A shruti list: Difference between revisions

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[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#72704 Original article] by ma1937, on the Yahoo tuning forum, is quoted here.
:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#72704 Original article] by ma1937, on the Yahoo tuning forum, is quoted here:</tt>''
 
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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:<blockquote>"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</blockquote>This quotation yields many insights... Below I have just listed the twenty-three and a half srutis he is referring to.
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:<blockquote>"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</blockquote>This quotation yields many insights... Below I have just listed the twenty-three and a half srutis he is referring to.
Line 233: Line 231:
! | Status
! | Status
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff; color: #000000;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step+Small step
! | Large step+Small step
Line 240: Line 237:
| | "half"
| | "half"
| | 18\19 &lt; g &lt; 1
| | 18\19 &lt; g &lt; 1
| | g = 37\38
| | g = ''19\20, 20\21, 21\22''
| | g = ''19\20, 20\21, 21\22''
| | 18g-17+1-g = 17g-16
| | 18g-17+1-g = 17g-16
Line 247: Line 243:
| rowspan="16" | full
| rowspan="16" | full
| | 9\19 &lt; g &lt; 1\2
| | 9\19 &lt; g &lt; 1\2
| | g = 37\76
| | g = ''10\21'', 11\23, 12\25
| | g = ''10\21'', 11\23, 12\25
| | 17g-8+1-2g = 15g-7
| | 17g-8+1-2g = 15g-7
Line 253: Line 248:
| | [[3L 16s]]
| | [[3L 16s]]
| | 6\19 &lt; g &lt; 1\3
| | 6\19 &lt; g &lt; 1\3
| | g = 37\114
| | g = ''7\22'', 8\25, 10\31
| | g = ''7\22'', 8\25, 10\31
| | 16g-5+1-3g = 13g-4
| | 16g-5+1-3g = 13g-4
Line 259: Line 253:
| | [[4L 15s]]
| | [[4L 15s]]
| | 14\19 &lt; g &lt; 3\4
| | 14\19 &lt; g &lt; 3\4
| | g = 113\152
| | g = 17\23, 20\27, 23\31
| | g = 17\23, 20\27, 23\31
| | 15g-11+3-4g = 11g-8
| | 15g-11+3-4g = 11g-8
Line 265: Line 258:
| | [[5L 14s]]
| | [[5L 14s]]
| | 15\19 &lt; g &lt; 4\5
| | 15\19 &lt; g &lt; 4\5
| | g = 151\190
| | g = 19\24, 23\29, 27\34
| | g = 19\24, 23\29, 27\34
| | 14g-11+4-5g = 9g-7
| | 14g-11+4-5g = 9g-7
Line 271: Line 263:
| | [[6L 13s]]
| | [[6L 13s]]
| | 3\19 &lt; g &lt; 1\6
| | 3\19 &lt; g &lt; 1\6
| | g = 37\228
| | g = 4\25, 5\31, 6/37
| | g = 4\25, 5\31, 6/37
| | 13g-2+1-6g = 7g-1
| | 13g-2+1-6g = 7g-1
Line 277: Line 268:
| | [[7L 12s]]
| | [[7L 12s]]
| | 8\19 &lt; g &lt; 3\7
| | 8\19 &lt; g &lt; 3\7
| | g = 113\266
| | g = 11\26, 14\33, 17\40
| | g = 11\26, 14\33, 17\40
| | 12g-5+3-7g = 5g-2
| | 12g-5+3-7g = 5g-2
Line 283: Line 273:
| | [[8L 11s]]
| | [[8L 11s]]
| | 7\19 &lt; g &lt; 3\8
| | 7\19 &lt; g &lt; 3\8
| | g = 113\304
| | g = 10\27, 13\35, 16\43
| | g = 10\27, 13\35, 16\43
| | 11g-4+3-8g = 3g-1
| | 11g-4+3-8g = 3g-1
Line 289: Line 278:
| | [[9L 10s]]
| | [[9L 10s]]
| | 2\19 &lt; g &lt; 1\9
| | 2\19 &lt; g &lt; 1\9
| | g = 37\342
| | g = 3\28, 4\37, 5\46
| | g = 3\28, 4\37, 5\46
| | 10g-1+1-9g = g
| | 10g-1+1-9g = g
Line 295: Line 283:
| | [[10L 9s]]
| | [[10L 9s]]
| | 17\19 &lt; g &lt; 9\10
| | 17\19 &lt; g &lt; 9\10
| | g = 341\380
| | g = 26\29, 35\39, 44\49
| | g = 26\29, 35\39, 44\49
| | 9g-8+9-10g = 1-g
| | 9g-8+9-10g = 1-g
Line 301: Line 288:
| | [[11L 8s]]
| | [[11L 8s]]
| | 12\19 &lt; g &lt; 7\11
| | 12\19 &lt; g &lt; 7\11
| | g = 265\418
| | g = 19\30, 26\41, 33\52
| | g = 19\30, 26\41, 33\52
| | 8g-5+7-11g = 2-3g
| | 8g-5+7-11g = 2-3g
Line 307: Line 293:
| | [[12L 7s]]
| | [[12L 7s]]
| | 11\19 &lt; g &lt; 7\12
| | 11\19 &lt; g &lt; 7\12
| | g = 265\456
| | g = 18\31, 25\43, 32\55
| | g = 18\31, 25\43, 32\55
| | 7g-4+7-12g = 3-5g
| | 7g-4+7-12g = 3-5g
Line 313: Line 298:
| | [[13L 6s]]
| | [[13L 6s]]
| | 16\19 &lt; g &lt; 11\13
| | 16\19 &lt; g &lt; 11\13
| | g = 417\494
| | g = 27\32, 38\45, 49\58
| | g = 27\32, 38\45, 49\58
| | 6g-5+11-13g = 6-7g
| | 6g-5+11-13g = 6-7g
Line 319: Line 303:
| | [[14L 5s]]
| | [[14L 5s]]
| | 4\19 &lt; g &lt; 3\14
| | 4\19 &lt; g &lt; 3\14
| | g = 113\532
| | g = 7\33, 10\47, 13\61
| | g = 7\33, 10\47, 13\61
| | 5g-1+3-14g = 2-9g
| | 5g-1+3-14g = 2-9g
Line 325: Line 308:
| | [[15L 4s]]
| | [[15L 4s]]
| | 5\19 &lt; g &lt; 4\15
| | 5\19 &lt; g &lt; 4\15
| | g = 151\570
| | g = 9\34, 13\49, 17\64
| | g = 9\34, 13\49, 17\64
| | 4g-1+4-15g = 3-11g
| | 4g-1+4-15g = 3-11g
Line 331: Line 313:
| | [[16L 3s]]
| | [[16L 3s]]
| | 13\19 &lt; g &lt; 11\16
| | 13\19 &lt; g &lt; 11\16
| | g = 417\608
| | g = 24\35, 35\51, 46\67
| | g = 24\35, 35\51, 46\67
| | 3g-2+11-16g = 9-13g
| | 3g-2+11-16g = 9-13g
Line 337: Line 318:
| | [[17L 2s]]
| | [[17L 2s]]
| | 10\19 &lt; g &lt; 9\17
| | 10\19 &lt; g &lt; 9\17
| | g = 341\646
| | g = 19\36, 28\53, 37\70
| | g = 19\36, 28\53, 37\70
| | 2g-1+9-17g = 8-15g
| | 2g-1+9-17g = 8-15g
Line 344: Line 324:
| | "half"
| | "half"
| | 1\19 &lt; g &lt; 1\18
| | 1\19 &lt; g &lt; 1\18
| | g = 37\684
| | g = 2\37, 3\55, 4\73
| | g = 2\37, 3\55, 4\73
| | g+1-18g = 1-17g
| | g+1-18g = 1-17g
Line 355: Line 334:
!''Status''
!''Status''
! |''Generator range''
! |''Generator range''
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
! |''Large step+Small step''
Line 362: Line 340:
|''"half"''
|''"half"''
| |<span style="line-height: 15.6000003814697px;">''22\23 &lt; g &lt; 1''</span>
| |<span style="line-height: 15.6000003814697px;">''22\23 &lt; g &lt; 1''</span>
| |''g = 45\46''
| |'''''g = 23\24, 24\25, 25\26'''''
| |'''''g = 23\24, 24\25, 25\26'''''
| |''22g-21+1-g = 21g-20''
| |''22g-21+1-g = 21g-20''
Line 369: Line 346:
| rowspan="20" |''full''
| rowspan="20" |''full''
| |''11\23 &lt; g &lt; 1\2''
| |''11\23 &lt; g &lt; 1\2''
| |''g = 45\92''
| |'''''g = 12\25, 13\27''', 14\29''
| |'''''g = 12\25, 13\27''', 14\29''
| |''21g-10+1-2g = 19g-9''
| |''21g-10+1-2g = 19g-9''
Line 375: Line 351:
| |''3L20s''
| |''3L20s''
| |''15\23 &lt; g &lt; 2\3''
| |''15\23 &lt; g &lt; 2\3''
| |''g = 91\138''
| |'''''g = 17\26,''''' ''19\29, 21\32''
| |'''''g = 17\26,''''' ''19\29, 21\32''
| |''20g-13+1-3g = 17g-12''
| |''20g-13+1-3g = 17g-12''
Line 381: Line 356:
| |''4L19s''
| |''4L19s''
| |''17\23 &lt; g &lt; 3\4''
| |''17\23 &lt; g &lt; 3\4''
| |''g = 137\184''
| |'''''g = 20\27,''''' ''23\31, 26\35''
| |'''''g = 20\27,''''' ''23\31, 26\35''
| |''19g-14+3-4g = 15g-11''
| |''19g-14+3-4g = 15g-11''
Line 387: Line 361:
| |''5L18s''
| |''5L18s''
| |''9\23 &lt; g &lt; 2\5''
| |''9\23 &lt; g &lt; 2\5''
| |''g = 91\230''
| |'''''g = 11\28''', 13\33, 15\38''
| |'''''g = 11\28''', 13\33, 15\38''
| |''18g-7+2-5g = 13g-5''
| |''18g-7+2-5g = 13g-5''
Line 393: Line 366:
| |''6L17s''
| |''6L17s''
| |''19\23 &lt; g &lt; 5\6''
| |''19\23 &lt; g &lt; 5\6''
| |''g = 229\276''
| |''g = 24\29, 29\35, 34\41''
| |''g = 24\29, 29\35, 34\41''
| |''17g-15+1-6g = 11g-14''
| |''17g-15+1-6g = 11g-14''
Line 399: Line 371:
