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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2017-01-04 | : This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2017-01-04 21:21:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>603103806</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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. Ratios given are exact. Cent values given are rounded to the nearest whole cent: | ||
Sa (1): [1/1; 000] | Sa (1): [1/1; 000] | ||
komal re (3): | komal re (3): | ||
| Line 29: | Line 25: | ||
ati komal re: [256/243; 090] | ati komal re: [256/243; 090] | ||
ati ati komal re: [25/24; 070] | ati ati komal re: [25/24; 070] | ||
Re (1 1/2): | Re (1 1/2): | ||
shuddha re: [9/8; 204] | shuddha re: [9/8; 204] | ||
"half"-status shuddha re: [10/9; 182] | "half"-status shuddha re: [10/9; 182] | ||
komal ga (3): | komal ga (3): | ||
| Line 53: | Line 43: | ||
shuddha Ma: [4/3; 498] | shuddha Ma: [4/3; 498] | ||
ekasruti Ma: [27/20; 520] | ekasruti Ma: [27/20; 520] | ||
tivra Ma (2 [1 3/4]): | tivra Ma (2 [1 3/4]): | ||
tivra(tar) Ma: [45/32; 590], [729/512; 612] | tivra(tar) Ma: [45/32; 590], [729/512; 612] | ||
(these two essentially inverses; maybe not entirely a true priority) | (these two essentially inverses; maybe not entirely a true priority) | ||
Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680]) | Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680]) | ||
komal dha (3): | komal dha (3): | ||
| Line 74: | Line 59: | ||
(these two hard to prioritize; maybe a toss-up) | (these two hard to prioritize; maybe a toss-up) | ||
(inverse ati ati komal ga: [128/75; 926]) | (inverse ati ati komal ga: [128/75; 926]) | ||
komal ni (2 [1 3/4]): | komal ni (2 [1 3/4]): | ||
komal ni: [9/5; 1018], [16/9; 996] | komal ni: [9/5; 1018], [16/9; 996] | ||
(these two hard to prioritize; maybe a toss-up) | (these two hard to prioritize; maybe a toss-up) | ||
Ni (1 1/2): | Ni (1 1/2): | ||
| Line 91: | Line 69: | ||
(inverse ati ati komal re: [48/25; 1130]) | (inverse ati ati komal re: [48/25; 1130]) | ||
// | |||
**Secondary functions and "artifact shrutis" i****ntroduced 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== | ==Regular temperaments of the full-status shrutis== | ||
| Line 152: | Line 158: | ||
<br /> | <br /> | ||
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:<br /> | 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:<br /> | ||
<br /> | <br /> | ||
Sa (1): [1/1; 000]<br /> | Sa (1): [1/1; 000]<br /> | ||
<br /> | <br /> | ||
komal re (3):<br /> | komal re (3):<br /> | ||
| Line 163: | Line 165: | ||
ati komal re: [256/243; 090]<br /> | ati komal re: [256/243; 090]<br /> | ||
ati ati komal re: [25/24; 070]<br /> | ati ati komal re: [25/24; 070]<br /> | ||
<br /> | <br /> | ||
Re (1 1/2):<br /> | Re (1 1/2):<br /> | ||
shuddha re: [9/8; 204]<br /> | shuddha re: [9/8; 204]<br /> | ||
&quot;half&quot;-status shuddha re: [10/9; 182]<br /> | &quot;half&quot;-status shuddha re: [10/9; 182]<br /> | ||
<br /> | <br /> | ||
komal ga (3):<br /> | komal ga (3):<br /> | ||
| Line 187: | Line 183: | ||
shuddha Ma: [4/3; 498]<br /> | shuddha Ma: [4/3; 498]<br /> | ||
ekasruti Ma: [27/20; 520]<br /> | ekasruti Ma: [27/20; 520]<br /> | ||
<br /> | <br /> | ||
tivra Ma (2 [1 3/4]):<br /> | tivra Ma (2 [1 3/4]):<br /> | ||
tivra(tar) Ma: [45/32; 590], [729/512; 612]<br /> | tivra(tar) Ma: [45/32; 590], [729/512; 612]<br /> | ||
(these two essentially inverses; maybe not entirely a true priority)<br /> | (these two essentially inverses; maybe not entirely a true priority)<br /> | ||
