Shruti (music)

For other uses, see Śruti (disambiguation).

Shruti or sruti (pronounced śruti) is a Sanskrit term, which in the context of Indian music, is the smallest interval of pitch that the human ear can detect. It has been used in several contexts throughout the history of Indian music.

Contexts

To know the real meaning of shruti, it is important to know the various contexts in which the term is used.

Ancient period: Grama system

Bharata Muni uses shruti to mean the interval between two notes such that the difference between them is perceptible. He formulates jatis, which are classes of melodic structures. These can be further grouped into two gramas—shadja-grama and madhyama-grama. The notes (svaras) are separated by intervals, as measured in shrutis.

The shadja-grama is given by the following division: Sa of four shrutis, Ri of three shrutis, Ga of two shrutis, Ma of four shrutis, Pa of four shrutis, Da of three shrutis and Ni of two shrutis. Bharata also describes an experiment to obtain the correct physical configuration of shruti in shadja grama, Sarana Chatushtai.

The madhyama-grama is the same, but the panchama (Pa) has to be diminished by one shruti. That is, the panchama of madhyama-grama is lower than that of shadja-grama by one shruti, according to Bharata. Shruti is only mentioned as a perceptual measure in the music of Bharata's time.

In both the gramas, Ri is three shrutis away from Sa – there are three perceptible intervals between Sa and Ri. The third of these is called trishruti rishabha (Ri). Likewise, the second interval is called dvishruti rishabha, and the first ekashruti rishabha.

Notes nine and 13 shrutis from each other are mutually samvādi (consonant). The notes that are at the distance of two and 20 shrutis are mutually vivādi (dissonant). The remaining ones, at the distance between 2 and 20 shrutis, are called anuvādi (assonant).

The shruti table below shows the mathematical ratios considered to correspond to the system described by Bharata and Dattila, along with the comparable notes in common Western 12-TET tuning and comparable notes in 53-TET tuning. The names of the 22 shrutis were provided by Śārñgadeva.

Shrutis				12-TET Notes		53-TET Notes		Perfect FIFTHs
Name	Ratio	Cents	Frequency (Hz)	Name	Frequency (Hz)	Note No.	Frequency (Hz)	FIFTH No.	Frequency (Hz)
Kṣobhinī	1	0	261.6256	C	261.6256	0	261.6256	0	261.6256
Tīvrā	256/243	90	275.6220	C♯	277.1826	4	275.6763	-5	275.622
Kumudvatī	16/15	112	279.0673			5	279.3053	7	279.3824
Mandā	10/9	182	290.6951	D	293.6648	8	290.4816	-10	290.3672
Chandovatī	9/8	203	294.3288			9	294.3056	2	294.3288
Dayāvatī	32/27	294	310.0747	D♯	311.1270	13	310.1114	-3	310.0747
Ranjanī	6/5	316	313.9507			14	314.1937	9	314.3052
Raktikā	5/4	386	327.0319	E	329.6275	17	326.7661	-8	326.6631
Raudrī	81/64	407	331.1198			18	331.0677	4	331.1199
Krodhā	4/3	498	348.8341	F	349.2282	22	348.8478	-1	348.8341
Vajrikā	27/20	519	353.1945			23	353.4401	11	353.5933
Prasāriṇī	45/32	590	367.9109	F♯	369.9944	26	367.5829	-6	367.496
Prīti	729/512	612	372.5098			27	372.4218	6	372.5098
Mārjanī	3/2	702	392.4383	G	391.9954	31	392.4229	1	392.4384
Kṣiti	128/81	792	413.4330	G♯	415.3047	35	413.4982	-4	413.433
Raktā	8/5	814	418.6009			36	418.9415	8	419.0736
Sandīpanī	5/3	884	436.0426	A	440.0000	39	435.7053	-9	435.5508
Ālāpinī	27/16	906	441.4931			40	441.441	3	441.4932
Madantī	16/9	996	465.1121	A♯	466.1638	44	465.1488	-2	465.1121
Rohiṇī	9/5	1017	470.9260			45	471.2721	10	471.4578
Ramyā	15/8	1088	490.5479	B	493.8833	48	490.1298	-7	489.9947
Ugrā	243/128	1110	496.6798			49	496.582	5	496.6798
Kṣobhinī	2	1200	523.2511	C	523.2511	53	523.2512	0	523.2511

The 53-TET approximation has a maximum error of 1.5%, while the perfect fifths approximation has a maximum error of 2%.

