Xenharmonic Wiki

OTC JI 22 sruti scale

Revision as of 22:22, 28 August 2016 by Wikispaces>spt3125 (**Imported revision 590312774 - Original comment: **)

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Original Wikitext content:

This page examines the [[omnitetrachordality]] of the 22-tone Indian 'sruti' scale, a 5-limit [[Just intonation|JI]] scale with three step sizes -- one of many possible theoretical tunings for Indian classical music.  (This scale may be found in the [[Scala]] archive as {{ indian.scl }}.)

||= **scale step** ||= **ratio** ||> **cents** ||= **name** ||
||=  0 ||= 1/1     ||>    0.000 ||= Sa ||
||=  1 ||= 256/243 ||>   90.225 ||= r1 ||
||=  2 ||= 16/15   ||>  111.731 ||= r2 ||
||=  3 ||= 10/9    ||>  182.404 ||= R3 ||
||=  4 ||= 9/8     ||>  203.910 ||= R4 ||
||=  5 ||= 32/27   ||>  294.135 ||= g1 ||
||=  6 ||= 6/5     ||>  315.641 ||= g2 ||
||=  7 ||= 5/4     ||>  386.314 ||= G3 ||
||=  8 ||= 81/64   ||>  407.820 ||= G4 ||
||=  9 ||= 4/3     ||>  498.045 ||= Ma ||
||= 10 ||= 27/20   ||>  519.551 ||= m2 ||
||= 11 ||= 45/32   ||>  590.224 ||= m3 ||
||= 12 ||= 729/512 ||>  611.730 ||= m4 ||
||= 13 ||= 3/2     ||>  701.955 ||= Pa ||
||= 14 ||= 128/81  ||>  792.180 ||= d1 ||
||= 15 ||= 8/5     ||>  813.686 ||= d2 ||
||= 16 ||= 5/3     ||>  884.359 ||= D3 ||
||= 17 ||= 27/16   ||>  905.865 ||= D4 ||
||= 18 ||= 16/9    ||>  996.090 ||= n1 ||
||= 19 ||= 9/5     ||> 1017.596 ||= n2 ||
||= 20 ||= 15/8    ||> 1088.269 ||= N3 ||
||= 21 ||= 243/128 ||> 1109.775 ||= N4 ||
||= 22 ||= 2/1     ||> 1200.000 ||= Sa ||

A = 256/243 (90.225 cents)
b = 81/80 (21.506 cents)
c = 25/24 (70.672 cents)

9/8 = A+2b+c
4/3 = 3A+4b+2c
2/1 = 7A+10b+5c

||= **interval** ||= **ratio** ||= **step size** ||
||=  1-2  ||= 256/243 ||= A ||
||=  2-3  ||= 81/80   ||= b ||
||=  3-4  ||= 25/24   ||= c ||
||=  4-5  ||= 81/80   ||= b ||
||=  5-6  ||= 256/243 ||= A ||
||=  6-7  ||= 81/80   ||= b ||
||=  7-8  ||= 25/24   ||= c ||
||=  8-9  ||= 81/80   ||= b ||
||=  9-10 ||= 256/243 ||= A ||
||= 10-11 ||= 81/80   ||= b ||
||= 11-12 ||= 25/24   ||= c ||
||= 12-13 ||= 81/80   ||= b ||
||= 13-14 ||= 256/243 ||= A ||
||= 14-15 ||= 256/243 ||= A ||
||= 15-16 ||= 81/80   ||= b ||
||= 16-17 ||= 25/24   ||= c ||
||= 17-18 ||= 81/80   ||= b ||
||= 18-19 ||= 256/243 ||= A ||
||= 19-20 ||= 81/80   ||= b ||
||= 20-21 ||= 25/24   ||= c ||
||= 21-22 ||= 81/80   ||= b ||
||= 22-1  ||= 256/243 ||= A ||