<br /> | <br /> | ||
Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680]) | Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680])<br /> | ||
<br /> | <br /> | ||
komal dha (3):<br /> | komal dha (3):<br /> | ||
| Line 208: | Line 199: | ||
(these two hard to prioritize; maybe a toss-up)<br /> | (these two hard to prioritize; maybe a toss-up)<br /> | ||
(inverse ati ati komal ga: [128/75; 926])<br /> | (inverse ati ati komal ga: [128/75; 926])<br /> | ||
<br /> | <br /> | ||
komal ni (2 [1 3/4]):<br /> | komal ni (2 [1 3/4]):<br /> | ||
komal ni: [9/5; 1018], [16/9; 996]<br /> | komal ni: [9/5; 1018], [16/9; 996]<br /> | ||
(these two hard to prioritize; maybe a toss-up)<br /> | (these two hard to prioritize; maybe a toss-up)<br /> | ||
<br /> | <br /> | ||
Ni (1 1/2):<br /> | Ni (1 1/2):<br /> | ||
| Line 225: | Line 209: | ||
(inverse ati ati komal re: [48/25; 1130])<br /> | (inverse ati ati komal re: [48/25; 1130])<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Regular temperaments of the full-status shrutis"></a><!-- ws:end:WikiTextHeadingRule: | <strong>Secondary functions and &quot;artifact shrutis&quot; i</strong><strong>ntroduced by using 19 or 22 (out of n) edo to simulate ragas</strong><br /> | ||
<br /> | |||
komal-ardha re (1): [250/243; 48]: 22<br /> | |||
<br /> | |||
ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 134], [~64/59; 138], [625/576; 141]: 19*<br /> | |||
<br /> | |||
inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22<br /> | |||
inverse ekasruti komal ni: [800/729; 160]: 22<br /> | |||
<br /> | |||
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19<br /> | |||
<br /> | |||
inverse komal re/tivratar Ma [320/243; 476]<br /> | |||
<br /> | |||
komal ga/komal ga; [36/25; 632]: 19<br /> | |||
inverse komal ga/komal ga; [25/18; 568]: 19<br /> | |||
ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22<br /> | |||
inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22<br /> | |||
<br /> | |||
komal re/tivratar Ma [243/160; 724]<br /> | |||
<br /> | |||
komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19<br /> | |||
<br /> | |||
ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22<br /> | |||
ekasruti komal ni: [729/400; 1040]: 22<br /> | |||
<br /> | |||
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*<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2> | |||
inverse komal-ardha re (1): [243/125; 1152]: 22<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Regular temperaments of the full-status shrutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->Regular temperaments of the full-status shrutis</h2> | |||
<strong>Note: generators in italics will generate a 19 (</strong><strong>diatonic)</strong> <strong>or 22 tone (superdiatonic) set which is too weakly tonal for serious practice</strong><br /> | <strong>Note: generators in italics will generate a 19 (</strong><strong>diatonic)</strong> <strong>or 22 tone (superdiatonic) set which is too weakly tonal for serious practice</strong><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h4&gt; --><h4 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h4> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Underlying"></a><!-- ws:end:WikiTextHeadingRule:6 -->Underlying</h1> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Quoted"></a><!-- ws:end:WikiTextHeadingRule:8 -->Quoted</h1> | ||
Revision as of 21:21, 4 January 2017
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author diagonalia and made on 2017-01-04 21:21:49 UTC.
