OTC JI 22 sruti scale

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

• Gallery of omnitetrachordal scales

References

• Noted as omnitetrachordal by Paul Erlich; date unknown.