A shruti list: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
|||
| Line 335: | Line 335: | ||
|- | |- | ||
! |Large-small numbers | ! |Large-small numbers | ||
!Status | |||
! |Generator range | ! |Generator range | ||
! |<span style="background-color: #ffffff;">Midpoint</span> | ! |<span style="background-color: #ffffff;">Midpoint</span> | ||
| Line 341: | Line 342: | ||
|- | |- | ||
| |1L22s | | |1L22s | ||
|"half" | |||
| |<span style="line-height: 15.6000003814697px;">22\23 < g < 1</span> | | |<span style="line-height: 15.6000003814697px;">22\23 < g < 1</span> | ||
| |g = 45\46 | | |g = 45\46 | ||
| Line 347: | Line 349: | ||
|- | |- | ||
| |2L21s | | |2L21s | ||
| rowspan="20" |full | |||
| |11\23 < g < 1\2 | | |11\23 < g < 1\2 | ||
| |g = 45\92 | | |g = 45\92 | ||
| Line 467: | Line 470: | ||
|- | |- | ||
| |22L1s | | |22L1s | ||
|"half" | |||
| |1\23 < g < 1\22 | | |1\23 < g < 1\22 | ||
| |g = 45\1012 | | |g = 45\1012 | ||
| Line 554: | Line 558: | ||
|- | |- | ||
| | [[11L 11s]] | | | [[11L 11s]] | ||
| | | | |"7/8" | ||
| | 1\22 < g < 1\11 | | | 1\22 < g < 1\11 | ||
| | g = 3\44 | | | g = 3\44 | ||
| Line 634: | Line 638: | ||
|- | |- | ||
! |Large-small numbers | ! |Large-small numbers | ||
!Status | |||
! |Generator range | ! |Generator range | ||
! |<span style="background-color: #ffffff;">Midpoint</span> | ! |<span style="background-color: #ffffff;">Midpoint</span> | ||
| Line 640: | Line 645: | ||
|- | |- | ||
| |1L25s | | |1L25s | ||
|"half" | |||
| |25\26 < g < 1 | | |25\26 < g < 1 | ||
| |g = 51\52 | | |g = 51\52 | ||
| Line 646: | Line 652: | ||
|- | |- | ||
| |2L24s | | |2L24s | ||
|"3/4" | |||
| |12\26 < g < 1\2 | | |12\26 < g < 1\2 | ||
| |g = 25\52 | | |g = 25\52 | ||
| Line 652: | Line 659: | ||
|- | |- | ||
| |3L23s | | |3L23s | ||
|full | |||
| |17\26 < g < 2\3 | | |17\26 < g < 2\3 | ||
| |g = 103\156 | | |g = 103\156 | ||
| Line 658: | Line 666: | ||
|- | |- | ||
| |4L22s | | |4L22s | ||
|"3/4" | |||
| |6\26 < g < 1\4 | | |6\26 < g < 1\4 | ||
| |g = 25\104 | | |g = 25\104 | ||
| Line 664: | Line 673: | ||
|- | |- | ||
| |5L21s | | |5L21s | ||
|full | |||
| |5\26 < g < 1\5 | | |5\26 < g < 1\5 | ||
| |g = 51\260 | | |g = 51\260 | ||
| Line 670: | Line 680: | ||
|- | |- | ||
| |6L20s | | |6L20s | ||
|"3/4" | |||
| |4\26 < g < 1\6 | | |4\26 < g < 1\6 | ||
| |g = 25\156 | | |g = 25\156 | ||
| Line 676: | Line 687: | ||
|- | |- | ||
| |7L19s | | |7L19s | ||
|full | |||
| |11\26 < g < 3\7 | | |11\26 < g < 3\7 | ||
| |g = 155\364 | | |g = 155\364 | ||
| Line 682: | Line 694: | ||
|- | |- | ||
| |8L18s | | |8L18s | ||
|"3/4" | |||
| |3\26 < g < 1\8 | | |3\26 < g < 1\8 | ||
| |g = 25\208 | | |g = 25\208 | ||
| Line 688: | Line 701: | ||
|- | |- | ||
| |9L17s | | |9L17s | ||
|full | |||
| |23\26 < g < 8\9 | | |23\26 < g < 8\9 | ||
| |g = 415\468 | | |g = 415\468 | ||
| Line 694: | Line 708: | ||
|- | |- | ||
| |10L16s | | |10L16s | ||
|"3/4" | |||
| |5\26 < g < 2\10 | | |5\26 < g < 2\10 | ||
| |g = 51\260 | | |g = 51\260 | ||
| Line 700: | Line 715: | ||
|- | |- | ||
| |11L15s | | |11L15s | ||
|full | |||
| |7\26 < g < 3\11 | | |7\26 < g < 3\11 | ||
| |g = 155\572 | | |g = 155\572 | ||
| Line 706: | Line 722: | ||
|- | |- | ||
| |12L14s | | |12L14s | ||
|"3/4" | |||
| |2\26 < g < 1\12 | | |2\26 < g < 1\12 | ||