The table below shows the Harmonic scales into shruti:

Name	Frequency (Hz)	Normalized (Freq/261.6256)	HARMONIC MULTIPLES = Normalized x n (n = 2,3,4,5,6,8,9,10,12,15,16,18,19,20,24,25,27,30,32)
Kṣobhinī	261.6256	1.000000	2	3	4	5	6	8	9	10	12	15	16	18	19	20	24	25	27	30	32
Tīvrā	275.622	1.053498													20
Kumudvatī	279.0673	1.066667										16								32
Mandā	290.6951	1.111111							10					20					30
Chandovatī	294.3288	1.125000						9					18				27				36
Dayāvatī	310.0747	1.185185																	32
Ranjanī	313.9507	1.200000				6				12		18				24		30		36
Raktikā	327.0319	1.250000			5			10			15		20			25	30				40
Raudrī	331.1198	1.265625													24
Krodhā	348.8341	1.333333		4			8		12		16	20		24			32		36	40
Vajrikā	353.1945	1.350000														27
Prasāriṇī	367.9109	1.406250																			45
Prīti	372.5098	1.423828													27
Mārjanī	392.4383	1.500000	3		6		9	12		15	18		24	27		30	36			45	48
Kṣiti	413.433	1.580247								16					30
Raktā	418.6009	1.600000				8						24				32		40		48
Sandīpanī	436.0426	1.666666		5			10		15		20	25		30			40		45	50
Ālāpinī	441.4931	1.687500													32						54
Madantī	465.1121	1.777777							16					32					48
Rohiṇī	470.926	1.800000				9				18		27				36		45		54
Ramyā	490.5479	1.875000						15					30				45				60
Ugrā	496.6798	1.898437													36
Kṣobhinī	523.2511	2.000000	4	6	8	10	12	16	18	20	24	30	32	36	38	40	48	50	54	60	64

As is shown, the harmonics in scales of shruti are multiples of prime numbers 2, 3, 5 and 19. There are no multiples of 7, 11, 13, 17, 23, etc., just of 19. In reality it is not 19, but 19.2, because 19.2/32 = 3/5, which means that the harmonic 19.2 becomes the harmonic 3 and all of the harmonics multiplies up by 5.

Medieval period: Mela system

By the time Venkatamakhin formulated the melakarta ("mela") system, the grama system was no longer in use. Unlike the grama system, the mela system uses the same starting swara. It forms the scales by varying the intervals of the subsequent swaras, and does not specify a fixed interval for a swara in terms of shrutis. For example, the intervals of kakali-nishada and shuddha-madhyama vary depending on the dhaivata and the gandhara that precede them, respectively. The interval of kakali-nishada is of three different shruti values depending on whether shuddha, panca-sruti or shat-shruti-dhaivata preceded it. Thus shruti as a measure of interval is not fully employed in the mela system.

Modern period: Controversy

In current practice of Carnatic music, shruti has several meanings. It is used by musicians in several contexts. For instance, the Tamil term "Oru kattai sruti (ஒரு கட்டை ஸ்ருதி)" means that the tonic is set to the pitch C or the first key. The Telugu term "Sruti chesuko (శ్రుతి చేసుకో)" is a way to correspond with the accompanying artists to tune their instruments.

In certain ragas, due to inflexions or gamakas on some of those 12 notes, listeners perceive a sharpened or flattened version of an existing note. Some scholars have attempted to fit such perceived new tones into the non-contextual Bharata's 22 shrutis, which lead to confusion and controversy. It was also wrongly attributed to Bharata, who proposed shruti in a completely different context.

Some scientific evidence shows that these intermediate tones perceived in the contemporary rendition of a raga do not hint at the existence of 22 shrutis. The number 22 is of no practical significance in the current performance of Carnatic and Hindustani music traditions, partly because different musicians use slightly different "shrutis" when performing the same raga. The phenomenon of intermediate tones is pursued as an active area of research in Indian Musicology, which says the number of perceptible intermediate tones may be less or more than 22. N. Ramanathan, a musicologist points this out and says that the idea of 22 shrutis is applicable only to the music system of Bharata's time.

An Indian monograph about shruti claims various opinions about the number (66, 53) of shrutis. In recent times it seems that the number of shrutis is broadly agreed upon to be 22. Recognizing the controversy over the number and the exact ratios of shruti intervals, it also says that not all shruti intervals are equal and known as pramana shruti (22%), nyuna shruti (70% cents) and purana shruti (90%). Еach shruti may be approximated in 53EDO system.

Ancient treatises on Indian classical music and performing arts

• Natya Shastra by Bharata
• Dattilam by Dattila
• Brihaddeshi by Matanga
• Abhinavabharati - Abhinava Gupta's commentary on Natya Shastra
• Sangita Ratnakara by Sarangadeva