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: 1×2x2×2x1×2x2=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 2×3x3x ….., no, no, something wrong! …..We get 1x(6)x2×1x(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.
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Cycle of 5th or Panchama cycle (x 3/2) |
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3/2 |
9/4 |
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9/8 |
27/16 |
81/32 |
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81/64 |
243/128 |
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4/3 |
2/1 |
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5/4 |
15/8 |
45/16 |
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45/32 |
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6/5 |
9/5 |
27/10 |
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27/20 |
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Cycle of 4th or Madhyama cycle (x 4/3) |
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3/2 |
2/1 |
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4/3 |
16/9 |
64/27 |
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32/27 |
128/81 |
512/243 |
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256/243 |
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5/4 |
5/3 |
20/9 |
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10/9 |
40/27 |
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6/5 |
8/5 |
32/15 |
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16/15 |
64/45 |
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The selected sruthi values are shown highlighted. We may arrange them in an ascending order as
below:
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
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