| |g = 25\312 | | |g = 25\312 | ||
| Line 712: | Line 729: | ||
|- | |- | ||
| |13L13s | | |13L13s | ||
|"7/8" | |||
| |1\26 < g < 1\13 | | |1\26 < g < 1\13 | ||
| |g = 3\52 | | |g = 3\52 | ||
| Line 718: | Line 736: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">14L12s</span> | | |<span style="line-height: 15.6000003814697px;">14L12s</span> | ||
|"3/4" | |||
| |11\26 < g < 6\14 | | |11\26 < g < 6\14 | ||
| |g = 155\364 | | |g = 155\364 | ||
| Line 724: | Line 743: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">15L11s</span> | | |<span style="line-height: 15.6000003814697px;">15L11s</span> | ||
|full | |||
| |19\26 < g < 11\15 | | |19\26 < g < 11\15 | ||
| |g = 571\780 | | |g = 571\780 | ||
| Line 730: | Line 750: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">16L10s</span> | | |<span style="line-height: 15.6000003814697px;">16L10s</span> | ||
|"3/4" | |||
| |8\26 < g < 5\16 | | |8\26 < g < 5\16 | ||
| |g = 129\416 | | |g = 129\416 | ||
| Line 736: | Line 757: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">17L9s</span> | | |<span style="line-height: 15.6000003814697px;">17L9s</span> | ||
|full | |||
| |3\26 < g < 2\17 | | |3\26 < g < 2\17 | ||
| |g = 103\884 | | |g = 103\884 | ||
| Line 742: | Line 764: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">18L</span>8s | | |<span style="line-height: 15.6000003814697px;">18L</span>8s | ||
|"3/4" | |||
| |10\26 < g < 7\18 | | |10\26 < g < 7\18 | ||
| |g = 181\468 | | |g = 181\468 | ||
| Line 748: | Line 771: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">19L</span>7s | | |<span style="line-height: 15.6000003814697px;">19L</span>7s | ||
|full | |||
| |15\26 < g < 11\19 | | |15\26 < g < 11\19 | ||
| |g = 571\988 | | |g = 571\988 | ||
| Line 754: | Line 778: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">20L</span>6s | | |<span style="line-height: 15.6000003814697px;">20L</span>6s | ||
|"3/4" | |||
| |9\26 < g < 7\20 | | |9\26 < g < 7\20 | ||
| |g = 181\520 | | |g = 181\520 | ||
| Line 760: | Line 785: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">21L</span>5s | | |<span style="line-height: 15.6000003814697px;">21L</span>5s | ||
|full | |||
| |21\26 < g < 17\21 | | |21\26 < g < 17\21 | ||
| |g = 883\1092 | | |g = 883\1092 | ||
| Line 766: | Line 792: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">22L</span>4s | | |<span style="line-height: 15.6000003814697px;">22L</span>4s | ||
|"3/4" | |||
| |7\26 < g < 6\22 | | |7\26 < g < 6\22 | ||
| |g = 155\572 | | |g = 155\572 | ||
| Line 772: | Line 799: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">23L</span>3s | | |<span style="line-height: 15.6000003814697px;">23L</span>3s | ||
|full | |||
| |9\26 < g < 8\23 | | |9\26 < g < 8\23 | ||
| |g = 415\1196 | | |g = 415\1196 | ||
| Line 778: | Line 806: | ||
|- | |- | ||
| |<span style="line-height: 15.6000003814697px;">24L</span>2s | | |<span style="line-height: 15.6000003814697px;">24L</span>2s | ||
|"3/4" | |||
| |1\26 < g < 1\24 | | |1\26 < g < 1\24 | ||
| |g = 25\312 | | |g = 25\312 | ||
| Line 784: | Line 813: | ||
|- | |- | ||
| |25L1s | | |25L1s | ||
|"half" | |||
| |1\26 < g < 1\25 | | |1\26 < g < 1\25 | ||
| |g = 51\1300 | | |g = 51\1300 | ||
Revision as of 23:55, 20 August 2019
Original article by ma1937, on the Yahoo tuning forum, is quoted here.
