lt; 33\52<br />
| |
| </td>
| |
| <td>-5+8g<br />
| |
| </td>
| |
| <td>-11g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L7s<br />
| |
| </td>
| |
| <td>11\19 &lt; g &lt; 7\12<br />
| |
| </td>
| |
| <td>g = 265\456<br />
| |
| </td>
| |
| <td>11\19 &lt; g &lt; 18\31<br />
| |
| </td>
| |
| <td>18\31 &lt; g &lt; 25\43<br />
| |
| </td>
| |
| <td>25\43 &lt; g &lt; 32\55<br />
| |
| </td>
| |
| <td>-4+7g<br />
| |
| </td>
| |
| <td>-12g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L6s<br />
| |
| </td>
| |
| <td>16\19 &lt; g &lt; 11\13<br />
| |
| </td>
| |
| <td>g = 417\494<br />
| |
| </td>
| |
| <td>16\19 &lt; g &lt; 27\32<br />
| |
| </td>
| |
| <td>27\32 &lt; g &lt; 38\45<br />
| |
| </td>
| |
| <td>38\45 &lt; g &lt; 49\58<br />
| |
| </td>
| |
| <td>-5+6g<br />
| |
| </td>
| |
| <td>-13g+11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L5s<br />
| |
| </td>
| |
| <td>4\19 &lt; g &lt; 3\14<br />
| |
| </td>
| |
| <td>g = 113\532<br />
| |
| </td>
| |
| <td>4\19 &lt; g &lt; 7\33<br />
| |
| </td>
| |
| <td>7\33 &lt; g &lt; 10\47<br />
| |
| </td>
| |
| <td>10\47 &lt; g &lt; 13\61<br />
| |
| </td>
| |
| <td>-1+5g<br />
| |
| </td>
| |
| <td>-14g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L4s<br />
| |
| </td>
| |
| <td>5\19 &lt; g &lt; 4\15<br />
| |
| </td>
| |
| <td>g = 151\570<br />
| |
| </td>
| |
| <td>5\19 &lt; g &lt; 9\34<br />
| |
| </td>
| |
| <td>9\34 &lt; g &lt; 13\49<br />
| |
| </td>
| |
| <td>13\49 &lt; g &lt; 17\64<br />
| |
| </td>
| |
| <td>-1+4g<br />
| |
| </td>
| |
| <td>-15g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L3s<br />
| |
| </td>
| |
| <td>13\19 &lt; g &lt; 11\16<br />
| |
| </td>
| |
| <td>g = 417\608<br />
| |
| </td>
| |
| <td>13\19 &lt; g &lt; 24\35<br />
| |
| </td>
| |
| <td>24\35 &lt; g &lt; 35\51<br />
| |
| </td>
| |
| <td>35\51 &lt; g &lt; 46\67<br />
| |
| </td>
| |
| <td>-2+3g<br />
| |
| </td>
| |
| <td>-16g+11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L2s<br />
| |
| </td>
| |
| <td>10\19 &lt; g &lt; 9\17<br />
| |
| </td>
| |
| <td>g = 341\646<br />
| |
| </td>
| |
| <td>10\19 &lt; g &lt; 19\36<br />
| |
| </td>
| |
| <td>19\36 &lt; g &lt; 28\53<br />
| |
| </td>
| |
| <td>28\53 &lt; g &lt; 37\70<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-17g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L1s<br />
| |
| </td>
| |
| <td>1\19 &lt; g &lt; 1\18<br />
| |
| </td>
| |
| <td>g = 37\684<br />
| |
| </td>
| |
| <td>1\19 &lt; g &lt; 2\37<br />
| |
| </td>
| |
| <td>2\37 &lt; g &lt; 3\55<br />
| |
| </td>
| |
| <td>3\55 &lt; g &lt;<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-18g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="x20"></a><!-- ws:end:WikiTextHeadingRule:32 -->20</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L19s<br />
| |
| </td>
| |
| <td>19\20 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 39\40<br />
| |
| </td>
| |
| <td>19\20 &lt; g &lt; 20\21<br />
| |
| </td>
| |
| <td>20\21 &lt; g &lt; 21\22<br />
| |
| </td>
| |
| <td>21\22 &lt; g &lt; 22\23<br />
| |
| </td>
| |
| <td>-18+19g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L18s<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 19\40<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 10\22<br />
| |
| </td>
| |
| <td>10\22 &lt; g &lt; 11\24<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 12\26<br />
| |
| </td>
| |
| <td>-4+9g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L17s<br />
| |
| </td>
| |
| <td>13\20 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 79\120<br />
| |
| </td>
| |
| <td>13\20 &lt; g &lt; 15\23<br />
| |
| </td>
| |
| <td>15\23 &lt; g &lt; 17\26<br />
| |
| </td>
| |
| <td>17\26 &lt; g &lt; 20\29<br />
| |
| </td>
| |
| <td>-11+17g<br />
| |
| </td>
| |
| <td>-3g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L16s<br />
| |
| </td>
| |
| <td>4\20 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 9\40<br />
| |
| </td>
| |
| <td>4\20 &lt; g &lt; 5\24<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 6\28<br />
| |
| </td>
| |
| <td>6\28 &lt; g &lt; 7\32<br />
| |
| </td>
| |
| <td>-3\4+4g<br />
| |
| </td>
| |
| <td>-g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L15s<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 7\40<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\25<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\30<br />
| |
| </td>
| |
| <td>5\30 &lt; g &lt; 6\35<br />
| |
| </td>
| |
| <td>-2\5+3g<br />
| |
| </td>
| |
| <td>-g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L14s<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 19\120<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 4\26<br />
| |
| </td>
| |
| <td>4\26 &lt; g &lt; 5\32<br />
| |
| </td>
| |
| <td>5\32 &lt; g &lt; 6\38<br />
| |
| </td>
| |
| <td>-1+7g<br />
| |
| </td>
| |
| <td>-3g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L13s<br />
| |
| </td>
| |
| <td>17\20 &lt; g &lt; 6\7<br />
| |
| </td>
| |
| <td>g = 239\280<br />
| |
| </td>
| |
| <td>17\20 &lt; g &lt; 23\27<br />
| |
| </td>
| |
| <td>23\27 &lt; g &lt; 29\34<br />
| |
| </td>
| |
| <td>29\34 &lt; g &lt; 35\41<br />
| |
| </td>
| |
| <td>-11+13g<br />
| |
| </td>
| |
| <td>-7g+6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L12s<br />
| |
| </td>
| |
| <td>2\20 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 9\80<br />
| |
| </td>
| |
| <td>2\20 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\36<br />
| |
| </td>
| |
| <td>4\36 &lt; g &lt; 5\44<br />
| |
| </td>
| |
| <td>-1\4+3g<br />
| |
| </td>
| |
| <td>-2g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L11s<br />
| |
| </td>
| |
| <td>11\20 &lt; g &lt; 5\9<br />
| |
| </td>
| |
| <td>g = 199\360<br />
| |
| </td>
| |
| <td>11\20 &lt; g &lt; 16\29<br />
| |
| </td>
| |
| <td>16\29 &lt; g &lt; 21\38<br />
| |
| </td>
| |
| <td>21\38 &lt; g &lt; 26\47<br />
| |
| </td>
| |
| <td>-6+11g<br />
| |
| </td>
| |
| <td>-9g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L10s<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 3\40<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 2\30<br />
| |
| </td>
| |
| <td>2\30 &lt; g &lt; 3\40<br />
| |
| </td>
| |
| <td>3\40 &lt; g &lt; 4\50<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L9s<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 5\11<br />
| |
| </td>
| |
| <td>g = 199\440<br />
| |
| </td>
| |
| <td>9\20 &lt; g &lt; 14\31<br />
| |
| </td>
| |
| <td>14\31 &lt; g &lt; 19\42<br />
| |
| </td>
| |
| <td>19\42 &lt; g &lt; 24\53<br />
| |
| </td>
| |
| <td>-4+9g<br />
| |
| </td>
| |
| <td>-11g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L8s<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 2\12<br />
| |
| </td>
| |
| <td>g = 19\120<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 5\32<br />
| |
| </td>
| |
| <td>5\32 &lt; g &lt; 7\44<br />
| |
| </td>
| |
| <td>7\44 &lt; g &lt; 9\56<br />
| |
| </td>
| |
| <td>-1\4+2g<br />
| |
| </td>
| |
| <td>-3g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L7s<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 2\13<br />
| |
| </td>
| |
| <td>g = 79\520<br />
| |
| </td>
| |
| <td>3\20 &lt; g &lt; 5\33<br />
| |
| </td>
| |
| <td>5\33 &lt; g &lt; 7\46<br />
| |
| </td>
| |
| <td>7\46 &lt; g &lt; 9\59<br />
| |
| </td>
| |
| <td>-1+7g<br />
| |
| </td>
| |
| <td>-13g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L6s<br />
| |
| </td>
| |
| <td>7\20 &lt; g &lt; 5\14<br />
| |
| </td>
| |
| <td>g = 99\280<br />
| |
| </td>
| |
| <td>7\20 &lt; g &lt; 12\34<br />
| |
| </td>
| |
| <td>12\34 &lt; g &lt; 17\48<br />
| |
| </td>
| |
| <td>17\48 &lt; g &lt; 22\62<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-7g+5\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L5s<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 1\15<br />
| |
| </td>
| |
| <td>g = 7\120<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 2\35<br />
| |
| </td>
| |
| <td>2\35 &lt; g &lt; 3\50<br />
| |
| </td>
| |
| <td>3\50 &lt; g &lt; 4\65<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-3g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L4s<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 1\16<br />
| |
| </td>
| |
| <td>g = 9\160<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 2\36<br />
| |
| </td>
| |
| <td>2\36 &lt; g &lt; 3\52<br />
| |
| </td>
| |
| <td>3\52 &lt; g &lt; 4\68<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-4g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L3s<br />
| |
| </td>
| |
| <td>7\20 &lt; g &lt; 6\17<br />
| |
| </td>
| |
| <td>g = 239\680<br />
| |
| </td>
| |
| <td>7\20 &lt; g &lt; 13\37<br />
| |
| </td>
| |
| <td>13\37 &lt; g &lt; 19\54<br />
| |
| </td>
| |
| <td>19\54 &lt; g &lt; 25\71<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-17g+6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L2s<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 1\18<br />
| |
| </td>
| |
| <td>g = 19\360<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 2\38<br />
| |
| </td>
| |
| <td>2\38 &lt; g &lt; 3\56<br />
| |
| </td>
| |
| <td>3\56 &lt; g &lt; 4\74<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-9g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L1s<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 1\19<br />
| |
| </td>
| |
| <td>g = 39\760<br />
| |
| </td>
| |
| <td>1\20 &lt; g &lt; 2\39<br />
| |
| </td>
| |
| <td>2\39 &lt; g &lt; 3\58<br />
| |
| </td>
| |
| <td>3\58 &lt; g &lt; 4\77<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-19g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="x21"></a><!-- ws:end:WikiTextHeadingRule:34 -->21</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L20s<br />
| |
| </td>
| |
| <td>20\21 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 41\42<br />
| |
| </td>
| |
| <td>20\21 &lt; g &lt; 21\22<br />
| |
| </td>
| |
| <td>21\22 &lt; g &lt; 22\23<br />
| |
| </td>
| |
| <td>22\23 &lt; g &lt; 23\24<br />
| |
| </td>
| |
| <td>-19+20g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L19s<br />
| |
| </td>
| |
| <td>10\21 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 41\84<br />
| |
| </td>
| |
| <td>10\21 &lt; g &lt; 11\23<br />
| |
| </td>
| |
| <td>11\23 &lt; g &lt; 12\25<br />
| |
| </td>
| |
| <td>12\25 &lt; g &lt; 13\27<br />
| |
| </td>
| |
| <td>-9+19g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L18s<br />
| |
| </td>
| |
| <td>6\21 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 13\42<br />
| |
| </td>
| |
| <td>6\21 &lt; g &lt; 7\24<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 8\27<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 9\30<br />
| |
| </td>
| |
| <td>-5\3+6g<br />
| |
| </td>
| |
| <td>-g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L17s<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 41\168<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 6\25<br />
| |
| </td>
| |
| <td>6\25 &lt; g &lt; 7\29<br />
| |
| </td>
| |
| <td>7\29 &lt; g &lt; 8\33<br />
| |
| </td>
| |
| <td>-4+17g<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L16s<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 41\210<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 5\26<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 6\31<br />
| |
| </td>
| |
| <td>6\31 &lt; g &lt; 7\37<br />
| |
| </td>
| |
| <td>-3+16g<br />
| |
| </td>
| |
| <td>-5g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L15s<br />
