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[http://launch.groups.yahoo.com/group/tuning/message/72704 Original article] by ma1937, on the Yahoo tuning forum, is quoted here.
{{Wikipedia|Shruti (music)}}
In [[Indian music]], the '''shruti''' or '''śruti''' is the smallest interval that the human ear can detect and a singer or musical instrument can produce.


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."</blockquote>Ali Akbar Khan
== List of shrutis ==
:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#72704 Original article] by Marc Savage (ma1937), on the Yahoo tuning forum, is quoted here:</tt>''


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.


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.
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:
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:
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 63: Line 65:
|75/64
|75/64
|274
|274
|
|inverse ekasruti shuddha dha:[~256/219, 273] is the schismatic tuning of this shruti
|-
|-
| rowspan="2" |Ga
| rowspan="2" |Ga
Line 69: Line 71:
|5/4
|5/4
|386
|386
|
|inverse "half"-status shuddha ga/"half"-status shuddha ga [384] is the schismatic tuning of this shruti
|-
|-
|"half"-status shuddha ga
|"half"-status shuddha ga
|81/64
|81/64
|408
|408
|
|inverse "half"-status shuddha ga/shuddha ga [512/405; 406] is the schismatic tuning of this shruti
|-
|-
| colspan="2" |(inverse ati ati komal dha)
| colspan="2" |(inverse ati ati komal dha)
Line 100: Line 102:
|729/512
|729/512
|612
|612
|-
| colspan="2" |(inverse ekasruti Ma)
|40/27
|680
|
|-
|-
| colspan="2" |Pa
| colspan="2" |Pa
|3/2
|3/2
|702
|702
|
|-
| colspan="2" |(inverse ekasruti Ma)
|40/27
|680
|
|
|-
|-
Line 115: Line 117:
|8/5
|8/5
|814
|814
|
|"half"-status shuddha ga/"half"-status shuddha ga [816] is the schismatic tuning of this shruti
|-
|-
|ati komal dha
|ati komal dha
|128/81
|128/81
|792
|792
|
|"half"-status shuddha ga/shuddha ga [405/256; 794] is the schismatic tuning of this shruti
|-
|-
|ati ati komal dha
|ati ati komal dha
Line 139: Line 141:
|128/75
|128/75
|926
|926
|
|ekasruti shuddha dha:[~219/128, 927] is the schismatic tuning of this shruti
|-
|-
| rowspan="2" |komal ni
| rowspan="2" |komal ni
Line 166: Line 168:
|
|
|}
|}
{{inaccessible}}
{{todo|inline=1|cleanup|review heading structure}}
'''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


'''Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 26 (out of n) edo to simulate ragas'''
inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23, 29


komal-ardha re (1): [250/243; 48]: 22, 23, 26  
inverse ati ati komal ga/Pa, komal re/komal re, inverse komal-ardha ni: [256/225; 224], [729/640; 226]: 22, 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
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19, 25*, 29


inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22, 26
ekasruti komal ga: [243/200; 338]: 25, 29


inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23
inverse inverse ati ati komal dha/inverse ati ati komal dha: [625/512; 344]: 25


komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19
inverse ekasruti komal dha, "half"-status shuddha re/"half"-status shuddha re [100/81; 365]; 23, 26, 29


inverse komal re/tivratar Ma [320/243; 476]: 23
inverse komal-ardha dha [162/125; 449]: 19, 29


inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23
(ati) ati komal re/shuddha ga, inverse komal re/tivratar Ma, inverse ekasruti Pa: [~13/10; 454], [320/243; 476]: 25, 29


komal ga/komal ga; [36/25; 631]: 19
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
inverse komal ga/komal ga; [25/18; 569]: 19


ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22
komal ga/komal ga; [36/25; 631]: 19


inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 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
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


komal re/tivratar Ma [243/160; 724]: 22, 23
inverse ati ati komal dha/inverse ati ati komal dha: [1024/625; 856]


komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19
inverse ekasruti komal ga: [400/243; 862]: 25, 29


ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22
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
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 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
inverse komal-ardha re (1): [243/125; 1152]: 22, 23, 26