The listing of the srutis of Indian classical music given below is based on decades of study of the srutis, study with several masters of Indian classical music, pitch analysis of recordings by several masters of raga performance, and the following quote by Ali Akbar Khan:
"I am still learning about the srutis. They reach to your heart and help you feel the ragas and the notes. In old theory, they say that there are twenty-two in number, but right now I feel that there are more like twenty-three and a half. There is only one sa and one pa. Komal re, komal ga, and komal dha all have three. Shuddha ma, tivra ma, shuddha dha, and komal ni each have two. And shuddha re, shuddha ga, and shuddha ni each have one and a half."
Ali Akbar Khan
This quotation yields many insights... Below I have just listed the twenty-three and a half srutis he is referring to.
In brief summary, Khansahib's list is basically the usually-given twenty-two srutis plus the three "ati ati komals" (ati ati komal re; ati ati komal ga; and ati ati komal dha). Though not on the usual list of 22 srutis, it is well-known that these notes do appear is some ragas. So really there are twenty-five notes on Khansahib's list. It's reduced to twenty-three and half because he gives "half" status to three notes that are usually considered srutis -- the lesser-used versions of shuddha re, shuddha ga, and shuddha ni. I think this is the most illuminating aspect of his comment.
With each set of srutis associated with a given note, the principal sruti is listed first, the others in descending order of significance. Ratios given are exact. Cent values given are rounded to the nearest whole cent:
| Principal | Shruti | Ratio | ¢
(approx) |
Remarks |
|---|---|---|---|---|
| Sa | 1/1 | 000 | ||
| komal re | komal re | 16/15 | 112 | |
| ati komal re | 256/243 | 090 | ||
| ati ati komal re | 25/24 | 070 | ||
| Re | shuddha re | 9/8 | 204 | |
| "half"-status shuddha re | 10/9 | 182 | ||
| komal ga | komal ga | 6/5 | 316 | |
| ati komal ga | 32/27 | 294 | ||
| ati ati komal ga | 75/64 | 274 | ||
| Ga | shuddha ga | 5/4 | 386 | |
| "half"-status shuddha ga | 81/64 | 408 | ||
| (inverse ati ati komal dha) | 32/25 | 428 | ||
| Ma | shuddha Ma | 4/3 | 498 | |
| ekasruti Ma | 27/20 | 520 | ||
| tivra Ma | tivra(tar) Ma | 45/32 | 590 | (these two essentially inverses; maybe not entirely a true priority) |
| 729/512 | 612 | |||
| Pa | 3/2 | 702 | ||
| (inverse ekasruti Ma) | 40/27 | 680 | ||
| komal dha | komal dha | 8/5 | 814 | |
| ati komal dha | 128/81 | 792 | ||
| ati ati komal dha | 25/16 | 772 | ||
| Dha | shuddha dha | 5/3 | 884 | (these two hard to prioritize; maybe a toss-up) |