| |
| </td>
| |
| <td>3\21 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 13\84<br />
| |
| </td>
| |
| <td>3\21 &lt; g &lt; 4\27<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 5\33<br />
| |
| </td>
| |
| <td>5\33 &lt; g &lt; 6\39<br />
| |
| </td>
| |
| <td>-2\3+5g<br />
| |
| </td>
| |
| <td>-2g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L14s<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 5\42<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\28<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\35<br />
| |
| </td>
| |
| <td>4\35 &lt; g &lt; 5\42<br />
| |
| </td>
| |
| <td>-1\7+2g<br />
| |
| </td>
| |
| <td>-g+1\7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L13s<br />
| |
| </td>
| |
| <td>13\21 &lt; g &lt; 5\8<br />
| |
| </td>
| |
| <td>g = 209\336<br />
| |
| </td>
| |
| <td>13\21 &lt; g &lt; 18\29<br />
| |
| </td>
| |
| <td>18\29 &lt; g &lt; 23\37<br />
| |
| </td>
| |
| <td>23\37 &lt; g &lt; 28\45<br />
| |
| </td>
| |
| <td>-8+13g<br />
| |
| </td>
| |
| <td>-8g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L12s<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 13\126<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\30<br />
| |
| </td>
| |
| <td>3\30 &lt; g &lt; 4\39<br />
| |
| </td>
| |
| <td>4\39 &lt; g &lt; 5\48<br />
| |
| </td>
| |
| <td>-1\3+4g<br />
| |
| </td>
| |
| <td>-3g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L11s<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 41\420<br />
| |
| </td>
| |
| <td>2\21 &lt; g &lt; 3\31<br />
| |
| </td>
| |
| <td>3\31 &lt; g &lt; 4\41<br />
| |
| </td>
| |
| <td>4\41 &lt; g &lt; 5\51<br />
| |
| </td>
| |
| <td>-1+11g<br />
| |
| </td>
| |
| <td>-10g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L10s<br />
| |
| </td>
| |
| <td>19\21 &lt; g &lt; 10\11<br />
| |
| </td>
| |
| <td>g = 419\462<br />
| |
| </td>
| |
| <td>19\21 &lt; g &lt; 29\32<br />
| |
| </td>
| |
| <td>29\32 &lt; g &lt; 39\43<br />
| |
| </td>
| |
| <td>39\43 &lt; g &lt; 49\54<br />
| |
| </td>
| |
| <td>-9+10g<br />
| |
| </td>
| |
| <td>-11g+10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L9s<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 3\12<br />
| |
| </td>
| |
| <td>g = 41\168<br />
| |
| </td>
| |
| <td>5\21 &lt; g &lt; 8\33<br />
| |
| </td>
| |
| <td>8\33 &lt; g &lt; 11\45<br />
| |
| </td>
| |
| <td>11\45 &lt; g &lt; 14\57<br />
| |
| </td>
| |
| <td>-2\3+3g<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L8s<br />
| |
| </td>
| |
| <td>8\21 &lt; g &lt; 5\13<br />
| |
| </td>
| |
| <td>g = 209\546<br />
| |
| </td>
| |
| <td>8\21 &lt; g &lt; 13\34<br />
| |
| </td>
| |
| <td>13\34 &lt; g &lt; 18\47<br />
| |
| </td>
| |
| <td>18\47 &lt; g &lt; 23\70<br />
| |
| </td>
| |
| <td>-3+8g<br />
| |
| </td>
| |
| <td>-13g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L7s<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 1\14<br />
| |
| </td>
| |
| <td>g = 5\84<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 2\35<br />
| |
| </td>
| |
| <td>2\35 &lt; g &lt; 3\49<br />
| |
| </td>
| |
| <td>3\49 &lt; g &lt; 4\63<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-2g+1\7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L6s<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 3\15<br />
| |
| </td>
| |
| <td>g = 41\210<br />
| |
| </td>
| |
| <td>4\21 &lt; g &lt; 7\36<br />
| |
| </td>
| |
| <td>7\36 &lt; g &lt; 10\51<br />
| |
| </td>
| |
| <td>10\51 &lt; g &lt; 13\66<br />
| |
| </td>
| |
| <td>-1\3+2g<br />
| |
| </td>
| |
| <td>-5g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L5s<br />
| |
| </td>
| |
| <td>17\21 &lt; g &lt; 13\16<br />
| |
| </td>
| |
| <td>g = 545\672<br />
| |
| </td>
| |
| <td>17\21 &lt; g &lt; 30\37<br />
| |
| </td>
| |
| <td>30\37 &lt; g &lt; 43\53<br />
| |
| </td>
| |
| <td>43\53 &lt; g &lt; 56\69<br />
| |
| </td>
| |
| <td>-4+5g<br />
| |
| </td>
| |
| <td>-16g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L4s<br />
| |
| </td>
| |
| <td>16\21 &lt; g &lt; 13\17<br />
| |
| </td>
| |
| <td>g = 545\714<br />
| |
| </td>
| |
| <td>16\21 &lt; g &lt; 29\38<br />
| |
| </td>
| |
| <td>29\38 &lt; g &lt; 42\55<br />
| |
| </td>
| |
| <td>42\55 &lt; g &lt; 55\72<br />
| |
| </td>
| |
| <td>-3+4g<br />
| |
| </td>
| |
| <td>-17g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L3s<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 1\18<br />
| |
| </td>
| |
| <td>g = 13\252<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 2\39<br />
| |
| </td>
| |
| <td>2\39 &lt; g &lt; 3\57<br />
| |
| </td>
| |
| <td>3\57 &lt; g &lt; 4\75<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-6g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L2s<br />
| |
| </td>
| |
| <td>11\21 &lt; g &lt; 10\19<br />
| |
| </td>
| |
| <td>g = 419\798<br />
| |
| </td>
| |
| <td>11\21 &lt; g &lt; 21\40<br />
| |
| </td>
| |
| <td>21\40 &lt; g &lt; 31\59<br />
| |
| </td>
| |
| <td>31\59 &lt; g &lt; 41\78<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-19g+10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L1s<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 1\20<br />
| |
| </td>
| |
| <td>g = 41\840<br />
| |
| </td>
| |
| <td>1\21 &lt; g &lt; 2\41<br />
| |
| </td>
| |
| <td>2\41 &lt; g &lt; 3\61<br />
| |
| </td>
| |
| <td>3\61 &lt; g &lt; 4/81<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-20g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="x22"></a><!-- ws:end:WikiTextHeadingRule:36 -->22</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L21s<br />
| |
| </td>
| |
| <td>21\22 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 43\44<br />
| |
| </td>
| |
| <td>21\22 &lt; g &lt; 22\23<br />
| |
| </td>
| |
| <td>22\23 &lt; g &lt; 23\24<br />
| |
| </td>
| |
| <td>23\24 &lt; g &lt; 24/25<br />
| |
| </td>
| |
| <td>-20+21g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L20s<br />
| |
| </td>
| |
| <td>10\22 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 21\44<br />
| |
| </td>
| |
| <td>10\22 &lt; g &lt; 11\24<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 12\26<br />
| |
| </td>
| |
| <td>12\26 &lt; g &lt; 13\28<br />
| |
| </td>
| |
| <td>-9\2+10g<br />
| |
| </td>
| |
| <td>-g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L19s<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 43\132<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 8\25<br />
| |
| </td>
| |
| <td>8\25 &lt; g &lt; 9\28<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 10\31<br />
| |
| </td>
| |
| <td>-6+19g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L18s<br />
| |
| </td>
| |
| <td>5\22 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 21\88<br />
| |
| </td>
| |
| <td>5\22 &lt; g &lt; 6\26<br />
| |
| </td>
| |
| <td>6\26 &lt; g &lt; 7\30<br />
| |
| </td>
| |
| <td>7\30 &lt; g &lt; 8\34<br />
| |
| </td>
| |
| <td>-2+9g<br />
| |
| </td>
| |
| <td>-2g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L17s<br />
| |
| </td>
| |
| <td>13\22 &lt; g &lt; 3\5<br />
| |
| </td>
| |
| <td>g = 131\220<br />
| |
| </td>
| |
| <td>13\22 &lt; g &lt; 16\27<br />
| |
| </td>
| |
| <td>16\27 &lt; g &lt; 19\32<br />
| |
| </td>
| |
| <td>19\32 &lt; g &lt; 22\37<br />
| |
| </td>
| |
| <td>-10+17g<br />
| |
| </td>
| |
| <td>-5g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L16s<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 2\6<br />
| |
| </td>
| |
| <td>g = 43\132<br />
| |
| </td>
| |
| <td>7\22 &lt; g &lt; 9\28<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 11\34<br />
| |
| </td>
| |
| <td>11\34 &lt; g &lt; 13\40<br />
| |
| </td>
| |
| <td>-5\2+8g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L15s<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 43\308<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 4\29<br />
| |
| </td>
| |
| <td>4\29 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>5\36 &lt; g &lt; 6\43<br />
| |
| </td>
| |
| <td>-2+15g<br />
| |
| </td>
| |
| <td>-7g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L14s<br />
| |
| </td>
| |
| <td>8\22 &lt; g &lt; 3\8<br />
| |
| </td>
| |
| <td>g = 65\176<br />
| |
| </td>
| |
| <td>8\22 &lt; g &lt; 11\30<br />
| |
| </td>
| |
| <td>11\30 &lt; g &lt; 14\38<br />
| |
| </td>
| |
| <td>14\38 &lt; g &lt; 17\46<br />
| |
| </td>
| |
| <td>-5\2+7g<br />
| |
| </td>
| |
| <td>-4g+3\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L13s<br />
| |
| </td>
| |
| <td>17\22 &lt; g &lt; 7\9<br />
| |
| </td>
| |
| <td>g = 307\396<br />
| |
| </td>
| |
| <td>17\22 &lt; g &lt; 24\31<br />
| |
| </td>
| |
| <td>24\31 &lt; g &lt; 31\40<br />
| |
| </td>
| |
| <td>31\40 &lt; g &lt; 38\49<br />
| |
| </td>
| |
| <td>-10+13g<br />
| |
| </td>
| |
| <td>-9g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L12s<br />
| |
| </td>
| |
| <td>2\22 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 21\220<br />
| |
| </td>
| |
| <td>2\22 &lt; g &lt; 3\32<br />
| |
| </td>
| |
| <td>3\32 &lt; g &lt; 4\42<br />
| |
| </td>
| |
| <td>4\42 &lt; g &lt; 5\52<br />
| |
| </td>
| |
| <td>-1\2+6g<br />
| |
| </td>
| |
| <td>-5g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L11s<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 1\11<br />
| |
| </td>
| |
| <td>g = 3\44<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 2\33<br />
| |
| </td>
| |
| <td>2\33 &lt; g &lt; 3\44<br />
| |
| </td>
| |
| <td>3\44 &lt; g &lt; 4\55<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L10s<br />
| |
| </td>
| |
| <td>9\22 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>g = 109\264<br />
| |
| </td>
| |
| <td>9\22 &lt; g &lt; 14\34<br />
| |
| </td>
| |
| <td>14\34 &lt; g &lt; 19\46<br />
| |
| </td>
| |
| <td>19\46 &lt; g &lt; 24\58<br />
| |
| </td>
| |
| <td>-2+5g<br />
| |
| </td>
| |
| <td>-6g+5\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L9s<br />
| |
| </td>
| |
| <td>5\22 &lt; g &lt; 3\13<br />
| |
| </td>
| |
| <td>g = 131\572<br />
| |
| </td>
| |
| <td>5\22 &lt; g &lt; 8\35<br />
| |
| </td>
| |
| <td>8\35 &lt; g &lt; 11\48<br />
| |
| </td>
| |
| <td>11\48 &lt; g &lt; 14\61<br />
| |
| </td>
| |
| <td>-2+9g<br />
| |
| </td>
| |
| <td>-13g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L8s<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 2\14<br />
| |
| </td>
| |
| <td>g = 43\308<br />
| |
| </td>
| |
| <td>3\22 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>5\36 &lt; g &lt; 7\50<br />
| |
| </td>
| |
| <td>7\50 &lt; g &lt; 9\64<br />
| |
| </td>
| |
| <td>4g-1\2<br />
| |
| </td>
| |
| <td>-7g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L7s<br />
| |
| </td>
| |
| <td>19\22 &lt; g &lt; 13\15<br />
| |
| </td>
| |
| <td>g = 571\660<br />
| |
| </td>
| |
| <td>19\22 &lt; g &lt; 32\37<br />
| |
| </td>
| |
| <td>32\37 &lt; g &lt; 45\52<br />
| |
| </td>
| |
| <td>45\52 &lt; g &lt; 58\67<br />
| |
| </td>
| |
| <td>-6+7g<br />
| |
| </td>
| |
| <td>-15g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L6s<br />
| |
| </td>
| |
| <td>4\22 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>g = 65\352<br />
| |
| </td>
| |
| <td>4\22 &lt; g &lt; 7\38<br />
| |
| </td>
| |
| <td>7\38 &lt; g &lt; 10\54<br />
| |
| </td>
| |
| <td>10\54 &lt; g &lt; 13\70<br />
| |
| </td>
| |
| <td>3g-1\2<br />
| |
| </td>
| |
| <td>-8g+3\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L5s<br />
| |
| </td>
| |
| <td>9\22 &lt; g &lt; 7\17<br />
| |
| </td>
| |