all modes:
|| {{ Abcb AbcbAbcbA AbcbAbcbA }} || {{ AbcbAbcbA bcbA AbcbAbcbA }} || ||
|| {{ bcbA bcbAbcbAA bcbAbcbAA }} || || ||
|| {{ cbAb cbAbcbAAb cbAbcbAAb }} || || ||
|| {{ bAbc bAbcbAAbc bAbcbAAbc }} || || ||
|| {{ Abcb AbcbAAbcb AbcbAAbcb }} || || {{ AbcbAbcbA AbcbAbcbA Abcb }} ||
|| {{ bcbA bcbAAbcbA bcbAAbcbA }} || || {{ bcbAbcbAA bcbAbcbAA bcbA }} ||
|| {{ cbAb cbAAbcbAb cbAAbcbAb }} || || {{ cbAbcbAAb cbAbcbAAb cbAb }} ||
|| {{ bAbc bAAbcbAbc bAAbcbAbc }} || || {{ bAbcbAAbc bAbcbAAbc bAbc }} ||
|| {{ Abcb AAbcbAbcb AAbcbAbcb }} || || {{ AbcbAAbcb AbcbAAbcb Abcb }} ||
|| {{ bcbA AbcbAbcbA AbcbAbcbA }} || || {{ bcbAAbcbA bcbAAbcbA bcbA }} ||
|| || || {{ cbAAbcbAb cbAAbcbAb cbAb }} ||
|| || || {{ bAAbcbAbc bAAbcbAbc bAbc }} ||
|| || || {{ AAbcbAbcb AAbcbAbcb Abcb }} ||
|| || {{ AbcbAbcbA Abcb AbcbAbcbA }} || {{ AbcbAbcbA AbcbAbcbA bcbA }} ||
|| || {{ bcbAbcbAA bcbA bcbAbcbAA }} || ||
|| || {{ cbAbcbAAb cbAb cbAbcbAAb }} || ||
|| || {{ bAbcbAAbc bAbc bAbcbAAbc }} || ||
|| || {{ AbcbAAbcb Abcb AbcbAAbcb }} || ||
|| || {{ bcbAAbcbA bcbA bcbAAbcbA }} || ||
|| || {{ cbAAbcbAb cbAb cbAAbcbAb }} || ||
|| || {{ bAAbcbAbc bAbc bAAbcbAbc }} || ||
|| || {{ AAbcbAbcb Abcb AAbcbAbcb }} || ||


lattice:
[[code]]
                     R3 -- D3 -- G3 -- N3 -- m3
                      |     |     |     |     |
   r1 -- d1 -- g1 -- n1 -- Ma -- Sa -- Pa -- R4 -- D4 -- G4 -- N4 -- m4
                           |      |     |     |     |
                           r2 -- d2 -- g2 -- n2 -- m2
5
|
1 -- 3
                     10     5     5    15    45
                      / --- / --- / --- / --- /
                      9     3     4     8    32
                      |     |     |     |     |
   256   128   32    16     4     1     3     9    27    81    243   729
    / --- / --- / --- / --- / --- / --- / --- / --- / --- / --- / --- /
   243    81   27     9     3     1     2     8    16    64    128   512
                            |     |     |     |     |
                           16     8     6     9    27
                            / --- / --- / --- / --- /
                           15     5     5     5    20
[[code]]


This scale could be considered a detempering of the following OTC scales with two step sizes:

[[OTC 17L 5s|OTC 17L+5s]] (A=L, b=L, c=s)
superpyth MOS
{{ AbcbAbcbAbcbAAbcbAbcbA }}
{{ LLsLLLsLLLsLLLLsLLLsLL }}

[[OTC 15L 7s|OTC 15L+7s]] (A=s, b=L, c=L)
porcupine MODMOS
{{ AbcbAbcbAbcbAAbcbAbcbA }}
{{ sLLLsLLLsLLLssLLLsLLLs }}

[[OTC 12L 10s|OTC 12L+10s]]  (A=L, b=s, c=L)
pajara MODMOS
{{ AbcbAbcbAbcbAAbcbAbcbA }}
{{ LsLsLsLsLsLsLLsLsLsLsL }} (form 1)


===See also===
* [[Gallery of omnitetrachordal scales]]

===References===
* Noted as omnitetrachordal by Paul Erlich; date unknown.