| 27/16 | 906 | |||
| (inverse ati ati komal ga) | 128/75 | 926 | ||
| komal ni | komal ni | 9/5 | 1018 | (these two hard to prioritize; maybe a toss-up) |
| 16/9 | 996 | |||
| Ni | shuddha ni | 15/8 | 1088 | |
| "half"-status shuddha ni | 243/128 | 1110 | ||
| (inverse ati ati komal re) | 48/25 | 1130 | ||
Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 26 (out of n) edo to simulate ragas
komal-ardha re (1): [250/243; 48]: 22, 23, 26
ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~64/59; 138], [625/576; 141]: 26
inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22, 26
inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19
inverse komal re/tivratar Ma [320/243; 476]: 23
inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23
komal ga/komal ga; [36/25; 631]: 19
inverse komal ga/komal ga; [25/18; 569]: 19
ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22
inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22
ati ati komal re/tivra(tar) Ma [375/256, 661; ~61/41, 682]: 22, 23
komal re/tivratar Ma [243/160; 724]: 22, 23
komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19
ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22
ekasruti komal ni, ekasruti Ma/ekasruti Ma: [729/400; 1040]: 22, 23
inverse ardha komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1067], [~59/32; 1062], [1152/625; 1059]: 26
inverse komal-ardha re (1): [243/125; 1152]: 22, 23, 26
Regular temperaments of the full-status shrutis
Note: generators in italics will generate a 19 (diatonic) or 22 tone (superdiatonic) set which is too weakly tonal for serious practice
Underlying
Excluding inverses
| Large-small numbers | Status | Generator range | Midpoint | Boundaries of propriety, maximum expressiveness, diatonicity | Large step+Small step |
|---|---|---|---|---|---|
| 1L 18s | "half" | 18\19 < g < 1 | g = 37\38 | g = 19\20, 20\21, 21\22 | 18g-17+1-g = 17g-16 |
| 2L 17s | full | 9\19 < g < 1\2 | g = 37\76 | g = 10\21, 11\23, 12\25 | 17g-8+1-2g = 15g-7 |
| 3L 16s | 6\19 < g < 1\3 | g = 37\114 | g = 7\22, 8\25, 10\31 | 16g-5+1-3g = 13g-4 | |
| 4L 15s | 14\19 < g < 3\4 | g = 113\152 | g = 17\23, 20\27, 23\31 | 15g-11+3-4g = 11g-8 | |
| 5L 14s | 15\19 < g < 4\5 | g = 151\190 | g = 19\24, 23\29, 27\34 | 14g-11+4-5g = 9g-7 | |
| 6L 13s | 3\19 < g < 1\6 | g = 37\228 | g = 4\25, 5\31, 6/37 | 13g-2+1-6g = 7g-1 | |
| 7L 12s | 8\19 < g < 3\7 | g = 113\266 | g = 11\26, 14\33, 17\40 | 12g-5+3-7g = 5g-2 | |
| 8L 11s | 7\19 < g < 3\8 | g = 113\304 | g = 10\27, 13\35, 16\43 | 11g-4+3-8g = 3g-1 | |
| 9L 10s | 2\19 < g < 1\9 | g = 37\342 | g = 3\28, 4\37, 5\46 | 10g-1+1-9g = g | |
