More on shruti-s

Hello ALL, I am thankful to all the Tuning Group members for their
active interest in the quest for the meaning of shruti. I do not think
I can convey how much all this means to me.

Let me try to make some points:

1. There was no Tanpura when jaati gaan and muoorchchhanaa were to the
fore -- until drupad and, later, khayal singing replaced jaati gaan.
According to one estimate, Tanpura may have been introduced around the
12th-13th century.

2. The concept of shruti has always been there -- the earliest
authentic reference would be Bharat Muni's Natyashastra.

Again, shruti means "heard" or "audible" in Sanskrit: it is sung (or
played), not in isolation, but as an integral part of singing. Shruti,
as apart from singing (or playing) can exist only for its analysis.
Any such analytical study would result in some hypothesis which would
then tested in context of singing.

3. Shruti-s are NOT equal. There are some musicians who believe they
are equal, but when there is a difference of opinion, we would always
go back to "pramaaNa" (authenticity) as found in Natyashastra or
Sangita-ratnakara.

As mentioned in the standard Sanskrit texts on music, there are five
classes of shruti-s: (1) dipta [pronounced deeptaa], meaning blazing,
brilliant; (2) ayata [pronounced aayataa], meaning spread over,
extended; (3) karuna [pronounced karuNaa], meaning compassion, pathos;
(4) mrudu, meaning tender; and (5) madhyaa, meaning moderate, medium.
So, various shruti-s were designed to perform differevt aesthetic
functions -- they cannot be equal.

4. About Danielou's opinions, I would humbly suggest we should stick
to the aesthetics and the related theory -- not mixing it with any
other considerations, however interesting they may be.

5. Bharat Muni did not refer to ANY mathematical terms or ratios or
fractions -- he refers only to three numerals: 9, 13 and 22. And if an
anecdote or legend cannot be supported by the texts, it is to be
discarded.

6. Sitar has a number of NOTES (20, 26 ...), not shruti-s.

7. As traditionally rendered, Hindustani music contains absolutely no
modulation.

8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
studied, using spectrograms. The shruti-s (perceived 'notes') reported
include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat) 7/4, Ni 15/8,
as also Ma 21/16, and Dha 27/16. These do not fully agree with the
traditional Indian gamut tables.

9. In practice, the contemporary Indian music may be said to be based
on 12 notes, JI, 5-limit, with shruti-s close to those 12 notes (the
12 notes themselves being shruti-s, of course). The singer does not
'stay' on the remaining 10 shruti-s usually, but tastefully touches
and passes through them.

Nevertheless, he DOES use all shruti-s, according to his sense of
aesthetics, even if mostly unknowingly. That is the reason "meend"
(glissando) is so very important in Indian music.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:

> 8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
> studied, using spectrograms. The shruti-s (perceived 'notes') reported
> include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat) 7/4, Ni 15/8,
> as also Ma 21/16, and Dha 27/16. These do not fully agree with the
> traditional Indian gamut tables.
>
> 9. In practice, the contemporary Indian music may be said to be based
> on 12 notes, JI, 5-limit, with shruti-s close to those 12 notes (the
> 12 notes themselves being shruti-s, of course). The singer does not
> 'stay' on the remaining 10 shruti-s usually, but tastefully touches
> and passes through them.

Even so, it doesn't look very 5-limit to me. If what you really have
contains both 1-5/4-3/2-7/4 and 3/2-15/8-9/4-21/8, then the septimal
nature of it all is evident.

Haresh, thank you very much for you comments!

> 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> or fractions -- he refers only to three numerals: 9, 13 and 22.

Hmm, suggests orwell?

> 8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
> studied, using spectrograms. The shruti-s (perceived 'notes')
> reported include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat)
> 7/4, Ni 15/8, as also Ma 21/16, and Dha 27/16. These do not fully
> agree with the traditional Indian gamut tables.

Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
was showing up in the spectrogram because it is part of the
timbre of the instrument. Do you have a citation for this
study?