| <td>g = 207\748<br />
| |
| </td>
| |
| <td>9\22 &lt; g &lt; 16\39<br />
| |
| </td>
| |
| <td>16\39 &lt; g &lt; 23\56<br />
| |
| </td>
| |
| <td>23\56 &lt; g &lt; 30\73<br />
| |
| </td>
| |
| <td>-2+5g<br />
| |
| </td>
| |
| <td>-17g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L4s<br />
| |
| </td>
| |
| <td>6\22 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>g = 109\396<br />
| |
| </td>
| |
| <td>6\22 &lt; g &lt; 11\40<br />
| |
| </td>
| |
| <td>11\40 &lt; g &lt; 16\58<br />
| |
| </td>
| |
| <td>16\58 &lt; g &lt; 21\76<br />
| |
| </td>
| |
| <td>-1\2+2g<br />
| |
| </td>
| |
| <td>-9g+5\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L3s<br />
| |
| </td>
| |
| <td>15\22 &lt; g &lt; 13\19<br />
| |
| </td>
| |
| <td>g = 571\836<br />
| |
| </td>
| |
| <td>15\22 &lt; g &lt; 28\41<br />
| |
| </td>
| |
| <td>28\41 &lt; g &lt; 41\60<br />
| |
| </td>
| |
| <td>41\60 &lt; g &lt; 54\79<br />
| |
| </td>
| |
| <td>-2+3g<br />
| |
| </td>
| |
| <td>-19g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L2s<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 1\20<br />
| |
| </td>
| |
| <td>g = 21\440<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 2\42<br />
| |
| </td>
| |
| <td>2\42 &lt; g &lt; 3\62<br />
| |
| </td>
| |
| <td>3\62 &lt; g &lt; 4\72<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-10g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L1s<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 1\21<br />
| |
| </td>
| |
| <td>g = 43\924<br />
| |
| </td>
| |
| <td>1\22 &lt; g &lt; 2\43<br />
| |
| </td>
| |
| <td>2\43 &lt; g &lt; 3\64<br />
| |
| </td>
| |
| <td>3\64 &lt; g &lt; 4\85<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-21g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="x23"></a><!-- ws:end:WikiTextHeadingRule:38 -->23</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L22s<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">22\23 &lt; g &lt; 1</span><br />
| |
| </td>
| |
| <td>g = 45\46<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">22\23 </span>&lt; g &lt; 23\24<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">23\24 </span>&lt; g &lt; 24\25<br />
| |
| </td>
| |
| <td>24\25 &lt; g &lt; 25\26<br />
| |
| </td>
| |
| <td>-21+22g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L21s<br />
| |
| </td>
| |
| <td>11\23 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 45\92<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">11\23 </span>&lt; g &lt; 12\25<br />
| |
| </td>
| |
| <td>12\25 &lt; g &lt; 13\27<br />
| |
| </td>
| |
| <td>13\27 &lt; g &lt; 14\29<br />
| |
| </td>
| |
| <td>-10+21g<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L20s<br />
| |
| </td>
| |
| <td>15\23 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 91\138<br />
| |
| </td>
| |
| <td>15\23 &lt; g &lt; 17\26<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">17\26 </span>&lt; g &lt; 19\29<br />
| |
| </td>
| |
| <td>19\29 &lt; g &lt; 21\32<br />
| |
| </td>
| |
| <td>-13+20g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L19s<br />
| |
| </td>
| |
| <td>17\23 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 137\184<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">17\23 </span>&lt; g &lt; 20\27<br />
| |
| </td>
| |
| <td>20\27 &lt; g &lt; 23\31<br />
| |
| </td>
| |
| <td>23\31 &lt; g &lt; 26\35<br />
| |
| </td>
| |
| <td>-14+19g<br />
| |
| </td>
| |
| <td>-4g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L18s<br />
| |
| </td>
| |
| <td>9\23 &lt; g &lt; 2\5<br />
| |
| </td>
| |
| <td>g = 91\230<br />
| |
| </td>
| |
| <td>9\23 &lt; g &lt; 11\28<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 13\33<br />
| |
| </td>
| |
| <td>13\33 &lt; g &lt; 15\38<br />
| |
| </td>
| |
| <td>-7+18g<br />
| |
| </td>
| |
| <td>-5g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L17s<br />
| |
| </td>
| |
| <td>19\23 &lt; g &lt; 5\6<br />
| |
| </td>
| |
| <td>g = 229\276<br />
| |
| </td>
| |
| <td>19\23 &lt; g &lt; 24\29<br />
| |
| </td>
| |
| <td>24\29 &lt; g &lt; 29\35<br />
| |
| </td>
| |
| <td>29\35 &lt; g &lt; 34\41<br />
| |
| </td>
| |
| <td>-15+17g<br />
| |
| </td>
| |
| <td>1-6g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L16s<br />
| |
| </td>
| |
| <td>13\23 &lt; g &lt; 4\7<br />
| |
| </td>
| |
| <td>g = 183\322<br />
| |
| </td>
| |
| <td>13\23 &lt; g &lt; 17\30<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">17\30 &lt; g &lt; 21\37</span><br />
| |
| </td>
| |
| <td>21\37 &lt; g &lt; 25\44<br />
| |
| </td>
| |
| <td>-9+16g<br />
| |
| </td>
| |
| <td>-7g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L15s<br />
| |
| </td>
| |
| <td>20\23 &lt; g &lt; 7\8<br />
| |
| </td>
| |
| <td>g = 321\368<br />
| |
| </td>
| |
| <td>20\23 &lt; g &lt; 27\31<br />
| |
| </td>
| |
| <td>27\31 &lt; g &lt; 34\39<br />
| |
| </td>
| |
| <td>34\39 &lt; g &lt; 41\47<br />
| |
| </td>
| |
| <td>-13+15g<br />
| |
| </td>
| |
| <td>-8g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L14s<br />
| |
| </td>
| |
| <td>5\23 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>g = 91\414<br />
| |
| </td>
| |
| <td>5\23 &lt; g &lt; 7\32<br />
| |
| </td>
| |
| <td>7\32 &lt; g &lt; 9\41<br />
| |
| </td>
| |
| <td>9\41 &lt; g &lt; 11\50<br />
| |
| </td>
| |
| <td>9g-7<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">11-14g</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L13s<br />
| |
| </td>
| |
| <td>16\23 &lt; g &lt; 7\10<br />
| |
| </td>
| |
| <td>g = 321\460<br />
| |
| </td>
| |
| <td>16\23 &lt; g &lt; 23\33<br />
| |
| </td>
| |
| <td>23\33 &lt; g &lt; 30\43<br />
| |
| </td>
| |
| <td>30\43 &lt; g &lt; 37\53<br />
| |
| </td>
| |
| <td>-9+13g<br />
| |
| </td>
| |
| <td>-10g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L12s<br />
| |
| </td>
| |
| <td>2\23 &lt; g &lt; 1\11<br />
| |
| </td>
| |
| <td>g = 45\506<br />
| |
| </td>
| |
| <td>2\23 &lt; g &lt; 3\34<br />
| |
| </td>
| |
| <td>3\34 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>4\45 &lt; g &lt; 5\56<br />
| |
| </td>
| |
| <td>-11g+1<br />
| |
| </td>
| |
| <td>12g-1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L11s<br />
| |
| </td>
| |
| <td>21\23 &lt; g &lt; 11\12<br />
| |
| </td>
| |
| <td>g = 505\552<br />
| |
| </td>
| |
| <td>21\23 &lt; g &lt; 32\35<br />
| |
| </td>
| |
| <td>32\35 &lt; g &lt; 43\47<br />
| |
| </td>
| |
| <td>43\47 &lt; g &lt; 54\59<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">11g-10</span><br />
| |
| </td>
| |
| <td>11-12g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L10s<br />
| |
| </td>
| |
| <td>7\23 &lt; g &lt; 4\13<br />
| |
| </td>
| |
| <td>g = 183\598<br />
| |
| </td>
| |
| <td>7\23 &lt; g &lt; 11\36<br />
| |
| </td>
| |
| <td>11\36 &lt; g &lt; 15\49<br />
| |
| </td>
| |
| <td>15\49 &lt; g &lt; 19\62<br />
| |
| </td>
| |
| <td>4-13g<br />
| |
| </td>
| |
| <td>10g-3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L9s<br />
| |
| </td>
| |
| <td>18\23 &lt; g &lt; 11\14<br />
| |
| </td>
| |
| <td>g = 505\644<br />
| |
| </td>
| |
| <td>18\23 &lt; g &lt; 29\37<br />
| |
| </td>
| |
| <td>29\37 &lt; g &lt; 40\51<br />
| |
| </td>
| |
| <td>40\51 &lt; g &lt; 51\65<br />
| |
| </td>
| |
| <td>14g-3<br />
| |
| </td>
| |
| <td>-9g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L8s<br />
| |
| </td>
| |
| <td>3\23 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>g = 91\690<br />
| |
| </td>
| |
| <td>3\23 &lt; g &lt; 5\38<br />
| |
| </td>
| |
| <td>5\38 &lt; g &lt; 7\53<br />
| |
| </td>
| |
| <td>7\53 &lt; g &lt; 9\68<br />
| |
| </td>
| |
| <td>2-15g<br />
| |
| </td>
| |
| <td>8g-1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L7s<br />
| |
| </td>
| |
| <td>10\23 &lt; g &lt; 7\16<br />
| |
| </td>
| |
| <td>g = 321\736<br />
| |
| </td>
| |
| <td>10\23 &lt; g &lt; 17\39<br />
| |
| </td>
| |
| <td>17\39 &lt; g &lt; 24\55<br />
| |
| </td>
| |
| <td>24\55 &lt; g &lt; 31\71<br />
| |
| </td>
| |
| <td>7g-3<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-16g+7</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L6s<br />
| |
| </td>
| |
| <td>4\23 &lt; g &lt; 3\17<br />
| |
| </td>
| |
| <td>g = 137\782<br />
| |
| </td>
| |
| <td>4\23 &lt; g &lt; 7\40<br />
| |
| </td>
| |
| <td>7\40 &lt; g &lt; 10\57<br />
| |
| </td>
| |
| <td>10\57 &lt; g &lt; 13\74<br />
| |
| </td>
| |
| <td>-1+6g<br />
| |
| </td>
| |
| <td>-17g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L5s<br />
| |
| </td>
| |
| <td>14\23 &lt; g &lt; 11\18<br />
| |
| </td>
| |
| <td>g = 505\828<br />
| |
| </td>
| |
| <td>14\23 &lt; g &lt; 25\41<br />
| |
| </td>
| |
| <td>25\41 &lt; g &lt; 36\59<br />
| |
| </td>
| |
| <td>36\59 &lt; g &lt; 47\77<br />
| |
| </td>
| |
| <td>11-18g<br />
| |
| </td>
| |
| <td>5g-4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L4s<br />
| |
| </td>
| |
| <td>6\23 &lt; g &lt; 5\19<br />
| |
| </td>
| |
| <td>g = 229\874<br />
| |
| </td>
| |
| <td>6\23 &lt; g &lt; 11\42<br />
| |
| </td>
| |
| <td>11\42 &lt; g &lt; 16\61<br />
| |
| </td>
| |
| <td>16\61 &lt; g &lt; 21\80<br />
| |
| </td>
| |
| <td>-1+4g<br />
| |
| </td>
| |
| <td>-19g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L3s<br />
| |
| </td>
| |
| <td>8\23 &lt; g &lt; 7\20<br />
| |
| </td>
| |
| <td>g = 321\920<br />
| |
| </td>
| |
| <td>8\23 &lt; g &lt; 15\43<br />
| |
| </td>
| |
| <td>15\43 &lt; g &lt; 22\63<br />
| |
| </td>
| |
| <td>22\63 &lt; g &lt; 29\83<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>-20g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L2s<br />
| |
| </td>
| |
| <td>12\23 &lt; g &lt; 11\21<br />
| |
| </td>
| |
| <td>g = 505\966<br />
| |
| </td>
| |
| <td>12\23 &lt; g &lt; 23\44<br />
| |
| </td>
| |
| <td>23\44 &lt; g &lt; 34\65<br />
| |
| </td>
| |
| <td>34\65 &lt; g &lt; 45\86<br />
| |
| </td>
| |
| <td>-1+2g<br />
| |
| </td>
| |
| <td>-21g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22L1s<br />
| |
| </td>
| |
| <td>1\23 &lt; g &lt; 1\22<br />
| |
| </td>
| |
| <td>g = 45\1012<br />
| |
| </td>
| |
| <td>1\23 &lt; g &lt; 2\45<br />
| |
| </td>
| |
| <td>2\45 &lt; g &lt; 3\67<br />
| |
| </td>
| |
| <td>3\67 &lt; g &lt; 4\89<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-22g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="x24"></a><!-- ws:end:WikiTextHeadingRule:40 -->24</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L23s<br />
| |
| </td>
| |
| <td>23\24 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 47\48<br />
| |
| </td>
| |
| <td>23\24 &lt; g &lt; 24\25<br />
| |
| </td>
| |
| <td>24\25 &lt; g &lt; 25\26<br />
| |
| </td>
| |
| <td>25\26 &lt; g &lt; 26\27<br />
| |
| </td>
| |
| <td>-22+23g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L22s<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 23\48<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 12\26<br />
| |
| </td>
| |
| <td>12\26 &lt; g &lt; 13\28<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 14\30<br />
| |
| </td>
| |
| <td>-g+1/2<br />
| |
| </td>
| |
| <td>-5+11g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L21s<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 15\48<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 8\27<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 9\30<br />
| |
| </td>
| |
| <td>9\30 &lt; g &lt; 10\33<br />
| |
| </td>
| |
| <td>2/3-2g<br />
| |
| </td>
| |
