A shruti list: Difference between revisions

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! | <span style="background-color: #ffffff; color: #000000;">Midpoint</span>
! | <span style="background-color: #ffffff; color: #000000;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
! |  
|-
|-
| | [[1L 18s]]
| | [[1L 18s]]
Line 221: Line 221:
| | g = 37\38
| | g = 37\38
| | g = ''19\20, 20\21, 21\22''
| | g = ''19\20, 20\21, 21\22''
| | 18g-17
| | 18g-17+1-g = 17g-16
| | 1-g
| |  
|-
|-
| | [[2L 17s]]
| | [[2L 17s]]
Line 229: Line 229:
| | g = 37\76
| | g = 37\76
| | g = ''10\21'', 11\23, 12\25
| | g = ''10\21'', 11\23, 12\25
| | 17g-8
| | 17g-8+1-2g = 15g-7
| | 1-2g
| |  
|-
|-
| | [[3L 16s]]
| | [[3L 16s]]
Line 236: Line 236:
| | g = 37\114
| | g = 37\114
| | g = ''7\22'', 8\25, 10\31
| | g = ''7\22'', 8\25, 10\31
| | 16g-5
| | 16g-5+1-3g = 13g-4
| | 1-3g
| |  
|-
|-
| | [[4L 15s]]
| | [[4L 15s]]
Line 250: Line 250:
| | g = 151\190
| | g = 151\190
| | g = 19\24, 23\29, 27\34
| | g = 19\24, 23\29, 27\34
| | 14g-11
| | 14g-11+4-5g = 9g-7
| | 4-5g
| |  
|-
|-
| | [[6L 13s]]
| | [[6L 13s]]
Line 257: Line 257:
| | g = 37\228
| | g = 37\228
| | g = 4\25, 5\31, 6/37
| | g = 4\25, 5\31, 6/37
| | 13g-2
| | 13g-2+1-6g = 7g-1
| | 1-6g
| |  
|-
|-
| | [[7L 12s]]
| | [[7L 12s]]
Line 264: Line 264:
| | g = 113\266
| | g = 113\266
| | g = 11\26, 14\33, 17\40
| | g = 11\26, 14\33, 17\40
| | 12g-5
| | 12g-5+3-7g = 5g=2
| | 3-7g
| |  
|-
|-
| | [[8L 11s]]
| | [[8L 11s]]
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| | g = 113\304
| | g = 113\304
| | g = 10\27, 13\35, 16\43
| | g = 10\27, 13\35, 16\43
| | 11g-4
| | 11g-4+3-8g = 3g-1
| | 3-8g
| |  
|-
|-
| | [[9L 10s]]
| | [[9L 10s]]
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| | g = 37\342
| | g = 37\342
| | g = 3\28, 4\37, 5\46
| | g = 3\28, 4\37, 5\46
| | 10g-1
| | 10g-1+1-9g = g
| | 1-9g
| |  
|-
|-
| | [[10L 9s]]
| | [[10L 9s]]
Line 285: Line 285:
| | g = 341\380
| | g = 341\380
| | g = 26\29, 35\39, 44\49
| | g = 26\29, 35\39, 44\49
| | 9g-8
| | 9g-8+9-10g = 1-g
| | 9-10g
| |  
|-
|-
| | [[11L 8s]]
| | [[11L 8s]]
Line 292: Line 292:
| | g = 265\418
| | g = 265\418
| | g = 19\30, 26\41, 33\52
| | g = 19\30, 26\41, 33\52
| | 8g-5
| | 8g-5+7-11g = 2-3g
| | 7-11g
| |  
|-
|-
| | [[12L 7s]]
| | [[12L 7s]]
Line 299: Line 299:
| | g = 265\456
| | g = 265\456
| | g = 18\31, 25\43, 32\55
| | g = 18\31, 25\43, 32\55
| | 7g-4
| | 7g-4+7-12g = 3-5g
| | 7-12g
| |  
|-
|-
| | [[13L 6s]]
| | [[13L 6s]]
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| | g = 417\494
| | g = 417\494
| | g = 27\32, 38\45, 49\58
| | g = 27\32, 38\45, 49\58
| | 6g-5
| | 6g-5+11-13g = 6-7g
| | 11-13g
| |  
|-
|-
| | [[14L 5s]]
| | [[14L 5s]]
Line 313: Line 313:
| | g = 113\532
| | g = 113\532
| | g = 7\33, 10\47, 13\61
| | g = 7\33, 10\47, 13\61
| | 5g-1
| | 5g-1+3-14g = 2-9g
| | 3-14g
| |  
|-
|-
| | [[15L 4s]]
| | [[15L 4s]]
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| | g = 151\570
| | g = 151\570
| | g = 9\34, 13\49, 17\64
| | g = 9\34, 13\49, 17\64
| | 4g-1
| | 4g-1+4-15g = 3-11g
| | 4-15g
| |  
|-
|-
| | [[16L 3s]]
| | [[16L 3s]]
Line 327: Line 327:
| | g = 417\608
| | g = 417\608
| | g = 24\35, 35\51, 46\67
| | g = 24\35, 35\51, 46\67
| | 3g-2
| | 3g-2+11-16g = 9-13g
| | 11-16g
| |  
|-
|-
| | [[17L 2s]]
| | [[17L 2s]]
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| | g = 341\646
| | g = 341\646
| | g = 19\36, 28\53, 37\70
| | g = 19\36, 28\53, 37\70
| | 2g-1
| | 2g-1+9-17g = 8-15g
| | 9-17g
| |  
|-
|-
| | [[18L 1s]]
| | [[18L 1s]]
Line 342: Line 342:
| | g = 37\684
| | g = 37\684
| | g = 2\37, 3\55, 4\73
| | g = 2\37, 3\55, 4\73
| | g
| | g+1-18g = 1-17g
| | 1-18g
| |  
|}
|}