| |''7L16s''
| |''7L16s''
| |''13\23 &lt; g &lt; 4\7''
| |''13\23 &lt; g &lt; 4\7''
| |''g = 183\322''
| |''g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44''
| |''g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44''
| |''16g-9+4-7g = 9g-5''
| |''16g-9+4-7g = 9g-5''
Line 405: Line 376:
| |''8L15s''
| |''8L15s''
| |''20\23 &lt; g &lt; 7\8''
| |''20\23 &lt; g &lt; 7\8''
| |''g = 321\368''
| |''g = 27\31, 34\39, 41\47''
| |''g = 27\31, 34\39, 41\47''
| |''15g-13+7-8g = 7g-6''
| |''15g-13+7-8g = 7g-6''
Line 411: Line 381:
| |''9L14s''
| |''9L14s''
| |''5\23 &lt; g &lt; 2\9''
| |''5\23 &lt; g &lt; 2\9''
| |''g = 91\414''
| |''g = 7\32, 9\41, 11\50''
| |''g = 7\32, 9\41, 11\50''
| |''14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>''
| |''14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>''
Line 417: Line 386:
| |''10L13s''
| |''10L13s''
| |''16\23 &lt; g &lt; 7\10''
| |''16\23 &lt; g &lt; 7\10''
| |''g = 321\460''
| |''g = 23\33, 30\43, 37\53''
| |''g = 23\33, 30\43, 37\53''
| |''13g-9+7-10g = 3g-2''
| |''13g-9+7-10g = 3g-2''
Line 423: Line 391:
| |''11L12s''
| |''11L12s''
| |''2\23 &lt; g &lt; 1\11''
| |''2\23 &lt; g &lt; 1\11''
| |''g = 45\506''
| |''g = 3\34, 4\45, 5\56''
| |''g = 3\34, 4\45, 5\56''
| |''12g-1+1-11g = g''
| |''12g-1+1-11g = g''
Line 429: Line 396:
| |''12L11s''
| |''12L11s''
| |''21\23 &lt; g &lt; 11\12''
| |''21\23 &lt; g &lt; 11\12''
| |''g = 505\552''
| |''g = 32\35, 43\47, 54\59''
| |''g = 32\35, 43\47, 54\59''
| |<span style="line-height: 15.6000003814697px;">''11g-10+11-12g = 1-g''</span>
| |<span style="line-height: 15.6000003814697px;">''11g-10+11-12g = 1-g''</span>
Line 435: Line 401:
| |''13L10s''
| |''13L10s''
| |''7\23 &lt; g &lt; 4\13''
| |''7\23 &lt; g &lt; 4\13''
| |''g = 183\598''
| |''g = 11\36, 15\49, 19\62''
| |''g = 11\36, 15\49, 19\62''
| |''10g-3+4-13g =1-3g''
| |''10g-3+4-13g =1-3g''
Line 441: Line 406:
| |''14L9s''
| |''14L9s''
| |''18\23 &lt; g &lt; 11\14''
| |''18\23 &lt; g &lt; 11\14''
| |''g = 505\644''
| |''g = 29\37, 40\51, 51\65''
| |''g = 29\37, 40\51, 51\65''
| |''9g-7+11-14g = 4-5g''
| |''9g-7+11-14g = 4-5g''
Line 447: Line 411:
| |''15L8s''
| |''15L8s''
| |''3\23 &lt; g &lt; 2\15''
| |''3\23 &lt; g &lt; 2\15''
| |''g = 91\690''
| |''g = 5\38, 7\53, 9\68''
| |''g = 5\38, 7\53, 9\68''
| |''8g-1+2-15g = 1-7g''
| |''8g-1+2-15g = 1-7g''
Line 453: Line 416:
| |''16L7s''
| |''16L7s''
| |''10\23 &lt; g &lt; 7\16''
| |''10\23 &lt; g &lt; 7\16''
| |''g = 321\736''
| |''g = 17\39, 24\55, 31\71''
| |''g = 17\39, 24\55, 31\71''
| |''7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>''
| |''7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>''
Line 459: Line 421:
| |''17L6s''
| |''17L6s''
| |''4\23 &lt; g &lt; 3\17''
| |''4\23 &lt; g &lt; 3\17''
| |''g = 137\782''
| |''g = 7\40, 10\57, 13\74''
| |''g = 7\40, 10\57, 13\74''
| |''6g-1+3-17g = 2-11g''
| |''6g-1+3-17g = 2-11g''
Line 465: Line 426:
| |''18L5s''
| |''18L5s''
| |''14\23 &lt; g &lt; 11\18''
| |''14\23 &lt; g &lt; 11\18''
| |''g = 505\828''
| |''g = 25\41, 36\59, 47\77''
| |''g = 25\41, 36\59, 47\77''
| |''5g-4+11-18g = 7-13g''
| |''5g-4+11-18g = 7-13g''
Line 471: Line 431:
| |''19L4s''
| |''19L4s''
| |''6\23 &lt; g &lt; 5\19''
| |''6\23 &lt; g &lt; 5\19''
| |''g = 229\874''
| |''g = 11\42, 16\61, 21\80''
| |''g = 11\42, 16\61, 21\80''
| |''4g-1+5-19g = 4-15g''
| |''4g-1+5-19g = 4-15g''
Line 477: Line 436:
| |''20L3s''
| |''20L3s''
| |''8\23 &lt; g &lt; 7\20''
| |''8\23 &lt; g &lt; 7\20''
| |''g = 321\920''
| |''g = 15\43, 22\63, 29\83''
| |''g = 15\43, 22\63, 29\83''
| |''3g-1+13-20g = 12-17g''
| |''3g-1+13-20g = 12-17g''
Line 483: Line 441:
| |''21L2s''
| |''21L2s''
| |''12\23 &lt; g &lt; 11\21''
| |''12\23 &lt; g &lt; 11\21''
| |''g = 505\966''
| |''g = 23\44, 34\65, 45\86''
| |''g = 23\44, 34\65, 45\86''
| |''2g-1+11-21g = 10-19g''
| |''2g-1+11-21g = 10-19g''
Line 490: Line 447:
|''"half"''
|''"half"''
| |''1\23 &lt; g &lt; 1\22''
| |''1\23 &lt; g &lt; 1\22''
| |''g = 45\1012''
| |''g = 2\45, 3\67, 4\89''
| |''g = 2\45, 3\67, 4\89''
| |''g+1-22g = 1-221''
| |''g+1-22g = 1-221''
Line 503: Line 459:
! | Status
! | Status
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff; color: #000000;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step+Small step
! | Large step+Small step
Line 510: Line 465:
| | "half"
| | "half"
| | 21\22 &lt; g &lt; 1
| | 21\22 &lt; g &lt; 1
| | g = 43\44
| | g = ''22\23,'' ''23\24,'' ''24\25''
| | g = ''22\23,'' ''23\24,'' ''24\25''
| | 21g-20+1-g = 20g-19
| | 21g-20+1-g = 20g-19
Line 517: Line 471:
| | "3/4"
| | "3/4"
| | 10\22 &lt; g &lt; 1\2
| | 10\22 &lt; g &lt; 1\2
| | g = 21\44
| | g = ''11\24,'' ''12\26'', 13\28
| | g = ''11\24,'' ''12\26'', 13\28
| | 10g-9\2+1\2-g = 9g-4
| | 10g-9\2+1\2-g = 9g-4
Line 524: Line 477:
| | full
| | full
| | 7\22 &lt; g &lt; 1\3
| | 7\22 &lt; g &lt; 1\3
| | g = 43\132
| | g = ''8\25'', 9\28, 10\31
| | g = ''8\25'', 9\28, 10\31
| | 19g-6+1-3g = 16g-5
| | 19g-6+1-3g = 16g-5
Line 531: Line 483:
| | "3/4"
| | "3/4"
| | 5\22 &lt; g &lt; 1\4
| | 5\22 &lt; g &lt; 1\4
| | g = 21\88
| | g = ''6\26'', 7\30, 8\34
| | g = ''6\26'', 7\30, 8\34
| | 9g-2+1\2-2g = 7g-3\2
| | 9g-2+1\2-2g = 7g-3\2
Line 538: Line 489:
| | full
| | full
| | 13\22 &lt; g &lt; 3\5
| | 13\22 &lt; g &lt; 3\5
| | g = 131\220
| | g = 16\27, 19\32, 22\37
| | g = 16\27, 19\32, 22\37
| | 17g-10+3-5g = 12g-7
| | 17g-10+3-5g = 12g-7
Line 545: Line 495:
| | "3/4"
| | "3/4"
| | 7\22 &lt; g &lt; 2\6
| | 7\22 &lt; g &lt; 2\6
| | g = 43\132
| | g = 9\28, 11\34, 13\40
| | g = 9\28, 11\34, 13\40
| | 8g-5\2+1-3g = 5g-2
| | 8g-5\2+1-3g = 5g-2
Line 552: Line 501:
| | full
| | full
| | 3\22 &lt; g &lt; 1\7
| | 3\22 &lt; g &lt; 1\7
| | g = 43\308
| | g = 4\29, 5\36, 6\43
| | g = 4\29, 5\36, 6\43
| | 15g-2+1-7g = 8g-1
| | 15g-2+1-7g = 8g-1
Line 559: Line 507:
| | "3/4"
| | "3/4"
| | 8\22 &lt; g &lt; 3\8
| | 8\22 &lt; g &lt; 3\8
| | g = 65\176
| | g = 11\30, 14\38, 17\46
| | g = 11\30, 14\38, 17\46
| | 7g-5\2+3\2-4g = 3g-2
| | 7g-5\2+3\2-4g = 3g-2
Line 566: Line 513:
| | full
| | full
| | 17\22 &lt; g &lt; 7\9
| | 17\22 &lt; g &lt; 7\9
| | g = 307\396
| | g = 24\31, 31\40, 38\49
| | g = 24\31, 31\40, 38\49
| | 13g-10+7-9g = 4g-3
| | 13g-10+7-9g = 4g-3
Line 573: Line 519:
| | "3/4"
| | "3/4"
| | 2\22 &lt; g &lt; 1\10
| | 2\22 &lt; g &lt; 1\10
| | g = 21\220
| | g = 3\32, 4\42, 5\52
| | g = 3\32, 4\42, 5\52
| | 6g-1\2+1\2-5g = g
| | 6g-1\2+1\2-5g = g
Line 580: Line 525:
| |"7/8"
| |"7/8"
| | 1\22 &lt; g &lt; 1\11
| | 1\22 &lt; g &lt; 1\11
| | g = 3\44
| | g = 2\33, 3\44, 4\55
| | g = 2\33, 3\44, 4\55
| | g + 1\11-g = 1\11
| | g + 1\11-g = 1\11
Line 587: Line 531:
| | "3/4"
| | "3/4"
| | 9\22 &lt; g &lt; 5\12
| | 9\22 &lt; g &lt; 5\12
| | g = 109\264
| | g = 14\34, 19\46, 24\58
| | g = 14\34, 19\46, 24\58
| | 5g-2+5\2-6g = 1\2-g
| | 5g-2+5\2-6g = 1\2-g
Line 594: Line 537:
| | full
| | full
| | 5\22 &lt; g &lt; 3\13
| | 5\22 &lt; g &lt; 3\13
