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


komal-ardha re (1): [250/243; 48]: 22, 23, 26
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19, 25*, 29


ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 133], [~64/59; 138], [625/576; 141]: 26
ekasruti komal ga: [243/200; 338]: 25, 29


inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22, 26
inverse inverse ati ati komal dha/inverse ati ati komal dha: [625/512; 344]: 25


inverse ekasruti komal ni, inverse ekasruti Ma/ekasruti Ma: [800/729; 160]: 22, 23
inverse ekasruti komal dha, "half"-status shuddha re/"half"-status shuddha re [100/81; 365]; 23, 26, 29


komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19
inverse komal-ardha dha [162/125; 449]: 19, 29


inverse komal re/tivratar Ma [320/243; 476]: 23
(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
inverse ati ati komal re/tivra(tar) Ma [512/375, 539; ~82/61, 518]: 22, 23, 25


komal ga/komal ga; [36/25; 631]: 19
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
 
inverse ati ati komal dha/inverse ati ati komal dha: [1024/625; 856]


komal re/tivratar Ma [243/160; 724]: 22, 23
inverse ekasruti komal ga: [400/243; 862]: 25, 29


komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19
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: [225/128; 976]: 22
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''
! |Generator range
!''Status''
! |<span style="background-color: #ffffff;">Midpoint</span>
! |''Generator range''
! |Boundaries of propriety, maximum expressiveness, diatonicity
! |''Boundaries of propriety, maximum expressiveness, diatonicity''
! |Large step+Small step
! |''Large step+Small step''
|-
|-
| |1L22s
| |''1L22s''
| |<span style="line-height: 15.6000003814697px;">22\23 &lt; g &lt; 1</span>
|''"half"''
| |g = 45\46
| |<span style="line-height: 15.6000003814697px;">''22\23 &lt; g &lt; 1''</span>
| |''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''
| |11\23 &lt; g &lt; 1\2
| rowspan="20" |''full''
| |g = 45\92
| |''11\23 &lt; g &lt; 1\2''
| |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''
| |1\23 &lt; g &lt; 1\22
|''"half"''
| |g = 45\1012
| |''1\23 &lt; g &lt; 1\22''
| |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 479: 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 486: 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 493: 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 500: 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 507: 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 514: 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 521: 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 528: 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 535: 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 542: 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 549: 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
|-
|-
| | [[11L 11s]]
| | [[11L 11s]]
| | full
| |"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 563: 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 570: 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 577: 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 584: 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 591: 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 598: 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 605: 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 612: 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 619: 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 626: 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 634: Line 592:
|-
|-
! |Large-small numbers
! |Large-small numbers
!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
|-
|-
| |1L25s
| |1L25s
|"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
|-
|-
| |2L24s
| |2L24s
|"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
|-
|-
| |3L23s
| |3L23s
|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
|-
|-
| |4L22s
| |4L22s
|"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>
|-
|-
| |5L21s
| |5L21s
|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
|-
|-
| |6L20s
| |6L20s
|"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
|-
|-
| |7L19s
| |7L19s
|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
|-
|-
| |8L18s
| |8L18s
|"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
|-
|-
| |9L17s
| |9L17s
|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
|-
|-
| |10L16s
| |10L16s
|"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
|-
|-
| |11L15s
| |11L15s
|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
|-
|-
| |12L14s
| |12L14s
|"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
|-
|-
| |13L13s
| |13L13s
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">14L12s</span>
| |<span style="line-height: 15.6000003814697px;">14L12s</span>
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">15L11s</span>
| |<span style="line-height: 15.6000003814697px;">15L11s</span>
|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
|-
|-
| |<span style="line-height: 15.6000003814697px;">16L10s</span>
| |<span style="line-height: 15.6000003814697px;">16L10s</span>
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">17L9s</span>
| |<span style="line-height: 15.6000003814697px;">17L9s</span>
|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
|-
|-
| |<span style="line-height: 15.6000003814697px;">18L</span>8s
| |<span style="line-height: 15.6000003814697px;">18L</span>8s
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">19L</span>7s
| |<span style="line-height: 15.6000003814697px;">19L</span>7s
|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
|-
|-
| |<span style="line-height: 15.6000003814697px;">20L</span>6s
| |<span style="line-height: 15.6000003814697px;">20L</span>6s
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">21L</span>5s
| |<span style="line-height: 15.6000003814697px;">21L</span>5s
|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
|-
|-
| |<span style="line-height: 15.6000003814697px;">22L</span>4s
| |<span style="line-height: 15.6000003814697px;">22L</span>4s
|"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
|-
|-
| |<span style="line-height: 15.6000003814697px;">23L</span>3s
| |<span style="line-height: 15.6000003814697px;">23L</span>3s
|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
|-
|-
| |<span style="line-height: 15.6000003814697px;">24L</span>2s
| |<span style="line-height: 15.6000003814697px;">24L</span>2s
|"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
|-
|-
| |25L1s
| |25L1s
|"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 }}

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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