> 9. In practice, the contemporary Indian music may be said to be
> based on 12 notes, JI, 5-limit, with shruti-s close to those
> 12 notes (the 12 notes themselves being shruti-s, of course).
> The singer does not 'stay' on the remaining 10 shruti-s usually,
> but tastefully touches and passes through them.

Now this is the first theory of Indian music I've heard that
I can really believe!

> Nevertheless, he DOES use all shruti-s, according to his sense
> of aesthetics, even if mostly unknowingly. That is the
> reason "meend" (glissando) is so very important in Indian music.

Yes, clearly there is a great degree of sensitivity and
attention to intonation in this music. The glissandi are
often profoundly beautiful.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>
> Haresh, thank you very much for you comments!
>
> > 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> > or fractions -- he refers only to three numerals: 9, 13 and 22.
>
> Hmm, suggests orwell?

Orwell isn't very fifths-oriented; magic and shrutar both have lower
complexity for fifths.

> Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
> was showing up in the spectrogram because it is part of the
> timbre of the instrument. Do you have a citation for this
> study?

That would be interesting. It's worth noting that the Modern Gamut to
Centaur via marvel gambit does produce these tetrads, separated by
fifths relationships. They are in othr words already approximately
present in the Modern Indian Gamut (MIG), and the tuning can be made
much better by smoothing it out via marvel. An optimal marvel-tempered
fifth is about 700 cents, a little flat, not sharp, but 22 *is* a
225/224 system, and magic or orwell tempers it out.

> > 9. In practice, the contemporary Indian music may be said to be
> > based on 12 notes, JI, 5-limit, with shruti-s close to those
> > 12 notes (the 12 notes themselves being shruti-s, of course).
> > The singer does not 'stay' on the remaining 10 shruti-s usually,
> > but tastefully touches and passes through them.
>
> Now this is the first theory of Indian music I've heard that
> I can really believe!

Except it doesn't correspond to the data he just gave.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>>>>>

> Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
> was showing up in the spectrogram because it is part of the
> timbre of the instrument. Do you have a citation for this
> study?
>>>>>

Thr reference:
http://www.tcs.tifr.res.in/~pandya/music/tanpura/papers/tanpura.pdf

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> Hello ALL, I am thankful to all the Tuning Group members for their
> active interest in the quest for the meaning of shruti.

> 2. The concept of shruti has always been there -- the earliest
> authentic reference would be Bharat Muni's Natyashastra.
Edition: M. Gosh
Vol 1, Chap:1-27 Calcutta 1967, ntyasastra
Vol 2, Chap:28-36 Calcutta 1956, gandharvaveda
both in sanscrite,
the engl. translation also by Gosh Calcutta 1967(first edition)
has become meanwhile the common accepted standard reference source
textbook for Bahratas writings.
>
> 3. Shruti-s are NOT equal. There are some musicians who believe they
> are equal,
of about absurde steps of virtual
1 200cents / 22 = ~54.5454545... cents each,
in the questionable try of logarithmic approximation
by western 20th-century theoreticans dreams aposteriori wrong.
I doubt that Bahrata knew already about the logarithm-concept in
order to yield such equal 22 subdivision of the octave, like in 12-et.
http://de.wikipedia.org/wiki/Srutis
says:
" Die 22 Töne ergeben sich aus unserer 12-tönigen pythagoräischen
Stimmung, nur werden hier die innerhalb der zwischen zwei beliebigen
Tönen der pythagoräischen Stimmung vorkommenden Frequenzverhältnisse
an den Grundton "angelegt"."
translation:
//The 22 tones result from our 12-tone Pythagorean tuning.
only the others inbetween two arbitrary chosen tones of that in given
Pythagorean tuning appearing frequency-ratois
become here "inserted" in relation the base tone (=sadja).//
>
So we may conclude from that all in all:
>
> -- they cannot be equal.
evidently.
> 5. Bharat Muni did not refer to ANY mathematical terms or ratios or
> fractions -- he refers only to three numerals: 9, 13 and 22.
Are you really sure about that?
> And if an
> anecdote or legend cannot be supported by the texts, it is to be
> discarded.
Confirm yourself about his legandary acustic experiments in:
Vol 2, Chap.28 p. 24ff, Gosh edition,
with the two different tuned "vinas"
(that were presumably antediluvianic bow-harps?),
in order to explain the meaning of: "pramana-shruti" for
converting "sa" into "magrama" by an Pythagorean comma.
>
>> Nevertheless, he DOES use all shruti-s, according to his sense of
> aesthetics, even if mostly unknowingly.
I.m.o: he knew very well what he exactly had tuned on his both vinas,
just in order to produce and express the desired and intended affects,
as desired conciously by will, determinated by his exact just tuning,
of the 22 shrutis, according his own instructions, as all musicians
do that too, that want to preserve still his old tradition seriously
as well as they are able do, like i try to follow Bachs own tuning
instructions:
http://www.strukturbildung.de/Andreas.Sparschuh/