==Regular temperaments of the full-status shrutis==
==Regular temperaments of the shrutis==
'''Note: generators in italics will generate a 19 (diatonic)''' '''or 22 tone (superdiatonic) set which is too weakly tonal for serious practice'''
'''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=
=Underlying full status shrutis=
Excluding inverses
Excluding inverses
{| class="wikitable"
{| class="wikitable"
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! | 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 222: Line 243:
| | "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 229: Line 249:
| 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 235: Line 254:
| | [[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 241: Line 259:
| | [[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 247: Line 264:
| | [[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 253: Line 269:
| | [[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 259: Line 274:
| | [[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 265: Line 279:
| | [[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 271: Line 284:
| | [[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 277: Line 289:
| | [[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 283: Line 294:
| | [[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 289: Line 299:
| | [[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 295: Line 304:
| | [[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 301: Line 309:
| | [[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 307: Line 314:
| | [[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 313: Line 319:
| | [[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 319: Line 324:
| | [[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 326: Line 330:
| | "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
|}
|}


Including inverses
''Including inverses''
{| class="wikitable"
{| class="wikitable"
|-
|-
! |Large-small numbers
! |''Large-small numbers''
!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
|-
|-
| |1L22s
| |''1L22s''
|"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
|-
|-
| |2L21s
| |''2L21s''
| 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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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>
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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>
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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>
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |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
|-
|-
| |22L1s
| |''22L1s''
|"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
|}
|}
=Quoted=
=Quoted=
=== Excluding "half" status shrutis ===
Excluding inverses
Excluding inverses
{| class="wikitable"
{| class="wikitable"
Line 483: Line 465:
! | 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 490: Line 471:
| | "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 497: Line 477:
| | "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 504: Line 483:
| | 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 511: Line 489:
| | "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 518: Line 495:
| | 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 525: Line 501:
| | "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 532: Line 507:
| | 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 539: Line 513:
| | "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 546: Line 519:
| | 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 553: Line 525:
| | "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 560: Line 531:
| |"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 567: Line 537:
| | "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 574: Line 543:
| | 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 581: Line 549:
| | "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 588: Line 555:
| | 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 595: Line 561:
| | "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 602: Line 567:
| | 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 609: Line 573:
