Indian music

Indian music is one of the major microtonal traditions of the world (along with the Middle Eastern family of traditions).

The unit of measurement in the Indian system is the shruti (sometimes spelled śruti, sruti or shruthi), which corresponds roughly to a quarter-tone. There are 22 shrutis per octave, 13 per fifth and 9 per fourth. A size of 4 shruti for the major whole tone follows from that. The step sizes of the heptatonic scales (shadja grama, madhyama grama) are given as sequences of 4, 3, and 2 shruti.

There is no single standardized non-ambiguous definition of the exact sizes of all shruti intervals.

An explanation about the shruti system and one traditional derivation of the 22 shrutis is available here.

Another example of a compilation of the shrutis, with explicit values of the intervals, can be found here.

The system has been approximated by 22edo, though the traditional tuning system is unequal, and split-shruti systems may approximated by the 22&34d (or 12&22 or even 10&12 generalized Diaschismic if simplicity or accuracy is no object) temperament.

The Wikipedia entry on shrutis gives a quite accurate approximation of the shruti system as a 22-note subset of 53edo. (See also a discussion on the Yahoo tuning list and immediately below for a duplication of the chart.

Shrutis				24-TET		106-TET
Name	Ratio	Cents	Frequency (Hz)		Name	Step	Cents
Chandovatī	1	0	261.6256		C	0
	36/35	49	269.1005	269.2918	C‡	4	45.28
Dayāvatī	256/243	90	275.6220	277.1826	D♭	8	90.57
Ranjanī	16/15	112	279.0673	277.1826	D♭	10	113.21
	49/45	147	284.8812	285.3047	DTemplate:Music	13	147.17
Ratikā	10/9	182	290.6951	293.6648	D	16	181.13
Raudrī	9/8	204	294.3288	293.6648	D	18	203.78
	81/70	253	302.73815	302.2698	D‡	22	249.06
Krodhā	32/27	294	310.0747	311.1270	E♭	26	294.34
Vajrikā	6/5	316	313.9507	311.1270	E♭	28	316.98
	11/9	347	319.7646	320.2437	E Template:Music	31	350.94
Prasāriṇī	5/4	386	327.0319	329.6275	E	34	384.91
Prīti	81/64	408	331.1198	329.6275	E	36	407.55
	35/27	449	339.14425	339.2864	E‡/F Template:Music	40	452.83
Mārjanī	4/3	498	348.8341	349.2282	F	44	498.11
Kṣhiti	27/20	519	353.1945	349.2282	F	46	520.75
	135/98	554	360.2046	359.4614	F‡	49	554.72
Raktā	45/32	590	367.9109	369.9944	F#	52	588.68
Sandīpanī	729/512	612	372.5098	369.9944	F#	54	611.32
	35/24	653	381.5373	380.8361	G Template:Music	58	656.6
Ālāpinī	3/2	702	392.4383	391.9954	G	62	701.89
	54/35	751	403.6509	403.4818	G‡	66	747.17
Madantī	128/81	792	413.4330	415.3047	A♭	70	792.45
Rohiṇī	8/5	814	418.6009	415.3047	A♭	72	815.09
	49/30	849	427.3218	427.47405	A‡	75	849.06
Ramyā	5/3	884	436.0426	440.0000	A	78	883.02
Ugrā	27/16	907	441.4931	440.0000	A	80	905.66
	243/140	955	454.1072	452.893	A Template:Music	84	950.94
Kṣobhinī	16/9	996	465.1121	466.1638	B♭	88	996.23
Tīvrā	9/5	1017	470.9260	466.1638	B♭	90	1018.87
	11/6	1050	479.6469	479.8234	B Template:Music	93	1052.83
Kumudvatī	15/8	1088	490.5479	493.8833	B	96	1086.79
Mandā	243/128	1110	496.6798	493.8833	B	98	1109.43
	35/18	1151	508.7164	508.3552	B‡/C Template:Music	102	1154.72
Chandovatī	2	1200	523.2511		C	106	1200

Some derivations in the light of modern temperament theory: Magic22 and Shrutar22 as srutis

Indian music

Other links