Tuning theory

[A Learner]

Hi,
Can someone throw some light on how the pitch scales vary for
different styles of music. To re-phrase it, the note C in western is
the equivalent of our 'Sa' right ? Do they have the same frequency base
(220Hz/440Hz) or is there a difference ? I understand that the
subsequent notes in the octave are computed as a twelfth root of two in
western and as fractions in our systems of music. Does hindustani and
carnatic share the same chromatic frequencies ?

Thanks
Kaarthik

[Ananth]

Kaarthik,

Now-a-days in Western music they use a tuning system called 'Equal
Temperament'. The concept is simple.. 1. Frequency of a note in a
higher octave is just a double than the same note in its immediate
lower octave. ie., C(5) = C(4) * 2
2. An octave contains 12 notes. So, they simply distribute the
frequencies equally to those 12 notes.

This is not the only tuning system there... they experimented a lot,
and this is the one which is widely in use today.

------------------------

Sa is not Equalent to 'C' always. That's an usual misconception. 'Sa
Ri Ga Ma..' is comparable to 'Do Re Mi Fa ..' in western... both are
'relative' signs. 'Sa' gets associated to a particular frequency/fixed
note when we decide the 'Sruthi'. Say for instance, if a singer sings
in '3 Kattai' sruthi (how to say it properly in English?), then his/her
'Sa' correspends to 'E'. 1 kattai Sa = C, 2 1/2 Kattai Sa = D#

Carnatic doesnt use 'Equal Temperament' Tuning. Again, I'm not sure
about whether we have any fixed base frequency, like western A=440
(there too some european orchestras tune to A=442).

Practically, a carnatic singer/instrumentalist can take any frequency
that's comfortable for them as the sruthi/sa, and calculate other notes
according to that. Even though they take a fixed keyboard note, like
'C' as Sa, then other notes may not fall on the same frequencies that
keyboard notes represent, because we dont use ET tuning. For instance,
if I take C as my sruthi, then 'G' will be slightly outof tune for my
Pa.

Mr. Arvind Krishnamurthy has done some interesting research in this
regard. You can find his papers here -
http://ccrma.stanford.edu/~arvindh/cmt/icmpapers.html

Regards,
Ananth.