| 10L 9s | 17\19 < g < 9\10 | g = 341\380 | g = 26\29, 35\39, 44\49 | 9g-8+9-10g = 1-g | |
| 11L 8s | 12\19 < g < 7\11 | g = 265\418 | g = 19\30, 26\41, 33\52 | 8g-5+7-11g = 2-3g | |
| 12L 7s | 11\19 < g < 7\12 | g = 265\456 | g = 18\31, 25\43, 32\55 | 7g-4+7-12g = 3-5g | |
| 13L 6s | 16\19 < g < 11\13 | g = 417\494 | g = 27\32, 38\45, 49\58 | 6g-5+11-13g = 6-7g | |
| 14L 5s | 4\19 < g < 3\14 | g = 113\532 | g = 7\33, 10\47, 13\61 | 5g-1+3-14g = 2-9g | |
| 15L 4s | 5\19 < g < 4\15 | g = 151\570 | g = 9\34, 13\49, 17\64 | 4g-1+4-15g = 3-11g | |
| 16L 3s | 13\19 < g < 11\16 | g = 417\608 | g = 24\35, 35\51, 46\67 | 3g-2+11-16g = 9-13g | |
| 17L 2s | 10\19 < g < 9\17 | g = 341\646 | g = 19\36, 28\53, 37\70 | 2g-1+9-17g = 8-15g | |
| 18L 1s | "half" | 1\19 < g < 1\18 | g = 37\684 | g = 2\37, 3\55, 4\73 | g+1-18g = 1-17g |
Including inverses
| Large-small numbers | Status | Generator range | Midpoint | Boundaries of propriety, maximum expressiveness, diatonicity | Large step+Small step |
|---|---|---|---|---|---|
| 1L22s | "half" | 22\23 < g < 1 | g = 45\46 | g = 23\24, 24\25, 25\26 | 22g-21+1-g = 21g-20 |
| 2L21s | full | 11\23 < g < 1\2 | g = 45\92 | g = 12\25, 13\27, 14\29 | 21g-10+1-2g = 19g-9 |
| 3L20s | 15\23 < g < 2\3 | g = 91\138 | g = 17\26, 19\29, 21\32 | 20g-13+1-3g = 17g-12 | |
| 4L19s | 17\23 < g < 3\4 | g = 137\184 | g = 20\27, 23\31, 26\35 | 19g-14+3-4g = 15g-11 | |
| 5L18s | 9\23 < g < 2\5 | g = 91\230 | g = 11\28, 13\33, 15\38 | 18g-7+2-5g = 13g-5 | |
| 6L17s | 19\23 < g < 5\6 | g = 229\276 | g = 24\29, 29\35, 34\41 | 17g-15+1-6g = 11g-14 | |
| 7L16s | 13\23 < g < 4\7 | g = 183\322 | g = 17\30, 21\37, 25\44 | 16g-9+4-7g = 9g-5 | |
| 8L15s | 20\23 < g < 7\8 | g = 321\368 | g = 27\31, 34\39, 41\47 | 15g-13+7-8g = 7g-6 | |
| 9L14s | 5\23 < g < 2\9 | g = 91\414 | g = 7\32, 9\41, 11\50 | 14g-7+2-9g = 5g-5 | |
| 10L13s | 16\23 < g < 7\10 | g = 321\460 | g = 23\33, 30\43, 37\53 | 13g-9+7-10g = 3g-2 | |
| 11L12s | 2\23 < g < 1\11 | g = 45\506 | g = 3\34, 4\45, 5\56 | 12g-1+1-11g = g | |
| 12L11s | 21\23 < g < 11\12 | g = 505\552 | g = 32\35, 43\47, 54\59 | 11g-10+11-12g = 1-g | |
| 13L10s | 7\23 < g < 4\13 | g = 183\598 | g = 11\36, 15\49, 19\62 | 10g-3+4-13g =1-3g | |
| 14L9s | 18\23 < g < 11\14 | g = 505\644 | g = 29\37, 40\51, 51\65 | 9g-7+11-14g = 4-5g | |
| 15L8s | 3\23 < g < 2\15 | g = 91\690 | g = 5\38, 7\53, 9\68 | 8g-1+2-15g = 1-7g | |
| 16L7s | 10\23 < g < 7\16 | g = 321\736 | g = 17\39, 24\55, 31\71 | 7g-3+7-16g = 4-9g | |
| 17L6s | 4\23 < g < 3\17 | g = 137\782 | g = 7\40, 10\57, 13\74 | 6g-1+3-17g = 2-11g | |