Original HTML content:

<html><head><title>OTC JI 22 sruti scale</title></head><body>This page examines the <a class="wiki_link" href="/omnitetrachordality">omnitetrachordality</a> of the 22-tone Indian 'sruti' scale, a 5-limit <a class="wiki_link" href="/Just%20intonation">JI</a> scale with three step sizes -- one of many possible theoretical tunings for Indian classical music.  (This scale may be found in the <a class="wiki_link" href="/Scala">Scala</a> archive as <tt> indian.scl </tt>.)<br />
<br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>scale step</strong><br />
</td>
        <td style="text-align: center;"><strong>ratio</strong><br />
</td>
        <td style="text-align: right;"><strong>cents</strong><br />
</td>
        <td style="text-align: center;"><strong>name</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: right;">0.000<br />
</td>
        <td style="text-align: center;">Sa<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: right;">90.225<br />
</td>
        <td style="text-align: center;">r1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">16/15<br />
</td>
        <td style="text-align: right;">111.731<br />
</td>
        <td style="text-align: center;">r2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">10/9<br />
</td>
        <td style="text-align: right;">182.404<br />
</td>
        <td style="text-align: center;">R3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">9/8<br />
</td>
        <td style="text-align: right;">203.910<br />
</td>
        <td style="text-align: center;">R4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">32/27<br />
</td>
        <td style="text-align: right;">294.135<br />
</td>
        <td style="text-align: center;">g1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">6/5<br />
</td>
        <td style="text-align: right;">315.641<br />
</td>
        <td style="text-align: center;">g2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">5/4<br />
</td>
        <td style="text-align: right;">386.314<br />
</td>
        <td style="text-align: center;">G3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">81/64<br />
</td>
        <td style="text-align: right;">407.820<br />
</td>
        <td style="text-align: center;">G4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">4/3<br />
</td>
        <td style="text-align: right;">498.045<br />
</td>
        <td style="text-align: center;">Ma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: center;">27/20<br />
</td>
        <td style="text-align: right;">519.551<br />
</td>
        <td style="text-align: center;">m2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: center;">45/32<br />
</td>
        <td style="text-align: right;">590.224<br />
</td>
        <td style="text-align: center;">m3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: center;">729/512<br />
</td>
        <td style="text-align: right;">611.730<br />
</td>
        <td style="text-align: center;">m4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">3/2<br />
</td>
        <td style="text-align: right;">701.955<br />
</td>
        <td style="text-align: center;">Pa<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">128/81<br />
</td>
        <td style="text-align: right;">792.180<br />
</td>
        <td style="text-align: center;">d1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">8/5<br />
</td>
        <td style="text-align: right;">813.686<br />
</td>
        <td style="text-align: center;">d2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">5/3<br />
</td>
        <td style="text-align: right;">884.359<br />
</td>
        <td style="text-align: center;">D3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">27/16<br />
</td>
        <td style="text-align: right;">905.865<br />
</td>
        <td style="text-align: center;">D4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: center;">16/9<br />
</td>
        <td style="text-align: right;">996.090<br />
</td>
        <td style="text-align: center;">n1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">9/5<br />
</td>
        <td style="text-align: right;">1017.596<br />
</td>
        <td style="text-align: center;">n2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">15/8<br />
</td>
        <td style="text-align: right;">1088.269<br />
</td>
        <td style="text-align: center;">N3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">243/128<br />
</td>
        <td style="text-align: right;">1109.775<br />
</td>
        <td style="text-align: center;">N4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
        <td style="text-align: right;">1200.000<br />
</td>
        <td style="text-align: center;">Sa<br />
</td>
    </tr>
</table>