| <td>-1/3+g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L20s<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 11\48<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 6\28<br />
| |
| </td>
| |
| <td>6\28 &lt; g &lt; 7\32<br />
| |
| </td>
| |
| <td>7\32 &lt; g &lt; 8\36<br />
| |
| </td>
| |
| <td>-1+5g<br />
| |
| </td>
| |
| <td>-g+1/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L19s<br />
| |
| </td>
| |
| <td>19\24 &lt; g &lt; 4\5<br />
| |
| </td>
| |
| <td>g = 191\240<br />
| |
| </td>
| |
| <td>19\24 &lt; g &lt; 23\29<br />
| |
| </td>
| |
| <td>23\29 &lt; g &lt; 27\34<br />
| |
| </td>
| |
| <td>27\34 &lt; g &lt; 31\39<br />
| |
| </td>
| |
| <td>-15+19g<br />
| |
| </td>
| |
| <td>-5g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L18s<br />
| |
| </td>
| |
| <td>3\24 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 7\48<br />
| |
| </td>
| |
| <td>3\24 &lt; g &lt; 4\30<br />
| |
| </td>
| |
| <td>4\30 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>5\36 &lt; g &lt; 6\42<br />
| |
| </td>
| |
| <td>-1\3+3g<br />
| |
| </td>
| |
| <td>1\6-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L17s<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt; 5\7<br />
| |
| </td>
| |
| <td>g = 239\336<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt; 22\31<br />
| |
| </td>
| |
| <td>22\31 &lt; g &lt; 27\38<br />
| |
| </td>
| |
| <td>27\38 &lt; g &lt; 32\455<br />
| |
| </td>
| |
| <td>5-17g<br />
| |
| </td>
| |
| <td>7g-2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L16s<br />
| |
| </td>
| |
| <td>2\24 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 5\48<br />
| |
| </td>
| |
| <td>2\24 &lt; g &lt; 3\32<br />
| |
| </td>
| |
| <td>3\32 &lt; g &lt; 4\40<br />
| |
| </td>
| |
| <td>4\40 &lt; g &lt; 5\48<br />
| |
| </td>
| |
| <td>-1\8+2g<br />
| |
| </td>
| |
| <td>-g+1\8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L15s<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 2\9<br />
| |
| </td>
| |
| <td>g = 31\144<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 7\33<br />
| |
| </td>
| |
| <td>7\33 &lt; g &lt; 9\42<br />
| |
| </td>
| |
| <td>9\42 &lt; g &lt; 11\51<br />
| |
| </td>
| |
| <td>5g-1<br />
| |
| </td>
| |
| <td>2\3-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L14s<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 3\10<br />
| |
| </td>
| |
| <td>g = 71\240<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 10\34<br />
| |
| </td>
| |
| <td>10\34 &lt; g &lt; 13\44<br />
| |
| </td>
| |
| <td>13\44 &lt; g &lt; 16\54<br />
| |
| </td>
| |
| <td>-4+7g<br />
| |
| </td>
| |
| <td>-3\2+5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L13s<br />
| |
| </td>
| |
| <td>13\24 &lt; g &lt; 6\11<br />
| |
| </td>
| |
| <td>g = 287\528<br />
| |
| </td>
| |
| <td>13\24 &lt; g &lt; 19\35<br />
| |
| </td>
| |
| <td>19\35 &lt; g &lt; 25\46<br />
| |
| </td>
| |
| <td>25|46 &lt; g &lt; 31\57<br />
| |
| </td>
| |
| <td>13g-7<br />
| |
| </td>
| |
| <td>-11g+6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L12s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 3\48<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\36<br />
| |
| </td>
| |
| <td>2\36 &lt; g &lt; 3\48<br />
| |
| </td>
| |
| <td>3\48 &lt; g &lt; 4\60<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\12-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L11s<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 6\13<br />
| |
| </td>
| |
| <td>g = 287\624<br />
| |
| </td>
| |
| <td>11\24 &lt; g &lt; 17\37<br />
| |
| </td>
| |
| <td>17\37 &lt; g &lt; 23\50<br />
| |
| </td>
| |
| <td>23\50 &lt; g &lt; 29\63<br />
| |
| </td>
| |
| <td>11g-5<br />
| |
| </td>
| |
| <td>6-13g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L10s<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt; 10\14<br />
| |
| </td>
| |
| <td>g = 239\336<br />
| |
| </td>
| |
| <td>17\24 &lt; g &lt; 27\38<br />
| |
| </td>
| |
| <td>27\38 &lt; g &lt; 37\52<br />
| |
| </td>
| |
| <td>37\52 &lt; g &lt; 47\66<br />
| |
| </td>
| |
| <td>3\2-5g<br />
| |
| </td>
| |
| <td>7g-2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L9s<br />
| |
| </td>
| |
| <td>3\24 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>g = 31\240<br />
| |
| </td>
| |
| <td>3\24 &lt; g &lt; 5\39<br />
| |
| </td>
| |
| <td>5\39 &lt; g &lt; 7\54<br />
| |
| </td>
| |
| <td>7\54 &lt; g &lt; 9\69<br />
| |
| </td>
| |
| <td>3g-1\3<br />
| |
| </td>
| |
| <td>-5g+2\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L8s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\16<br />
| |
| </td>
| |
| <td>g = 5\96<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\40<br />
| |
| </td>
| |
| <td>2\40 &lt; g &lt; 3\56<br />
| |
| </td>
| |
| <td>3\56 &lt; g &lt; 4\72<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\8-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L7s<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 5\17<br />
| |
| </td>
| |
| <td>g = 239\816<br />
| |
| </td>
| |
| <td>7\24 &lt; g &lt; 12\41<br />
| |
| </td>
| |
| <td>12\41 &lt; g &lt; 17\58<br />
| |
| </td>
| |
| <td>17\58 &lt; g &lt; 22\75<br />
| |
| </td>
| |
| <td>-7g+4<br />
| |
| </td>
| |
| <td>17g-12<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L6s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\18<br />
| |
| </td>
| |
| <td>g = 7\144<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\42<br />
| |
| </td>
| |
| <td>2\42 &lt; g &lt; 3\60<br />
| |
| </td>
| |
| <td>3\60 &lt; g &lt; 4\78<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\6-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L5s<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 4\19<br />
| |
| </td>
| |
| <td>g = 191\912<br />
| |
| </td>
| |
| <td>5\24 &lt; g &lt; 9\43<br />
| |
| </td>
| |
| <td>9\43 &lt; g &lt; 13\62<br />
| |
| </td>
| |
| <td>13\62 &lt; g &lt; 17\81<br />
| |
| </td>
| |
| <td>-5g+4<br />
| |
| </td>
| |
| <td>-15+19g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L4s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\20<br />
| |
| </td>
| |
| <td>g = 11\240<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\44<br />
| |
| </td>
| |
| <td>2\44 &lt; g &lt; 3\64<br />
| |
| </td>
| |
| <td>3\64 &lt; g &lt; 4\84<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-5g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L3s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\21<br />
| |
| </td>
| |
| <td>g = 15\336<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\45<br />
| |
| </td>
| |
| <td>2\45 &lt; g &lt; 3\66<br />
| |
| </td>
| |
| <td>3\66 &lt; g &lt; 4\87<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-7g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22L2s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\22<br />
| |
| </td>
| |
| <td>g = 23\264<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\46<br />
| |
| </td>
| |
| <td>2\46 &lt; g &lt; 3\68<br />
| |
| </td>
| |
| <td>3\68 &lt; g &lt; 4\90<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-11g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23L1s<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 1\23<br />
| |
| </td>
| |
| <td>g = 47\1104<br />
| |
| </td>
| |
| <td>1\24 &lt; g &lt; 2\47<br />
| |
| </td>
| |
| <td>2\47 &lt; g &lt; 3\70<br />
| |
| </td>
| |
| <td>3\70 &lt; g &lt; 4\93<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-23g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="x25"></a><!-- ws:end:WikiTextHeadingRule:42 -->25</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L24s<br />
| |
| </td>
| |
| <td>24\25 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 49\50<br />
| |
| </td>
| |
| <td>24\25 &lt; g &lt; 25\26<br />
| |
| </td>
| |
| <td>25\26 &lt; g &lt; 26\27<br />
| |
| </td>
| |
| <td>26\27 &lt; g &lt; 27\28<br />
| |
| </td>
| |
| <td>-23+24g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L23s<br />
| |
| </td>
| |
| <td>12\25 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 49\100<br />
| |
| </td>
| |
| <td>12\25 &lt; g &lt; 13\27<br />
| |
| </td>
| |
| <td>13\27 &lt; g &lt; 14\29<br />
| |
| </td>
| |
| <td>14\29 &lt; g &lt; 15\31<br />
| |
| </td>
| |
| <td>2g-11<br />
| |
| </td>
| |
| <td>1-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L22s<br />
| |
| </td>
| |
| <td>8\25 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 49\150<br />
| |
| </td>
| |
| <td>8\25 &lt; g &lt; 9\28<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 10\31<br />
| |
| </td>
| |
| <td>10\31 &lt; g &lt; 11\34<br />
| |
| </td>
| |
| <td>-7+22g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L21s<br />
| |
| </td>
| |
| <td>6\25 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 49\200<br />
| |
| </td>
| |
| <td>6\25 &lt; g &lt; 7\29<br />
| |
| </td>
| |
| <td>7\29 &lt; g &lt; 8\33<br />
| |
| </td>
| |
| <td>8\33 &lt; g &lt; 9\37<br />
| |
| </td>
| |
| <td>-5+21g<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L20s<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 9\50<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\30<br />
| |
| </td>
| |
| <td>5\30 &lt; g &lt; 6\35<br />
| |
| </td>
| |
| <td>6\35 &lt; g &lt; 7\40<br />
| |
| </td>
| |
| <td>-3\5+4g<br />
| |
| </td>
| |
| <td>1\5-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L19s<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 49\300<br />
| |
| </td>
| |
| <td>4\25 &lt; g &lt; 5\31<br />
| |
| </td>
| |
| <td>5\31 &lt; g &lt; 6\37<br />
| |
| </td>
| |
| <td>6\37 &lt; g &lt; 7\43<br />
| |
| </td>
| |
| <td>-3+19g<br />
| |
| </td>
| |
| <td>-6g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L18s<br />
| |
| </td>
| |
| <td>7\25 &lt; g &lt; 2\7<br />
| |
| </td>
| |
| <td>g = 99\350<br />
| |
| </td>
| |
| <td>7\25 &lt; g &lt; 9\32<br />
| |
| </td>
| |
| <td>9\32 &lt; g &lt; 11\39<br />
| |
| </td>
| |
| <td>11\39 &lt; g &lt; 13\46<br />
| |
| </td>
| |
| <td>-5+18g<br />
| |
| </td>
| |
| <td>-7g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L17s<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 49\400<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 4\33<br />
| |
| </td>
| |
| <td>4\33 &lt; g &lt; 5\41<br />
| |
| </td>
| |
| <td>5\41 &lt; g &lt; 6\47<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">17g-2</span><br />
| |
| </td>
| |
| <td>1-8g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L16s<br />
| |
| </td>
| |
| <td>11\25 &lt; g &lt; 4\9<br />
| |
| </td>
| |
| <td>g = 199\450<br />
| |
| </td>
| |
| <td>11\25 &lt; g &lt; 15\34<br />
| |
| </td>
| |
| <td>15\34 &lt; g &lt; 19\43<br />
| |
| </td>
| |
| <td>19\43 &lt; g &lt; 23\52<br />
| |
| </td>
| |
| <td>-7+16g<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-9g+4</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L15s<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 1\10<br />
| |
| </td>
| |
| <td>g = 9\100<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 3\35<br />
| |
| </td>
| |
| <td>3\35 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>4\45 &lt; g &lt; 5\55<br />
| |
| </td>
| |
| <td>-1\5+3g<br />
| |
| </td>
| |
| <td>1\5-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L14s<br />
| |
| </td>
| |
| <td>9\25 &lt; g &lt; 4\11<br />
| |
| </td>
| |
| <td>g = 199\550<br />
| |
| </td>
| |
| <td>9\25 &lt; g &lt; 13\36<br />
| |
| </td>
| |
| <td>13\36 &lt; g &lt; 17\47<br />
| |
| </td>
| |
| <td>17\47 &lt; g &lt; 21\58<br />
| |
| </td>
| |
| <td>14g-5<br />
| |
| </td>
| |