| 18L5s | 14\23 < g < 11\18 | g = 505\828 | g = 25\41, 36\59, 47\77 | 5g-4+11-18g = 7-13g | |
| 19L4s | 6\23 < g < 5\19 | g = 229\874 | g = 11\42, 16\61, 21\80 | 4g-1+5-19g = 4-15g | |
| 20L3s | 8\23 < g < 7\20 | g = 321\920 | g = 15\43, 22\63, 29\83 | 3g-1+13-20g = 12-17g | |
| 21L2s | 12\23 < g < 11\21 | g = 505\966 | g = 23\44, 34\65, 45\86 | 2g-1+11-21g = 10-19g | |
| 22L1s | "half" | 1\23 < g < 1\22 | g = 45\1012 | g = 2\45, 3\67, 4\89 | g+1-22g = 1-221 |
Quoted
Excluding inverses
| Large-small numbers | Status | Generator range | Midpoint | Boundaries of propriety, maximum expressiveness, diatonicity | Large step+Small step |
|---|---|---|---|---|---|
| 1L 21s | "half" | 21\22 < g < 1 | g = 43\44 | g = 22\23, 23\24, 24\25 | 21g-20+1-g = 20g-19 |
| 2L 20s | "3/4" | 10\22 < g < 1\2 | g = 21\44 | g = 11\24, 12\26, 13\28 | 10g-9\2+1\2-g = 9g-4 |
| 3L 19s | full | 7\22 < g < 1\3 | g = 43\132 | g = 8\25, 9\28, 10\31 | 19g-6+1-3g = 16g-5 |
| 4L 18s | "3/4" | 5\22 < g < 1\4 | g = 21\88 | g = 6\26, 7\30, 8\34 | 9g-2+1\2-2g = 7g-3\2 |
| 5L 17s | full | 13\22 < g < 3\5 | g = 131\220 | g = 16\27, 19\32, 22\37 | 17g-10+3-5g = 12g-7 |
| 6L 16s | "3/4" | 7\22 < g < 2\6 | g = 43\132 | g = 9\28, 11\34, 13\40 | 8g-5\2+1-3g = 5g-2 |
| 7L 15s | full | 3\22 < g < 1\7 | g = 43\308 | g = 4\29, 5\36, 6\43 | 15g-2+1-7g = 8g-1 |
| 8L 14s | "3/4" | 8\22 < g < 3\8 | g = 65\176 | g = 11\30, 14\38, 17\46 | 7g-5\2+3\2-4g = 3g-2 |
| 9L 13s | full | 17\22 < g < 7\9 | g = 307\396 | g = 24\31, 31\40, 38\49 | 13g-10+7-9g = 4g-3 |
| 10L 12s | "3/4" | 2\22 < g < 1\10 | g = 21\220 | g = 3\32, 4\42, 5\52 | 6g-1\2+1\2-5g = g |
| 11L 11s | "7/8" | 1\22 < g < 1\11 | g = 3\44 | g = 2\33, 3\44, 4\55 | g + 1\11-g = 1\11 |
| 12L 10s | "3/4" | 9\22 < g < 5\12 | g = 109\264 | g = 14\34, 19\46, 24\58 | 5g-2+5\2-6g = 1\2-g |
| 13L 9s | full | 5\22 < g < 3\13 | g = 131\572 | g = 8\35, 11\48, 14\61 | 9g-2+3-13g = 1-4g |
| 14L 8s | "3/4" | 3\22 < g < 2\14 | g = 43\308 | g = 5\36, 7\50, 9\64 | 4g-1\2+1-7g = 1\2-3g |
| 15L 7s | full | 19\22 < g < 13\15 | g = 571\660 | g = 32\37, 45\52, 58\67 | 7g-6+13-15g = 7-8g |
| 16L 6s | "3/4" | 4\22 < g < 3\16 | g = 65\352 | g = 7\38, 10\54, 13\70 | 3g-1\2+3\2-8g = 1-5g |
| 17L 5s | full | 9\22 < g < 7\17 | g = 207\748 | g = 16\39, 23\56, 30\73 | 5g-2+7-17g = 5-12g |
| 18L 4s | "3/4" | 6\22 < g < 5\18 | g = 109\396 | g = 11\40, 16\58, 21\76 | 2g-1\2+5\2-9g = 2-7g |
| 19L 3s | full | 15\22 < g < 13\19 | g = 571\836 | g = 28\41, 41\60, 54\79 | 3g-2+13-19g = 11-16g |
| 20L 2s | "3/4" | 1\22 < g < 1\20 | g = 21\440 | g = 2\42, 3\62, 4\72 | g+1\2-10g = 1\2-9g |
| 21L 1s | "half" | 1\22 < g < 1\21 | g = 43\924 | g = 2\43, 3\64, 4\85 | g+1-21g = 1-20g |
