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A shruti list: Difference between revisions

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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.
:''<tt>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_63593.html#72704 Original article] by ma1937, on the Yahoo tuning forum, is quoted here:</tt>''


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
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.
 
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 61:
|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 67:
|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 98:
|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 113:
|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 137:
|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
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|}
|}


'''Secondary functions and "artifact shrutis" introduced by using 19 or 22 or 23 or 26 (out of n) edo to simulate ragas'''
'''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


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


komal re/tivratar Ma [243/160; 724]: 22, 23
inverse (ati) ati komal re/shuddha ga, komal re/tivratar Ma, ekasruti Pa: [~20/13; 746], [243/160; 724]: 25, 29


komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19
komal-ardha dha [125/81; 751]: 19


ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22
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
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"
Line 215: 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 222: 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 229: 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 235: 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 241: 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 247: 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 253: 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 259: 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 265: 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 271: 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 277: 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 283: 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 289: 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 295: 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 301: 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 307: 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 313: 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 319: 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 326: 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
|}
|}


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 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 490: 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 497: 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 504: 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 511: 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 518: 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 525: 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 532: 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 539: 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 546: 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 553: 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 560: 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 567: 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 574: 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 581: 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 588: 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 595: 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 602: 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 609: 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 616: 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 623: 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 630: 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 640: 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 647: 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 654: 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 661: 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 668: 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 675: 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 682: 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 689: 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 696: 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 703: 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 710: 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 717: 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 724: 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 731: 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 738: 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 745: 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 752: 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 759: 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 766: 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 773: 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 780: 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 787: 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 794: 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 801: 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 808: 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 815: 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
|}
|}
=== ''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]]
{{Todo| discuss title | cleanup }}
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