| <td>-11g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L13s<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 49\600<br />
| |
| </td>
| |
| <td>2\25 &lt; g &lt; 3\37<br />
| |
| </td>
| |
| <td>3\37 &lt; g &lt; 4\49<br />
| |
| </td>
| |
| <td>4\49 &lt; g &lt; 5\61<br />
| |
| </td>
| |
| <td>13g-1<br />
| |
| </td>
| |
| <td>1-12g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L12s<br />
| |
| </td>
| |
| <td>23\25 &lt; g &lt; 12\13<br />
| |
| </td>
| |
| <td>g = 599\650<br />
| |
| </td>
| |
| <td>23\25 &lt; g &lt; 35\38<br />
| |
| </td>
| |
| <td>35\38 &lt; g &lt; 47\51<br />
| |
| </td>
| |
| <td>47\51 &lt; g &lt; 59\64<br />
| |
| </td>
| |
| <td>12g-11<br />
| |
| </td>
| |
| <td>12-13g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L11s<br />
| |
| </td>
| |
| <td>16\25 &lt; g &lt; 9\14<br />
| |
| </td>
| |
| <td>g = 449\700<br />
| |
| </td>
| |
| <td>16\25 &lt; g &lt; 25\39<br />
| |
| </td>
| |
| <td>25\39 &lt; g &lt; 34\53<br />
| |
| </td>
| |
| <td>34\53 &lt; g &lt; 43\67<br />
| |
| </td>
| |
| <td>-7+11g<br />
| |
| </td>
| |
| <td>-14g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L10s<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 2\15<br />
| |
| </td>
| |
| <td>g = 19\150<br />
| |
| </td>
| |
| <td>3\25 &lt; g &lt; 5\40<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">5\40 </span>&lt; g &lt; 7\55<br />
| |
| </td>
| |
| <td>7\55 &lt; g &lt; 9\70<br />
| |
| </td>
| |
| <td>-2g+1\5<br />
| |
| </td>
| |
| <td>3g-2\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L9s<br />
| |
| </td>
| |
| <td>14\25 &lt; g &lt; 9\16<br />
| |
| </td>
| |
| <td>g = 449\800<br />
| |
| </td>
| |
| <td>14\25 &lt; g &lt; 23\41<br />
| |
| </td>
| |
| <td>23\41 &lt; g &lt; 32\57<br />
| |
| </td>
| |
| <td>32\57 &lt; g &lt; 41\73<br />
| |
| </td>
| |
| <td>9g-5<br />
| |
| </td>
| |
| <td>9-16g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L8s<br />
| |
| </td>
| |
| <td>22\25 &lt; g &lt; 15\17<br />
| |
| </td>
| |
| <td>g = 749\850<br />
| |
| </td>
| |
| <td>22\25 &lt; g &lt; 37\42<br />
| |
| </td>
| |
| <td>37\42 &lt; g &lt; 52\59<br />
| |
| </td>
| |
| <td>52\59 &lt; g &lt; 67\76<br />
| |
| </td>
| |
| <td>8g-7<br />
| |
| </td>
| |
| <td>-17g+15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L7s<br />
| |
| </td>
| |
| <td>18\25 &lt; g &lt; 13\18<br />
| |
| </td>
| |
| <td>g = 649\900<br />
| |
| </td>
| |
| <td>18\25 &lt; g &lt; 31\43<br />
| |
| </td>
| |
| <td>31\43 &lt; g &lt; 44\61<br />
| |
| </td>
| |
| <td>44\61 &lt; g &lt; 57\79<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>1\6-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L6s<br />
| |
| </td>
| |
| <td>21\25 &lt; g &lt; 16\19<br />
| |
| </td>
| |
| <td>g = 799\950<br />
| |
| </td>
| |
| <td>21\25 &lt; g &lt; 37\44<br />
| |
| </td>
| |
| <td>37\44 &lt; g &lt; 53\63<br />
| |
| </td>
| |
| <td>53\63 &lt; g &lt; 69\82<br />
| |
| </td>
| |
| <td>-19g+16<br />
| |
| </td>
| |
| <td>-5+6g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L5s<br />
| |
| </td>
| |
| <td>1\25 &lt; g &lt; 1\20<br />
| |
| </td>
| |
| <td>g = 9\200<br />
| |
| </td>
| |
| <td>1\25 &lt; g &lt; 2\45<br />
| |
| </td>
| |
| <td>2\45 &lt; g &lt; 3\65<br />
| |
| </td>
| |
| <td>3\65 &lt; g &lt; 4\85<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-4g+1\5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L4s<br />
| |
| </td>
| |
| <td>16\21 &lt; g &lt; 19\25<br />
| |
| </td>
| |
| <td>g = 799\1050<br />
| |
| </td>
| |
| <td>19\25 &lt; g &lt; 35\46<br />
| |
| </td>
| |
| <td>35\46 &lt; g &lt; 51\67<br />
| |
| </td>
| |
| <td>51\67 &lt; g &lt; 71\88<br />
| |
| </td>
| |
| <td>4g-3<br />
| |
| </td>
| |
| <td>-21g+16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22L3s<br />
| |
| </td>
| |
| <td>17\25 &lt; g &lt; 15\22<br />
| |
| </td>
| |
| <td>g = 749\1100<br />
| |
| </td>
| |
| <td>17\25 &lt; g &lt; 32\47<br />
| |
| </td>
| |
| <td>32\47 &lt; g &lt; 47\69<br />
| |
| </td>
| |
| <td>47\69 &lt; g &lt; 62\91<br />
| |
| </td>
| |
| <td>3g-2<br />
| |
| </td>
| |
| <td>-22g+15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23L2s<br />
| |
| </td>
| |
| <td>13\25 &lt; g &lt; 12\23<br />
| |
| </td>
| |
| <td>g = 599\1150<br />
| |
| </td>
| |
| <td>13\25 &lt; g &lt; 25\48<br />
| |
| </td>
| |
| <td>25\48 &lt; g &lt; 37\71<br />
| |
| </td>
| |
| <td>37\71 &lt; g &lt; 49\94<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| <td>23g-11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24L1s<br />
| |
| </td>
| |
| <td>1\25 &lt; g &lt; 1\24<br />
| |
| </td>
| |
| <td>g = 49\1200<br />
| |
| </td>
| |
| <td>1\25 &lt; g &lt; 2\49<br />
| |
| </td>
| |
| <td>2\49 &lt; g &lt; 3\73<br />
| |
| </td>
| |
| <td>3\73 &lt; g &lt; 4\97<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-24g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="x26"></a><!-- ws:end:WikiTextHeadingRule:44 -->26</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L25s<br />
| |
| </td>
| |
| <td>25\26 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 51\52<br />
| |
| </td>
| |
| <td>25\26 &lt; g &lt; 26\27<br />
| |
| </td>
| |
| <td>26\27 &lt; g &lt; 27\28<br />
| |
| </td>
| |
| <td>27\28 &lt; g &lt; 28\29<br />
| |
| </td>
| |
| <td>-24+25g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L24s<br />
| |
| </td>
| |
| <td>12\26 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 25\52<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">12\26</span> &lt; g &lt; 13\28<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 14\30<br />
| |
| </td>
| |
| <td>14\30 &lt; g &lt; 15\32<br />
| |
| </td>
| |
| <td>12g-11\2<br />
| |
| </td>
| |
| <td>1\2-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L23s<br />
| |
| </td>
| |
| <td>17\26 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 103\156<br />
| |
| </td>
| |
| <td>17\26 &lt; g &lt; 19\29<br />
| |
| </td>
| |
| <td>19\29 &lt; g &lt; 21\32<br />
| |
| </td>
| |
| <td>21\32 &lt; g &lt; 23\35<br />
| |
| </td>
| |
| <td>-15+23g<br />
| |
| </td>
| |
| <td>2-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L22s<br />
| |
| </td>
| |
| <td>6\26 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 25\104<br />
| |
| </td>
| |
| <td>6\26 &lt; g &lt; 7\30<br />
| |
| </td>
| |
| <td>7\30 &lt; g &lt; 8\34<br />
| |
| </td>
| |
| <td>8\34 &lt; g &lt; 9\38<br />
| |
| </td>
| |
| <td>11g-5\2<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-2g+1\2</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L21s<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 1\5<br />
| |
| </td>
| |
| <td>g = 51\260<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 6\31<br />
| |
| </td>
| |
| <td>6\31 &lt; g &lt; 7\36<br />
| |
| </td>
| |
| <td>7\36 &lt; g &lt; 8\41<br />
| |
| </td>
| |
| <td>-4+21g<br />
| |
| </td>
| |
| <td>1-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L20s<br />
| |
| </td>
| |
| <td>4\26 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 25\156<br />
| |
| </td>
| |
| <td>4\26 &lt; g &lt; 5\32<br />
| |
| </td>
| |
| <td>5\32 &lt; g &lt; 6\38<br />
| |
| </td>
| |
| <td>6\38 &lt; g &lt; 7\44<br />
| |
| </td>
| |
| <td>-3\2+10g<br />
| |
| </td>
| |
| <td>-3g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L19s<br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 3\7<br />
| |
| </td>
| |
| <td>g = 155\364<br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 14\33<br />
| |
| </td>
| |
| <td>14\33 &lt; g &lt; 17\40<br />
| |
| </td>
| |
| <td>17\40 &lt; g &lt; 20\47<br />
| |
| </td>
| |
| <td>-8+19g<br />
| |
| </td>
| |
| <td>-7g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L18s<br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 25\208<br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 4\34<br />
| |
| </td>
| |
| <td>4\34 &lt; g &lt; 5\42<br />
| |
| </td>
| |
| <td>5\42 &lt; g &lt; 6\50<br />
| |
| </td>
| |
| <td>9g-1<br />
| |
| </td>
| |
| <td>1\2-4g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L17s<br />
| |
| </td>
| |
| <td>23\26 &lt; g &lt; 8\9<br />
| |
| </td>
| |
| <td>g = 415\468<br />
| |
| </td>
| |
| <td>23\26 &lt; g &lt; 31\35<br />
| |
| </td>
| |
| <td>31\35 &lt; g &lt; 39\44<br />
| |
| </td>
| |
| <td>39\44 &lt; g &lt; 47\53<br />
| |
| </td>
| |
| <td>-15+17g<br />
| |
| </td>
| |
| <td>-9g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L16s<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 2\10<br />
| |
| </td>
| |
| <td>g = 51\260<br />
| |
| </td>
| |
| <td>5\26 &lt; g &lt; 7\36<br />
| |
| </td>
| |
| <td>7\36 &lt; g &lt; 9\46<br />
| |
| </td>
| |
| <td>9\46 &lt; g &lt; 11\56<br />
| |
| </td>
| |
| <td>-3\2+8g<br />
| |
| </td>
| |
| <td>1-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L15s<br />
| |
| </td>
| |
| <td>7\26 &lt; g &lt; 3\11<br />
| |
| </td>
| |
| <td>g = 155\572<br />
| |
| </td>
| |
| <td>7\26 &lt; g &lt; 10\37<br />
| |
| </td>
| |
| <td>10\37 &lt; g &lt; 13\48<br />
| |
| </td>
| |
| <td>13\48 &lt; g &lt; 16\59<br />
| |
| </td>
| |
| <td>15g-4<br />
| |
| </td>
| |
| <td>-11g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L14s<br />
| |
| </td>
| |
| <td>2\26 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 25\312<br />
| |
| </td>
| |
| <td>2\26 &lt; g &lt; 3\38<br />
| |
| </td>
| |
| <td>3\38 &lt; g &lt; 4\50<br />
| |
| </td>
| |
| <td>4\50 &lt; g &lt; 5\62<br />
| |
| </td>
| |
| <td>7g-1\2<br />
| |
| </td>
| |
| <td>1\2-6g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L13s<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 1\13<br />
| |
| </td>
| |
| <td>g = 3\52<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 2\39<br />
| |
| </td>
| |
| <td>2\39 &lt; g &lt; 3\52<br />
| |
| </td>
| |
| <td>3\52 &lt; g &lt; 4\65<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">14L12s</span><br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 6\14<br />
| |
| </td>
| |
| <td>g = 155\364<br />
| |
| </td>
| |
| <td>11\26 &lt; g &lt; 17\40<br />
| |
| </td>
| |
| <td>17\40 &lt; g &lt; 23\54<br />
| |
| </td>
| |
| <td>23\54 &lt; g &lt; 29\68<br />
| |
| </td>
| |
| <td>6g-5\2<br />
| |
| </td>
| |
| <td>3-7g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">15L11s</span><br />
| |
| </td>
| |
| <td>19\26 &lt; g &lt; 11\15<br />
| |
| </td>
| |
| <td>g = 571\780<br />
| |
| </td>
| |
| <td>19\26 &lt; g &lt; 30\41<br />
| |
| </td>
| |
| <td>30\41 &lt; g &lt; 41\56<br />
| |
| </td>
| |
| <td>41\56 &lt; g &lt; 52\71<br />
| |
| </td>
| |
| <td>-8+11g<br />
| |
| </td>
| |
| <td>-15g+11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">16L10s</span><br />
| |
| </td>
| |
| <td>8\26 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>g = 129\416<br />
| |
| </td>
| |
| <td>8\26 &lt; g &lt; 13\42<br />
| |
| </td>
| |
| <td>13\42 &lt; g &lt; 18\58<br />
| |
| </td>
| |
| <td>18\58 &lt; g &lt; 23\74<br />
| |
| </td>
| |
| <td>-8g+13\2<br />
| |
| </td>
| |
| <td>5g-4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">17L9s</span><br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 2\17<br />
| |
| </td>
| |
| <td>g = 103\884<br />
| |
| </td>
| |
| <td>3\26 &lt; g &lt; 5\43<br />
| |
| </td>
| |
| <td>5\43 &lt; g &lt; 7\60<br />
| |
| </td>
| |
| <td>7\60 &lt; g &lt; 9\77<br />
| |
| </td>
| |
| <td>9g-1<br />
| |
| </td>
| |
| <td>2-17g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">18L</span>8s<br />
| |
| </td>
| |
| <td>10\26 &lt; g &lt; 7\18<br />
| |
| </td>
| |
