RE: Demisemitones

Gary,

A "syntonic meantone temperament" -- or meantone temperament, for short
-- is one in which there is NO pitch difference between the dominant of
the dominant and the submediant of
the subdominant.

I would not consider 17tet a meantone temperament because it is not
consistent within the 5-limit (i.e., the best approximation of a 4/3
plus the best approximation of a 5/4 does not equal the best
approximation of a 5/3).



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From: PErlich@Acadian-Asset.com
Subject: RE: Tuning of the 2nd sruti
PostedDate: 02-09-97 18:53:39
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>>I've had a look through the ragas defined on srutis in Manuel Op
>>De Coul's mode list. Some of them imply a diaschisma=0, but
>>some are probably schismatic. The plot thickens ...
>
>Unfortunately for theorists, practice does not always conform to the
>theoretical value schisma=1 sruti. Being only 2 cents, it should not be
>surprising that musicians would tend to ignore it in practice. The most
>common occurence of this practice is at sruti 12, which can be used as
>729/512 (611.730 cents) or 64/45 (609.776 cents) depending on the situation.
>But the diaschismatic interpretation of the sruti system implies that 729/512
>is 12 srutis while 64/45 is 11. Perhaps the best theoretical remedy would be
>to consider a 10-sruti schisma-augmented perfect fourth (499.999 cents) a
>consonant interval in its own right, and fix 729/512 as the correct tuning of
>sruti 12.



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From: jloffink@pdq.net
Subject: Re: harmonic patrol
PostedDate: 03-09-97 06:32:54
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Paul Erlich wrote:

>Unfortunately for theorists, practice does not always conform to the
>theoretical value schisma=1 sruti. Being only 2 cents, it should not be
>surprising that musicians would tend to ignore it in practice. The most
>common occurence of this practice is at sruti 12, which can be used as
>729/512 (611.730 cents) or 64/45 (609.776 cents) depending on the situation.
>But the diaschismatic interpretation of the sruti system implies that 729/512
>is 12 srutis while 64/45 is 11. Perhaps the best theoretical remedy would be
>to consider a 10-sruti schisma-augmented perfect fourth (499.999 cents) a
>consonant interval in its own right, and fix 729/512 as the correct tuning of
>sruti 12.

On the evidence I've got, which is purely the modes Manuel put on
this list as well as the FTP site, I wouldn't say that a schisma
is even theoretically 1 sruti. As it took me a while to sort this
out, I'll share my thoughts with the list.

First, the sruti scale I'm using is:

s p r p s p r p s|p r p s|s p r p s p r p s

With s a limma, r a chromatic semitone and p a syntonic comma. I
think these work out as:

(s) ( 8 -5 0)
(r) = (-3 -1 2)H
(p) (-4 4 -1)

Setting a schisma=0 means s=p+r. Setting a diaschisma=0 means s=r.

Most of the scales work as 5-limit harmony with the just version
of this scale. In some cases the schismic and diaschismic
approximations both work. The following scale doesn't make sense
to me:

3 2 4 3 2 4 4 Gandhaara Grama (Sarngadeva der. ma-grama)

I suggest that Pa should be flat by p rather than s, so that the
interval of 3 steps separating the tetrachords is a minor tone.
Either this uses a different version of the sruti scale, or it is
assumed that people will guess the correct tuning. Or, my
interpretation is wrong.


This scale works as a diaschismic but not a schismic scale:

2 6 1 4 2 6 1 Raga Bhairav

I'm assuming the intervals of 6 steps should be just minor thirds,
but I have no proof of this.


I think the following scales imply schismic tuning:

1 4 6 2 1 7 1 Raga Todi
1 7 1 4 2 2 4 1 Raga Saurastra
1 4 7 1 1 6 2 Raga Varali

The intervals of 7 steps aren't right for diaschismic major thirds,
so I'm assuming they should be schismic minor thirds. The upper
tetrachord of Varali suggests the same _diaschismic_ approximation
as in Bhairav above! That's consistent with the sruti scale being
a kind of well temperament with no single interpretation.
Because the tonic is always sruti 0, you don't have to worry
about transpositional invariance, so this sort of thing is
allowed. Then again, the 6 steps could denote a Pythagorean
minor third (5 -3)H.


There are also some that may have 7-prime-limit intervals. The
following is the only one that doesn't work schismically:

4 2 4 3 3 3 3 Gandhaara Grama (Narada der. sa-grama)

The middle of the three 3's is 2s+p. This can't be a minor tone.
I suggest it should be the interval (-1 1 1 -1)H or 15/14. It
can be better represented as either r+r+p or s+p. The two are
identical in a schismic temperament, and the former is the
diaschismic equivalent of 2s+p. One of the other 3's will be
(2 0 -2 1)H to compensate. It's also possible that all the 3's
are supposed to be roughly equal intervals, and no 7-limit
interpretation is intended.



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From: mr88cet@texas.net
Subject: 2-D FFTs
PostedDate: 06-09-97 01:15:48
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Graham Breed wrote:
> The following scale doesn't make sense
> to me:
> 3 2 4 3 2 4 4 Gandhaara Grama (Sarngadeva der. ma-grama)

That's not so surprising. The Gandhaara Grama or ga-grama for short
was already obsolete in the time of Bharata. (Grama by the way means
"tone system", or "basic scale".) The descriptions that survived are
only vague. It's said to be a scale more for the gods than for the
people. It has less fifths than the sa-grama and ma-grama. Several
authors tried to deduce what it could have been, an alteration of
the sa-grama or ma-grama. The possibility that appears in most books
is 3 2 4 3 3 3 4, given by the 13th century author Sarngadeva in the
book Sangita Ratnakara. So these modes are only theoretical, it's
unlikely that any one is used in practice.