Revision as of 01:14, 23 June 2019

Original article by ma1937, on the Yahoo tuning forum, is quoted here.

The listing of the srutis of Indian classical music given below is based on decades of study of the srutis, study with several masters of Indian classical music, pitch analysis of recordings by several masters of raga performance, and the following quote by Ali Akbar Khan:

"I am still learning about the srutis. They reach to your heart and help you feel the ragas and the notes. In old theory, they say that there are twenty-two in number, but right now I feel that there are more like twenty-three and a half. There is only one sa and one pa. Komal re, komal ga, and komal dha all have three. Shuddha ma, tivra ma, shuddha dha, and komal ni each have two. And shuddha re, shuddha ga, and shuddha ni each have one and a half."

Ali Akbar Khan

This quotation yields many insights... Below I have just listed the twenty-three and a half srutis he is referring to.

In brief summary, Khansahib's list is basically the usually-given twenty-two srutis plus the three "ati ati komals" (ati ati komal re; ati ati komal ga; and ati ati komal dha). Though not on the usual list of 22 srutis, it is well-known that these notes do appear is some ragas. So really there are twenty-five notes on Khansahib's list. It's reduced to twenty-three and half because he gives "half" status to three notes that are usually considered srutis -- the lesser-used versions of shuddha re, shuddha ga, and shuddha ni. I think this is the most illuminating aspect of his comment.

With each set of srutis associated with a given note, the principal sruti is listed first, the others in descending order of significance. Ratios given are exact. Cent values given are rounded to the nearest whole cent:

Principal Shruti Ratio ¢

(approx)

Remarks
Sa 1/1 000
komal re komal re 16/15 112
ati komal re 256/243 090
ati ati komal re 25/24 070
Re shuddha re 9/8 204
"half"-status shuddha re 10/9 182
komal ga komal ga 6/5 316
ati komal ga 32/27 294
ati ati komal ga 75/64 274
Ga shuddha ga 5/4 386
"half"-status shuddha ga 81/64 408
(inverse ati ati komal dha) 32/25 428
Ma shuddha Ma 4/3 498
ekasruti Ma 27/20 520
tivra Ma tivra(tar) Ma 45/32 590 (these two essentially inverses; maybe not entirely a true priority)
729/512 612
Pa 3/2 702
(inverse ekasruti Ma) 40/27 680
komal dha komal dha 8/5 814
ati komal dha 128/81 792
ati ati komal dha 25/16 772
Dha shuddha dha 5/3 884 (these two hard to prioritize; maybe a toss-up)
27/16 906
(inverse ati ati komal ga) 128/75 926
komal ni komal ni 9/5 1018 (these two hard to prioritize; maybe a toss-up)
16/9 996
Ni shuddha ni 15/8 1088
"half"-status shuddha ni 243/128 1110
(inverse ati ati komal re) 48/25 1130

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

komal-ardha re (1): [250/243; 48]: 22

ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 134], [~64/59; 138], [625/576; 141]: 19*

inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22

inverse ekasruti komal ni: [800/729; 160]: 22

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

inverse komal re/tivratar Ma [320/243; 476]

komal ga/komal ga; [36/25; 632]: 19

inverse komal ga/komal ga; [25/18; 568]: 19

ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22

inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22

komal re/tivratar Ma [243/160; 724]

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

ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22

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

inverse ardha komal re (1 3/4), inverse ati ati komal re/ati ati komal re: [50/27; 1066], [~59/32; 1062], [1152/625; 1059]: 19*

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

Regular temperaments of the full-status shrutis

Note: generators in italics will generate a 19 (diatonic) or 22 tone (superdiatonic) set which is too weakly tonal for serious practice