| <td>g = 181\468<br />
| |
| </td>
| |
| <td>10\26 &lt; g &lt; 17\44<br />
| |
| </td>
| |
| <td>17\44 &lt; g &lt; 24\62<br />
| |
| </td>
| |
| <td>24\62 &lt; g &lt; 31\80<br />
| |
| </td>
| |
| <td>8g-7<br />
| |
| </td>
| |
| <td>-9g+7\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">19L</span>7s<br />
| |
| </td>
| |
| <td>15\26 &lt; g &lt; 11\19<br />
| |
| </td>
| |
| <td>g = 571\988<br />
| |
| </td>
| |
| <td>15\26 &lt; g &lt; 26\45<br />
| |
| </td>
| |
| <td>26\45 &lt; g &lt; 37\64<br />
| |
| </td>
| |
| <td>37\64 &lt; g &lt; 48\83<br />
| |
| </td>
| |
| <td>11-19g<br />
| |
| </td>
| |
| <td>-4+7g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">20L</span>6s<br />
| |
| </td>
| |
| <td>9\26 &lt; g &lt; 7\20<br />
| |
| </td>
| |
| <td>g = 181\520<br />
| |
| </td>
| |
| <td>9\26 &lt; g &lt; 16\46<br />
| |
| </td>
| |
| <td>16\46 &lt; g &lt; 23\66<br />
| |
| </td>
| |
| <td>23\66 &lt; g &lt; 30\86<br />
| |
| </td>
| |
| <td>-1+3g<br />
| |
| </td>
| |
| <td>7\2-10g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">21L</span>5s<br />
| |
| </td>
| |
| <td>21\26 &lt; g &lt; 17\21<br />
| |
| </td>
| |
| <td>g = 883\1092<br />
| |
| </td>
| |
| <td>21\26 &lt; g &lt; 38\47<br />
| |
| </td>
| |
| <td>38\47 &lt; g &lt; 55\68<br />
| |
| </td>
| |
| <td>55\68 &lt; g &lt; 72\89<br />
| |
| </td>
| |
| <td>5g-4<br />
| |
| </td>
| |
| <td>-21g+16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">22L</span>4s<br />
| |
| </td>
| |
| <td>7\26 &lt; g &lt; 6\22<br />
| |
| </td>
| |
| <td>g = 155\572<br />
| |
| </td>
| |
| <td>7\26 &lt; g &lt; 13\48<br />
| |
| </td>
| |
| <td>13\48 &lt; g &lt; 19\70<br />
| |
| </td>
| |
| <td>19\70 &lt; g &lt; 25\92<br />
| |
| </td>
| |
| <td>2g-1\2<br />
| |
| </td>
| |
| <td>-11g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">23L</span>3s<br />
| |
| </td>
| |
| <td>9\26 &lt; g &lt; 8\23<br />
| |
| </td>
| |
| <td>g = 415\1196<br />
| |
| </td>
| |
| <td>9\26 &lt; g &lt; 17\49<br />
| |
| </td>
| |
| <td>17\49 &lt; g &lt; 25\72<br />
| |
| </td>
| |
| <td>25\72 &lt; g &lt; 33/95<br />
| |
| </td>
| |
| <td>3g-1<br />
| |
| </td>
| |
| <td>-23g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">24L</span>2s<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 1\24<br />
| |
| </td>
| |
| <td>g = 25\312<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 2\50<br />
| |
| </td>
| |
| <td>2\50 &lt; g &lt; 3\74<br />
| |
| </td>
| |
| <td>3\74 &lt; g &lt; 4\98<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-12g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25L1s<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 1\25<br />
| |
| </td>
| |
| <td>g = 51\1300<br />
| |
| </td>
| |
| <td>1\26 &lt; g &lt; 2\51<br />
| |
| </td>
| |
| <td>2\51&lt; g &lt; 3\76<br />
| |
| </td>
| |
| <td>3\76 &lt; g &lt; 4\101<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-25g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="x27"></a><!-- ws:end:WikiTextHeadingRule:46 -->27</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L26s<br />
| |
| </td>
| |
| <td>26\27 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 53\54<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">26\27 &lt; g &lt; 27\28</span><br />
| |
| </td>
| |
| <td>27\28 &lt; g &lt; 28\29<br />
| |
| </td>
| |
| <td>28\29 &lt; g &lt; 29\30<br />
| |
| </td>
| |
| <td>-25+26g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L25s<br />
| |
| </td>
| |
| <td>13\27 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 53\108<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">13</span>\27 &lt; g &lt; 14\29<br />
| |
| </td>
| |
| <td>14\29 &lt; g &lt; 15\31<br />
| |
| </td>
| |
| <td>15\31 &lt; g &lt; 16\33<br />
| |
| </td>
| |
| <td>25g-12<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L24s<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 17\54<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 9\30<br />
| |
| </td>
| |
| <td>9\30 &lt; g &lt; 10\33<br />
| |
| </td>
| |
| <td>10\33 &lt; g &lt; 11\36<br />
| |
| </td>
| |
| <td>-7\3+8g<br />
| |
| </td>
| |
| <td>1-3-g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L23s<br />
| |
| </td>
| |
| <td>20\27 &lt; g &lt; 3\4<br />
| |
| </td>
| |
| <td>g = 161\216<br />
| |
| </td>
| |
| <td>20\27 &lt; g &lt; 23\31<br />
| |
| </td>
| |
| <td>23\31 &lt; g &lt; 26\35<br />
| |
| </td>
| |
| <td>26\35 &lt; g &lt; 29\39<br />
| |
| </td>
| |
| <td>23g-17<br />
| |
| </td>
| |
| <td>-4g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L22s<br />
| |
| </td>
| |
| <td>16\27 &lt; g &lt; 3\5<br />
| |
| </td>
| |
| <td>g = 161\270<br />
| |
| </td>
| |
| <td>16\27 &lt; g &lt; 19\32<br />
| |
| </td>
| |
| <td>19\32 &lt; g &lt; 22\37<br />
| |
| </td>
| |
| <td>22\37 &lt; g &lt; 25\42<br />
| |
| </td>
| |
| <td>-13+22g<br />
| |
| </td>
| |
| <td>3-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L21s<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 1\6<br />
| |
| </td>
| |
| <td>g = 17\108<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 5\33<br />
| |
| </td>
| |
| <td>5\33 &lt; g &lt; 6\39<br />
| |
| </td>
| |
| <td>6\39 &lt; g &lt; 7\45<br />
| |
| </td>
| |
| <td>-1+7g<br />
| |
| </td>
| |
| <td>-2g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L20s<br />
| |
| </td>
| |
| <td>23\27 &lt; g &lt; 6\7<br />
| |
| </td>
| |
| <td>g = 323\378<br />
| |
| </td>
| |
| <td>23\27 &lt; g &lt; 29\34<br />
| |
| </td>
| |
| <td>29\34 &lt; g &lt; 35\41<br />
| |
| </td>
| |
| <td>35\41 &lt; g &lt; 41\48<br />
| |
| </td>
| |
| <td>-17+20g<br />
| |
| </td>
| |
| <td>-7g+6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L19s<br />
| |
| </td>
| |
| <td>10\27 &lt; g &lt; 3\8<br />
| |
| </td>
| |
| <td>g = 161\432<br />
| |
| </td>
| |
| <td>10\27 &lt; g &lt; 13\35<br />
| |
| </td>
| |
| <td>13\35 &lt; g &lt; 16\43<br />
| |
| </td>
| |
| <td>16\43 &lt; g &lt; 19\51<br />
| |
| </td>
| |
| <td>19g-7<br />
| |
| </td>
| |
| <td>3-8g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L18s<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 5\54<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\36<br />
| |
| </td>
| |
| <td>3\36 &lt; g &lt; 4\45<br />
| |
| </td>
| |
| <td>4\45 &lt; g &lt; 5\54<br />
| |
| </td>
| |
| <td>-1\9+2g<br />
| |
| </td>
| |
| <td>-g+1\9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L17s<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 3\10<br />
| |
| </td>
| |
| <td>g = 161\540<br />
| |
| </td>
| |
| <td>8\27 &lt; g &lt; 11\37<br />
| |
| </td>
| |
| <td>11\37 &lt; g &lt; 14\47<br />
| |
| </td>
| |
| <td>14\47 &lt; g &lt; 17\57<br />
| |
| </td>
| |
| <td>-5+17g<br />
| |
| </td>
| |
| <td>3-10g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L16s<br />
| |
| </td>
| |
| <td>22\27 &lt; g &lt; 9\11<br />
| |
| </td>
| |
| <td>g = 485\594<br />
| |
| </td>
| |
| <td>22\27 &lt; g &lt; 31\38<br />
| |
| </td>
| |
| <td>31\38 &lt; g &lt; 40\49<br />
| |
| </td>
| |
| <td>40\49 &lt; g &lt; 49\60<br />
| |
| </td>
| |
| <td>16g-13<br />
| |
| </td>
| |
| <td>-11g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L15s<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 17\216<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\39<br />
| |
| </td>
| |
| <td>3\39 &lt; g &lt; 4\51<br />
| |
| </td>
| |
| <td>4\51 &lt; g &lt; 5\63<br />
| |
| </td>
| |
| <td>5g-1\3<br />
| |
| </td>
| |
| <td>1\3-4g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L14s<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 1\13<br />
| |
| </td>
| |
| <td>g = 53\702<br />
| |
| </td>
| |
| <td>2\27 &lt; g &lt; 3\40<br />
| |
| </td>
| |
| <td>3\40 &lt; g &lt; 4\53<br />
| |
| </td>
| |
| <td>4\53 &lt; g &lt; 5\66<br />
| |
| </td>
| |
| <td>14g-1<br />
| |
| </td>
| |
| <td>-13g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L13s<br />
| |
| </td>
| |
| <td>25\27 &lt; g &lt; 13\14<br />
| |
| </td>
| |
| <td>g = 701\756<br />
| |
| </td>
| |
| <td>25\27 &lt; g &lt; 38\41<br />
| |
| </td>
| |
| <td>38\41 &lt; g &lt; 51\55<br />
| |
| </td>
| |
| <td>51\55 &lt; g &lt; 64\69<br />
| |
| </td>
| |
| <td>13g-12<br />
| |
| </td>
| |
| <td>13-14g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L12s<br />
| |
| </td>
| |
| <td>7\27 &lt; g &lt; 4\15<br />
| |
| </td>
| |
| <td>g = 71\270<br />
| |
| </td>
| |
| <td>7\27 &lt; g &lt; 11\42<br />
| |
| </td>
| |
| <td>11\42 &lt; g &lt; 15\57<br />
| |
| </td>
| |
| <td>15\57 &lt; g &lt; 19\72<br />
| |
| </td>
| |
| <td>-4+4g<br />
| |
| </td>
| |
| <td>-5g+14\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L11s<br />
| |
| </td>
| |
| <td>5\27 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>g = 161\864<br />
| |
| </td>
| |
| <td>5\27 &lt; g &lt; 8\43<br />
| |
| </td>
| |
| <td>8\43 &lt; g &lt; 11\59<br />
| |
| </td>
| |
| <td>11\59 &lt; g &lt; 14\75<br />
| |
| </td>
| |
| <td>11g-2<br />
| |
| </td>
| |
| <td>-16g+3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L10s<br />
| |
| </td>
| |
| <td>19\27 &lt; g &lt; 12\17<br />
| |
| </td>
| |
| <td>g = 647\918<br />
| |
| </td>
| |
| <td>19\27 &lt; g &lt; 31\44<br />
| |
| </td>
| |
| <td>31\44 &lt; g &lt; 43\61<br />
| |
| </td>
| |
| <td>43\61 &lt; g &lt; 55\78<br />
| |
| </td>
| |
| <td>10g-7<br />
| |
| </td>
| |
| <td>12-17g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L9s<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 1\18<br />
| |
| </td>
| |
| <td>g = 5\108<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 2\45<br />
| |
| </td>
| |
| <td>2\45 &lt; g &lt; 3\63<br />
| |
| </td>
| |
| <td>3\63 &lt; g &lt; 4\81<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-2g+1\9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L8s<br />
| |
| </td>
| |
| <td>17\27 &lt; g &lt; 12\19<br />
| |
| </td>
| |
| <td>g = 647\1026<br />
| |
| </td>
| |
| <td>17\27 &lt; g &lt; 29\46<br />
| |
| </td>
| |
| <td>29\46 &lt; g &lt; 41\65<br />
| |
| </td>
| |
| <td>41\65 &lt; g &lt; 53\84<br />
| |
| </td>
| |
| <td>-5+8g<br />
| |
| </td>
| |
| <td>12-19g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L7s<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>g = 161\1080<br />
| |
| </td>
| |
| <td>4\27 &lt; g &lt; 7\47<br />
| |
| </td>
| |
| <td>7\47 &lt; g &lt; 10\67<br />
| |
| </td>
| |
| <td>10\67 &lt; g &lt; 13\87<br />
| |
| </td>
| |
| <td>-1+7g<br />
| |
| </td>
| |
| <td>3-20g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L6s<br />
| |
| </td>
| |
| <td>5\27 &lt; g &lt; 4\21<br />
| |
| </td>
| |
| <td>g = 71\378<br />
| |
| </td>
| |
| <td>5\27 &lt; g &lt; 9\48<br />
| |
| </td>
| |
| <td>9\48 &lt; g &lt; 13\69<br />
| |
| </td>
| |
| <td>13\69 &lt; g &lt; 17\90<br />
| |
| </td>
| |
| <td>2g-1\3<br />
| |
| </td>
| |
| <td>-7g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22L5s<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">11</span>\27 &lt; g &lt; 9\22<br />
| |
| </td>
| |
| <td>g = 485\1188<br />
| |
| </td>
| |
| <td>11\27 &lt; g &lt; 20\49<br />
| |
| </td>
| |
| <td>20\49 &lt; g &lt; 29\71<br />
| |
| </td>
| |
| <td>29\71 &lt; g &lt; 38\93<br />
| |
| </td>
| |
| <td>5g-2<br />
| |
| </td>
| |
| <td>-22g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23L4s<br />
| |
| </td>
| |
| <td>7\27 &lt; g &lt; 6\23<br />
| |
| </td>
| |
| <td>g = 323\1242<br />
| |
| </td>
| |
| <td>7\27 &lt; g &lt; 13\50<br />
| |
| </td>
| |
| <td>13\50 &lt; g &lt; 19\73<br />
| |
| </td>
| |
| <td>19\73 &lt; g &lt; 25\96<br />
