Swaras, Swarasthanas and Sruthis

When I started my musical expedition, I was told there are seven notes in any music- Sa, Ri, Ga, Ma, Pa, Da, Ni or Do, Re, Mi, Fa, So, La, Ti. Remember the song from Sound of Music – “if you know the notes to sing you, you can sing `most anything”. In India we call them as saptha-swaras. We hear that this is the basis of any music in the world. One day I took out my mother’s old harmonium and was trying to play these notes on them. I played the white keys Sa to Sa, one octave of eight notes and was very pleased with it.


Hey, But what are these five black keys sitting between those whites?


“They are additional notes in an octave.”


You mean, there are 12 notes instead of seven? But what are they called? I have never heard any other swaras except the ones mentioned above.


“These additional five notes are the variations of the five swaras, Ri, Ga, Ma, Da and N.   … Yes, Sa and Pa are constants without variations.”


You mean there are 12 swaras instead of 7.


“No. There are only seven swaras, but we have 12 sruthis.”


Then may I call them, S,R1,R2,G1,G2,M1,M2,P,D1,D2,N1 and N2.


“Yes you may”.


Oh, it means one can make 32 basic scales, calculated as: 1x2x2x2x1x2x2=32.


“Yes, 32 `pure’ scales, as some people may call it”


What do you mean? How do you get any more scales and why are they impure?


“There are: a R3 in the same place as G1, a G0 in the same place as R2, a D3 in the same place as N1 and a N0 in the same place as D2. These are considered ‘impure’ with vivadi dosha as they take the place of another note.”


Then why have them?


“Because there are already melodies existing in scales using these notes, even before the grammar on music was compiled”


Okay. Going back to basic scales, now we get 2x3x3x ….., no, no, something wrong! …..We get 1x(6)x2x1x(6) = 72. Now, I see! So these are called the ‘72-Melakarthas’ or basic scales. Right?


“Very good. You are quite sharp to get it right”.


I hope, at least now we can codify all our ancient ragas within these 72 scales.


“Yes and No. We will discuss this later.”


Now we have 12 sruthis, 16 swarasthanas and 7 swaras. Are these same for all music including western music?


“In Western music, they call these 12 sruthis as semitones. The groups of 7 notes taken from these twelve semitones are called scales. One major change took place in about 17th century. Perhaps in an attempt to standardize the frequencies of these 12 tones, they made them go in a geometric progression from a base frequency of 240 Hz to 480 Hz. (like from lower Sa to upper Sa).  This division of the octave into twelve ‘tones’ which have equal ratio between adjacent keys (the ratio equalling to 12th root of 2 = 1.059) is peculiar to Western music. This geometric arrangement of frequencies of the 12 notes in an octave is called an ‘Equally tempered’ arrangement. Most western musical instruments were tuned to such an arrangement, including the harmonium your mother had.”


Oh my God. May be that is why harmonium is not accepted as a karnatic classical instrument. In such a tuning how do they ensure consonance between notes?


“Luckily music world still has another way of tuning these notes, generally called `Just Tempered’ where such consonances you have mentioned are taken care of. But that is not the only reason why harmonium is not accepted in carnatic music platform. Harmonium or any fixed key instruments like keyboards cannot produce anything other than these 12 tones.   


Hey, Hey, Wait. First it was seven notes (Saptha swaras). Then we settled for 12 sruthis. Now why and where are these sruthis other than these 12?  I am confused.


“Many carnatic musicians and musicologists stress that a large number of our ancient ragas cannot be produced with only these 12 sruthis”


Any examples?.


“I have heard them say that ragas Saveri, Gowla and Mayamalavagowla theoretically use the same suddha rishaba, but in actual usage they are different. Same they say about madhyama of Raga Varali.”


Uhm…! Now where are we heading to?


“If we strictly go by consonance ratios of 3/2(Pa), 4/3(Ma) or 5/4(Ga) alone we can get infinite frequency intervals within an octave (one sthayi). But human ear in general cannot distinguish between two frequencies with an interval ratio less than 81/80. This ratio 81/80 is known as pramana sruthi (Systonic Comma). Avoiding such intervals and satisfying the consonance ratios as above we are able to derive 22 sruthis in an octave. Musicologists quote ancient texts of Silappadikaram, a tamil epic by Ilango Adigal and Natya Sastra by Sage Bharata in Sanskrit (both dated between 2nd century BC and 2nd Century AD) and concludes that our ancient musical tradition had in fact 22 sruthis as basis. There are some slight disagreements on the actual values of these 22 sruthis but in general they are accepted. Even Hindustani musicians have agreed to this 22-sruthi concept.”


