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Accuracy of Pitch [Jan. 8th, 2006|09:14 pm]
Arvind Narayanan
 [ Tags | music ]

I've been doing a bit of Carnatic-related coding recently. Here's a couple of graphs comparing the accuracy of pitch of a beginner and an expert, who shall be nameless. The range is one octave - the lower sa is at 0 and the upper sa is at 12. The difference is obvious. Surprisingly, the expert has some room for improvement too. Computers can greatly enhance Carnatic learning, but most practitioners are too tradition-bound to go near them.

Pitch graph - beginner

Pitch graph - expert

Another thing this graph shows is that the claim made by many people that the equally tempered scale is not suitable for Carnatic is baseless - the deviation from perfect pitch of even the expert (2-4 hertz) is greater than the difference between the 22-shruti scale and the equally tempered 12-note scale (at most 1 hertz).

 From: (Anonymous)2006-01-08 10:59 am (UTC) (Link)
I am Sandeep. Why should one go for the equally tempered scale at all ( why not 1, 16/15,... )?

Also do you have similar results for hindustAni? There are some hindustAni guys who tell me that only in hindustAni music do people actually sing the 22 notes perfectly; they have given some arguments based on the sequences of notes in rAgas that, say, multAni and miyAn kI tODi. I cannot distinguish between, say trishruti RShabhaM, catushruti RShabhaM and
2^(2/12). Another thing is, I have heard that shyAma shAstri began his
"birAna varAlicci" with trishruti RShabham. Should this be true, it seems
possible that there existed guys who had an ear fine enough to distinguish between such frequencies. May be one should hunt in traditional homes or so for people who claim they can sing these and cross-check. Similarly I saw in one of sAmbamUrtis books some ancient Indian text mentions "experiments" to illustrate the 22 shrutis but haven't bothered to procure those or check.

Also do you know how constant the tALam cycles are, atleast for
expert singers and mRdangists? As an aside I think it is laziness/inertia and not tradition that prevents musicians from approaching computers. I would like people to use time checking devices right from beginning to ensure that their kAla-pramANa is impeccable and also get their 22 shrutis right from the beginning, if possible.

Thanks a lot man.
From:
2006-01-08 11:36 am (UTC)

### kAlapramANa

Have a look here.
 From: 2006-01-08 11:46 am (UTC) (Link)
We want to use equi-tempered for the obvious reason that instrumentalists can use the same instrument no matter what the base pitch of the vocalist. In ancient Tam land, they used the yazh with the tonic scale. They went on adding strings to the yazh to keep up with the different possibilities to the point where no one could keep track of the mess any more. This is the same reason that equi-tempered is used EVERYWHERE IN THE WORLD. I don't want to rehash those reasons.

As for Hindustani - I have heard all knowledgeable people say that hindustani singers have much better accuracy of pitch than carnatic. I am positive that no human cannot sing the 22 notes perfectly. Actually "22 shrutis" is bogus - there are infinitely many shrutis in the tonic scale (for want of a better name) and different people choose a different subset of the shrutis and call them the 22 shrutis. Anyway, the difference between a tonic P and an equi-tempered P is 0.2 hertz! No one can distinguish the two. But other notes may have as much as a 1 hz difference, which can possibly be sung differently by hindustani singers. It is slightly possible that some highly accomplished Carnatic singers can also do that.

 From: 2006-01-08 12:01 pm (UTC) (Link)
I am clueless about mridangam; mssnlayam should know much better.

Your idea of "experiments" is interesting - finding the pitch resolution of the human ear. Wikipedia says:

Frequency resolution of the ear is, in the middle range, about 2 Hz. That is, changes in pitch larger than 2 Hz can be perceived. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a (low-)frequency difference pitch. This effect of phase variance upon the resultant sound is known as 'beating'. (http://en.wikipedia.org/wiki/Psychoacoustics)

I guess what one needs to measure is the resolution when two notes are sung not at the same time but one after the other (i.e, can one tell the difference between S followed by tri-R and S followed by chathur-R). I'm guessing the resolution must be somewhere around 1 hz.

P.S my source for history of tam music is Rangaramanuja Iyengar's book.
 From: (Anonymous)2006-01-08 12:09 pm (UTC) (Link)
I am Sandeep. Well, these 22 shrutis are those that approximate the 12 notes, and most of them are in small integer ratios. And how exactly does one conclude that notes of 1 hz difference can possibly be sung differently but the 22 shrutis cannot be reproduced perfectly? And can you give any reference to the claim that everywhere else in the world people use the equally tempered scale? And in carnatic music we use instruments like violin, vINa etc. - for these and almost any instrument that can play gamakams, I doubt if it is at all possible to accurately reproduce differences of the order of 1hz ( think of what small distance the finger will have to move through ). As it is violinists etc. don't find any difficulty tuning their instrument to different shrutis and junta don't seem to notice the $\epsilon$ differences that may occur. That being the case, I don't see how shifting to equally tempered scales will be of any help whatsoever. Also there is this issue that if the ears were actually fine enough to notice such differences then the equally tempered notes not being small integral multiples of each other should produce very close harmonics simultaneously ( for instance twice the madhyasthAyi pan~camam and thrice the madhyasthAyi ShaDjam will play from the tanpura or whatever ) which would be jarring. Thanks.
 From: 2006-01-08 09:38 pm (UTC) (Link)
My reference for the ubiquity of the equitempered scale is from some book I read long ago. Clearly it was an exaggeration to say that all world music uses it; but it is definitely very widespread. For example wikipedia says that arab music uses the 24-tone equi-tempered scale.
From:
2006-01-08 11:03 am (UTC)

### Methodology?

Could you please provide more information about the methodology? What did you measure? Did you make them sing each note and measure the pitch?

One more issue. My understanding is that the Carnatic scale is not equally-tempered, i.e. the frequencies are not spaced equally apart on the log scale. The notes in Western music and Carnatic music have different frequencies (though they are close to each other).
From:
2006-01-08 11:53 am (UTC)

### Re: Methodology?

I would say that there is no "Carnatic scale". The scale is defined by the pitch at which you sing, and your instruments are tuned to produce. My point here is that pitch variations of even expert carnatic singers are so much that it is not possible to pinpointedly say that it follows one scale or the other. The errors are much greater than the difference between scales.

As for instruments, I'm not knowledgeable about their construction, but as far as I can see they must necessarily be equi-tempered, otherwise you need a colossal number of strings (see my post above).

BTW, wikipedia outrightly claims that modern carnatic uses the chromatic (equitempered) scale.

As for methodology, as you said I took a sample of each of them singing each note (flat, no gamakam) and measured the pitch.