Re: The ass that can sing in all gramas [was: [tuning] Shruti Researching]

Klaus and Haresh!
Amiya Dasgupta who worked with Erv Wilson on examining the shutis being used came to the
conclusion that now in North India they use only 17 of the 22 theoretical shutis. Amiya could
hear the difference of 2 cents when someone would try to trick him. Although we have his book that
he used to teach out of at Cal Arts, we have been hoping to make sure that his family doesn't have
any latter material before we put this up as part of the Wilson Archives.
On the other hand as opposed to the harmonic series, Amiya would recognize subharmonic flute
scales as belonging to certain ragas. He believed that many of the original melodies could have
first developed on the flute and later pythagorean versions of the scales were used on string
instruments.

klaus schmirler wrote:

> Dear Haresh, dear tuners,
>
> I started reading this list about a month ago, looking for clues to
> evaluate an idea I have about the 22 srutis--an essay in historical
> reconstruction, if you will, and quite different from your intent;
> actually, I will argue that you are trying to give meaning to a word
> that has been misunderstood for centuries because the underlying
> practice is no longer there. I have to confess that my sources are not
> necessarily reliable (the internet :o}[not only]), that I have a hard
> time telling apart the Northern and Southern traditions and generally
> don't know much about Indian music..., but if I only faintly consider
> making a fool of myself with my theories, this seems the right time to
> do so. Here we go:
>
> Assumption #1 The concept of the 22 srutis is more ancient and very
> likely different from their interpretation in terms of just and
> pythagorean values (which were probably imported from Arabian
> theorists--likely with a change in actual musical practice--in the time
> of the moguls at the latest).
>
> Assumption #2 The srutis define a grid on which to place the 7 svaras.
> If you come up with scales that are modes of each other (maybe with a
> comma difference here or there) such a fine grid seems like overkill. So
> it is reasonable to assume that there were scale genera with distinct
> interval sizes, and srutis were used to relate quite different types of
> scales. The unequivocal equation of 4 sruti=9/8, 3 sruti=10/9, and 2
> sruti=16/15 that you find is probably too simple and inaccurate; it may,
> on the other hand, be assumed that srutis of different sizes are taken
> from a harmonic series, where *one* grouping of four sruti equals 9/8
> &c. And finally, if you want to define a grid, you don't go by your
> voice, you take an instrument. This instrument was the vina.
>
> Assumption #3 (Concerning some gestalt aspects of interval cognition, a
> topic I couldn't find anything on. Glad about hints!) Going by my
> totally subjective personal experience, there is no succesive interval
> in the continuum that stands out like 9/8. From there I can extrapolate
> 10/9 to find 5/4, and I can divide it into 17/16 and 18/17. To openly
> generalize, I posit that there is something in the ear/brain connection
> that can adjust ("tune") smaller units ("intervals") so that they yield
> a larger unit that is "simpler" (is this a definition of "harmonic"?).
> The 9/8 is a natural starting point.
>
> The vina has four strings, two pairs an octave apart that are tuned to a
> 4/3.
> The problem: How to place your frets for a specific type of music.
>
> Let us assume you already have determined the places of 4/3 and 3/2. You
> divide the 9/8 between them into four parts by ear (=with all the
> accuracy you need); the possibly idealized intervals are 33/32, 34/33,
> 35/34, and 36/35.
> Then you extrapolate the intervals downwards: 32/31, 31/30. These give
> you 16/15.
> Extrapolate further. After 3 times, you have 10/9: 28/27, 29/28, 30/29
> (i.e., 30/27).
> You also have a 4/3: 28/27, 29/28, ... 35/34, 36/35, i.e., 36/27.
>
> The nine intervals on the lowest open string are (28, 29, 30, ... 35,
> 36)/27. Sharing a possible fret, they correspond exactly to these nine
> intervals in the 4/3 string: (112, 116, 120, ... 140, 144)/81. Another
> 9/8 is needed to complete the octave. Again: divide 4 times (36/32). On
> the higher string, four more intervals are added: (33, 34, 35, 36)/18.
> 9+9+4=22: the sruti.
>
> The interesting part
>
> Three scale genera or grama were reported and identified by their sruti
> steps.
>
> The least problematic is Shadja Grama, 4-3-2-4-4-3-2, which yields a
> well known sequence when started right in the middle (the fifth sruti)
> of the lower tetrachord:
> 9/8, 5/4, 4/3, 3/2, 27/16. 15/8
> is available on the pair of strings tuned an octave higher. (All 22
> sruti from this starting point are
> _1/1_, 33/32, 17/16, 35/32, _9/8_; 7/6, 29/24, _5/4_, 31/24, _4/3_,
> 11/8, 17/12, 35/24, _3/2_, 99/64, 51/32, 105/64, _27/16_;; 7/4, 29/16,
> _15/8,_ 31/16. _2/1_.)
> [";": string 4/3 up, ";;": string 3/2 up]
>
> Madhyama Grama (4-3-4-2-4-3-2) is said to start on Pa (the fifth degree)
> which makes many commentators rotate the scale they determined in the
> first place. No need to do this here: You start counting from the 4/3
> string which makes the lowest available tone a 3/2. Extinct for quite
> some time; I don't remember and can't find whether it was still used in
> the Mogul era.
> 8/7, 5/4, 45/32, 3/2, 12/7, 15/8
> selected from
> _1/1_, 29/28, 15/14, 31/28, _8/7_, 33/28, 17/14, _5/4_, 9/7 297/224,
> 153/112, _45/32_, 81/56;; _3/2_, 87/56, 45/28, 93/56, _12/7_, 99/56,
> 51/28, _15/8_, 27/14, _2/1_.
> The same count of four sruti that gave 9/8 in Shadja Grama gives 8/7
> here, showing the inadequacy of 22-ET to approximate the sruti.
>
> Lastly, there is Gandara Grama (4-3-2-4-3-3-3), described as either
> nonexistent--apparently there is a fable, where an ass declares himself
> able to sing in all three gramas, not knowing that Gandara Grama is a
> mere theoretical construction to please some god--or as being extinct
> for a long time, having a high tessitura and being kept secret by hunter
> societies. With this setup of sruti, however, you find a scale
> reminiscent (except for the seventh harmonic being lowered to allow for
> another 9/8-10/9 grouping) of alphorns, jaws harps and musical bows if
> you start from the top of the higher tetrachord and does have a high
> tessitura on the vina:
> 9/8, 5/4, 3/2, 5/3, 11/6
> taken from
> _1/1_, 33/32, 17/16, 35/32, _9/8_;; 7/6, 29/24, _5/4_, 31/24, _4/3_,
> 11/8, 17/12, 35/24, _3/2_; 14/9, 29/18, _5/3_, 31/18, 16/9, _11/6_,
> 17/9, 35/18, _2/1_.
>
> I take the fact that there are often more than seven "good" but unused
> intervals available from a given starting note as a strong indication
> that the purpose of the sruti was indeed to regulate the seven svaras
> themselves for a given style, not to account for a certain number of
> ornamental notes. The ornaments themselves are a different matter--very
> much to learn for a singer, if he wants to stick to the generating
> pattern of the sruti on the vina, and probably regarded as superfluous
> by the vina player himself as soon as he is done with fretting his
> instrument. (Were there female musicians?)
>
> Ready to be murdered
>
> Klaus Schmirler

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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