- The original revision id was 603103806.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[http://launch.groups.yahoo.com/group/tuning/message/72704|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: Sa (1): [1/1; 000] komal re (3): komal re: [16/15; 112] ati komal re: [256/243; 090] ati ati komal re: [25/24; 070] Re (1 1/2): shuddha re: [9/8; 204] "half"-status shuddha re: [10/9; 182] komal ga (3): komal ga: [6/5; 316] ati komal ga: [32/27; 294] ati ati komal ga: [75/64; 274] Ga (1 1/2): shuddha ga: [5/4; 386] "half"-status shuddha ga: [81/64; 408] (inverse ati ati komal dha: [32/25; 428]) Ma (2): shuddha Ma: [4/3; 498] ekasruti Ma: [27/20; 520] tivra Ma (2 [1 3/4]): tivra(tar) Ma: [45/32; 590], [729/512; 612] (these two essentially inverses; maybe not entirely a true priority) Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680]) komal dha (3): komal dha: [8/5; 814] ati komal dha: [128/81; 792] ati ati komal dha: [25/16; 772] Dha (2 [1 3/4]): shuddha dha: [5/3; 884], [27/16; 906] (these two hard to prioritize; maybe a toss-up) (inverse ati ati komal ga: [128/75; 926]) komal ni (2 [1 3/4]): komal ni: [9/5; 1018], [16/9; 996] (these two hard to prioritize; maybe a toss-up) Ni (1 1/2): 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" i****ntroduced 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 ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || || 1L18s || "half" || 18\19 < g < 1 || g = 37\38 || g = //19\20, 20\21, 21\22// || 18g-17 || 1-g || || 2L17s || full || 9\19 < g < 1\2 || g = 37\76 || g = //10\21//, 11\23, 12\25 || 17g-8 || 1-2g || || 3L16s || full || 6\19 < g < 1\3 || g = 37\114 || g = //7\22//, 8\25, 10\31 || 16g-5 || 1-3g || || 4L15s || full || 14\19 < g < 3\4 || g = 113\152 || g = 17\23, 20\27, 23\31 || 15g-11 || 3-4g || || 5L14s || full || 15\19 < g < 4\5 || g = 151\190 || g = 19\24, 23\29, 27\34 || 14g-11 || 4-5g || || 6L13s || full || 3\19 < g < 1\6 || g = 37\228 || g = 4\25, 5\31, 6/37 || 13g-2 || 1-6g || || 7L12s || full || 8\19 < g < 3\7 || g = 113\266 || g = 11\26, 14\33, 17\40 || 12g-5 || 3-7g || || 8L11s || full || 7\19 < g < 3\8 || g = 113\304 || g = 10\27, 13\35, 16\43 || 11g-4 || 3-8g || || 9L10s || full || 2\19 < g < 1\9 || g = 37\342 || g = 3\28, 4\37, 5\46 || 10g-1 || 1-9g || || 10L9s || full || 17\19 < g < 9\10 || g = 341\380 || g = 26\29, 35\39, 44\49 || 9g-8 || 9-10g || || 11L8s || full || 12\19 < g < 7\11 || g = 265\418 || g = 19\30, 26\41, 33\52 || 8g-5 || 7-11g || || 12L7s || full || 11\19 < g < 7\12 || g = 265\456 || g = 18\31, 25\43, 32\55 || 7g-4 || 7-12g || || 13L6s || full || 16\19 < g < 11\13 || g = 417\494 || g = 27\32, 38\45, 49\58 || 6g-5 || 11-13g || || 14L5s || full || 4\19 < g < 3\14 || g = 113\532 || g = 7\33, 10\47, 13\61 || 5g-1 || 3-14g || || 15L4s || full || 5\19 < g < 4\15 || g = 151\570 || g = 9\34, 13\49, 17\64 || 4g-1 || 4-15g || || 16L3s || full || 13\19 < g < 11\16 || g = 417\608 || g = 24\35, 35\51, 46\67 || 3g-2 || 11-16g || || 17L2s || full || 10\19 < g < 9\17 || g = 341\646 || g = 19\36, 28\53, 37\70 || 2g-1 || 9-17g || || 18L1s || "half" || 1\19 < g < 1\18 || g = 37\684 || g = 2\37, 3\55, 4\73 || g || 1-18g || =Quoted= ||~ Large-small numbers ||~ Status ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || || 1L21s || "half" || 21\22 < g < 1 || g = 43\44 || g = //22\23,// //23\24,// //24/25// || 21g-20 || 1-g || || 2L20s || "3/4" || 10\22 < g < 1\2 || g = 21\44 || g = //11\24,// //12\26//, 13\28 || 10g-9\2 || 1\2-g || || 3L19s || full || 7\22 < g < 1\3 || g = 43\132 || g = //8\25//, 9\28, 10\31 || 19g-6 || 1-3g || || 4L18s || "3/4" || 5\22 < g < 1\4 || g = 21\88 || g = //6\26//, 7\30, 8\34 || 9g-2 || 1\2-2g || || 5L17s || full || 13\22 < g < 3\5 || g = 131\220 || g = 16\27, 19\32, 22\37 || 17g-10 || 3-5g || || 6L16s || "3/4" || 7\22 < g < 2\6 || g = 43\132 || g = 9\28, 11\34, 13\40 || 8g-5\2 || 1-3g || || 7L15s || full || 3\22 < g < 1\7 || g = 43\308 || g = 4\29, 5\36, 6\43 || 15g-2 || 1-7g || || 8L14s || "3/4" || 8\22 < g < 3\8 || g = 65\176 || g = 11\30, 14\38, 17\46 || 7g-5\2 || 3\2-4g || || 9L13s || full || 17\22 < g < 7\9 || g = 307\396 || g = 24\31, 31\40, 38\49 || 13g-10 || 7-9g || || 10L12s || "3/4" || 2\22 < g < 1\10 || g = 21\220 || g = 3\32, 4\42, 5\52 || 6g-1\2 || 1\2-5g || || 11L11s || full || 1\22 < g < 1\11 || g = 3\44 || g = 2\33, 3\44, 4\55 || g || 1\11-g || || 12L10s || "3/4" || 9\22 < g < 5\12 || g = 109\264 || g = 14\34, 19\46, 24\58 || 5g-2 || 5\2-6g || || 13L9s || full || 5\22 < g < 3\13 || g = 131\572 || g = 8\35, 11\48, 14\61 || 9g-2 || 3-13g || || 14L8s || "3/4" || 3\22 < g < 2\14 || g = 43\308 || g = 5\36, 7\50, 9\64 || 4g-1\2 || 1-7g || || 15L7s || full || 19\22 < g < 13\15 || g = 571\660 || g = 32\37, 45\52, 58\67 || 7g-6 || 13-15g || || 16L6s || "3/4" || 4\22 < g < 3\16 || g = 65\352 || g = 7\38, 10\54, 13\70 || 3g-1\2 || 3\2-8g || || 17L5s || full || 9\22 < g < 7\17 || g = 207\748 || g = 16\39, 23\56, 30\73 || 5g-2 || 7-17g || || 18L4s || "3/4" || 6\22 < g < 5\18 || g = 109\396 || g = 11\40, 16\58, 21\76 || 2g-1\2 || 5\2-9g || || 19L3s || full || 15\22 < g < 13\19 || g = 571\836 || g = 28\41, 41\60, 54\79 || 3g-2 || 13-19g || || 20L2s || "3/4" || 1\22 < g < 1\20 || g = 21\440 || g = 2\42, 3\62, 4\72 || g || 1\2-10g || || 21L1s || "half" || 1\22 < g < 1\21 || g = 43\924 || g = 2\43, 3\64, 4\85 || g || 1-21g ||
Original HTML content:
<html><head><title>A shruti list</title></head><body><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/72704" rel="nofollow">Original article</a> by ma1937, on the Yahoo tuning forum, is quoted here.<br />
<br />
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:<br />
<br />
"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."<br />
Ali Akbar Khan<br />
<br />
This quotation yields many insights... Below I have just listed the twenty-three and a half srutis he is referring to.<br />
<br />
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.<br />
<br />
