Shruti

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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.

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]

Ma (2):
shuddha Ma: [4/3; 498]
ekasruti Ma: [27/20; 520]

tivra Ma (2):
tivra Ma: [45/32; 590]
tivratar Ma: [729/512; 612]

Pa (1): [3/2; 702]

komal dha (3):
komal dha: [8/5; 814]
ati komal dha: [128/81; 792]
ati ati komal dha: [25/16; 772]

Dha (2):
shuddha dha: [5/3; 884]
shuddha dha: [27/16; 906]

komal ni (2):
komal ni: [9/5; 1018]
komal ni: [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]

==Regular temperaments of the full-status shrutis== 
**Note: generators in italics will generate a 22 tone set which is too weakly tonal for serious practice**
||~ Large-small numbers ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step ||
|| 1L21s || 21\22 < g < 1 || g = 43\44 || g = //22\23,// //23\24,// //24/25// || 21g-20 || 1-g ||
|| 2L20s || 10\22 < g < 1\2 || g = 21\44 || g = //11\24,// //12\26//, 13\28 || 10g-9\2 || 1\2-g ||
|| 3L19s || 7\22 < g < 1\3 || g = 43\132 || g = //8\25//, 9\28, 10\31 || 19g-6 || 1-3g ||
|| 4L18s || 5\22 < g < 1\4 || g = 21\88 || g = //6\26//, 7\30, 8\34 || 9g-2 || 1\2-2g ||
|| 5L17s || 13\22 < g < 3\5 || g = 131\220 || g = 16\27, 19\32, 22\37 || 17g-10 || 3-5g ||
|| 6L16s || 7\22 < g < 2\6 || g = 43\132 || g = 9\28, 11\34, 13\40 || 8g-5\2 || 1-3g ||
|| 7L15s || 3\22 < g < 1\7 || g = 43\308 || g = 4\29, 5\36, 6\43 || 15g-2 || 1-7g ||
|| 8L14s || 8\22 < g < 3\8 || g = 65\176 || g = 11\30, 14\38, 17\46 || 7g-5\2 || 3\2-4g ||
|| 9L13s || 17\22 < g < 7\9 || g = 307\396 || g = 24\31, 31\40, 38\49 || 13g-10 || 7-9g ||
|| 10L12s || 2\22 < g < 1\10 || g = 21\220 || g = 3\32, 4\42, 5\52 || 6g-1\2 || 1\2-5g ||
|| 11L11s || 1\22 < g < 1\11 || g = 3\44 || g = 2\33, 3\44, 4\55 || g || 1\11-g ||
|| 12L10s || 9\22 < g < 5\12 || g = 109\264 || g = 14\34, 19\46, 24\58 || 5g-2 || 5\2-6g ||
|| 13L9s || 5\22 < g < 3\13 || g = 131\572 || g = 8\35, 11\48, 14\61 || 9g-2 || 3-13g ||
|| 14L8s || 3\22 < g < 2\14 || g = 43\308 || g = 5\36, 7\50, 9\64 || 4g-1\2 || 1-7g ||
|| 15L7s || 19\22 < g < 13\15 || g = 571\660 || g = 32\37, 45\52, 58\67 || 7g-6 || 13-15g ||
|| 16L6s || 4\22 < g < 3\16 || g = 65\352 || g = 7\38, 10\54, 13\70 || 3g-1\2 || 3\2-8g ||
|| 17L5s || 9\22 < g < 7\17 || g = 207\748 || g = 16\39, 23\56, 30\73 || 5g-2 || 7-17g ||
|| 18L4s || 6\22 < g < 5\18 || g = 109\396 || g = 11\40, 16\58, 21\76 || 2g-1\2 || 5\2-9g ||
|| 19L3s || 15\22 < g < 13\19 || g = 571\836 || g = 28\41, 41\60, 54\79 || 3g-2 || 13-19g ||
|| 20L2s || 1\22 < g < 1\20 || g = 21\440 || g = 2\42, 3\62, 4\72 || g || 1\2-10g ||
|| 21L1s || 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 />
&quot;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.&quot;<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 &quot;ati ati komals&quot; (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 &quot;half&quot; 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 />
&quot;half&quot;-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 />
&quot;half&quot;-status shuddha ga: [81/64; 408]<br />
<br />
Ma (2):<br />
shuddha Ma: [4/3; 498]<br />
ekasruti Ma: [27/20; 520]<br />
<br />
tivra Ma (2):<br />
tivra Ma: [45/32; 590]<br />
tivratar Ma: [729/512; 612]<br />
<br />
Pa (1): [3/2; 702]<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):<br />
shuddha dha: [5/3; 884]<br />
shuddha dha: [27/16; 906]<br />
<br />
komal ni (2):<br />
komal ni: [9/5; 1018]<br />
komal ni: [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 />
&quot;half&quot;-status shuddha ni: [243/128; 1110]<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:0 -->Regular temperaments of the full-status shrutis</h2>
 <strong>Note: generators in italics will generate a 22 tone set which is too weakly tonal for serious practice</strong><br />


<table class="wiki_table">
    <tr>
        <th>Large-small numbers<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>21\22 &lt; g &lt; 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>10\22 &lt; g &lt; 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>7\22 &lt; g &lt; 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>5\22 &lt; g &lt; 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>13\22 &lt; g &lt; 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>7\22 &lt; g &lt; 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>3\22 &lt; g &lt; 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>8\22 &lt; g &lt; 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>17\22 &lt; g &lt; 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>2\22 &lt; g &lt; 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>1\22 &lt; g &lt; 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>9\22 &lt; g &lt; 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>5\22 &lt; g &lt; 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\22 &lt; g &lt; 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>19\22 &lt; g &lt; 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>4\22 &lt; g &lt; 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>9\22 &lt; g &lt; 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>6\22 &lt; g &lt; 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>15\22 &lt; g &lt; 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>1\22 &lt; g &lt; 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>1\22 &lt; g &lt; 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>