<br />
A = 256/243 (90.225 cents)<br />
b = 81/80 (21.506 cents)<br />
c = 25/24 (70.672 cents)<br />
<br />
9/8 = A+2b+c<br />
4/3 = 3A+4b+2c<br />
2/1 = 7A+10b+5c<br />
<br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>interval</strong><br />
</td>
        <td style="text-align: center;"><strong>ratio</strong><br />
</td>
        <td style="text-align: center;"><strong>step size</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1-2<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2-3<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3-4<br />
</td>
        <td style="text-align: center;">25/24<br />
</td>
        <td style="text-align: center;">c<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4-5<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5-6<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6-7<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7-8<br />
</td>
        <td style="text-align: center;">25/24<br />
</td>
        <td style="text-align: center;">c<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8-9<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9-10<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10-11<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11-12<br />
</td>
        <td style="text-align: center;">25/24<br />
</td>
        <td style="text-align: center;">c<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12-13<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13-14<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14-15<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15-16<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16-17<br />
</td>
        <td style="text-align: center;">25/24<br />
</td>
        <td style="text-align: center;">c<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17-18<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18-19<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19-20<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20-21<br />
</td>
        <td style="text-align: center;">25/24<br />
</td>
        <td style="text-align: center;">c<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21-22<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: center;">b<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22-1<br />
</td>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: center;">A<br />
</td>
    </tr>
</table>

<br />
<br />
all modes:<br />


<table class="wiki_table">
    <tr>
        <td><tt> Abcb AbcbAbcbA AbcbAbcbA </tt><br />
</td>
        <td><tt> AbcbAbcbA bcbA AbcbAbcbA </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> bcbA bcbAbcbAA bcbAbcbAA </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> cbAb cbAbcbAAb cbAbcbAAb </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> bAbc bAbcbAAbc bAbcbAAbc </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> Abcb AbcbAAbcb AbcbAAbcb </tt><br />
</td>
        <td><br />
</td>
        <td><tt> AbcbAbcbA AbcbAbcbA Abcb </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> bcbA bcbAAbcbA bcbAAbcbA </tt><br />
</td>
        <td><br />
</td>
        <td><tt> bcbAbcbAA bcbAbcbAA bcbA </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> cbAb cbAAbcbAb cbAAbcbAb </tt><br />
</td>
        <td><br />
</td>
        <td><tt> cbAbcbAAb cbAbcbAAb cbAb </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> bAbc bAAbcbAbc bAAbcbAbc </tt><br />
</td>
        <td><br />
</td>
        <td><tt> bAbcbAAbc bAbcbAAbc bAbc </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> Abcb AAbcbAbcb AAbcbAbcb </tt><br />
</td>
        <td><br />
</td>
        <td><tt> AbcbAAbcb AbcbAAbcb Abcb </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> bcbA AbcbAbcbA AbcbAbcbA </tt><br />
</td>
        <td><br />
</td>
        <td><tt> bcbAAbcbA bcbAAbcbA bcbA </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> cbAAbcbAb cbAAbcbAb cbAb </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> bAAbcbAbc bAAbcbAbc bAbc </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> AAbcbAbcb AAbcbAbcb Abcb </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> AbcbAbcbA Abcb AbcbAbcbA </tt><br />
</td>
        <td><tt> AbcbAbcbA AbcbAbcbA bcbA </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> bcbAbcbAA bcbA bcbAbcbAA </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> cbAbcbAAb cbAb cbAbcbAAb </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> bAbcbAAbc bAbc bAbcbAAbc </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> AbcbAAbcb Abcb AbcbAAbcb </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> bcbAAbcbA bcbA bcbAAbcbA </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> cbAAbcbAb cbAb cbAAbcbAb </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> bAAbcbAbc bAbc bAAbcbAbc </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> AAbcbAbcb Abcb AAbcbAbcb </tt><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
lattice:<br />
<!-- ws:start:WikiTextCodeRule:0:
&lt;pre class=&quot;text&quot;&gt;                     R3 &amp;#45;- D3 &amp;#45;- G3 &amp;#45;- N3 &amp;#45;- m3&lt;br/&gt;                      |     |     |     |     |&lt;br/&gt;   r1 &amp;#45;- d1 &amp;#45;- g1 &amp;#45;- n1 &amp;#45;- Ma &amp;#45;- Sa &amp;#45;- Pa &amp;#45;- R4 &amp;#45;- D4 &amp;#45;- G4 &amp;#45;- N4 &amp;#45;- m4&lt;br/&gt;                           |      |     |     |     |&lt;br/&gt;                           r2 &amp;#45;- d2 &amp;#45;- g2 &amp;#45;- n2 &amp;#45;- m2&lt;br/&gt;5&lt;br/&gt;|&lt;br/&gt;1 &amp;#45;- 3&lt;br/&gt;                     10     5     5    15    45&lt;br/&gt;                      / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- /&lt;br/&gt;                      9     3     4     8    32&lt;br/&gt;                      |     |     |     |     |&lt;br/&gt;   256   128   32    16     4     1     3     9    27    81    243   729&lt;br/&gt;    / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- /&lt;br/&gt;   243    81   27     9     3     1     2     8    16    64    128   512&lt;br/&gt;                            |     |     |     |     |&lt;br/&gt;                           16     8     6     9    27&lt;br/&gt;                            / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- / &amp;#45;&amp;#45;- /&lt;br/&gt;                           15     5     5     5    20&lt;/pre&gt;
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</style><pre class="text">                     R3 -- D3 -- G3 -- N3 -- m3
                      |     |     |     |     |
   r1 -- d1 -- g1 -- n1 -- Ma -- Sa -- Pa -- R4 -- D4 -- G4 -- N4 -- m4
                           |      |     |     |     |
                           r2 -- d2 -- g2 -- n2 -- m2
5
|
1 -- 3
                     10     5     5    15    45
                      / --- / --- / --- / --- /
                      9     3     4     8    32
                      |     |     |     |     |
   256   128   32    16     4     1     3     9    27    81    243   729
    / --- / --- / --- / --- / --- / --- / --- / --- / --- / --- / --- /
   243    81   27     9     3     1     2     8    16    64    128   512
                            |     |     |     |     |
                           16     8     6     9    27
                            / --- / --- / --- / --- /
                           15     5     5     5    20</pre>

