OTC JI 22 sruti scale

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This page examines the omnitetrachordality of the 22-tone Indian 'sruti' scale, a 5-limit 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
0-1-2-3-4 256/243-81/80-25/24-81/80 A-b-c-b
4-5-6-7-8 256/243-81/80-25/24-81/80 A-b-c-b
8-9-10-11-12 256/243-81/80-25/24-81/80 A-b-c-b
12-13 256/243 A
13-14-15-16-17 256/243-81/80-25/24-81/80 A-b-c-b
17-18-19-20-21 256/243-81/80-25/24-81/80 A-b-c-b
21-22 256/243 A

all modes:

Abcb AbcbAbcbA AbcbAbcbA AbcbAbcbA bcbA AbcbAbcbA AbcbAbcbA AbcbAbcbA Abcb
bcbA bcbAbcbAA bcbAbcbAA AbcbAbcbA Abcb AbcbAbcbA bcbAbcbAA bcbAbcbAA bcbA
cbAb cbAbcbAAb cbAbcbAAb bcbAbcbAA bcbA bcbAbcbAA cbAbcbAAb cbAbcbAAb cbAb
bAbc bAbcbAAbc bAbcbAAbc cbAbcbAAb cbAb cbAbcbAAb bAbcbAAbc bAbcbAAbc bAbc
Abcb AbcbAAbcb AbcbAAbcb bAbcbAAbc bAbc bAbcbAAbc AbcbAAbcb AbcbAAbcb Abcb
bcbA bcbAAbcbA bcbAAbcbA AbcbAAbcb Abcb AbcbAAbcb bcbAAbcbA bcbAAbcbA bcbA
cbAb cbAAbcbAb cbAAbcbAb bcbAAbcbA bcbA bcbAAbcbA cbAAbcbAb cbAAbcbAb cbAb
bAbc bAAbcbAbc bAAbcbAbc cbAAbcbAb cbAb cbAAbcbAb bAAbcbAbc bAAbcbAbc bAbc
Abcb AAbcbAbcb AAbcbAbcb bAAbcbAbc bAbc bAAbcbAbc AAbcbAbcb AAbcbAbcb Abcb
bcbA AbcbAbcbA AbcbAbcbA AAbcbAbcb Abcb AAbcbAbcb AbcbAbcbA AbcbAbcbA bcbA

lattice:

                     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

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

OTC 17L+5s (A=L, b=L, c=s)

superpyth MOS

AbcbAbcbAbcbAAbcbAbcbA

LLsLLLsLLLsLLLLsLLLsLL

OTC 15L+7s (A=s, b=L, c=L)

porcupine MODMOS

AbcbAbcbAbcbAAbcbAbcbA

sLLLsLLLsLLLssLLLsLLLs

OTC 12L+10s (A=L, b=s, c=L)

pajara MODMOS

AbcbAbcbAbcbAAbcbAbcbA

LsLsLsLsLsLsLLsLsLsLsL (form 1)

See also

References

  • Noted as omnitetrachordal by Paul Erlich; date unknown.