Including inverses
| Large-small numbers | Status | Generator range | Midpoint | Boundaries of propriety, maximum expressiveness, diatonicity | Large step+Small step |
|---|---|---|---|---|---|
| 1L25s | "half" | 25\26 < g < 1 | g = 51\52 | g = 26\27, 27\28, 28\29 | 25g-24+1-g = 24g-23 |
| 2L24s | "3/4" | 12\26 < g < 1\2 | g = 25\52 | g = 13\28, 14\30, 15\32 | 12g-11\2+1\2-g = 11g-5 |
| 3L23s | full | 17\26 < g < 2\3 | g = 103\156 | g = 19\29, 21\32, 23\35 | 23g-15+2-3g = 20g-13 |
| 4L22s | "3/4" | 6\26 < g < 1\4 | g = 25\104 | g = 7\30, 8\34, 9\38 | 11g-5\2+1\2-2g = 9g-2 |
| 5L21s | full | 5\26 < g < 1\5 | g = 51\260 | g = 6\31, 7\36, 8\41 | 21g-4+1-5g = 16g-3 |
| 6L20s | "3/4" | 4\26 < g < 1\6 | g = 25\156 | g = 5\32, 6\38, 7\44 | 10g-3\2+1\2-3g = 7g-1 |
| 7L19s | full | 11\26 < g < 3\7 | g = 155\364 | g = 14\33, 17\40, 20\47 | 19g-8+3-7g = 12g-5 |
| 8L18s | "3/4" | 3\26 < g < 1\8 | g = 25\208 | g = 4\34, 5\42, 6\50 | 9g-1+1\2-4g = 5g-1\2 |
| 9L17s | full | 23\26 < g < 8\9 | g = 415\468 | g = 31\35, 39\44, 47\53 | 17g-15+8-9g = 8g-7 |
| 10L16s | "3/4" | 5\26 < g < 2\10 | g = 51\260 | g = 7\36, 9\46, 11\56 | 8g-3\2+1-5g = 3g-1\2 |
| 11L15s | full | 7\26 < g < 3\11 | g = 155\572 | g = 10\37, 13\48, 16\59 | 15g-4+3-11g = 4g-1 |
| 12L14s | "3/4" | 2\26 < g < 1\12 | g = 25\312 | g = 3\38, 4\50, 5\62 | 7g-1\2+1\2-6g = g |
| 13L13s | "7/8" | 1\26 < g < 1\13 | g = 3\52 | g = 2\39, 3\52, 4\65 | g+1\13-g = 1\13 |
| 14L12s | "3/4" | 11\26 < g < 6\14 | g = 155\364 | g = 17\40, 23\54, 29\68 | 6g-5\2+3-7g = 1\2-g |
| 15L11s | full | 19\26 < g < 11\15 | g = 571\780 | g = 30\41, 41\56, 52\71 | 11g-8+11-15g = 3-4g |
| 16L10s | "3/4" | 8\26 < g < 5\16 | g = 129\416 | g = 13\42, 18\58, 23\74 | 5g-3\2+5\2-8g = 1-3g |
| 17L9s | full | 3\26 < g < 2\17 | g = 103\884 | g = 5\43, 7\60, 9\77 | 9g-1+2-17g = 1-8g |
| 18L8s | "3/4" | 10\26 < g < 7\18 | g = 181\468 | g = 17\44, 24\62, 31\80 | 4g-7\2+7-9g = 7\2-5g |
| 19L7s | full | 15\26 < g < 11\19 | g = 571\988 | g = 26\45, 37\64, 48\83 | 7g-4+11-19g = 7-12g |
| 20L6s | "3/4" | 9\26 < g < 7\20 | g = 181\520 | g = 16\46, 23\66, 30\86 | 3g-1+7\2-10g = 5\2-7g |
| 21L5s | full | 21\26 < g < 17\21 | g = 883\1092 | g = 38\47, 55\68, 72\89 | 5g-4+16-21g = 12-16g |
| 22L4s | "3/4" | 7\26 < g < 6\22 | g = 155\572 | g = 13\48, 19\70, 25\92 | 2g-1\2+3-11g = 5\2-9g |
| 23L3s | full | 9\26 < g < 8\23 | g = 415\1196 | g = 17\49, 25\72, 33/95 | 3g-1+8-23g = 7-20g |
| 24L2s | "3/4" | 1\26 < g < 1\24 | g = 25\312 | g = 2\50, 3\74, 4\98 | g+1\2-12g = 1\2-11g |
| 25L1s | "half" | 1\26 < g < 1\25 | g = 51\1300 | g = 2\51, 3\76, 4\101 | g+1-25g = 1-24g |