Those srutis again

Gregg Gibson writes:

> You may wish to consult the most famous of all Indian musical theorists,
> Sarngadeva, ...

I've lamented before on this list the (apparent?) absence of primary
sources on Indian music in English. I won't reproduce the quote,
but suffice to say it doesn't convince _me_ that Sarngadeva was
using equal temperament. This is all irrelevant to contemporary
music, of course. I'll bet there are more recent theorists than
Sarngadeva who imply that 1/4 comma meantone is the basis of
European music.

Incidentally, I wasn't previously aware of the Levy article (book?)
either. Could you give details?

> Innumerable other authorities, both traditional and modern, say much the
> same thing. It is true that other authorities give - very slightly -
> unequal scales (Ellis, for example), and one, the quite untrustworthy
> Westerner Danielou, constructs a highly unequal 22-tone
> pseudo-pythagorean system, apparently out of thin air.

B C Deva, in "The Music of India: A Scientific Study" gives an unequal,
just 22 note scale. Having at least the pretence of scientific rigour,
he goes on to measure it against an instrument. Alas, I didn't realise
I was going to get into an argument about this, so I didn't take proper
notes. The measured scale is more than 8 cents out from the
theoretical one. However, most of the commas are preserved at about 20
cents, so we certainly aren't talking about equal temperament.

This scale has a certain contemporary relevence. I did come across it
on the Web. Try hypatia.ucsc.edu:70/1/RELATED/Batish/Archives/Rago1

T V Subba Rao's "Studies in Indian Music", my primary (alright, only)
source on the South Indian tradition, explicitly states that the srutis
are not 22 or 24 equal.

> Ravi Shankar, as
> I recall, says he uses 22 pitches in the octave - I don't remember
> whether equal, nearly equal, or unequal.

Hariprasad Chaurasia says the same in this month's Wire. The 22 note
scale is dead in North India, but it's ghost still haunts those who
refuse to admit of more than 12 notes to the octave :-)

> My own opinion, however, is that while the 22-tone equal does seem to
> enjoy some instrumental use in India, the evidence - very scanty,
> admittedly - supports 19-tone equal for Indian vocal music.

I'm more for 12 pitch classes, boring though that may be.

>> As there is no modulation in Indian music, 436-cents thirds
>> will never arise, even if you follow Gregg's highly suspect
>> argument.
>
> Alas, the incommensurability of the thirds and fifths in 22-tone equal
> does not arise only when modulation is employed, which I have always
> been very careful to note. If, taking C as tonic, we tune by fifths of
> 709 cents, we have a G of 709 cents and a B of 1145 cents. These two
> intervals form a 'major third' of 436 cents. 22-tone equal melody is a
> tissue of such badly, indeed unrecognizably mistuned consonances.

It is true that there is no way of specifying a major scale with 7
notes from a non-meantone temperament such that all thirds and
fifths are in tune. However, I don't see this is being such a big
problem. Neither, presumably, did Bharata, whose gramas give the
following major scales:

Sa-grama 4 3 2 4 4 3 2
Ma-grama 4 3 2 4 3 4 2

Each scale contains a mistuned fifth, which Bharata did claim as
a dissonance. Bharata's srutis are nominally equal, however I
still do not see why these scales could not be just. The interval
of 8 srutis would then be a Pythagorean major third of 408 cents.
This scale sounds fine, melodically, to my ears. In Ma-grama, only
one (minor) third is mistuned.

All of which is very interesting, but says nothing about the
subsequent millenium. Subba Rao allowed for a note in a raga to have
more than one sruti interpretation, but I don' t have a reference to
hand. Although he didn't give any examples of how a scale or phrase
should be tuned in terms of srutis, the implication is obviously that
mistuned consonances can be avoided.

> To
> pretend that Indian singers use major thirds of 436 cents is
> contradicted by all the studies I have seen. They may well use an
> interval between the major third and perfect fourth for purposes of
> ornament, but certainly not as the usual diatonic interval.

6 of the 17 Sa-Ga intervals measured by Jairazbhoy and Stone in
"Intonation in Present Day North Indian Classical Music" are larger
than 408 cents, although a 22 note scale is obviously not being used.
The largest third of 439 cents is >436. This comes from the flautist
Pannalal Ghosh. The largest vocal third is 405 cents from Gangoobai
Hangal. None of this contradicts the spirit of what Gregg says.


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From: gbreed@cix.compulink.co.uk (Graham Breed)
Subject: 19 equal and modal genera
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