| | "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 616: Line 579:
| | 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 623: Line 585:
| | "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 630: Line 591:
| | "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 640: Line 600:
!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 647: Line 606:
|"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 654: Line 612:
|"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 661: Line 618:
|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 668: Line 624:
|"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 675: Line 630:
|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 682: Line 636:
|"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 689: Line 642:
|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 696: Line 648:
|"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 703: Line 654:
|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 710: Line 660:
|"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 717: Line 666:
|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 724: Line 672:
|"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 731: Line 678:
|"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 738: Line 684:
|"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 745: Line 690:
|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 752: Line 696:
|"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 759: Line 702:
|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 766: Line 708:
|"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 773: Line 714:
|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 780: Line 720:
|"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 787: Line 726:
|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 794: Line 732:
|"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 801: Line 738:
|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 808: Line 744:
|"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 815: Line 750:
|"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
|}
|}
=== ''Including "half" status shrutis'' ===
''Excluding inverses''
{| class="wikitable"
|-
! |''Large-small numbers''
!''Status''
! |''Generator range''
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
|-
| |''1L24s''
|''"half"''
| |''24\25 &lt; g &lt; 1''
| |'''''g = 25\26, 26\27, 27\28'''''
| |''24g-23+1-g = 23g-22''
|-
| |''2L23s''
| rowspan="3" |''full''
| |''12\25 &lt; g &lt; 1\2''
| |'''''g = 13\27, 14\29, 15\31'''''
| |''23g-11+1-2g = 21g-10''
|-
| |''3L22s''
| |''8\25 &lt; g &lt; 1\3''
| |'''''g = 9\28, 10\31,''''' ''11\34''
| |''22g-7+1-3g = 19g-6''
|-
| |''4L21s''
| |''6\25 &lt; g &lt; 1\4''
| |'''''g = 7\29''', 8\33, 9\37''
| |''21g-5+1-4g = 17g-4''
|-
| |''5L20s''
|''"7/8"''
| |''4\25 &lt; g &lt; 1\5''
| |'''''g = 5\30,''' 6\35, 7\40''
| |''4g-3\5+1\5-g = 3g-2\5''
|-
| |''6L19s''
| rowspan="4" |''full''
| |''4\25 &lt; g &lt; 1\6''
| |'''''g = 5\31,''''' ''6\37, 7\43''
| |''19g-3+1-6g = 13g-2''
|-
| |''7L18s''
| |''7\25 &lt; g &lt; 2\7''
| |''g = 9\32, 11\39, 13\46''
| |''18g-5+2-7g = 11g-3''
|-
| |''8L17s''
| |''3\25 &lt; g &lt; 1\8''
| |''g = 4\33, 5\41, 6\47''
| |<span style="line-height: 15.6000003814697px;">''17g-2+1-8g = 9g-1''</span>
|-
| |''9L16s''
| |''11\25 &lt; g &lt; 4\9''
| |''g = 15\34, 19\43, 23\52''
| |''16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>''
|-
| |''10L15s''
|''"7/8"''
| |''2\25 &lt; g &lt; 1\10''
| |''g = 3\35, 4\45, 5\55''
| |''3g-1\5+1\5-2g = g''
|-
| |''11L14s''
| rowspan="4" |''full''
| |''9\25 &lt; g &lt; 4\11''
| |''g = 13\36, 17\47, 21\58''
| |''14g-5+4-11g = 3g-1''
|-
| |''12L13s''
| |''2\25 &lt; g &lt; 1\12''
| |''g = 3\37, 4\49, 5\61''
| |''13g-1+1-12g = g''
|-
| |''13L12s''
| |''23\25 &lt; g &lt; 12\13''
| |''g = 35\38, 47\51, 59\64''
| |''12g-11+12-13g = 1-g''
|-
| |''14L11s''
| |''16\25 &lt; g &lt; 9\14''
| |''g = 25\39, 34\53, 43\67''
| |''11g-7+9-14g = 2-3g''
|-
| |''15L10s''
|''"7/8"''
| |''3\25 &lt; g &lt; 2\15''
| |''g = 5\40, 7\55, 9\70''
| |''2g-1\5+2\5-3g = 1\5-g''
|-
| |''16L9s''
| rowspan="4" |''full''
| |''14\25 &lt; g &lt; 9\16''
| |''g = 23\41, 32\57, 41\73''
| |''9g-5+9-16g = 4-7g''