Ooof…! I think this is enough for the day


“Well, I also think so. Let me just give you a table showing one acceptable set of 22-sruthis. You may study it when you have time”


Okay. , bye and thanks.


“Bye, bye”



Derivation of 22 Sruthis

(By consonance ratios)

One possible way of deriving the 22 Sruthis used in carnatic music is shown as below.                                                                                                                                                      

Cycle of 5th or Panchama cycle (x 3/2)



























































Cycle of 4th or Madhyama cycle (x 4/3)























































































The selected sruthi values are shown highlighted. We may arrange them in an ascending order as


 1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32 :

: 64/45, 40/27, 3/2, 128/81, 8/5, 5/3. 27/16, 16/9, 9/5, 15/8, 243/128, 2                                  

It may be seen there are actually 24 sruthi values (including 1 and 2, the ends of an octave, Sa to Sa). The 12th sruthi is repeated as 45/32 and 64/45. They are away from each other by less than a pramana sruthi of 81/80. Hence only one of these two will be considered. Hence we get 23 sruthis, i.e 22-intervals in an octave.


It is possible Sri. Venkatamakhi considered the following 12 notes for the Melakartha scheme (or did he use the Equi-Tempered notes of western music?):

1, 16/15, 9/8, 6/5, 5/4, 4/3, 40/27, 3/2, 8/5, 27/16, 9/5, 15/8, 2 

– – – – – – – – -/oooooo/- – – – – – – – –






10 Responses to “Swaras, Swarasthanas and Sruthis”

  1. Mohan Jayaraman Says:

    Very informative, though I didn’t understand the last part as it went above my head.

    Thanks for visiting my blog – http://7swara.blogspot.com

  2. Dr.Vidyadhar Oke Says:

    Dear Sir,
    You may be delighted to know that now, a patented 22-shruti-harmonium is created and such harmoniums in all 12 scales are available with me. You may visit my above website for hearing 22 shrutis in all 12 scales, for videos on 22-shruti-harmonium, and 22-shruti-metallophone, and other related information.
    Best Regards,
    Dr.Vidyadhar Oke

  3. Ragas in Indian Music – FAQ2 « OPEN MIND Says:

    […] https://lvnaga.wordpress.com/2008/09/15/swaras-swarasthanas-and-sruthis/  […]

  4. Amritheshwary Says:

    This blog is very informative . I didn’t undertand the last part regrding 22 sruthis and other calculations.

    Expecting more informations regarding carnatic music.


  5. sahiti Says:

    useful and informative thanks alot

  6. Ravindra Says:

    Excellent and extremely informative. Thank yu very much. I wish to know more and more

  7. N S Rao Says:

    Kindly confirm that in respect of notes, in carnatic music the 7 notes are distributed among 22 sruthis among 7 notes, while in hindustani music it is not. Thanq

    • Nagarajan Says:

      I am not very familiar with Hindustani system as it has evolved now, though the origin and grammar for both Carnatic and Hindustani systems are same. Hindustani system has approved and adopted the 12-notes concept almost completely. They are quite comfortable with Harmonium tuned on this basis. Though Carnatic system also has adopted the 12-note concept with the evolution of 72-Melakartha scheme, it still uses minute notes (Nutpa-sruthis), on the basis of 22-sruthi system. Yes, in Carnatic music the 7-notes maps into all the 22-sruthis. I am not so sure of Hindustani system. I am directing this question to Dr. Vidhyadhar Oak, an expert in both the systems of Indian Music. (drvidyadharoke@yahoo.com). Thanks for your comment and the query. – Nagarajan.

  8. N S Rao Says:

    By way of correction to /improvement of what I said: I now state that
    1, Hundustani music has/uses 12 swaras and distributed the 22 sruthis among 12 swara sthanas.
    2.Carbatic music has and uses 12 swaras and dustrubuted 22 sruthis aming 16 swarasthanas,

    May I hope some one will confirm this observation


  9. Komaravolu Nageswara Rao Says:

    I am a lay man in music.
    My interest is to know:
    1- what are those 64 swara mentioned by historian-advocate Oak?
    2- How are those related to the 16 swara in our alphabets?
    3-If 16 x 4 = 64, then what that 4 indicates?
    4- Are these 64 variations in swara linked to 64 Yogini [not the tantra type] or to the musical steps or both?
    5- Can the swara sthana or the swara can be arranged systematically in to the 64 squares of the Chess board?
    I thought that vyanjana [consonants] came into use ever since the man started covering his body, as he lost the perfect mastery on the 64 swara ever since. In this context I take swara as Vowels.
    please guide me.
    Thanks a lot.

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