> That is the reason "meend"
> (glissando) is so very important in Indian music.
as an effective contrast in relation to the ordinary fixe 22 tones,
that your additional "meed" needs to refer to
22 backbone vertebrae of the fundamental sound-scale.
Shrutis work even without glissando, but none glissando without
shrutis.
>
kind regards
Andreas

> > Haresh, thank you very much for you comments!
> >
> > > 5. Bharat Muni did not refer to ANY mathematical terms or
> > > ratios or fractions -- he refers only to three numerals:
> > > 9, 13 and 22.
> >
> > Hmm, suggests orwell?
>
> Orwell isn't very fifths-oriented; magic and shrutar both have
> lower complexity for fifths.

Do you know of another system with 9, 13, and 22?

> > > 9. In practice, the contemporary Indian music may be said to be
> > > based on 12 notes, JI, 5-limit, with shruti-s close to those
> > > 12 notes (the 12 notes themselves being shruti-s, of course).
> > > The singer does not 'stay' on the remaining 10 shruti-s usually,
> > > but tastefully touches and passes through them.
> >
> > Now this is the first theory of Indian music I've heard that
> > I can really believe!
>
> Except it doesn't correspond to the data he just gave.

Even if that data does reflect the tuning of the strings of the
Tanpura, it wouldn't mean the sitar or voice would necessarily
use the same scale.

-Carl

> > Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
> > was showing up in the spectrogram because it is part of the
> > timbre of the instrument. Do you have a citation for this
> > study?
>
> Thr reference:
> http://www.tcs.tifr.res.in/~pandya/music/tanpura/papers/tanpura.pdf

Thank you!

So, this paper says immediately that it is looking for tones
that are in the texture, not the individual strings. I would
have expected septimal intervals to be present in the texture.
Though I do not typically hear them out prominently, I am sure
one could do so, and perhaps I will try the next time I am
listening!

-Carl

Here is their test file:

http://www.tcs.tifr.res.in/~pandya/music/tanpura/papers/tanpura/node6.html

I hear 21/16 at around the 25% point of the cycle.
I hear 7/4 briefly at the end of the cycle.
The 21/16 is a lot easier to spot than the 7/4 for me.

On Tue, 31 Jan 2006, Carl Lumma wrote:

>>> Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
>>> was showing up in the spectrogram because it is part of the
>>> timbre of the instrument. Do you have a citation for this
>>> study?
>>
>> Thr reference:
>> http://www.tcs.tifr.res.in/~pandya/music/tanpura/papers/tanpura.pdf
>
> Thank you!
>
> So, this paper says immediately that it is looking for tones
> that are in the texture, not the individual strings. I would
> have expected septimal intervals to be present in the texture.
> Though I do not typically hear them out prominently, I am sure
> one could do so, and perhaps I will try the next time I am
> listening!
>
> -Carl
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>

>Here is their test file:

Thanks Magnus. But listening to this, I don't gain any insight
beyond 'Indian music is based around a harmonics-rich drone',
which we knew already. The melodic scales could still be anything.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
>
> > > Haresh, thank you very much for you comments!
> > >
> > > > 5. Bharat Muni did not refer to ANY mathematical terms or
> > > > ratios or fractions -- he refers only to three numerals:
> > > > 9, 13 and 22.
> > >
> > > Hmm, suggests orwell?
> >
> > Orwell isn't very fifths-oriented; magic and shrutar both have
> > lower complexity for fifths.
>
> Do you know of another system with 9, 13, and 22?