<!-- ws:end:WikiTextCodeRule:0 --><br />
<br />
This scale could be considered a detempering of the following OTC scales with two step sizes:<br />
<br />
<a class="wiki_link" href="/OTC%2017L%205s">OTC 17L+5s</a> (A=L, b=L, c=s)<br />
superpyth MOS<br />
<tt> AbcbAbcbAbcbAAbcbAbcbA </tt><br />
<tt> LLsLLLsLLLsLLLLsLLLsLL </tt><br />
<br />
<a class="wiki_link" href="/OTC%2015L%207s">OTC 15L+7s</a> (A=s, b=L, c=L)<br />
porcupine MODMOS<br />
<tt> AbcbAbcbAbcbAAbcbAbcbA </tt><br />
<tt> sLLLsLLLsLLLssLLLsLLLs </tt><br />
<br />
<a class="wiki_link" href="/OTC%2012L%2010s">OTC 12L+10s</a>  (A=L, b=s, c=L)<br />
pajara MODMOS<br />
<tt> AbcbAbcbAbcbAAbcbAbcbA </tt><br />
<tt> LsLsLsLsLsLsLLsLsLsLsL </tt> (form 1)<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:1 -->See also</h3>
<ul><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h3&gt; --><h3 id="toc1"><a name="x--References"></a><!-- ws:end:WikiTextHeadingRule:3 -->References</h3>
<ul><li>Noted as omnitetrachordal by Paul Erlich; date unknown.</li></ul></body></html>
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