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:<br />
<br />
Sa (1): [1/1; 000]<br />
<br />
komal re (3):<br />
komal re: [16/15; 112]<br />
ati komal re: [256/243; 090]<br />
ati ati komal re: [25/24; 070]<br />
<br />
Re (1 1/2):<br />
shuddha re: [9/8; 204]<br />
"half"-status shuddha re: [10/9; 182]<br />
<br />
komal ga (3):<br />
komal ga: [6/5; 316]<br />
ati komal ga: [32/27; 294]<br />
ati ati komal ga: [75/64; 274]<br />
<br />
Ga (1 1/2):<br />
shuddha ga: [5/4; 386]<br />
"half"-status shuddha ga: [81/64; 408]<br />
(inverse ati ati komal dha: [32/25; 428])<br />
<br />
Ma (2):<br />
shuddha Ma: [4/3; 498]<br />
ekasruti Ma: [27/20; 520]<br />
<br />
tivra Ma (2 [1 3/4]):<br />
tivra(tar) Ma: [45/32; 590], [729/512; 612]<br />
(these two essentially inverses; maybe not entirely a true priority)<br />
<br />
Pa (1): [3/2; 702] (inverse ekasruti Ma: [40/27; 680])<br />
<br />
komal dha (3):<br />
komal dha: [8/5; 814]<br />
ati komal dha: [128/81; 792]<br />
ati ati komal dha: [25/16; 772]<br />
<br />
Dha (2 [1 3/4]):<br />
shuddha dha: [5/3; 884], [27/16; 906]<br />
(these two hard to prioritize; maybe a toss-up)<br />
(inverse ati ati komal ga: [128/75; 926])<br />
<br />
komal ni (2 [1 3/4]):<br />
komal ni: [9/5; 1018], [16/9; 996]<br />
(these two hard to prioritize; maybe a toss-up)<br />
<br />
Ni (1 1/2):<br />
shuddha ni: [15/8; 1088]<br />
"half"-status shuddha ni: [243/128; 1110]<br />
(inverse ati ati komal re: [48/25; 1130])<br />
<br />
<br />
<strong>Secondary functions and "artifact shrutis" i</strong><strong>ntroduced by using 19 or 22 (out of n) edo to simulate ragas</strong><br />
<br />
komal-ardha re (1): [250/243; 48]: 22<br />
<br />
ardha komal re (1 3/4), ati ati komal re/ati ati komal re: [27/25; 134], [~64/59; 138], [625/576; 141]: 19*<br />
<br />
inverse ati ati komal ga/Pa, komal re/komal re: [256/225; 224]: 22<br />
inverse ekasruti komal ni: [800/729; 160]: 22<br />
<br />
komal-ardha ga (1 3/4): [144/125; 246], [125/108; 252]: 19<br />
<br />
inverse komal re/tivratar Ma [320/243; 476]<br />
<br />
komal ga/komal ga; [36/25; 632]: 19<br />
inverse komal ga/komal ga; [25/18; 568]: 19<br />
ati ati komal ga/ati ati komal ga: [~563/410; 548]: 22<br />
inverse ati ati komal ga/ati ati komal ga: [~820/563; 652]: 22<br />
<br />
komal re/tivratar Ma [243/160; 724]<br />
<br />
komal-ardha ga (1 3/4): [125/72; 954], [216/125; 948]: 19<br />
<br />
ati ati komal ga/Pa, inverse komal re/komal re: [225/128; 976]: 22<br />
ekasruti komal ni: [729/400; 1040]: 22<br />
<br />
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*<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h2>
inverse komal-ardha re (1): [243/125; 1152]: 22<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Regular temperaments of the full-status shrutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->Regular temperaments of the full-status shrutis</h2>