| |
| </td>
| |
| <td>4g-1<br />
| |
| </td>
| |
| <td>-23g+6<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24L3s<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 1\24<br />
| |
| </td>
| |
| <td>g = 17\432<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 2\51<br />
| |
| </td>
| |
| <td>2/51 &lt; g &lt; 3\75<br />
| |
| </td>
| |
| <td>3\75 &lt; g &lt; 4\99<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-8g+1\3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25L2s<br />
| |
| </td>
| |
| <td>14\27 &lt; g &lt; 13\25<br />
| |
| </td>
| |
| <td>g = 701\1350<br />
| |
| </td>
| |
| <td>14\27 &lt; g &lt; 27\52<br />
| |
| </td>
| |
| <td>27\52 &lt; g &lt; 40\77<br />
| |
| </td>
| |
| <td>40\77 &lt; g &lt; 53\102<br />
| |
| </td>
| |
| <td>2g-1<br />
| |
| </td>
| |
| <td>-25g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26L1s<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 1\26<br />
| |
| </td>
| |
| <td>g = 53\1404<br />
| |
| </td>
| |
| <td>1\27 &lt; g &lt; 2\53<br />
| |
| </td>
| |
| <td>2\53 &lt; g &lt; 3\79<br />
| |
| </td>
| |
| <td>3\79 &lt; g &lt; 4\105<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-26g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="x28"></a><!-- ws:end:WikiTextHeadingRule:48 -->28</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L27s<br />
| |
| </td>
| |
| <td>27\28 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 55\56<br />
| |
| </td>
| |
| <td>27\28 &lt; g &lt; 28\29<br />
| |
| </td>
| |
| <td>28\29 &lt; g &lt; 29\30<br />
| |
| </td>
| |
| <td>29\30 &lt; g &lt; 30\31<br />
| |
| </td>
| |
| <td>-26+27g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L26s<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 27\56<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 14\30<br />
| |
| </td>
| |
| <td>14\30 &lt; g &lt; 15\32<br />
| |
| </td>
| |
| <td>15\32 &lt; g &lt; 16\34<br />
| |
| </td>
| |
| <td>13g-6<br />
| |
| </td>
| |
| <td>-2g+1\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L25s<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 1\3<br />
| |
| </td>
| |
| <td>g = 55\168<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 10\31<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">10\31 &lt; g &lt; 11\34</span><br />
| |
| </td>
| |
| <td>11\34 &lt; g &lt; 12\37<br />
| |
| </td>
| |
| <td>-8+25g<br />
| |
| </td>
| |
| <td>1-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L24s<br />
| |
| </td>
| |
| <td>6\28 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 13\56<br />
| |
| </td>
| |
| <td>6\28 &lt; g &lt; 7\32<br />
| |
| </td>
| |
| <td>7\32 &lt; g &lt; 8\36<br />
| |
| </td>
| |
| <td>8\36 &lt; g &lt; 9\40<br />
| |
| </td>
| |
| <td>6g-5\4<br />
| |
| </td>
| |
| <td>-g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L23s<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 2\5<br />
| |
| </td>
| |
| <td>g = 111\280<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 13\33<br />
| |
| </td>
| |
| <td>13\33 &lt; g &lt; 15\38<br />
| |
| </td>
| |
| <td>15\38 &lt; g &lt; 17\43<br />
| |
| </td>
| |
| <td>-9+23g<br />
| |
| </td>
| |
| <td>2-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L22s<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 2\6<br />
| |
| </td>
| |
| <td>g = 55\168<br />
| |
| </td>
| |
| <td>9\28 &lt; g &lt; 11\34<br />
| |
| </td>
| |
| <td>11\34 &lt; g &lt; 13\40<br />
| |
| </td>
| |
| <td>13\40 &lt; g &lt; 15\46<br />
| |
| </td>
| |
| <td>-7\2+11g<br />
| |
| </td>
| |
| <td>-3g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L21s<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 7\56<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\35<br />
| |
| </td>
| |
| <td>4\35 &lt; g &lt; 5\42<br />
| |
| </td>
| |
| <td>5\42 &lt; g &lt; 6\49<br />
| |
| </td>
| |
| <td>-2\7+3g<br />
| |
| </td>
| |
| <td>-g+1\7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L20s<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 1\8<br />
| |
| </td>
| |
| <td>g = 13\112<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\36<br />
| |
| </td>
| |
| <td>4\36 &lt; g &lt; 5\44<br />
| |
| </td>
| |
| <td>5\44 &lt; g &lt; 6\52<br />
| |
| </td>
| |
| <td>5g-1\2<br />
| |
| </td>
| |
| <td>1\4-2g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L19s<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 1\9<br />
| |
| </td>
| |
| <td>g = 55\504<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 4\37<br />
| |
| </td>
| |
| <td>4\37 &lt; g &lt; 5\46<br />
| |
| </td>
| |
| <td>5\46 &lt; g &lt; 6\55<br />
| |
| </td>
| |
| <td>-2+19g<br />
| |
| </td>
| |
| <td>-9g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L18s<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 4\10<br />
| |
| </td>
| |
| <td>g = 111\280<br />
| |
| </td>
| |
| <td>11\28 &lt; g &lt; 15\38<br />
| |
| </td>
| |
| <td>15\38 &lt; g &lt; 19\48<br />
| |
| </td>
| |
| <td>19\48 &lt; g &lt; 23\58<br />
| |
| </td>
| |
| <td>-7\2+4g<br />
| |
| </td>
| |
| <td>2-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L17s<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 2\11<br />
| |
| </td>
| |
| <td>g = 111\616<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 7\39<br />
| |
| </td>
| |
| <td>7\39 &lt; g &lt; 9\50<br />
| |
| </td>
| |
| <td>9\50 &lt; g &lt; 11\61<br />
| |
| </td>
| |
| <td>17g-3<br />
| |
| </td>
| |
| <td>-11g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L16s<br />
| |
| </td>
| |
| <td>2\28 &lt; g &lt; 1\12<br />
| |
| </td>
| |
| <td>g = 13\168<br />
| |
| </td>
| |
| <td>2\28 &lt; g &lt; 3\40<br />
| |
| </td>
| |
| <td>3\40 &lt; g &lt; 4\52<br />
| |
| </td>
| |
| <td>4\52 &lt; g &lt; 5\64<br />
| |
| </td>
| |
| <td>4g-1\4<br />
| |
| </td>
| |
| <td>1\4-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L15s<br />
| |
| </td>
| |
| <td>15\28 &lt; g &lt; 7\13<br />
| |
| </td>
| |
| <td>g = 391\728<br />
| |
| </td>
| |
| <td>15\28 &lt; g &lt; 22\41<br />
| |
| </td>
| |
| <td>22\41 &lt; g &lt; 29\54<br />
| |
| </td>
| |
| <td>29\54 &lt; g &lt; 36\67<br />
| |
| </td>
| |
| <td>15g-8<br />
| |
| </td>
| |
| <td>-13g+7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L14s<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 1\14<br />
| |
| </td>
| |
| <td>g = 3\56<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 2\42<br />
| |
| </td>
| |
| <td>2\42 &lt; g &lt; 3\56<br />
| |
| </td>
| |
| <td>3\56 &lt; g &lt; 4\70<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-g+1\14<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">15L13s</span><br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 7\15<br />
| |
| </td>
| |
| <td>g = 391\840<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 20\43<br />
| |
| </td>
| |
| <td>20\43 &lt; g &lt; 27\58<br />
| |
| </td>
| |
| <td>27\58 &lt; g &lt; 34\73<br />
| |
| </td>
| |
| <td>13g-6<br />
| |
| </td>
| |
| <td>7-15g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">16L12s</span><br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 3\16<br />
| |
| </td>
| |
| <td>g = 41\224<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 8\44<br />
| |
| </td>
| |
| <td>8\44 &lt; g &lt; 11\60<br />
| |
| </td>
| |
| <td>11\60 &lt; g &lt; 14\76<br />
| |
| </td>
| |
| <td>-1\2+3g<br />
| |
| </td>
| |
| <td>-4g+3\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">17L11s</span><br />
| |
| </td>
| |
| <td>23\28 &lt; g &lt; 14\17<br />
| |
| </td>
| |
| <td>g = 783\952<br />
| |
| </td>
| |
| <td>23\28 &lt; g &lt; 37\45<br />
| |
| </td>
| |
| <td>37\45 &lt; g &lt; 51\62<br />
| |
| </td>
| |
| <td>51\62 &lt; g &lt; 65\79<br />
| |
| </td>
| |
| <td>11g-9<br />
| |
| </td>
| |
| <td>-17g+13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">18L10s</span><br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 2\18<br />
| |
| </td>
| |
| <td>g = 55\504<br />
| |
| </td>
| |
| <td>3\28 &lt; g &lt; 5\46<br />
| |
| </td>
| |
| <td>5\46 &lt; g &lt; 7\64<br />
| |
| </td>
| |
| <td>7\64 &lt; g &lt; 9\82<br />
| |
| </td>
| |
| <td>5g-1\2<br />
| |
| </td>
| |
| <td>1-9g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">19L9s</span><br />
| |
| </td>
| |
| <td>25\28 &lt; g &lt; 17\19<br />
| |
| </td>
| |
| <td>g = 951\1064<br />
| |
| </td>
| |
| <td>25\28 &lt; g &lt; 42\47<br />
| |
| </td>
| |
| <td>42\47 &lt; g &lt; 59\66<br />
| |
| </td>
| |
| <td>59\66 &lt; g &lt; 76\85<br />
| |
| </td>
| |
| <td>9g-8<br />
| |
| </td>
| |
| <td>-19g+17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">20L</span>8s<br />
| |
| </td>
| |
| <td>4\28 &lt; g &lt; 3\20<br />
| |
| </td>
| |
| <td>g = 41\280<br />
| |
| </td>
| |
| <td>4\28 &lt; g &lt; 7\48<br />
| |
| </td>
| |
| <td>7\48 &lt; g &lt; 10\68<br />
| |
| </td>
| |
| <td>10\68 &lt; g &lt; 13\88<br />
| |
| </td>
| |
| <td>-1\4+2g<br />
| |
| </td>
| |
| <td>3\4-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">21L7s</span><br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 1\21<br />
| |
| </td>
| |
| <td>g = 7\168<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 2\49<br />
| |
| </td>
| |
| <td>2\49 &lt; g &lt; 3\70<br />
| |
| </td>
| |
| <td>3\70 &lt; g &lt; 4\91<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-1\7+3g</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">22L</span>6s<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 4\22<br />
| |
| </td>
| |
| <td>g = 111\616<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 9\50<br />
| |
| </td>
| |
| <td>9\50 &lt; g &lt; 13\72<br />
| |
| </td>
| |
| <td>13\72 &lt; g &lt; 17\94<br />
| |
| </td>
| |
| <td>3g-1\2<br />
| |
| </td>
| |
| <td>-11g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">23L</span>5s<br />
| |
| </td>
| |
| <td>17\28 &lt; g &lt; 14\23<br />
| |
| </td>
| |
| <td>g = 783\1288<br />
| |
| </td>
| |
| <td>17\28 &lt; g &lt; 31\51<br />
| |
| </td>
| |
| <td>31\51 &lt; g &lt; 45\74<br />
| |
| </td>
| |
| <td>45\74 &lt; g &lt; 59\97<br />
| |
| </td>
| |
| <td>5g-3<br />
| |
| </td>
| |
| <td>-23g+14<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">24L</span>4s<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 1\24<br />
| |
| </td>
| |
| <td>g = 13\336<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 2\52<br />
| |
| </td>
| |
| <td>2\52 &lt; g &lt; 3\76<br />
| |
| </td>
| |
| <td>3\76 &lt; g &lt; 4\100<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-6g+1\4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">25L</span>3s<br />
| |
| </td>
| |
| <td>19\28 &lt; g &lt; 17\25<br />
| |
| </td>
| |
| <td>g = 951\1400<br />
| |
| </td>
| |
| <td>19\28 &lt; g &lt; 36\53<br />
| |
| </td>
| |
| <td>36\53 &lt; g &lt; 53\78<br />
| |
| </td>
| |
| <td>53\76 &lt; g &lt; 70\103<br />
| |
| </td>
| |
| <td>3g-2<br />
| |
| </td>
| |
| <td>-25g+17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><span style="line-height: 15.6000003814697px;">26L</span>2s<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 12\26<br />
| |
| </td>
| |
| <td>g = 391\728<br />
| |
| </td>
| |
| <td>13\28 &lt; g &lt; 25\54<br />
| |
| </td>
| |
| <td>25\54 &lt; g &lt; 37\80<br />
| |
| </td>
| |
| <td>37\80 &lt; g &lt; 49\106<br />
| |
| </td>
| |
| <td>g-1\2<br />
| |
| </td>
| |
| <td>-13g+19\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27L1s<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 1\27<br />
| |
| </td>
| |
| <td>g = 55\1512<br />
| |
| </td>
| |
| <td>1\28 &lt; g &lt; 2\55<br />