|-
| |''17L8s''
| |''22\25 &lt; g &lt; 15\17''
| |''g = 37\42, 52\59, 67\76''
| |''8g-7+15-17g = 8-9g''
|-
| |''18L7s''
| |''18\25 &lt; g &lt; 13\18''
| |''g = 31\43, 44\61, 57\79''
| |''7g-5+13-18g = 8-11g''
|-
| |''19L6s''
| |''21\25 &lt; g &lt; 16\19''
| |''g = 37\44, 53\63, 69\82''
| |''6g-5+16-19g = 11-13g''
|-
| |''20L5s''
|''"7/8"''
| |''1\25 &lt; g &lt; 1\20''
| |''g = 2\45, 3\65, 4\85''
| |''g+1\5-4g = 1\5-3g''
|-
| |''21L4s''
| rowspan="3" |''full''
| |''16\21 &lt; g &lt; 19\25''
| |''g = 35\46, 51\67, 71\88''
| |''4g-3+16-21g = 13-17g''
|-
| |''22L3s''
| |''17\25 &lt; g &lt; 15\22''
| |''g = 32\47, 47\69, 62\91''
| |''3g-2+15-22g = 13-19g''
|-
| |''23L2s''
| |''13\25 &lt; g &lt; 12\23''
| |''g = 25\48, 37\71, 49\94''
| |''2g-1+11-23g = 10-21g''
|-
| |''24L1s''
|''"half"''
| |''1\25 &lt; g &lt; 1\24''
| |''g = 2\49, 3\73, 4\97''
| |''g+1-24g = 1-23g''
|}
''Including inverses''
{| class="wikitable"
|-
! |''Large-small numbers''
!''Status''
! |''Generator range''
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |''Large step+Small step''
|-
| |''1L28s''
|''"half"''
| |''28\29 &lt; g &lt; 1''
| |'''''g = 29\30, 30\31, 31\32'''''
| |''28g-27+1-g = 27g-26''
|-
| |''2L27s''
| rowspan="26" |''full''
| |''14\29 &lt; g &lt; 1\2''
| |'''''g = 15\31, 16\33, 17\35'''''
| |''27g-13+1-2g = 25g-12''
|-
| |''3L26s''
| |''19\29 &lt; g &lt; 2\3''
| |'''''g = 21\32, 23\35''', 25\38''
| |''26g-17+2-3g = 23g-15''
|-
| |''4L25s''
| |''7\29 &lt; g &lt; 1\4''
| |''g = '''8\33,''' 9\37, 10\41''
| |''25g-6+1-4g = 21g-5''
|-
| |''5L24s''
| |''23\29 &lt; g &lt; 4\5''
| |''g = '''27\34''', 31\39, 35\44''
| |''24g-19+4-5g = 19g-15''
|-
| |''6L23s''
| |''24\29 &lt; g &lt; 5\6''
| |''g = '''29\35''', 34\41, 39\47''
| |''23g-19+5-6g = 17g-14''
|-
| |''7L22s''
| |''4\29 &lt; g &lt; 1\7''
| |''g = '''5\36''', 6\43, 7\50''
| |''22g-3+1-7g = 15g-2''
|-
| |''8L21s''
| |''18\29 &lt; g &lt; 5\8''
| |''g = 23\37, 28\45, 33\53''
| |<span style="line-height: 15.6000003814697px;">''21g-13+5-8g = 13g-8''</span>
|-
| |''9L20s''
| |''16\29 &lt; g &lt; 5\9''
| |''g = 21\38, 26\47, 31\56''
| |''20g-11+5-9g = 11g-6''
|-
| |''10L19s''
| |''26\29 &lt; g &lt; 9\10''
| |''g = 35\39, 44\49, 53\59''
| |''19g-17+9-10g = 9g-8''
|-
| |''11L18s''
| |''21\29 &lt; g &lt; 8\11''
| |''g = 29\40, 37\51, 45\62''
| |''18g-13+8-11g = 7g-2''
|-
| |''12L17s''
| |''12\29 &lt; g &lt; 5\12''
| |''g = 17\41, 22\53, 27\65''
| |''17g-7+5-12g = 5g-2''
|-
| |''13L16s''
| |''20\29 &lt; g &lt; 9\13''
| |''g = 29\42, 38\55, 47\68''
| |''16g+11+9-13g = 3g-2''
|-
| |''14L15s''
| |''2\29 &lt; g &lt; 1\14''
| |''g = 3\43, 4\57, 5\71''
| |''15g-1+1-14g = g''
|-
| |''15L14s''
| |''27\29 &lt; g &lt; 14\15''
| |''g = 41\44, 55\59, 69\74''
| |''14g-13+14-15g = 1-g''
|-
| |''16L13s''
| |''9\29 &lt; g &lt; 5\16''
| |''g = 14\45, 19\61, 24\77''
| |''13g-4+5-16g = 1-3g''
|-
| |''17L12s''
| |''17\29 &lt; g &lt; 10\17''
| |''g = 27\46, 37\63, 47\80''
| |''12g-5+7-17g = 2-5g''
|-
| |''18L11s''
| |''8\29 &lt; g &lt; 5\18''
| |''g = 13\47, 18\65, 23\83''
| |''11g-3+5-18g = 2-7g''
|-
| |''19L10s''
| |''3\29 &lt; g &lt; 2\19''
| |''g = 5\48, 7\67, 9\86''
| |''10g-1+2-19g = 1-9g''
|-
| |''20L9s''
| |''13\29 &lt; g &lt; 9\20''
| |''g = 22\49, 31\69, 40\89''
| |''9g-5+9-20g = 4-11g''
|-
| |''21L8s''
| |''11\29 &lt; g &lt; 8\21''
| |''g = 19\50, 27\71, 35\92''
| |''8g-3+8-21g = 5-13g''
|-
| |''22L7s''
| |''25\29 &lt; g &lt; 19\22''
| |''g = 44\51, 63\73, 82\95''
| |''7g-6+9-22g = 3-16g''
|-
| |''23L6s''
| |''5\29 &lt; g &lt; 4\23''
| |''g = 9\52, 13\75, 17\98''
| |''6g-1+4-23g = 3-17g''
|-
| |''24L5s''
| |''6\29 &lt; g &lt; 5\24''
| |''g = 11\53, 16\77, 21\101''
| |''5g-9+5-24g = 4-19g''
|-
| |''25L4s''
| |''22\29 &lt; g &lt; 19\25''
| |''g = 41\54, 60\79, 79\104''
| |''4g-3+19-25g = 16-21g''
|-
| |''26L3s''
| |''10\29 &lt; g &lt; 9\26''
| |''g = 19\55, 28\81, 37\107''
| |''3g-1+9-26g = 8-23g''
|-
| |''27L2s''
| |''15\29 &lt; g &lt; 14\27''
| |''g = 29\56, 43\83, 57\110''
| |''2g-1+17-27g = 16-25g''
|-
| |''28L1s''
|''"half"''
| |''1\29 &lt; g &lt; 1\28''
| |''g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113''
| |''g+1-28g = 1-27g''
|}
[[Category:Indian music]]
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