<strong>Note: generators in italics will generate a 19 (</strong><strong>diatonic)</strong> <strong>or 22 tone (superdiatonic) set which is too weakly tonal for serious practice</strong><br />
<!-- ws:start:WikiTextHeadingRule:4:<h4> --><h4 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h4>
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Underlying"></a><!-- ws:end:WikiTextHeadingRule:6 -->Underlying</h1>
<table class="wiki_table">
<tr>
<th>Large-small numbers<br />
</th>
<th>Status<br />
</th>
<th>Generator range<br />
</th>
<th><span style="background-color: #ffffff; color: #000000;">Midpoint</span><br />
</th>
<th>Boundaries of propriety, maximum expressiveness, diatonicity<br />
</th>
<th>Large step<br />
</th>
<th>Small step<br />
</th>
</tr>
<tr>
<td>1L18s<br />
</td>
<td>"half"<br />
</td>
<td>18\19 < g < 1<br />
</td>
<td>g = 37\38<br />
</td>
<td>g = <em>19\20, 20\21, 21\22</em><br />
</td>
<td>18g-17<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L17s<br />
</td>
<td>full<br />
</td>
<td>9\19 < g < 1\2<br />
</td>
<td>g = 37\76<br />
</td>
<td>g = <em>10\21</em>, 11\23, 12\25<br />
</td>
<td>17g-8<br />
</td>
<td>1-2g<br />
</td>
</tr>
<tr>
<td>3L16s<br />
</td>
<td>full<br />
</td>
<td>6\19 < g < 1\3<br />
</td>
<td>g = 37\114<br />
</td>
<td>g = <em>7\22</em>, 8\25, 10\31<br />
</td>
<td>16g-5<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L15s<br />
</td>
<td>full<br />
</td>
<td>14\19 < g < 3\4<br />
</td>
<td>g = 113\152<br />
</td>
<td>g = 17\23, 20\27, 23\31<br />
</td>
<td>15g-11<br />
</td>
<td>3-4g<br />
</td>
</tr>
<tr>
<td>5L14s<br />
</td>
<td>full<br />
</td>
<td>15\19 < g < 4\5<br />
</td>
<td>g = 151\190<br />
</td>
<td>g = 19\24, 23\29, 27\34<br />
</td>
<td>14g-11<br />
</td>
<td>4-5g<br />
</td>
</tr>
<tr>
<td>6L13s<br />
</td>
<td>full<br />
</td>
<td>3\19 < g < 1\6<br />
</td>
<td>g = 37\228<br />
</td>
<td>g = 4\25, 5\31, 6/37<br />
</td>
<td>13g-2<br />
</td>
<td>1-6g<br />
</td>
</tr>
<tr>
<td>7L12s<br />
</td>
<td>full<br />
</td>
<td>8\19 < g < 3\7<br />
</td>
<td>g = 113\266<br />
</td>
<td>g = 11\26, 14\33, 17\40<br />
</td>
<td>12g-5<br />
</td>
<td>3-7g<br />
</td>
</tr>
<tr>
<td>8L11s<br />
</td>
<td>full<br />
</td>
<td>7\19 < g < 3\8<br />
</td>
<td>g = 113\304<br />
</td>
<td>g = 10\27, 13\35, 16\43<br />
</td>
<td>11g-4<br />
</td>
<td>3-8g<br />
</td>
</tr>
<tr>
<td>9L10s<br />
</td>
<td>full<br />
</td>
<td>2\19 < g < 1\9<br />
</td>
<td>g = 37\342<br />
</td>
<td>g = 3\28, 4\37, 5\46<br />
</td>
<td>10g-1<br />
</td>
<td>1-9g<br />
</td>
</tr>
<tr>
<td>10L9s<br />
</td>
<td>full<br />
</td>
<td>17\19 < g < 9\10<br />
</td>
<td>g = 341\380<br />
</td>
<td>g = 26\29, 35\39, 44\49<br />
</td>
<td>9g-8<br />
</td>
<td>9-10g<br />
</td>
</tr>
<tr>
<td>11L8s<br />
</td>
<td>full<br />
</td>
<td>12\19 < g < 7\11<br />
</td>
<td>g = 265\418<br />
</td>
<td>g = 19\30, 26\41, 33\52<br />
</td>
<td>8g-5<br />
</td>
<td>7-11g<br />
</td>
</tr>
<tr>
<td>12L7s<br />
</td>
<td>full<br />
</td>
<td>11\19 < g < 7\12<br />
</td>
<td>g = 265\456<br />