| |
| </td>
| |
| <td>2\55 &lt; g &lt; 3\82<br />
| |
| </td>
| |
| <td>3\82 &lt; g &lt; 4\109<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-27g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="x29"></a><!-- ws:end:WikiTextHeadingRule:50 -->29</h1>
| |
|
| |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <th>Large-small numbers<br />
| |
| </th>
| |
| <th>Generator range<br />
| |
| </th>
| |
| <th><span style="background-color: #ffffff;">Midpoint</span><br />
| |
| </th>
| |
| <th>Range of propriety<br />
| |
| </th>
| |
| <th>Range of maximum expressiveness<br />
| |
| </th>
| |
| <th><span style="display: block; text-align: center;">Top</span><span style="display: block; text-align: center;">range of diatonicity</span><br />
| |
| </th>
| |
| <th>Large step<br />
| |
| </th>
| |
| <th>Small step<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1L28s<br />
| |
| </td>
| |
| <td>28\29 &lt; g &lt; 1<br />
| |
| </td>
| |
| <td>g = 57\58<br />
| |
| </td>
| |
| <td>28\29 &lt; g &lt; 29\30<br />
| |
| </td>
| |
| <td>29\30 &lt; g &lt; 30\31<br />
| |
| </td>
| |
| <td>30\31 &lt; g &lt; 31\32<br />
| |
| </td>
| |
| <td>-27+28g<br />
| |
| </td>
| |
| <td>-g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2L27s<br />
| |
| </td>
| |
| <td>14\29 &lt; g &lt; 1\2<br />
| |
| </td>
| |
| <td>g = 57\116<br />
| |
| </td>
| |
| <td>14\29 &lt; g &lt; 15\31<br />
| |
| </td>
| |
| <td>15\31 &lt; g &lt; 16\33<br />
| |
| </td>
| |
| <td>16\33 &lt; g &lt; 17\35<br />
| |
| </td>
| |
| <td>27g-13<br />
| |
| </td>
| |
| <td>-2g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3L26s<br />
| |
| </td>
| |
| <td>19\29 &lt; g &lt; 2\3<br />
| |
| </td>
| |
| <td>g = 115\174<br />
| |
| </td>
| |
| <td>19\29 &lt; g &lt; 21\32<br />
| |
| </td>
| |
| <td>21\32 &lt; g &lt; 23\35<br />
| |
| </td>
| |
| <td>23\35 &lt; g &lt; 25\38<br />
| |
| </td>
| |
| <td>-17+23g<br />
| |
| </td>
| |
| <td>2-3g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4L25s<br />
| |
| </td>
| |
| <td>7\29 &lt; g &lt; 1\4<br />
| |
| </td>
| |
| <td>g = 57\232<br />
| |
| </td>
| |
| <td>7\29 &lt; g &lt; 8\33<br />
| |
| </td>
| |
| <td>8\33 &lt; g &lt; 9\37<br />
| |
| </td>
| |
| <td>9\37 &lt; g &lt; 10\41<br />
| |
| </td>
| |
| <td>25g-6<br />
| |
| </td>
| |
| <td>-4g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5L24s<br />
| |
| </td>
| |
| <td>23\29 &lt; g &lt; 4\5<br />
| |
| </td>
| |
| <td>g = 231\290<br />
| |
| </td>
| |
| <td>23\29 &lt; g &lt; 27\34<br />
| |
| </td>
| |
| <td>27\34 &lt; g &lt; 31\39<br />
| |
| </td>
| |
| <td>31\39 &lt; g &lt; 35\44<br />
| |
| </td>
| |
| <td>-19+24g<br />
| |
| </td>
| |
| <td>4-5g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6L23s<br />
| |
| </td>
| |
| <td>24\29 &lt; g &lt; 5\6<br />
| |
| </td>
| |
| <td>g = 289\348<br />
| |
| </td>
| |
| <td>24\29 &lt; g &lt; 29\35<br />
| |
| </td>
| |
| <td>29\35 &lt; g &lt; 34\41<br />
| |
| </td>
| |
| <td>34\41 &lt; g &lt; 39\47<br />
| |
| </td>
| |
| <td>-19+23g<br />
| |
| </td>
| |
| <td>-6g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7L22s<br />
| |
| </td>
| |
| <td>4\29 &lt; g &lt; 1\7<br />
| |
| </td>
| |
| <td>g = 57\406<br />
| |
| </td>
| |
| <td>4\29 &lt; g &lt; 5\36<br />
| |
| </td>
| |
| <td>5\36 &lt; g &lt; 6\43<br />
| |
| </td>
| |
| <td>6\43 &lt; g &lt; 7\50<br />
| |
| </td>
| |
| <td>-3+22g<br />
| |
| </td>
| |
| <td>-7g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8L21s<br />
| |
| </td>
| |
| <td>18\29 &lt; g &lt; 5\8<br />
| |
| </td>
| |
| <td>g = 289\464<br />
| |
| </td>
| |
| <td>18\29 &lt; g &lt; 23\37<br />
| |
| </td>
| |
| <td>23\37 &lt; g &lt; 28\45<br />
| |
| </td>
| |
| <td>28\45 &lt; g &lt; 33\53<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-13+21g</span><br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">-8g+5</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9L20s<br />
| |
| </td>
| |
| <td>16\29 &lt; g &lt; 5\9<br />
| |
| </td>
| |
| <td>g = 289\522<br />
| |
| </td>
| |
| <td>16\29 &lt; g &lt; 21\38<br />
| |
| </td>
| |
| <td>21\38 &lt; g &lt; 26\47<br />
| |
| </td>
| |
| <td>26\47 &lt; g &lt; 31\56<br />
| |
| </td>
| |
| <td>-11+20g<br />
| |
| </td>
| |
| <td>-9g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10L19s<br />
| |
| </td>
| |
| <td>26\29 &lt; g &lt; 9\10<br />
| |
| </td>
| |
| <td>g = 521\580<br />
| |
| </td>
| |
| <td>26\29 &lt; g &lt; 35\39<br />
| |
| </td>
| |
| <td>35\39 &lt; g &lt; 44\49<br />
| |
| </td>
| |
| <td>44\49 &lt; g &lt; 53\59<br />
| |
| </td>
| |
| <td>-17+19g<br />
| |
| </td>
| |
| <td>9-10g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11L18s<br />
| |
| </td>
| |
| <td>21\29 &lt; g &lt; 8\11<br />
| |
| </td>
| |
| <td>g = 463\638<br />
| |
| </td>
| |
| <td>21\29 &lt; g &lt; 29\40<br />
| |
| </td>
| |
| <td>29\40 &lt; g &lt; 37\51<br />
| |
| </td>
| |
| <td>37\51 &lt; g &lt; 45\62<br />
| |
| </td>
| |
| <td>18g-13<br />
| |
| </td>
| |
| <td>-11g+8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12L17s<br />
| |
| </td>
| |
| <td>12\29 &lt; g &lt; 5\12<br />
| |
| </td>
| |
| <td>g = 289\696<br />
| |
| </td>
| |
| <td>12\29 &lt; g &lt; 17\41<br />
| |
| </td>
| |
| <td>17\41 &lt; g &lt; 22\53<br />
| |
| </td>
| |
| <td>22\53 &lt; g &lt; 27\65<br />
| |
| </td>
| |
| <td>17g-7<br />
| |
| </td>
| |
| <td>5-12g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13L16s<br />
| |
| </td>
| |
| <td>20\29 &lt; g &lt; 9\13<br />
| |
| </td>
| |
| <td>g = 521\754<br />
| |
| </td>
| |
| <td>20\29 &lt; g &lt; 29\42<br />
| |
| </td>
| |
| <td>29\42 &lt; g &lt; 38\55<br />
| |
| </td>
| |
| <td>38\55 &lt; g &lt; 47\68<br />
| |
| </td>
| |
| <td>16g+11<br />
| |
| </td>
| |
| <td>-13g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14L15s<br />
| |
| </td>
| |
| <td>2\29 &lt; g &lt; 1\14<br />
| |
| </td>
| |
| <td>g = 57\812<br />
| |
| </td>
| |
| <td>2\29 &lt; g &lt; 3\43<br />
| |
| </td>
| |
| <td>3\43 &lt; g &lt; 4\57<br />
| |
| </td>
| |
| <td>4\57 &lt; g &lt; 5\71<br />
| |
| </td>
| |
| <td>15g-1<br />
| |
| </td>
| |
| <td>-14g+1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15L14s<br />
| |
| </td>
| |
| <td>27\29 &lt; g &lt; 14\15<br />
| |
| </td>
| |
| <td>g = 811\870<br />
| |
| </td>
| |
| <td>27\29 &lt; g &lt; 41\44<br />
| |
| </td>
| |
| <td>41\44 &lt; g &lt; 55\59<br />
| |
| </td>
| |
| <td>55\59 &lt; g &lt; 69\74<br />
| |
| </td>
| |
| <td>14g-13<br />
| |
| </td>
| |
| <td>14-15g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16L13s<br />
| |
| </td>
| |
| <td>9\29 &lt; g &lt; 5\16<br />
| |
| </td>
| |
| <td>g = 289\928<br />
| |
| </td>
| |
| <td>9\29 &lt; g &lt; 14\45<br />
| |
| </td>
| |
| <td>14\45 &lt; g &lt; 19\61<br />
| |
| </td>
| |
| <td>19\61 &lt; g &lt; 24\77<br />
| |
| </td>
| |
| <td>-4+13g<br />
| |
| </td>
| |
| <td>-16g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17L12s<br />
| |
| </td>
| |
| <td>17\29 &lt; g &lt; 10\17<br />
| |
| </td>
| |
| <td>g = 579\986<br />
| |
| </td>
| |
| <td>17\29 &lt; g &lt; 27\46<br />
| |
| </td>
| |
| <td>27\46 &lt; g &lt; 37\63<br />
| |
| </td>
| |
| <td>37\63 &lt; g &lt; 47\80<br />
| |
| </td>
| |
| <td>17g-7<br />
| |
| </td>
| |
| <td>-12g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18L11s<br />
| |
| </td>
| |
| <td>8\29 &lt; g &lt; 5\18<br />
| |
| </td>
| |
| <td>g = 289\1044<br />
| |
| </td>
| |
| <td>8\29 &lt; g &lt; 13\47<br />
| |
| </td>
| |
| <td>13\47 &lt; g &lt; 18\65<br />
| |
| </td>
| |
| <td>18\65 &lt; g &lt; 23\83<br />
| |
| </td>
| |
| <td>11g-3<br />
| |
| </td>
| |
| <td>5-18g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19L10s<br />
| |
| </td>
| |
| <td>3\29 &lt; g &lt; 2\19<br />
| |
| </td>
| |
| <td>g = 115\1102<br />
| |
| </td>
| |
| <td>3\29 &lt; g &lt; 5\48<br />
| |
| </td>
| |
| <td>5\48 &lt; g &lt; 7\67<br />
| |
| </td>
| |
| <td>7\67 &lt; g &lt; 9\86<br />
| |
| </td>
| |
| <td>10g-1<br />
| |
| </td>
| |
| <td>-19g+2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20L9s<br />
| |
| </td>
| |
| <td>13\29 &lt; g &lt; 9\20<br />
| |
| </td>
| |
| <td>g = 521\1160<br />
| |
| </td>
| |
| <td>13\29 &lt; g &lt; 22\49<br />
| |
| </td>
| |
| <td>22\49 &lt; g &lt; 31\69<br />
| |
| </td>
| |
| <td>31\69 &lt; g &lt; 40\89<br />
| |
| </td>
| |
| <td>9-20g<br />
| |
| </td>
| |
| <td>-5+11g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21L8s<br />
| |
| </td>
| |
| <td>11\29 &lt; g &lt; 8\21<br />
| |
| </td>
| |
| <td>g = 463\1216<br />
| |
| </td>
| |
| <td>11\29 &lt; g &lt; 19\50<br />
| |
| </td>
| |
| <td>19\50 &lt; g &lt; 27\71<br />
| |
| </td>
| |
| <td>27\71 &lt; g &lt; 35\92<br />
| |
| </td>
| |
| <td>8g-3<br />
| |
| </td>
| |
| <td>8-21g<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22L7s<br />
| |
| </td>
| |
| <td>25\29 &lt; g &lt; 19\22<br />
| |
| </td>
| |
| <td>g = 1001\1274<br />
| |
| </td>
| |
| <td>25\29 &lt; g &lt; 44\51<br />
| |
| </td>
| |
| <td>44\51 &lt; g &lt; 63\73<br />
| |
| </td>
| |
| <td>63\73 &lt; g &lt; 82\95<br />
| |
| </td>
| |
| <td>7g-6<br />
| |
| </td>
| |
| <td>-22g+9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23L6s<br />
| |
| </td>
| |
| <td>5\29 &lt; g &lt; 4\23<br />
| |
| </td>
| |
| <td>g = 231\1332<br />
| |
| </td>
| |
| <td>5\28 &lt; g &lt; 9\52<br />
| |
| </td>
| |
| <td>9\52 &lt; g &lt; 13\75<br />
| |
| </td>
| |
| <td>13\75 &lt; g &lt; 17\98<br />
| |
| </td>
| |
| <td>6g-1<br />
| |
| </td>
| |
| <td>-23g+4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24L5s<br />
| |
| </td>
| |
| <td>6\29 &lt; g &lt; 5\24<br />
| |
| </td>
| |
| <td>g = 289\1392<br />
| |
| </td>
| |
| <td>6\29 &lt; g &lt; 11\53<br />
| |
| </td>
| |
| <td>11\53 &lt; g &lt; 16\77<br />
| |
| </td>
| |
| <td>16\77 &lt; g &lt; 21\101<br />
| |
| </td>
| |
| <td>5g-9<br />
| |
| </td>
| |
| <td>-24g+5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25L4s<br />
| |
| </td>
| |
| <td>22\29 &lt; g &lt; 19\25<br />
| |
| </td>
| |
| <td>g = 1001\1450<br />
| |
| </td>
| |
| <td>22\29 &lt; g &lt; 41\54<br />
| |
| </td>
| |
| <td>41\54 &lt; g &lt; 60\79<br />
| |
| </td>
| |
| <td>60\79 &lt; g &lt; 79\104<br />
| |
| </td>
| |
| <td>4g-3<br />
| |
| </td>
| |
| <td>-25g+19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26L3s<br />
| |
| </td>
| |
| <td>10\29 &lt; g &lt; 9\26<br />
| |
| </td>
| |
| <td>g = 521\1508<br />
| |
| </td>
| |
| <td>10\29 &lt; g &lt; 19\55<br />
| |
| </td>
| |
| <td>19\55 &lt; g &lt; 28\81<br />
| |
| </td>
| |
| <td>28\81 &lt; g &lt; 37\107<br />
| |
| </td>
| |
| <td>3g-1<br />
| |
| </td>
| |
| <td>-26g+19\2<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27L2s<br />
| |
| </td>
| |
| <td>15\29 &lt; g &lt; 14\27<br />
| |
| </td>
| |
| <td>g = 811\1564<br />
| |
| </td>
| |
| <td>15\29 &lt; g &lt; 29\56<br />
| |
| </td>
| |
| <td>29\56 &lt; g &lt; 43\83<br />
| |
| </td>
| |
| <td>43\83 &lt; g &lt; 57\110<br />
| |
| </td>
| |
| <td>2g-1<br />
| |
| </td>
| |
| <td>-27g+17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28L1s<br />
| |
| </td>
| |
| <td>1\29 &lt; g &lt; 1\28<br />
| |
| </td>
| |
| <td>g = 57\1622<br />
| |
| </td>
| |
| <td>1\29 &lt; g &lt; 2\57<br />
| |
| </td>
| |
| <td><span style="line-height: 15.6000003814697px;">2\57 &lt; g &lt; 3\85</span><br />
| |
| </td>
| |
| <td>3\85 &lt; g &lt; 4\113<br />
| |
| </td>
| |
| <td>g<br />
| |
| </td>
| |
| <td>-28g+1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |