Re: [tuning] probable 3==5 and possible 3==7 bridges in Indian tuning

Joe!

Joe Monzo wrote:

> As I state in my webpage, altho there is apparently no evidence,
> I think it's entirely possible that musicians in ancient India used
> an extended system tuned by ear in Pythagorean ratios, and then
> used the concept of schismatic substitution in order to incorporate
> Pythagorean ratios which closely approximated 5-limit ones, to
> provide subset scales in pseudo-5-limit-JI. But the actual
> ratios still would have been Pythagorean.

> Of course, I'm also willing to allow that over a (relatively
> short?) period of time, good musicians could have gotten to the
> point where they altered the tuning of those schismatic
> substitutions by ear so that they really *were* 5-limit ratios.

this is what Amiya Dasgupta stated is the case. He worked with Erv on the shruti system and
are trying to make a contact to put their joint papers on-line. In the mean time see
http://www.anaphoria.com/trans22.html
It is my understanding that they now only use 17 of the tones. This scale is discussed
http://www.anaphoria.com/genus.html .

I have been told that the use of the 7th harmonic in Indian music was confined to erotic
ragas. Hence their "reluctance" to talk about it!

Does anyone know how much all this had an influence on La Monte WTP.

>
>
> Then, going back to my reference to the recent Tuning List
> postings, there's also the observation that the interval between
> 3^-7 (= ~1086 cents) and 3^7 (= ~114 cents) is ~ 973 cents,
> pretty darn close to a 'harmonic 7th' of ~969 cents. With
> this sound available in their tuning system, I have no problem
> extrapolating the data to reach the assumption that the ancient
> Indian musicians also could have used 7-limit (or Pythagorean
> pseudo-7-limit) ratios in their music.
>
> -monz

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

PLEASE! DON'T SEND ANY MESSAGES TO FOLLOWING ADRESS!!
BARBARAD@CYBERHIGHWAY.NET

I AM SICK RECEVING THIS MASSAGES I DO NOT NOW WHERE THEY COM FROM

Kraig Grady wrote:

> I have been told that the use of the 7th harmonic in Indian music was
> confined to erotic ragas. Hence their "reluctance" to talk about it!
>
> Does anyone know how much all this had an influence on La Monte WTP.

Not realy, but I asked once if raga was 7 limit and Marian
Zazeela looked thoughtful and said yes. Michael Harrison told me
it depends on the gharana (liniage, stylistic school).

db

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* 49/32 R a d i o "all microtonal, all the time"
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*
* http://www.virtulink.com/immp/lookhere.htm

I was always told that 7 is implied not designated in Raga via meeds and gamak

David Beardsley wrote:

> Kraig Grady wrote:
>
> > I have been told that the use of the 7th harmonic in Indian music was
> > confined to erotic ragas. Hence their "reluctance" to talk about it!
> >
> > Does anyone know how much all this had an influence on La Monte WTP.
>
> Not realy, but I asked once if raga was 7 limit and Marian
> Zazeela looked thoughtful and said yes. Michael Harrison told me
> it depends on the gharana (liniage, stylistic school).
>
> db
>
> --
> * D a v i d B e a r d s l e y
> * xouoxno@virtulink.com
> *
> * 49/32 R a d i o "all microtonal, all the time"
> * M E L A v i r t u a l d r e a m house monitor
> *
> * http://www.virtulink.com/immp/lookhere.htm
>
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The inteval we're talking about, the 3.80¢ "septimal schisma", is
the
225/224 (I think that's called the "septimal kleisma", and it's
7.71¢) minus two schismas (1.95¢ each).

If it were used to get 7-limit intervals from the sruti system, the
7:4 interval would occur in two places in the 12-pitch Modern Indian
Gamut, a subset of the ancient sruti system -- between srutis #2 and
#20 (ratios 16/15 and 15/8, once schismas are taken into account),
and between #15 and #11 (8/5 and 45/32).

Each of those 7:4 intervals can be completed to either an otonal or
utonal 7-limit tetrad, using only srutis in the Modern Indian Gamut:

4:5:6:7: #2 #9 #15 #20 (16/15 4/3 8/5 15/8 )
#15 #0 #6 #11 ( 8/5 1/1 6/5 45/32)

1/(7:6:5:4): #2 #7 #13 #20 (16/15 5/4 3/2 15/8 )
#15 #20 #4 #11 ( 8/5 15/8 9/8 45/32)

Does this mean that the Modern Indian Gamut implies, or is even
capable of 7-limit harmony? I would have to say, not really. All
harmony in Indian music is mediated by the drone of 1/1 and 3/2 (or
sometimes 1/1 and 4/3, or the dissonant drone of 1/1 and 15/8), and
none of the chords above includes the drone. Although you may find
one of the drone notes in the any of the chords above, you will not
find both. And it is the drone that implies the harmony. Indian music
does not use free combinations of simultaneous notes -- at any given
time, only one note is sounding that is not part of the drone. So
real 7-limit harmony would require approximations to pitches like
7/6, 7/4, 12/7, 8/7 -- approximations not found even in the complete
sruti system.