</td>
<td>g = 18\31, 25\43, 32\55<br />
</td>
<td>7g-4<br />
</td>
<td>7-12g<br />
</td>
</tr>
<tr>
<td>13L6s<br />
</td>
<td>full<br />
</td>
<td>16\19 < g < 11\13<br />
</td>
<td>g = 417\494<br />
</td>
<td>g = 27\32, 38\45, 49\58<br />
</td>
<td>6g-5<br />
</td>
<td>11-13g<br />
</td>
</tr>
<tr>
<td>14L5s<br />
</td>
<td>full<br />
</td>
<td>4\19 < g < 3\14<br />
</td>
<td>g = 113\532<br />
</td>
<td>g = 7\33, 10\47, 13\61<br />
</td>
<td>5g-1<br />
</td>
<td>3-14g<br />
</td>
</tr>
<tr>
<td>15L4s<br />
</td>
<td>full<br />
</td>
<td>5\19 < g < 4\15<br />
</td>
<td>g = 151\570<br />
</td>
<td>g = 9\34, 13\49, 17\64<br />
</td>
<td>4g-1<br />
</td>
<td>4-15g<br />
</td>
</tr>
<tr>
<td>16L3s<br />
</td>
<td>full<br />
</td>
<td>13\19 < g < 11\16<br />
</td>
<td>g = 417\608<br />
</td>
<td>g = 24\35, 35\51, 46\67<br />
</td>
<td>3g-2<br />
</td>
<td>11-16g<br />
</td>
</tr>
<tr>
<td>17L2s<br />
</td>
<td>full<br />
</td>
<td>10\19 < g < 9\17<br />
</td>
<td>g = 341\646<br />
</td>
<td>g = 19\36, 28\53, 37\70<br />
</td>
<td>2g-1<br />
</td>
<td>9-17g<br />
</td>
</tr>
<tr>
<td>18L1s<br />
</td>
<td>"half"<br />
</td>
<td>1\19 < g < 1\18<br />
</td>
<td>g = 37\684<br />
</td>
<td>g = 2\37, 3\55, 4\73<br />
</td>
<td>g<br />
</td>
<td>1-18g<br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Quoted"></a><!-- ws:end:WikiTextHeadingRule:8 -->Quoted</h1>
<table class="wiki_table">
<tr>
<th>Large-small numbers<br />
</th>
<th>Status<br />
</th>
<th>Generator range<br />
</th>
<th><span style="background-color: #ffffff; color: #000000;">Midpoint</span><br />
</th>
<th>Boundaries of propriety, maximum expressiveness, diatonicity<br />
</th>
<th>Large step<br />
</th>
<th>Small step<br />
</th>
</tr>
<tr>
<td>1L21s<br />
</td>
<td>"half"<br />
</td>
<td>21\22 < g < 1<br />
</td>
<td>g = 43\44<br />
</td>
<td>g = <em>22\23,</em> <em>23\24,</em> <em>24/25</em><br />
</td>
<td>21g-20<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L20s<br />
</td>
<td>"3/4"<br />
</td>
<td>10\22 < g < 1\2<br />
</td>
<td>g = 21\44<br />
</td>
<td>g = <em>11\24,</em> <em>12\26</em>, 13\28<br />
</td>
<td>10g-9\2<br />
</td>
<td>1\2-g<br />
</td>
</tr>
<tr>
<td>3L19s<br />
</td>
<td>full<br />
</td>
<td>7\22 < g < 1\3<br />
</td>
<td>g = 43\132<br />
</td>
<td>g = <em>8\25</em>, 9\28, 10\31<br />
</td>
<td>19g-6<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L18s<br />
</td>
<td>"3/4"<br />
</td>
<td>5\22 < g < 1\4<br />
</td>
<td>g = 21\88<br />
</td>
<td>g = <em>6\26</em>, 7\30, 8\34<br />
</td>
<td>9g-2<br />
</td>
<td>1\2-2g<br />
</td>
</tr>
<tr>
<td>5L17s<br />
</td>
<td>full<br />
</td>
<td>13\22 < g < 3\5<br />
</td>
<td>g = 131\220<br />
</td>
<td>g = 16\27, 19\32, 22\37<br />
</td>
<td>17g-10<br />
</td>
<td>3-5g<br />
</td>
</tr>
<tr>
<td>6L16s<br />
</td>
<td>"3/4"<br />
</td>
<td>7\22 < g < 2\6<br />
</td>
<td>g = 43\132<br />
</td>
<td>g = 9\28, 11\34, 13\40<br />
</td>
<td>8g-5\2<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L15s<br />