| | g = 131\572
| | g = 8\35, 11\48, 14\61
| | g = 8\35, 11\48, 14\61
| | 9g-2+3-13g = 1-4g
| | 9g-2+3-13g = 1-4g
Line 601: Line 543:
| | "3/4"
| | "3/4"
| | 3\22 &lt; g &lt; 2\14
| | 3\22 &lt; g &lt; 2\14
| | g = 43\308
| | g = 5\36, 7\50, 9\64
| | g = 5\36, 7\50, 9\64
| | 4g-1\2+1-7g = 1\2-3g
| | 4g-1\2+1-7g = 1\2-3g
Line 608: Line 549:
| | full
| | full
| | 19\22 &lt; g &lt; 13\15
| | 19\22 &lt; g &lt; 13\15
| | g = 571\660
| | g = 32\37, 45\52, 58\67
| | g = 32\37, 45\52, 58\67
| | 7g-6+13-15g = 7-8g
| | 7g-6+13-15g = 7-8g
Line 615: Line 555:
| | "3/4"
| | "3/4"
| | 4\22 &lt; g &lt; 3\16
| | 4\22 &lt; g &lt; 3\16
| | g = 65\352
| | g = 7\38, 10\54, 13\70
| | g = 7\38, 10\54, 13\70
| | 3g-1\2+3\2-8g = 1-5g
| | 3g-1\2+3\2-8g = 1-5g
Line 622: Line 561:
| | full
| | full
| | 9\22 &lt; g &lt; 7\17
| | 9\22 &lt; g &lt; 7\17
| | g = 207\748
| | g = 16\39, 23\56, 30\73
| | g = 16\39, 23\56, 30\73
| | 5g-2+7-17g = 5-12g
| | 5g-2+7-17g = 5-12g
Line 629: Line 567:
| | "3/4"
| | "3/4"
| | 6\22 &lt; g &lt; 5\18
| | 6\22 &lt; g &lt; 5\18
| | g = 109\396
| | g = 11\40, 16\58, 21\76
| | g = 11\40, 16\58, 21\76
| | 2g-1\2+5\2-9g = 2-7g
| | 2g-1\2+5\2-9g = 2-7g
Line 636: Line 573:
| | full
| | full
| | 15\22 &lt; g &lt; 13\19
| | 15\22 &lt; g &lt; 13\19
| | g = 571\836
| | g = 28\41, 41\60, 54\79
| | g = 28\41, 41\60, 54\79
| | 3g-2+13-19g = 11-16g
| | 3g-2+13-19g = 11-16g
Line 643: Line 579:
| | "3/4"
| | "3/4"
| | 1\22 &lt; g &lt; 1\20
| | 1\22 &lt; g &lt; 1\20
| | g = 21\440
| | g = 2\42, 3\62, 4\72
| | g = 2\42, 3\62, 4\72
| | g+1\2-10g = 1\2-9g
| | g+1\2-10g = 1\2-9g
Line 650: Line 585:
| | "half"
| | "half"
| | 1\22 &lt; g &lt; 1\21
| | 1\22 &lt; g &lt; 1\21
| | g = 43\924
| | g = 2\43, 3\64, 4\85
| | g = 2\43, 3\64, 4\85
| | g+1-21g = 1-20g
| | g+1-21g = 1-20g
Line 660: Line 594:
!Status
!Status
! |Generator range
! |Generator range
! |<span style="background-color: #ffffff;">Midpoint</span>
! |Boundaries of propriety, maximum expressiveness, diatonicity
! |Boundaries of propriety, maximum expressiveness, diatonicity
! |Large step+Small step
! |Large step+Small step
Line 667: Line 600:
|"half"
|"half"
| |25\26 &lt; g &lt; 1
| |25\26 &lt; g &lt; 1
| |g = 51\52
| |''g = 26\27, 27\28, 28\29''
| |''g = 26\27, 27\28, 28\29''
| |25g-24+1-g = 24g-23
| |25g-24+1-g = 24g-23
Line 674: Line 606:
|"3/4"
|"3/4"
| |12\26 &lt; g &lt; 1\2
| |12\26 &lt; g &lt; 1\2
| |g = 25\52
| |''g = 13\28, 14\30, 15\32''
| |''g = 13\28, 14\30, 15\32''
| |12g-11\2+1\2-g = 11g-5
| |12g-11\2+1\2-g = 11g-5
Line 681: Line 612:
|full
|full
| |17\26 &lt; g &lt; 2\3
| |17\26 &lt; g &lt; 2\3
| |g = 103\156
| |g = ''19\29'', ''21\32'', 23\35
| |g = ''19\29'', ''21\32'', 23\35
| |23g-15+2-3g = 20g-13
| |23g-15+2-3g = 20g-13
Line 688: Line 618:
|"3/4"
|"3/4"
| |6\26 &lt; g &lt; 1\4
| |6\26 &lt; g &lt; 1\4
| |g = 25\104
| |g = ''7\30'', 8\34, 9\38
| |g = ''7\30'', 8\34, 9\38
| |11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span>
| |11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span>
Line 695: Line 624:
|full
|full
| |5\26 &lt; g &lt; 1\5
| |5\26 &lt; g &lt; 1\5
| |g = 51\260
| |g = ''6\31'', 7\36, 8\41
| |g = ''6\31'', 7\36, 8\41
| |21g-4+1-5g = 16g-3
| |21g-4+1-5g = 16g-3
Line 702: Line 630:
|"3/4"
|"3/4"
| |4\26 &lt; g &lt; 1\6
| |4\26 &lt; g &lt; 1\6
| |g = 25\156
| |g = ''5\32'', 6\38, 7\44
| |g = ''5\32'', 6\38, 7\44
| |10g-3\2+1\2-3g = 7g-1
| |10g-3\2+1\2-3g = 7g-1
Line 709: Line 636:
|full
|full
| |11\26 &lt; g &lt; 3\7
| |11\26 &lt; g &lt; 3\7
| |g = 155\364
| |g = 14\33, 17\40, 20\47
| |g = 14\33, 17\40, 20\47
| |19g-8+3-7g = 12g-5
| |19g-8+3-7g = 12g-5
Line 716: Line 642:
|"3/4"
|"3/4"
| |3\26 &lt; g &lt; 1\8
| |3\26 &lt; g &lt; 1\8
| |g = 25\208
| |g = 4\34, 5\42, 6\50
| |g = 4\34, 5\42, 6\50
| |9g-1+1\2-4g = 5g-1\2
| |9g-1+1\2-4g = 5g-1\2
Line 723: Line 648:
|full
|full
| |23\26 &lt; g &lt; 8\9
| |23\26 &lt; g &lt; 8\9
| |g = 415\468
| |g = 31\35, 39\44, 47\53
| |g = 31\35, 39\44, 47\53
| |17g-15+8-9g = 8g-7
| |17g-15+8-9g = 8g-7
Line 730: Line 654:
|"3/4"
|"3/4"
| |5\26 &lt; g &lt; 2\10
| |5\26 &lt; g &lt; 2\10
| |g = 51\260
| |g = 7\36, 9\46, 11\56
| |g = 7\36, 9\46, 11\56
| |8g-3\2+1-5g = 3g-1\2
| |8g-3\2+1-5g = 3g-1\2
Line 737: Line 660:
|full
|full
| |7\26 &lt; g &lt; 3\11
| |7\26 &lt; g &lt; 3\11
| |g = 155\572
| |g = 10\37, 13\48, 16\59
| |g = 10\37, 13\48, 16\59
| |15g-4+3-11g = 4g-1
| |15g-4+3-11g = 4g-1
Line 744: Line 666:
|"3/4"
|"3/4"
| |2\26 &lt; g &lt; 1\12
| |2\26 &lt; g &lt; 1\12
| |g = 25\312
| |g = 3\38, 4\50, 5\62
| |g = 3\38, 4\50, 5\62
| |7g-1\2+1\2-6g = g
| |7g-1\2+1\2-6g = g
Line 751: Line 672:
|"7/8"
|"7/8"
| |1\26 &lt; g &lt; 1\13
| |1\26 &lt; g &lt; 1\13
| |g = 3\52
| |g = 2\39, 3\52, 4\65
| |g = 2\39, 3\52, 4\65
| |g+1\13-g = 1\13
| |g+1\13-g = 1\13
Line 758: Line 678:
|"3/4"
|"3/4"
| |11\26 &lt; g &lt; 6\14
| |11\26 &lt; g &lt; 6\14
| |g = 155\364
| |g = 17\40, 23\54, 29\68
| |g = 17\40, 23\54, 29\68
| |6g-5\2+3-7g = 1\2-g
| |6g-5\2+3-7g = 1\2-g
Line 765: Line 684:
|full
|full
| |19\26 &lt; g &lt; 11\15
| |19\26 &lt; g &lt; 11\15
| |g = 571\780
| |g = 30\41, 41\56, 52\71
| |g = 30\41, 41\56, 52\71
| |11g-8+11-15g = 3-4g
| |11g-8+11-15g = 3-4g
Line 772: Line 690:
|"3/4"
|"3/4"
| |8\26 &lt; g &lt; 5\16
| |8\26 &lt; g &lt; 5\16
| |g = 129\416
| |g = 13\42, 18\58, 23\74
| |g = 13\42, 18\58, 23\74
| |5g-3\2+5\2-8g = 1-3g
| |5g-3\2+5\2-8g = 1-3g
Line 779: Line 696:
|full
|full
| |3\26 &lt; g &lt; 2\17
| |3\26 &lt; g &lt; 2\17
| |g = 103\884
| |g = 5\43, 7\60, 9\77
| |g = 5\43, 7\60, 9\77
| |9g-1+2-17g = 1-8g
| |9g-1+2-17g = 1-8g
Line 786: Line 702:
|"3/4"
|"3/4"
| |10\26 &lt; g &lt; 7\18
| |10\26 &lt; g &lt; 7\18
| |g = 181\468
| |g = 17\44, 24\62, 31\80
| |g = 17\44, 24\62, 31\80
| |4g-7\2+7-9g = 7\2-5g
| |4g-7\2+7-9g = 7\2-5g
Line 793: Line 708:
|full
|full
| |15\26 &lt; g &lt; 11\19
| |15\26 &lt; g &lt; 11\19
| |g = 571\988
| |g = 26\45, 37\64, 48\83
| |g = 26\45, 37\64, 48\83
| |7g-4+11-19g = 7-12g
| |7g-4+11-19g = 7-12g
Line 800: Line 714:
|"3/4"
|"3/4"
| |9\26 &lt; g &lt; 7\20
| |9\26 &lt; g &lt; 7\20
| |g = 181\520
| |g = 16\46, 23\66, 30\86
| |g = 16\46, 23\66, 30\86
| |3g-1+7\2-10g = 5\2-7g
| |3g-1+7\2-10g = 5\2-7g
Line 807: Line 720:
|full
|full
| |21\26 &lt; g &lt; 17\21
| |21\26 &lt; g &lt; 17\21
| |g = 883\1092
| |g = 38\47, 55\68, 72\89
| |g = 38\47, 55\68, 72\89
| |5g-4+16-21g = 12-16g
| |5g-4+16-21g = 12-16g
Line 814: Line 726:
|"3/4"
|"3/4"
| |7\26 &lt; g &lt; 6\22
| |7\26 &lt; g &lt; 6\22
| |g = 155\572
| |g = 13\48, 19\70, 25\92
| |g = 13\48, 19\70, 25\92
| |2g-1\2+3-11g = 5\2-9g
| |2g-1\2+3-11g = 5\2-9g
Line 821: Line 732:
|full
|full
| |9\26 &lt; g &lt; 8\23
| |9\26 &lt; g &lt; 8\23
| |g = 415\1196
| |g = 17\49, 25\72, 33/95
| |g = 17\49, 25\72, 33/95
| |3g-1+8-23g = 7-20g
| |3g-1+8-23g = 7-20g
Line 828: Line 738:
|"3/4"
|"3/4"
| |1\26 &lt; g &lt; 1\24
| |1\26 &lt; g &lt; 1\24
| |g = 25\312
| |g = 2\50, 3\74, 4\98
| |g = 2\50, 3\74, 4\98