The 22-tone sruti system is by no means uncontroversial, but
experiments where musicians tune instruments or oscillators have
produced tunings that are in good agreement with the theoretical
values. There are many theories as to why there are 22. One
connection that has been made is, there are 7 natural tones and 22
srutis, which is a clear reference to 22/7 (pi).


> This scale works as a diaschismic but not a schismic scale:
> 2 6 1 4 2 6 1 Raga Bhairav
> I'm assuming the intervals of 6 steps should be just minor thirds,
> but I have no proof of this.

The sixth sruti is 6/5 (or seventh if you start counting at 1) but in
this case it would be 1 7 1 4 1 7 1 for just minor thirds (ignoring
schismas).

Paul Erlich wrote:

>Perhaps the best theoretical remedy would be
>to consider a 10-sruti schisma-augmented perfect fourth (499.999 cents) a
>consonant interval in its own right, and fix 729/512 as the correct
>tuning of sruti 12.

The value 729/512 instead of 64/45 also makes the scale inversionally
symmetrical around the interval 6/5-5/4.

Manuel Op de Coul coul@ezh.nl



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From: Manuel.Op.de.Coul@ezh.nl
Subject: Announcement of concert
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Manuel Op de Coul wrote:

>The 22-tone sruti system is by no means uncontroversial, but
>experiments where musicians tune instruments or oscillators have
>produced tunings that are in good agreement with the theoretical
>values.

I would be very interested in your source for these experiments, if you
have it handy. If the tuning of the srutis is controversial, then how can
the experimenters have "theoretical values" to check recordings against?

By the way, I mentioned earlier that the first mention of precise tunings
that I know of comes from the Hrdayakautaka of Hrdaya Narayana of the late
17th century. I should have said that they are tunings of the 12 svaras,
not the 22 srutis. Also, there is an ambiguity in the text that can lead to
two different interpretations for some pitches. Here they are, reduced to
ratios:

interpretation #1 interpretation #2
(Bhatkande) (Levy)
1/1 1/1
27/25 27/25
9/8 9/8
6/5 6/5
54/43 72/57
4/3 4/3
162/113 36/25
3/2 3/2
18/11 18/11
27/16 12/7
9/5 9/5
81/43 36/19
2/1 2/1

Like some of our correspondents, Fox-Strangeways considered Bharata's 4
srutis to be a major tone (9/8) 3 to be a minor tone (10/9) and 2 to be a
just semitone (16/15). However, there is no direct evidence for this
interpretation in Bharata, nor in any of the treatises that I know of for
more than a millineum following him.

In fact, Bharata, like medieval European writers, considers the 3rd to be
in the "assonant" (anuvadi) category -- that is, neither consonant nor
dissonant. It could be argued that a 5/4 third would be considered
consonant, though such a judgement is also very culturally bound. Notice
that Narayana's tuning of the major third in both interpretations above is
a rather complex ratio.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



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From: Manuel.Op.de.Coul@ezh.nl
Subject: RE: sruti details
PostedDate: 12-09-97 07:24:59
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>In fact, Bharata, like medieval European writers, considers the 3rd to be
>in the "assonant" (anuvadi) category -- that is, neither consonant nor
>dissonant.

I'm responding to my own message because I didn't express this correctly.
The Europeans, of course, did not have an "assonant" category. Medieval
writers considered the third dissonant, presumably because of the
Pythagorean heritage; that is, the Pythagorean major third (C-E) is 81/64,
a relatively complex ratio and somewhat dissonant to my ears too. I meant
to compare the fact that in both cases the ratios are rather complex and in
neither case are they considered consonant. Whether this is significant I'm
not sure. Certainly the terms most writers now freely translate as
"consonant" or "dissonant" may have had different meanings for medieval
Europeans and medieval Indians.


^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



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From: Peter.Blasser@oberlin.edu
Subject: x
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Bill Alves wrote:

> By the way, I mentioned earlier that the first mention of precise tunings
> that I know of comes from the Hrdayakautaka of Hrdaya Narayana of the late
> 17th century. I should have said that they are tunings of the 12 svaras,
> not the 22 srutis. Also, there is an ambiguity in the text that can lead to
> two different interpretations for some pitches. Here they are, reduced to
> ratios:

The ambiguity in your definition is the difference between
27/16 and 12/7. This is log2(12/7)-log2(27/16) = 0.022720
octaves. Assuming the simplest interpretation of the 22
srutis, 22tet, the uncertainty is 1/44 = 0.022727 octaves.
It is not, therefore, correct to say that this is
significantly more precise than Bharata. The two
definitions of svaras are, however incompatible. By the
C17th, the 22 srutis were of only historical importance,
so I wouldn't expect agreement. We must also ask: is
this a North or South Indian scale?

For a bit of pedantry, couldn't 72/57 be 24/19?

To state my own position: whether or not the standard srutis
were ever used by musicians, it is a very good theory.
Whether or not 5-limit harmony was ever intended, enough
scales are consistent with it that I don't believe this is
a coincidence. I don't follow a diaschismic interpretation
any more, as I think my more recent posts made clear. I
could do with a longer list of ragas defined on srutis.

This "anuvadi" is consistent with what I know of modern
Indian theory. I'm perfectly happy with fourths and fifths
and being perfect and thirds imperfect "consonances".

Are any of these primary sources available in English
translation?


P.S. apologies for my unwarranted comment in the
demisemitone discussion. I regretted it not long after
I sent that message. There are some intelligent and
knowledgeable people on this list, and I appreciate the
attention you're giving me.



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