</td>
<td>full<br />
</td>
<td>3\22 < g < 1\7<br />
</td>
<td>g = 43\308<br />
</td>
<td>g = 4\29, 5\36, 6\43<br />
</td>
<td>15g-2<br />
</td>
<td>1-7g<br />
</td>
</tr>
<tr>
<td>8L14s<br />
</td>
<td>"3/4"<br />
</td>
<td>8\22 < g < 3\8<br />
</td>
<td>g = 65\176<br />
</td>
<td>g = 11\30, 14\38, 17\46<br />
</td>
<td>7g-5\2<br />
</td>
<td>3\2-4g<br />
</td>
</tr>
<tr>
<td>9L13s<br />
</td>
<td>full<br />
</td>
<td>17\22 < g < 7\9<br />
</td>
<td>g = 307\396<br />
</td>
<td>g = 24\31, 31\40, 38\49<br />
</td>
<td>13g-10<br />
</td>
<td>7-9g<br />
</td>
</tr>
<tr>
<td>10L12s<br />
</td>
<td>"3/4"<br />
</td>
<td>2\22 < g < 1\10<br />
</td>
<td>g = 21\220<br />
</td>
<td>g = 3\32, 4\42, 5\52<br />
</td>
<td>6g-1\2<br />
</td>
<td>1\2-5g<br />
</td>
</tr>
<tr>
<td>11L11s<br />
</td>
<td>full<br />
</td>
<td>1\22 < g < 1\11<br />
</td>
<td>g = 3\44<br />
</td>
<td>g = 2\33, 3\44, 4\55<br />
</td>
<td>g<br />
</td>
<td>1\11-g<br />
</td>
</tr>
<tr>
<td>12L10s<br />
</td>
<td>"3/4"<br />
</td>
<td>9\22 < g < 5\12<br />
</td>
<td>g = 109\264<br />
</td>
<td>g = 14\34, 19\46, 24\58<br />
</td>
<td>5g-2<br />
</td>
<td>5\2-6g<br />
</td>
</tr>
<tr>
<td>13L9s<br />
</td>
<td>full<br />
</td>
<td>5\22 < g < 3\13<br />
</td>
<td>g = 131\572<br />
</td>
<td>g = 8\35, 11\48, 14\61<br />
</td>
<td>9g-2<br />
</td>
<td>3-13g<br />
</td>
</tr>
<tr>
<td>14L8s<br />
</td>
<td>"3/4"<br />
</td>
<td>3\22 < g < 2\14<br />
</td>
<td>g = 43\308<br />
</td>
<td>g = 5\36, 7\50, 9\64<br />
</td>
<td>4g-1\2<br />
</td>
<td>1-7g<br />
</td>
</tr>
<tr>
<td>15L7s<br />
</td>
<td>full<br />
</td>
<td>19\22 < g < 13\15<br />
</td>
<td>g = 571\660<br />
</td>
<td>g = 32\37, 45\52, 58\67<br />
</td>
<td>7g-6<br />
</td>
<td>13-15g<br />
</td>
</tr>
<tr>
<td>16L6s<br />
</td>
<td>"3/4"<br />
</td>
<td>4\22 < g < 3\16<br />
</td>
<td>g = 65\352<br />
</td>
<td>g = 7\38, 10\54, 13\70<br />
</td>
<td>3g-1\2<br />
</td>
<td>3\2-8g<br />
</td>
</tr>
<tr>
<td>17L5s<br />
</td>
<td>full<br />
</td>
<td>9\22 < g < 7\17<br />
</td>
<td>g = 207\748<br />
</td>
<td>g = 16\39, 23\56, 30\73<br />
</td>
<td>5g-2<br />
</td>
<td>7-17g<br />
</td>
</tr>
<tr>
<td>18L4s<br />
</td>
<td>"3/4"<br />
</td>
<td>6\22 < g < 5\18<br />
</td>
<td>g = 109\396<br />
</td>
<td>g = 11\40, 16\58, 21\76<br />
</td>
<td>2g-1\2<br />
</td>
<td>5\2-9g<br />
</td>
</tr>
<tr>
<td>19L3s<br />
</td>
<td>full<br />
</td>
<td>15\22 < g < 13\19<br />
</td>
<td>g = 571\836<br />
</td>
<td>g = 28\41, 41\60, 54\79<br />
</td>
<td>3g-2<br />
</td>
<td>13-19g<br />
</td>
</tr>
<tr>
<td>20L2s<br />
</td>
<td>"3/4"<br />
</td>
<td>1\22 < g < 1\20<br />
</td>
<td>g = 21\440<br />
</td>
<td>g = 2\42, 3\62, 4\72<br />
</td>
<td>g<br />
</td>
<td>1\2-10g<br />
</td>
</tr>
<tr>
<td>21L1s<br />
</td>
<td>"half"<br />
</td>
<td>1\22 < g < 1\21<br />
</td>
<td>g = 43\924<br />
</td>
<td>g = 2\43, 3\64, 4\85<br />
</td>
<td>g<br />
</td>
<td>1-21g<br />
</td>
</tr>
</table>
</body></html>