| |g+1\2-12g = 1\2-11g
| |g+1\2-12g = 1\2-11g
Line 835: Line 744:
|"half"
|"half"
| |1\26 &lt; g &lt; 1\25
| |1\26 &lt; g &lt; 1\25
| |g = 51\1300
| |g = 2\51, 3\76, 4\101
| |g = 2\51, 3\76, 4\101
| |g+1-25g = 1-24g
| |g+1-25g = 1-24g
Line 847: Line 755:
!''Status''
!''Status''
! |''Generator range''
! |''Generator range''
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
! |''Large step+Small step''
Line 854: Line 761:
|''"half"''
|''"half"''
| |''24\25 &lt; g &lt; 1''
| |''24\25 &lt; g &lt; 1''
| |''g = 49\50''
| |'''''g = 25\26, 26\27, 27\28'''''
| |'''''g = 25\26, 26\27, 27\28'''''
| |''24g-23+1-g = 23g-22''
| |''24g-23+1-g = 23g-22''
Line 861: Line 767:
| rowspan="3" |''full''
| rowspan="3" |''full''
| |''12\25 &lt; g &lt; 1\2''
| |''12\25 &lt; g &lt; 1\2''
| |''g = 49\100''
| |'''''g = 13\27, 14\29, 15\31'''''
| |'''''g = 13\27, 14\29, 15\31'''''
| |''23g-11+1-2g = 21g-10''
| |''23g-11+1-2g = 21g-10''
Line 867: Line 772:
| |''3L22s''
| |''3L22s''
| |''8\25 &lt; g &lt; 1\3''
| |''8\25 &lt; g &lt; 1\3''
| |''g = 49\150''
| |'''''g = 9\28, 10\31,''''' ''11\34''
| |'''''g = 9\28, 10\31,''''' ''11\34''
| |''22g-7+1-3g = 19g-6''
| |''22g-7+1-3g = 19g-6''
Line 873: Line 777:
| |''4L21s''
| |''4L21s''
| |''6\25 &lt; g &lt; 1\4''
| |''6\25 &lt; g &lt; 1\4''
| |''g = 49\200''
| |'''''g = 7\29''', 8\33, 9\37''
| |'''''g = 7\29''', 8\33, 9\37''
| |''21g-5+1-4g = 17g-4''
| |''21g-5+1-4g = 17g-4''
Line 880: Line 783:
|''"7/8"''
|''"7/8"''
| |''4\25 &lt; g &lt; 1\5''
| |''4\25 &lt; g &lt; 1\5''
| |''g = 9\50''
| |'''''g = 5\30,''' 6\35, 7\40''
| |'''''g = 5\30,''' 6\35, 7\40''
| |''4g-3\5+1\5-g = 3g-2\5''
| |''4g-3\5+1\5-g = 3g-2\5''
Line 887: Line 789:
| rowspan="4" |''full''
| rowspan="4" |''full''
| |''4\25 &lt; g &lt; 1\6''
| |''4\25 &lt; g &lt; 1\6''
| |''g = 49\300''
| |'''''g = 5\31,''''' ''6\37, 7\43''
| |'''''g = 5\31,''''' ''6\37, 7\43''
| |''19g-3+1-6g = 13g-2''
| |''19g-3+1-6g = 13g-2''
Line 893: Line 794:
| |''7L18s''
| |''7L18s''
| |''7\25 &lt; g &lt; 2\7''
| |''7\25 &lt; g &lt; 2\7''
| |''g = 99\350''
| |''g = 9\32, 11\39, 13\46''
| |''g = 9\32, 11\39, 13\46''
| |''18g-5+2-7g = 11g-3''
| |''18g-5+2-7g = 11g-3''
Line 899: Line 799:
| |''8L17s''
| |''8L17s''
| |''3\25 &lt; g &lt; 1\8''
| |''3\25 &lt; g &lt; 1\8''
| |''g = 49\400''
| |''g = 4\33, 5\41, 6\47''
| |''g = 4\33, 5\41, 6\47''
| |<span style="line-height: 15.6000003814697px;">''17g-2+1-8g = 9g-1''</span>
| |<span style="line-height: 15.6000003814697px;">''17g-2+1-8g = 9g-1''</span>
Line 905: Line 804:
| |''9L16s''
| |''9L16s''
| |''11\25 &lt; g &lt; 4\9''
| |''11\25 &lt; g &lt; 4\9''
| |''g = 199\450''
| |''g = 15\34, 19\43, 23\52''
| |''g = 15\34, 19\43, 23\52''
| |''16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>''
| |''16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>''
Line 912: Line 810:
|''"7/8"''
|''"7/8"''
| |''2\25 &lt; g &lt; 1\10''
| |''2\25 &lt; g &lt; 1\10''
| |''g = 9\100''
| |''g = 3\35, 4\45, 5\55''
| |''g = 3\35, 4\45, 5\55''
| |''3g-1\5+1\5-2g = g''
| |''3g-1\5+1\5-2g = g''
Line 919: Line 816:
| rowspan="4" |''full''
| rowspan="4" |''full''
| |''9\25 &lt; g &lt; 4\11''
| |''9\25 &lt; g &lt; 4\11''
| |''g = 199\550''
| |''g = 13\36, 17\47, 21\58''
| |''g = 13\36, 17\47, 21\58''
| |''14g-5+4-11g = 3g-1''
| |''14g-5+4-11g = 3g-1''
Line 925: Line 821:
| |''12L13s''
| |''12L13s''
| |''2\25 &lt; g &lt; 1\12''
| |''2\25 &lt; g &lt; 1\12''
| |''g = 49\600''
| |''g = 3\37, 4\49, 5\61''
| |''g = 3\37, 4\49, 5\61''
| |''13g-1+1-12g = g''
| |''13g-1+1-12g = g''
Line 931: Line 826:
| |''13L12s''
| |''13L12s''
| |''23\25 &lt; g &lt; 12\13''
| |''23\25 &lt; g &lt; 12\13''
| |''g = 599\650''
| |''g = 35\38, 47\51, 59\64''
| |''g = 35\38, 47\51, 59\64''
| |''12g-11+12-13g = 1-g''
| |''12g-11+12-13g = 1-g''
Line 937: Line 831:
| |''14L11s''
| |''14L11s''
| |''16\25 &lt; g &lt; 9\14''
| |''16\25 &lt; g &lt; 9\14''
| |''g = 449\700''
| |''g = 25\39, 34\53, 43\67''
| |''g = 25\39, 34\53, 43\67''
| |''11g-7+9-14g = 2-3g''
| |''11g-7+9-14g = 2-3g''
Line 944: Line 837:
|''"7/8"''
|''"7/8"''
| |''3\25 &lt; g &lt; 2\15''
| |''3\25 &lt; g &lt; 2\15''
| |''g = 19\150''
| |''g = 5\40, 7\55, 9\70''
| |''g = 5\40, 7\55, 9\70''
| |''2g-1\5+2\5-3g = 1\5-g''
| |''2g-1\5+2\5-3g = 1\5-g''
Line 951: Line 843:
| rowspan="4" |''full''
| rowspan="4" |''full''
| |''14\25 &lt; g &lt; 9\16''
| |''14\25 &lt; g &lt; 9\16''
| |''g = 449\800''
| |''g = 23\41, 32\57, 41\73''
| |''g = 23\41, 32\57, 41\73''
| |''9g-5+9-16g = 4-7g''
| |''9g-5+9-16g = 4-7g''
Line 957: Line 848:
| |''17L8s''
| |''17L8s''
| |''22\25 &lt; g &lt; 15\17''
| |''22\25 &lt; g &lt; 15\17''
| |''g = 749\850''
| |''g = 37\42, 52\59, 67\76''
| |''g = 37\42, 52\59, 67\76''
| |''8g-7+15-17g = 8-9g''
| |''8g-7+15-17g = 8-9g''
Line 963: Line 853:
| |''18L7s''
| |''18L7s''
| |''18\25 &lt; g &lt; 13\18''
| |''18\25 &lt; g &lt; 13\18''
| |''g = 649\900''
| |''g = 31\43, 44\61, 57\79''
| |''g = 31\43, 44\61, 57\79''
| |''7g-5+13-18g = 8-11g''
| |''7g-5+13-18g = 8-11g''
Line 969: Line 858:
| |''19L6s''
| |''19L6s''
| |''21\25 &lt; g &lt; 16\19''
| |''21\25 &lt; g &lt; 16\19''
| |''g = 799\950''
| |''g = 37\44, 53\63, 69\82''
| |''g = 37\44, 53\63, 69\82''
| |''6g-5+16-19g = 11-13g''
| |''6g-5+16-19g = 11-13g''
Line 976: Line 864:
|''"7/8"''
|''"7/8"''
| |''1\25 &lt; g &lt; 1\20''
| |''1\25 &lt; g &lt; 1\20''
| |''g = 9\200''
| |''g = 2\45, 3\65, 4\85''
| |''g = 2\45, 3\65, 4\85''
| |''g+1\5-4g = 1\5-3g''
| |''g+1\5-4g = 1\5-3g''
Line 983: Line 870:
| rowspan="3" |''full''
| rowspan="3" |''full''
| |''16\21 &lt; g &lt; 19\25''
| |''16\21 &lt; g &lt; 19\25''
| |''g = 799\1050''
| |''g = 35\46, 51\67, 71\88''
| |''g = 35\46, 51\67, 71\88''
| |''4g-3+16-21g = 13-17g''
| |''4g-3+16-21g = 13-17g''
Line 989: Line 875:
| |''22L3s''
| |''22L3s''
| |''17\25 &lt; g &lt; 15\22''
| |''17\25 &lt; g &lt; 15\22''
| |''g = 749\1100''
| |''g = 32\47, 47\69, 62\91''
| |''g = 32\47, 47\69, 62\91''
| |''3g-2+15-22g = 13-19g''
| |''3g-2+15-22g = 13-19g''
Line 995: Line 880:
| |''23L2s''
| |''23L2s''
| |''13\25 &lt; g &lt; 12\23''
| |''13\25 &lt; g &lt; 12\23''
| |''g = 599\1150''
| |''g = 25\48, 37\71, 49\94''
| |''g = 25\48, 37\71, 49\94''
| |''2g-1+11-23g = 10-21g''
| |''2g-1+11-23g = 10-21g''
Line 1,002: Line 886:
|''"half"''
|''"half"''
| |''1\25 &lt; g &lt; 1\24''
| |''1\25 &lt; g &lt; 1\24''
| |''g = 49\1200''
| |''g = 2\49, 3\73, 4\97''
| |''g = 2\49, 3\73, 4\97''
| |''g+1-24g = 1-23g''
| |''g+1-24g = 1-23g''
Line 1,012: Line 895:
!''Status''
!''Status''
! |''Generator range''
! |''Generator range''
! |<span style="background-color: #ffffff;">''Midpoint''</span>
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
! |''Large step+Small step''
Line 1,019: Line 901:
|''"half"''
|''"half"''
| |''28\29 &lt; g &lt; 1''
| |''28\29 &lt; g &lt; 1''
| |''g = 57\58''
| |'''''g = 29\30, 30\31, 31\32'''''
| |'''''g = 29\30, 30\31, 31\32'''''
| |''28g-27+1-g = 27g-26''
| |''28g-27+1-g = 27g-26''
Line 1,026: Line 907:
| rowspan="26" |''full''
| rowspan="26" |''full''
| |''14\29 &lt; g &lt; 1\2''
| |''14\29 &lt; g &lt; 1\2''
| |''g = 57\116''
| |'''''g = 15\31, 16\33, 17\35'''''
| |'''''g = 15\31, 16\33, 17\35'''''
| |''27g-13+1-2g = 25g-12''
| |''27g-13+1-2g = 25g-12''
Line 1,032: Line 912:
| |''3L26s''
| |''3L26s''
| |''19\29 &lt; g &lt; 2\3''
| |''19\29 &lt; g &lt; 2\3''
| |''g = 115\174''
| |'''''g = 21\32, 23\35''', 25\38''
| |'''''g = 21\32, 23\35''', 25\38''
| |''26g-17+2-3g = 23g-15''
| |''26g-17+2-3g = 23g-15''
Line 1,038: Line 917:
| |''4L25s''
| |''4L25s''
| |''7\29 &lt; g &lt; 1\4''
| |''7\29 &lt; g &lt; 1\4''
| |''g = 57\232''
| |''g = '''8\33,''' 9\37, 10\41''
| |''g = '''8\33,''' 9\37, 10\41''
| |''25g-6+1-4g = 21g-5''
| |''25g-6+1-4g = 21g-5''
Line 1,044: Line 922:
| |''5L24s''
| |''5L24s''
| |''23\29 &lt; g &lt; 4\5''
| |''23\29 &lt; g &lt; 4\5''
| |''g = 231\290''
| |''g = '''27\34''', 31\39, 35\44''
| |''g = '''27\34''', 31\39, 35\44''
| |''24g-19+4-5g = 19g-15''
| |''24g-19+4-5g = 19g-15''
Line 1,050: Line 927:
| |''6L23s''
| |''6L23s''
| |''24\29 &lt; g &lt; 5\6''
| |''24\29 &lt; g &lt; 5\6''
| |''g = 289\348''
| |''g = '''29\35''', 34\41, 39\47''
| |''g = '''29\35''', 34\41, 39\47''
| |''23g-19+5-6g = 17g-14''
| |''23g-19+5-6g = 17g-14''
Line 1,056: Line 932:
| |''7L22s''
| |''7L22s''
| |''4\29 &lt; g &lt; 1\7''
| |''4\29 &lt; g &lt; 1\7''
| |''g = 57\406''
| |''g = '''5\36''', 6\43, 7\50''
| |''g = '''5\36''', 6\43, 7\50''
| |''22g-3+1-7g = 15g-2''
| |''22g-3+1-7g = 15g-2''
Line 1,062: Line 937:
| |''8L21s''
| |''8L21s''
| |''18\29 &lt; g &lt; 5\8''
| |''18\29 &lt; g &lt; 5\8''
| |''g = 289\464''
| |''g = 23\37, 28\45, 33\53''
| |''g = 23\37, 28\45, 33\53''
| |<span style="line-height: 15.6000003814697px;">''21g-13+5-8g = 13g-8''</span>
| |<span style="line-height: 15.6000003814697px;">''21g-13+5-8g = 13g-8''</span>
Line 1,068: Line 942:
| |''9L20s''
| |''9L20s''
| |''16\29 &lt; g &lt; 5\9''
| |''16\29 &lt; g &lt; 5\9''
| |''g = 289\522''
| |''g = 21\38, 26\47, 31\56''
| |''g = 21\38, 26\47, 31\56''
| |''20g-11+5-9g = 11g-6''
| |''20g-11+5-9g = 11g-6''
Line 1,074: Line 947:
| |''10L19s''
| |''10L19s''
| |''26\29 &lt; g &lt; 9\10''
| |''26\29 &lt; g &lt; 9\10''
| |''g = 521\580''
| |''g = 35\39, 44\49, 53\59''
| |''g = 35\39, 44\49, 53\59''
| |''19g-17+9-10g = 9g-8''
| |''19g-17+9-10g = 9g-8''
Line 1,080: Line 952:
| |''11L18s''
| |''11L18s''
| |''21\29 &lt; g &lt; 8\11''
| |''21\29 &lt; g &lt; 8\11''
| |''g = 463\638''
| |''g = 29\40, 37\51, 45\62''
| |''g = 29\40, 37\51, 45\62''
| |''18g-13+8-11g = 7g-2''
| |''18g-13+8-11g = 7g-2''
Line 1,086: Line 957:
| |''12L17s''
| |''12L17s''
| |''12\29 &lt; g &lt; 5\12''
| |''12\29 &lt; g &lt; 5\12''
| |''g = 289\696''
| |''g = 17\41, 22\53, 27\65''
| |''g = 17\41, 22\53, 27\65''
| |''17g-7+5-12g = 5g-2''
| |''17g-7+5-12g = 5g-2''
Line 1,092: Line 962:
| |''13L16s''
| |''13L16s''
| |''20\29 &lt; g &lt; 9\13''
| |''20\29 &lt; g &lt; 9\13''
| |''g = 521\754''
| |''g = 29\42, 38\55, 47\68''
| |''g = 29\42, 38\55, 47\68''
| |''16g+11+9-13g = 3g-2''
| |''16g+11+9-13g = 3g-2''
Line 1,098: Line 967:
| |''14L15s''
| |''14L15s''
| |''2\29 &lt; g &lt; 1\14''
| |''2\29 &lt; g &lt; 1\14''
| |''g = 57\812''
| |''g = 3\43, 4\57, 5\71''
| |''g = 3\43, 4\57, 5\71''
| |''15g-1+1-14g = g''
| |''15g-1+1-14g = g''
Line 1,104: Line 972:
| |''15L14s''
| |''15L14s''
| |''27\29 &lt; g &lt; 14\15''
| |''27\29 &lt; g &lt; 14\15''
| |''g = 811\870''
| |''g = 41\44, 55\59, 69\74''
| |''g = 41\44, 55\59, 69\74''
| |''14g-13+14-15g = 1-g''
| |''14g-13+14-15g = 1-g''
Line 1,110: Line 977:
| |''16L13s''
| |''16L13s''
| |''9\29 &lt; g &lt; 5\16''
| |''9\29 &lt; g &lt; 5\16''
| |''g = 289\928''
| |''g = 14\45, 19\61, 24\77''
| |''g = 14\45, 19\61, 24\77''
| |''13g-4+5-16g = 1-3g''
| |''13g-4+5-16g = 1-3g''
Line 1,116: Line 982:
| |''17L12s''
| |''17L12s''
| |''17\29 &lt; g &lt; 10\17''
| |''17\29 &lt; g &lt; 10\17''
| |''g = 579\986''
| |''g = 27\46, 37\63, 47\80''
| |''g = 27\46, 37\63, 47\80''
| |''12g-5+7-17g = 2-5g''
| |''12g-5+7-17g = 2-5g''
Line 1,122: Line 987:
| |''18L11s''
| |''18L11s''
| |''8\29 &lt; g &lt; 5\18''
| |''8\29 &lt; g &lt; 5\18''
| |''g = 289\1044''
| |''g = 13\47, 18\65, 23\83''
| |''g = 13\47, 18\65, 23\83''
| |''11g-3+5-18g = 2-7g''
| |''11g-3+5-18g = 2-7g''
Line 1,128: Line 992:
| |''19L10s''
| |''19L10s''
| |''3\29 &lt; g &lt; 2\19''
| |''3\29 &lt; g &lt; 2\19''
| |''g = 115\1102''
| |''g = 5\48, 7\67, 9\86''
| |''g = 5\48, 7\67, 9\86''
| |''10g-1+2-19g = 1-9g''
| |''10g-1+2-19g = 1-9g''
Line 1,134: Line 997:
| |''20L9s''
| |''20L9s''
| |''13\29 &lt; g &lt; 9\20''
| |''13\29 &lt; g &lt; 9\20''
| |''g = 521\1160''
| |''g = 22\49, 31\69, 40\89''
| |''g = 22\49, 31\69, 40\89''
| |''9g-5+9-20g = 4-11g''
| |''9g-5+9-20g = 4-11g''
Line 1,140: Line 1,002:
| |''21L8s''
| |''21L8s''
| |''11\29 &lt; g &lt; 8\21''
| |''11\29 &lt; g &lt; 8\21''
| |''g = 463\1216''
| |''g = 19\50, 27\71, 35\92''
| |''g = 19\50, 27\71, 35\92''
| |''8g-3+8-21g = 5-13g''
| |''8g-3+8-21g = 5-13g''
Line 1,146: Line 1,007:
| |''22L7s''
| |''22L7s''
| |''25\29 &lt; g &lt; 19\22''
| |''25\29 &lt; g &lt; 19\22''
| |''g = 1001\1274''
| |''g = 44\51, 63\73, 82\95''
| |''g = 44\51, 63\73, 82\95''
| |''7g-6+9-22g = 3-16g''
| |''7g-6+9-22g = 3-16g''
Line 1,152: Line 1,012:
| |''23L6s''
| |''23L6s''
| |''5\29 &lt; g &lt; 4\23''
| |''5\29 &lt; g &lt; 4\23''
| |''g = 231\1332''
| |''g = 9\52, 13\75, 17\98''
| |''g = 9\52, 13\75, 17\98''
| |''6g-1+4-23g = 3-17g''
| |''6g-1+4-23g = 3-17g''
Line 1,158: Line 1,017:
| |''24L5s''
| |''24L5s''
| |''6\29 &lt; g &lt; 5\24''
| |''6\29 &lt; g &lt; 5\24''
| |''g = 289\1392''
| |''g = 11\53, 16\77, 21\101''
| |''g = 11\53, 16\77, 21\101''
| |''5g-9+5-24g = 4-19g''
| |''5g-9+5-24g = 4-19g''
Line 1,164: Line 1,022:
| |''25L4s''
| |''25L4s''
| |''22\29 &lt; g &lt; 19\25''
| |''22\29 &lt; g &lt; 19\25''
| |''g = 1001\1450''
| |''g = 41\54, 60\79, 79\104''
| |''g = 41\54, 60\79, 79\104''
| |''4g-3+19-25g = 16-21g''
| |''4g-3+19-25g = 16-21g''
Line 1,170: Line 1,027:
| |''26L3s''
| |''26L3s''
| |''10\29 &lt; g &lt; 9\26''
| |''10\29 &lt; g &lt; 9\26''
| |''g = 521\1508''
| |''g = 19\55, 28\81, 37\107''
| |''g = 19\55, 28\81, 37\107''
| |''3g-1+9-26g = 8-23g''
| |''3g-1+9-26g = 8-23g''
Line 1,176: Line 1,032:
| |''27L2s''
| |''27L2s''
| |''15\29 &lt; g &lt; 14\27''
| |''15\29 &lt; g &lt; 14\27''
| |''g = 811\1564''
| |''g = 29\56, 43\83, 57\110''
| |''g = 29\56, 43\83, 57\110''
| |''2g-1+17-27g = 16-25g''
| |''2g-1+17-27g = 16-25g''
Line 1,183: Line 1,038:
|''"half"''
|''"half"''
| |''1\29 &lt; g &lt; 1\28''
| |''1\29 &lt; g &lt; 1\28''
| |''g = 57\1622''
| |''g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113''
| |''g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113''
| |''g+1-28g = 1-27g''
| |''g+1-28g = 1-27g''
|}
|}
[[Category:Indian music]]
{{Todo| discuss title | cleanup }}