In other words, due to the fixed nature of the harmony in Indian
music, any operative bridges must be affixed at one end to the
central pitch, the drone. Since the Pythagorean chain that forms the
basis of the Indian system only extends 11 steps in either direction
from the center, there are not enough perfect fifths in any operative
harmonic interval for the septimal schisma to play a role in Indian
music as we know it.

Of course we have no idea what ancient Indian music sounded like, and
the preponderance of 22-tone systems among 7-limit periodicity blocks
is suggestive, but I've have to say that there's no evidence that the
sruti system, as a Pythagorean chain with possible schismatic
substitutions, was ever associated with 7-limit harmony. 5-limit,
almost certainly yes; 7-limit, it doesn't look that way.

Nevertheless, the first part of this message shows that a modern
composer using a fixed-pitch 12-tone Indian instrument, such as the
santoor, could exploit four full consonant 7-limit tetrads, if she
chose to drop the drone, or to create polyharmony against the drone.

While periodicity can be useful for new music, and may be relevant to older
traditions, it's not likely to be relevant to contemporary practice in
Hindustani or Karnatik musics. While both share or claim the classical
Sanskrit theoretical traditions, there have been several important changes
in musical practice over the centuries that have created a substantial gap
between theory and practice. Chief among these is the introduction (some
four centuries ago) of a continuously sounding drone, adding an unavoidable
vertical element to traditions that appear to have been previously strictly
monophonic. Whereas the classical theoretical approach attempted to account
for all pitches used through the application of linear series of one sort or
another, the addition of the drone undoubtedly changed the conditions
through which musicians determined their intonation.

I have not personally heard septimal intervals used in Hindustani music with
any consistancy (indeed many singers or players seem to savor trying out
every intonational possibility they can for a given pitch during the
_Alap_). In South Indian music, however, the 7/4 appears prominently in the
obligatory ornamentation (_gamaka_) in some Ragas, and is played or sung
consistantly in both _Alapana_ and in forms with fast tempi. The two
musicians with whom I am most familiar, T. Viswanathan and
K.V.Narayanaswami, teach singers and players to tune this pitch directly to
the drone, not as the product of some long sequence of intervals.

--- In tuning@egroups.com, "Daniel Wolf" <djwolf@s...> wrote:
> While periodicity can be useful for new music, and may be relevant
to older
> traditions, it's not likely to be relevant to contemporary practice
in
> Hindustani or Karnatik musics.

I didn't mean to suggest it would. But periodicity block arguments
are relevant to explaining why exactly 12 notes are currently
recognized in these musics.

While both share or claim the classical
> Sanskrit theoretical traditions, there have been several important
changes
> in musical practice over the centuries that have created a
substantial gap
> between theory and practice. Chief among these is the introduction
(some
> four centuries ago) of a continuously sounding drone, adding an
unavoidable
> vertical element to traditions that appear to have been previously
strictly
> monophonic. Whereas the classical theoretical approach attempted
to account
> for all pitches used through the application of linear series of
one sort or
> another, the addition of the drone undoubtedly changed the
conditions
> through which musicians determined their intonation.

This is the thrust behind the way Lentz and I have explained the
schimatic substitutions giving the 5-limit ratios commonly ascribed
to Indian music.
>
> I have not personally heard septimal intervals used in Hindustani
music with
> any consistancy (indeed many singers or players seem to savor
trying out
> every intonational possibility they can for a given pitch during
the
> _Alap_). In South Indian music, however, the 7/4 appears
prominently in the
> obligatory ornamentation (_gamaka_) in some Ragas, and is played or
sung
> consistantly in both _Alapana_ and in forms with fast tempi. The
two
> musicians with whom I am most familiar, T. Viswanathan and
> K.V.Narayanaswami, teach singers and players to tune this pitch
directly to
> the drone, not as the product of some long sequence of intervals.

Yes, gospel singers and others who use ornamentation which involves
continuous sweeps of the frequency spectrum, will naturally treat
prominent local minima of harmonic dissonance (such as 7/4 against a
1/1-3/2 harmony) in a special way, despite (or perhaps savoring)
the "dissonance" they may create with the operative scalar framework
that dominates their melodic language.