Underlying

Large-small numbers Status Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 18s "half" 18\19 < g < 1 g = 37\38 g = 19\20, 20\21, 21\22 18g-17+1-g = 17g-16
2L 17s full 9\19 < g < 1\2 g = 37\76 g = 10\21, 11\23, 12\25 17g-8+1-2g = 15g-7
3L 16s 6\19 < g < 1\3 g = 37\114 g = 7\22, 8\25, 10\31 16g-5+1-3g = 13g-4
4L 15s 14\19 < g < 3\4 g = 113\152 g = 17\23, 20\27, 23\31 15g-11 3-4g
5L 14s 15\19 < g < 4\5 g = 151\190 g = 19\24, 23\29, 27\34 14g-11+4-5g = 9g-7
6L 13s 3\19 < g < 1\6 g = 37\228 g = 4\25, 5\31, 6/37 13g-2+1-6g = 7g-1
7L 12s 8\19 < g < 3\7 g = 113\266 g = 11\26, 14\33, 17\40 12g-5+3-7g = 5g=2
8L 11s 7\19 < g < 3\8 g = 113\304 g = 10\27, 13\35, 16\43 11g-4+3-8g = 3g-1
9L 10s 2\19 < g < 1\9 g = 37\342 g = 3\28, 4\37, 5\46 10g-1+1-9g = g
10L 9s 17\19 < g < 9\10 g = 341\380 g = 26\29, 35\39, 44\49 9g-8+9-10g = 1-g
11L 8s 12\19 < g < 7\11 g = 265\418 g = 19\30, 26\41, 33\52 8g-5+7-11g = 2-3g
12L 7s 11\19 < g < 7\12 g = 265\456 g = 18\31, 25\43, 32\55 7g-4+7-12g = 3-5g
13L 6s 16\19 < g < 11\13 g = 417\494 g = 27\32, 38\45, 49\58 6g-5+11-13g = 6-7g
14L 5s 4\19 < g < 3\14 g = 113\532 g = 7\33, 10\47, 13\61 5g-1+3-14g = 2-9g
15L 4s 5\19 < g < 4\15 g = 151\570 g = 9\34, 13\49, 17\64 4g-1+4-15g = 3-11g
16L 3s 13\19 < g < 11\16 g = 417\608 g = 24\35, 35\51, 46\67 3g-2+11-16g = 9-13g
17L 2s 10\19 < g < 9\17 g = 341\646 g = 19\36, 28\53, 37\70 2g-1+9-17g = 8-15g
18L 1s "half" 1\19 < g < 1\18 g = 37\684 g = 2\37, 3\55, 4\73 g+1-18g = 1-17g

Quoted

Large-small numbers Status Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L 21s "half" 21\22 < g < 1 g = 43\44 g = 22\23, 23\24, 24\25 21g-20 1-g
2L 20s "3/4" 10\22 < g < 1\2 g = 21\44 g = 11\24, 12\26, 13\28 10g-9\2 1\2-g
3L 19s full 7\22 < g < 1\3 g = 43\132 g = 8\25, 9\28, 10\31 19g-6 1-3g
4L 18s "3/4" 5\22 < g < 1\4 g = 21\88 g = 6\26, 7\30, 8\34 9g-2 1\2-2g
5L 17s full 13\22 < g < 3\5 g = 131\220 g = 16\27, 19\32, 22\37 17g-10 3-5g
6L 16s "3/4" 7\22 < g < 2\6 g = 43\132 g = 9\28, 11\34, 13\40 8g-5\2 1-3g
7L 15s full 3\22 < g < 1\7 g = 43\308 g = 4\29, 5\36, 6\43 15g-2 1-7g
8L 14s "3/4" 8\22 < g < 3\8 g = 65\176 g = 11\30, 14\38, 17\46 7g-5\2 3\2-4g
9L 13s full 17\22 < g < 7\9 g = 307\396 g = 24\31, 31\40, 38\49 13g-10 7-9g
10L 12s "3/4" 2\22 < g < 1\10 g = 21\220 g = 3\32, 4\42, 5\52 6g-1\2 1\2-5g
11L 11s full 1\22 < g < 1\11 g = 3\44 g = 2\33, 3\44, 4\55 g 1\11-g
12L 10s "3/4" 9\22 < g < 5\12 g = 109\264 g = 14\34, 19\46, 24\58 5g-2 5\2-6g
13L 9s full 5\22 < g < 3\13 g = 131\572 g = 8\35, 11\48, 14\61 9g-2 3-13g
14L 8s "3/4" 3\22 < g < 2\14 g = 43\308 g = 5\36, 7\50, 9\64 4g-1\2 1-7g
15L 7s full 19\22 < g < 13\15 g = 571\660 g = 32\37, 45\52, 58\67 7g-6 13-15g
16L 6s "3/4" 4\22 < g < 3\16 g = 65\352 g = 7\38, 10\54, 13\70 3g-1\2 3\2-8g
17L 5s full 9\22 < g < 7\17 g = 207\748 g = 16\39, 23\56, 30\73 5g-2 7-17g
18L 4s "3/4" 6\22 < g < 5\18 g = 109\396 g = 11\40, 16\58, 21\76 2g-1\2 5\2-9g
19L 3s full 15\22 < g < 13\19 g = 571\836 g = 28\41, 41\60, 54\79 3g-2 13-19g
20L 2s "3/4" 1\22 < g < 1\20 g = 21\440 g = 2\42, 3\62, 4\72 g 1\2-10g
21L 1s "half" 1\22 < g < 1\21 g = 43\924 g = 2\43, 3\64, 4\85 g 1-21g
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