Latest revision as of 09:07, 29 August 2023

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. Most 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 inverse ekasruti shuddha dha:[~256/219, 273] is the schismatic tuning of this shruti
Ga shuddha ga 5/4 386 inverse "half"-status shuddha ga/"half"-status shuddha ga [384] is the schismatic tuning of this shruti
"half"-status shuddha ga 81/64 408 inverse "half"-status shuddha ga/shuddha ga [512/405; 406] is the schismatic tuning of this shruti
(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
(inverse ekasruti Ma) 40/27 680
Pa 3/2 702
komal dha komal dha 8/5 814 "half"-status shuddha ga/"half"-status shuddha ga [816] is the schismatic tuning of this shruti
ati komal dha 128/81 792 "half"-status shuddha ga/shuddha ga [405/256; 794] is the schismatic tuning of this shruti
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 ekasruti shuddha dha:[~219/128, 927] is the schismatic tuning of this shruti
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 25 or 26 or 29 (out of n) edo to simulate ragas

komal-ardha re (1): [250/243; 48]: 22, 23. 25, 26, 29

ekasruti komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~13/12; 138], [625/576; 141]: 25, 26

inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23, 29

inverse ati ati komal ga/Pa, komal re/komal re, inverse komal-ardha ni: [256/225; 224], [729/640; 226]: 22, 26

komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19, 25*, 29

ekasruti komal ga: [243/200; 338]: 25, 29

inverse inverse ati ati komal dha/inverse ati ati komal dha: [625/512; 344]: 25

inverse ekasruti komal dha, "half"-status shuddha re/"half"-status shuddha re [100/81; 365]; 23, 26, 29

inverse komal-ardha dha [162/125; 449]: 19, 29

(ati) ati komal re/shuddha ga, inverse komal re/tivratar Ma, inverse ekasruti Pa: [~13/10; 454], [320/243; 476]: 25, 29

inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23, 25

ati ati komal ga/ati ati komal ga: [~56/41; 548]: 22

inverse komal ga/komal ga; [25/18; 569]: 19

komal ga/komal ga; [36/25; 631]: 19

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, 25

inverse (ati) ati komal re/shuddha ga, komal re/tivratar Ma, ekasruti Pa: [~20/13; 746], [243/160; 724]: 25, 29

komal-ardha dha [125/81; 751]: 19

ekasruti komal dha, inverse "half"-status shuddha re/"half"-status shuddha re [81/50; 835]: 23, 26, 29

inverse ati ati komal dha/inverse ati ati komal dha: [1024/625; 856]

inverse ekasruti komal ga: [400/243; 862]: 25, 29

komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19, 25*, 29

ati ati komal ga/Pa, inverse komal re/komal re, komal-ardha ni: [225/128; 976], [1280/729; 974]: 22, 26

ekasruti komal ni, ekasruti Ma/ekasruti Ma: [729/400; 1040]: 22, 23

inverse ekasruti komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1067], [~24/13; 1062], [1152/625; 1059]: 26

inverse komal-ardha re (1): [243/125; 1152]: 22, 23, 26

Regular temperaments of the shrutis

Note:

  • generators in (bold) italics will generate a 19/23 (diatonic) or 22/25/26/29 tone (superdiatonic) set which is too weakly tonal for serious practice
  • all 23, 25 and 29 tone temperaments given in italics due to either not necessarily possessing "real" Ma/Pa or counting "half" status shrutis as full status, thus messing up what the 25 and 29 tone temperaments should technically be

Underlying full status shrutis

Excluding inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 18s "half" 18\19 < g < 1 g = 19\20, 20\21, 21\22 18g-17+1-g = 17g-16
2L 17s full 9\19 < g < 1\2 g = 10\21, 11\23, 12\25 17g-8+1-2g = 15g-7
3L 16s 6\19 < g < 1\3 g = 7\22, 8\25, 10\31 16g-5+1-3g = 13g-4
4L 15s 14\19 < g < 3\4 g = 17\23, 20\27, 23\31 15g-11+3-4g = 11g-8
5L 14s 15\19 < g < 4\5 g = 19\24, 23\29, 27\34 14g-11+4-5g = 9g-7
6L 13s 3\19 < g < 1\6 g = 4\25, 5\31, 6/37 13g-2+1-6g = 7g-1
7L 12s 8\19 < g < 3\7 g = 11\26, 14\33, 17\40 12g-5+3-7g = 5g-2
8L 11s 7\19 < g < 3\8 g = 10\27, 13\35, 16\43 11g-4+3-8g = 3g-1
9L 10s 2\19 < g < 1\9 g = 3\28, 4\37, 5\46 10g-1+1-9g = g
10L 9s 17\19 < g < 9\10 g = 26\29, 35\39, 44\49 9g-8+9-10g = 1-g
11L 8s 12\19 < g < 7\11 g = 19\30, 26\41, 33\52 8g-5+7-11g = 2-3g
12L 7s 11\19 < g < 7\12 g = 18\31, 25\43, 32\55 7g-4+7-12g = 3-5g
13L 6s 16\19 < g < 11\13 g = 27\32, 38\45, 49\58 6g-5+11-13g = 6-7g
14L 5s 4\19 < g < 3\14 g = 7\33, 10\47, 13\61 5g-1+3-14g = 2-9g
15L 4s 5\19 < g < 4\15 g = 9\34, 13\49, 17\64 4g-1+4-15g = 3-11g
16L 3s 13\19 < g < 11\16 g = 24\35, 35\51, 46\67 3g-2+11-16g = 9-13g
17L 2s 10\19 < g < 9\17 g = 19\36, 28\53, 37\70 2g-1+9-17g = 8-15g
18L 1s "half" 1\19 < g < 1\18 g = 2\37, 3\55, 4\73 g+1-18g = 1-17g

Including inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L22s "half" 22\23 < g < 1 g = 23\24, 24\25, 25\26 22g-21+1-g = 21g-20
2L21s full 11\23 < g < 1\2 g = 12\25, 13\27, 14\29 21g-10+1-2g = 19g-9
3L20s 15\23 < g < 2\3 g = 17\26, 19\29, 21\32 20g-13+1-3g = 17g-12
4L19s 17\23 < g < 3\4 g = 20\27, 23\31, 26\35 19g-14+3-4g = 15g-11
5L18s 9\23 < g < 2\5 g = 11\28, 13\33, 15\38 18g-7+2-5g = 13g-5
6L17s 19\23 < g < 5\6 g = 24\29, 29\35, 34\41 17g-15+1-6g = 11g-14
7L16s 13\23 < g < 4\7 g = 17\30, 21\37, 25\44 16g-9+4-7g = 9g-5
8L15s 20\23 < g < 7\8 g = 27\31, 34\39, 41\47 15g-13+7-8g = 7g-6
9L14s 5\23 < g < 2\9 g = 7\32, 9\41, 11\50 14g-7+2-9g = 5g-5
10L13s 16\23 < g < 7\10 g = 23\33, 30\43, 37\53 13g-9+7-10g = 3g-2
11L12s 2\23 < g < 1\11 g = 3\34, 4\45, 5\56 12g-1+1-11g = g
12L11s 21\23 < g < 11\12 g = 32\35, 43\47, 54\59 11g-10+11-12g = 1-g
13L10s 7\23 < g < 4\13 g = 11\36, 15\49, 19\62 10g-3+4-13g =1-3g
14L9s 18\23 < g < 11\14 g = 29\37, 40\51, 51\65 9g-7+11-14g = 4-5g
15L8s 3\23 < g < 2\15 g = 5\38, 7\53, 9\68 8g-1+2-15g = 1-7g
16L7s 10\23 < g < 7\16 g = 17\39, 24\55, 31\71 7g-3+7-16g = 4-9g
17L6s 4\23 < g < 3\17 g = 7\40, 10\57, 13\74 6g-1+3-17g = 2-11g
18L5s 14\23 < g < 11\18 g = 25\41, 36\59, 47\77 5g-4+11-18g = 7-13g
19L4s 6\23 < g < 5\19 g = 11\42, 16\61, 21\80 4g-1+5-19g = 4-15g
20L3s 8\23 < g < 7\20 g = 15\43, 22\63, 29\83 3g-1+13-20g = 12-17g
21L2s 12\23 < g < 11\21 g = 23\44, 34\65, 45\86 2g-1+11-21g = 10-19g
22L1s "half" 1\23 < g < 1\22 g = 2\45, 3\67, 4\89 g+1-22g = 1-221

Quoted

Excluding "half" status shrutis

Excluding inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 21s "half" 21\22 < g < 1 g = 22\23, 23\24, 24\25 21g-20+1-g = 20g-19
2L 20s "3/4" 10\22 < g < 1\2 g = 11\24, 12\26, 13\28 10g-9\2+1\2-g = 9g-4
3L 19s full 7\22 < g < 1\3 g = 8\25, 9\28, 10\31 19g-6+1-3g = 16g-5
4L 18s "3/4" 5\22 < g < 1\4 g = 6\26, 7\30, 8\34 9g-2+1\2-2g = 7g-3\2
5L 17s full 13\22 < g < 3\5 g = 16\27, 19\32, 22\37 17g-10+3-5g = 12g-7
6L 16s "3/4" 7\22 < g < 2\6 g = 9\28, 11\34, 13\40 8g-5\2+1-3g = 5g-2
7L 15s full 3\22 < g < 1\7 g = 4\29, 5\36, 6\43 15g-2+1-7g = 8g-1
8L 14s "3/4" 8\22 < g < 3\8 g = 11\30, 14\38, 17\46 7g-5\2+3\2-4g = 3g-2
9L 13s full 17\22 < g < 7\9 g = 24\31, 31\40, 38\49 13g-10+7-9g = 4g-3
10L 12s "3/4" 2\22 < g < 1\10 g = 3\32, 4\42, 5\52 6g-1\2+1\2-5g = g
11L 11s "7/8" 1\22 < g < 1\11 g = 2\33, 3\44, 4\55 g + 1\11-g = 1\11
12L 10s "3/4" 9\22 < g < 5\12 g = 14\34, 19\46, 24\58 5g-2+5\2-6g = 1\2-g
13L 9s full 5\22 < g < 3\13 g = 8\35, 11\48, 14\61 9g-2+3-13g = 1-4g
14L 8s "3/4" 3\22 < g < 2\14 g = 5\36, 7\50, 9\64 4g-1\2+1-7g = 1\2-3g
15L 7s full 19\22 < g < 13\15 g = 32\37, 45\52, 58\67 7g-6+13-15g = 7-8g
16L 6s "3/4" 4\22 < g < 3\16 g = 7\38, 10\54, 13\70 3g-1\2+3\2-8g = 1-5g
17L 5s full 9\22 < g < 7\17 g = 16\39, 23\56, 30\73 5g-2+7-17g = 5-12g
18L 4s "3/4" 6\22 < g < 5\18 g = 11\40, 16\58, 21\76 2g-1\2+5\2-9g = 2-7g
19L 3s full 15\22 < g < 13\19 g = 28\41, 41\60, 54\79 3g-2+13-19g = 11-16g
20L 2s "3/4" 1\22 < g < 1\20 g = 2\42, 3\62, 4\72 g+1\2-10g = 1\2-9g
21L 1s "half" 1\22 < g < 1\21 g = 2\43, 3\64, 4\85 g+1-21g = 1-20g

Including inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L25s "half" 25\26 < g < 1 g = 26\27, 27\28, 28\29 25g-24+1-g = 24g-23
2L24s "3/4" 12\26 < g < 1\2 g = 13\28, 14\30, 15\32 12g-11\2+1\2-g = 11g-5
3L23s full 17\26 < g < 2\3 g = 19\29, 21\32, 23\35 23g-15+2-3g = 20g-13
4L22s "3/4" 6\26 < g < 1\4 g = 7\30, 8\34, 9\38 11g-5\2+1\2-2g = 9g-2
5L21s full 5\26 < g < 1\5 g = 6\31, 7\36, 8\41 21g-4+1-5g = 16g-3
6L20s "3/4" 4\26 < g < 1\6 g = 5\32, 6\38, 7\44 10g-3\2+1\2-3g = 7g-1
7L19s full 11\26 < g < 3\7 g = 14\33, 17\40, 20\47 19g-8+3-7g = 12g-5
8L18s "3/4" 3\26 < g < 1\8 g = 4\34, 5\42, 6\50 9g-1+1\2-4g = 5g-1\2
9L17s full 23\26 < g < 8\9 g = 31\35, 39\44, 47\53 17g-15+8-9g = 8g-7
10L16s "3/4" 5\26 < g < 2\10 g = 7\36, 9\46, 11\56 8g-3\2+1-5g = 3g-1\2
11L15s full 7\26 < g < 3\11 g = 10\37, 13\48, 16\59 15g-4+3-11g = 4g-1
12L14s "3/4" 2\26 < g < 1\12 g = 3\38, 4\50, 5\62 7g-1\2+1\2-6g = g
13L13s "7/8" 1\26 < g < 1\13 g = 2\39, 3\52, 4\65 g+1\13-g = 1\13
14L12s "3/4" 11\26 < g < 6\14 g = 17\40, 23\54, 29\68 6g-5\2+3-7g = 1\2-g
15L11s full 19\26 < g < 11\15 g = 30\41, 41\56, 52\71 11g-8+11-15g = 3-4g
16L10s "3/4" 8\26 < g < 5\16 g = 13\42, 18\58, 23\74 5g-3\2+5\2-8g = 1-3g
17L9s full 3\26 < g < 2\17 g = 5\43, 7\60, 9\77 9g-1+2-17g = 1-8g
18L8s "3/4" 10\26 < g < 7\18 g = 17\44, 24\62, 31\80 4g-7\2+7-9g = 7\2-5g
19L7s full 15\26 < g < 11\19 g = 26\45, 37\64, 48\83 7g-4+11-19g = 7-12g
20L6s "3/4" 9\26 < g < 7\20 g = 16\46, 23\66, 30\86 3g-1+7\2-10g = 5\2-7g
21L5s full 21\26 < g < 17\21 g = 38\47, 55\68, 72\89 5g-4+16-21g = 12-16g
22L4s "3/4" 7\26 < g < 6\22 g = 13\48, 19\70, 25\92 2g-1\2+3-11g = 5\2-9g
23L3s full 9\26 < g < 8\23 g = 17\49, 25\72, 33/95 3g-1+8-23g = 7-20g
24L2s "3/4" 1\26 < g < 1\24 g = 2\50, 3\74, 4\98 g+1\2-12g = 1\2-11g
25L1s "half" 1\26 < g < 1\25 g = 2\51, 3\76, 4\101 g+1-25g = 1-24g

Including "half" status shrutis

Excluding inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L24s "half" 24\25 < g < 1 g = 25\26, 26\27, 27\28 24g-23+1-g = 23g-22
2L23s full 12\25 < g < 1\2 g = 13\27, 14\29, 15\31 23g-11+1-2g = 21g-10
3L22s 8\25 < g < 1\3 g = 9\28, 10\31, 11\34 22g-7+1-3g = 19g-6
4L21s 6\25 < g < 1\4 g = 7\29, 8\33, 9\37 21g-5+1-4g = 17g-4
5L20s "7/8" 4\25 < g < 1\5 g = 5\30, 6\35, 7\40 4g-3\5+1\5-g = 3g-2\5
6L19s full 4\25 < g < 1\6 g = 5\31, 6\37, 7\43 19g-3+1-6g = 13g-2
7L18s 7\25 < g < 2\7 g = 9\32, 11\39, 13\46 18g-5+2-7g = 11g-3
8L17s 3\25 < g < 1\8 g = 4\33, 5\41, 6\47 17g-2+1-8g = 9g-1
9L16s 11\25 < g < 4\9 g = 15\34, 19\43, 23\52 16g-7+4-9g = 3-7g
10L15s "7/8" 2\25 < g < 1\10 g = 3\35, 4\45, 5\55 3g-1\5+1\5-2g = g
11L14s full 9\25 < g < 4\11 g = 13\36, 17\47, 21\58 14g-5+4-11g = 3g-1
12L13s 2\25 < g < 1\12 g = 3\37, 4\49, 5\61 13g-1+1-12g = g
13L12s 23\25 < g < 12\13 g = 35\38, 47\51, 59\64 12g-11+12-13g = 1-g
14L11s 16\25 < g < 9\14 g = 25\39, 34\53, 43\67 11g-7+9-14g = 2-3g
15L10s "7/8" 3\25 < g < 2\15 g = 5\40, 7\55, 9\70 2g-1\5+2\5-3g = 1\5-g
16L9s full 14\25 < g < 9\16 g = 23\41, 32\57, 41\73 9g-5+9-16g = 4-7g
17L8s 22\25 < g < 15\17 g = 37\42, 52\59, 67\76 8g-7+15-17g = 8-9g
18L7s 18\25 < g < 13\18 g = 31\43, 44\61, 57\79 7g-5+13-18g = 8-11g
19L6s 21\25 < g < 16\19 g = 37\44, 53\63, 69\82 6g-5+16-19g = 11-13g
20L5s "7/8" 1\25 < g < 1\20 g = 2\45, 3\65, 4\85 g+1\5-4g = 1\5-3g
21L4s full 16\21 < g < 19\25 g = 35\46, 51\67, 71\88 4g-3+16-21g = 13-17g
22L3s 17\25 < g < 15\22 g = 32\47, 47\69, 62\91 3g-2+15-22g = 13-19g
23L2s 13\25 < g < 12\23 g = 25\48, 37\71, 49\94 2g-1+11-23g = 10-21g
24L1s "half" 1\25 < g < 1\24 g = 2\49, 3\73, 4\97 g+1-24g = 1-23g

Including inverses

Large-small numbers Status Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L28s "half" 28\29 < g < 1 g = 29\30, 30\31, 31\32 28g-27+1-g = 27g-26
2L27s full 14\29 < g < 1\2 g = 15\31, 16\33, 17\35 27g-13+1-2g = 25g-12
3L26s 19\29 < g < 2\3 g = 21\32, 23\35, 25\38 26g-17+2-3g = 23g-15
4L25s 7\29 < g < 1\4 g = 8\33, 9\37, 10\41 25g-6+1-4g = 21g-5
5L24s 23\29 < g < 4\5 g = 27\34, 31\39, 35\44 24g-19+4-5g = 19g-15
6L23s 24\29 < g < 5\6 g = 29\35, 34\41, 39\47 23g-19+5-6g = 17g-14
7L22s 4\29 < g < 1\7 g = 5\36, 6\43, 7\50 22g-3+1-7g = 15g-2
8L21s 18\29 < g < 5\8 g = 23\37, 28\45, 33\53 21g-13+5-8g = 13g-8
9L20s 16\29 < g < 5\9 g = 21\38, 26\47, 31\56 20g-11+5-9g = 11g-6
10L19s 26\29 < g < 9\10 g = 35\39, 44\49, 53\59 19g-17+9-10g = 9g-8
11L18s 21\29 < g < 8\11 g = 29\40, 37\51, 45\62 18g-13+8-11g = 7g-2
12L17s 12\29 < g < 5\12 g = 17\41, 22\53, 27\65 17g-7+5-12g = 5g-2
13L16s 20\29 < g < 9\13 g = 29\42, 38\55, 47\68 16g+11+9-13g = 3g-2
14L15s 2\29 < g < 1\14 g = 3\43, 4\57, 5\71 15g-1+1-14g = g
15L14s 27\29 < g < 14\15 g = 41\44, 55\59, 69\74 14g-13+14-15g = 1-g
16L13s 9\29 < g < 5\16 g = 14\45, 19\61, 24\77 13g-4+5-16g = 1-3g
17L12s 17\29 < g < 10\17 g = 27\46, 37\63, 47\80 12g-5+7-17g = 2-5g
18L11s 8\29 < g < 5\18 g = 13\47, 18\65, 23\83 11g-3+5-18g = 2-7g
19L10s 3\29 < g < 2\19 g = 5\48, 7\67, 9\86 10g-1+2-19g = 1-9g
20L9s 13\29 < g < 9\20 g = 22\49, 31\69, 40\89 9g-5+9-20g = 4-11g
21L8s 11\29 < g < 8\21 g = 19\50, 27\71, 35\92 8g-3+8-21g = 5-13g
22L7s 25\29 < g < 19\22 g = 44\51, 63\73, 82\95 7g-6+9-22g = 3-16g
23L6s 5\29 < g < 4\23 g = 9\52, 13\75, 17\98 6g-1+4-23g = 3-17g
24L5s 6\29 < g < 5\24 g = 11\53, 16\77, 21\101 5g-9+5-24g = 4-19g
25L4s 22\29 < g < 19\25 g = 41\54, 60\79, 79\104 4g-3+19-25g = 16-21g
26L3s 10\29 < g < 9\26 g = 19\55, 28\81, 37\107 3g-1+9-26g = 8-23g
27L2s 15\29 < g < 14\27 g = 29\56, 43\83, 57\110 2g-1+17-27g = 16-25g
28L1s "half" 1\29 < g < 1\28 g = 2\57, 3\85, 4\113 g+1-28g = 1-27g
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