I guess you are thinking of MOS here, but I think the 9, 13, 22 refers
to mappings of fourths, fifths, and octaves. Hence, I think it is
saying that there is some connection to 22-et.

Hi Gene.
You wrote:

> I guess you are thinking of MOS here, but I think the 9, 13, 22 refers
> to mappings of fourths, fifths, and octaves. Hence, I think it is
> saying that there is some connection to 22-et.

But he said 13 shrutis was to be a third, didn't he?

Sorry, I meant 9 shrutis.

> I guess you are thinking of MOS here, but I think the 9, 13, 22 refers
> to mappings of fourths, fifths, and octaves. Hence, I think it is
> saying that there is some connection to 22-et.

A) If 9|13|22 shrutis are to make a third|fifth|octave, respectively, then
they can't be equal.
B) Whatever the truth is, I "vote" for unequal shrutis.

9|13|22 shrutis make a fourth|fifth|octave, respectively.

Regards,
Haresh.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@c...> wrote:
>
> > I guess you are thinking of MOS here, but I think the 9, 13, 22 refers
> > to mappings of fourths, fifths, and octaves. Hence, I think it is
> > saying that there is some connection to 22-et.
>
> A) If 9|13|22 shrutis are to make a third|fifth|octave,
respectively, then
> they can't be equal.
> B) Whatever the truth is, I "vote" for unequal shrutis.
>

> > > > > 5. Bharat Muni did not refer to ANY mathematical terms or
> > > > > ratios or fractions -- he refers only to three numerals:
> > > > > 9, 13 and 22.
> > > >
> > > > Hmm, suggests orwell?
> > >
> > > Orwell isn't very fifths-oriented; magic and shrutar both have
> > > lower complexity for fifths.
> >
> > Do you know of another system with 9, 13, and 22?
>
> I guess you are thinking of MOS here, but I think the 9, 13, 22
> refers to mappings of fourths, fifths, and octaves. Hence, I
> think it is saying that there is some connection to 22-et.

Oh!

-Carl

Haresh, what about modulations of the tetrachord - however scarce - a fourth
or a fifth above the fundamental tone? That would be enough information to
deterimine the key.

Cordially,
Ozan

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 31 Ocak 2006 Sal� 6:36
Subject: [tuning] More on shruti-s

> Hello ALL, I am thankful to all the Tuning Group members for their
> active interest in the quest for the meaning of shruti. I do not think
> I can convey how much all this means to me.
>
> Let me try to make some points:
>
> 1. There was no Tanpura when jaati gaan and muoorchchhanaa were to the
> fore -- until drupad and, later, khayal singing replaced jaati gaan.
> According to one estimate, Tanpura may have been introduced around the
> 12th-13th century.
>
> 2. The concept of shruti has always been there -- the earliest
> authentic reference would be Bharat Muni's Natyashastra.
>
> Again, shruti means "heard" or "audible" in Sanskrit: it is sung (or
> played), not in isolation, but as an integral part of singing. Shruti,
> as apart from singing (or playing) can exist only for its analysis.
> Any such analytical study would result in some hypothesis which would
> then tested in context of singing.
>
> 3. Shruti-s are NOT equal. There are some musicians who believe they
> are equal, but when there is a difference of opinion, we would always
> go back to "pramaaNa" (authenticity) as found in Natyashastra or
> Sangita-ratnakara.
>
> As mentioned in the standard Sanskrit texts on music, there are five
> classes of shruti-s: (1) dipta [pronounced deeptaa], meaning blazing,
> brilliant; (2) ayata [pronounced aayataa], meaning spread over,
> extended; (3) karuna [pronounced karuNaa], meaning compassion, pathos;
> (4) mrudu, meaning tender; and (5) madhyaa, meaning moderate, medium.
> So, various shruti-s were designed to perform differevt aesthetic
> functions -- they cannot be equal.
>
> 4. About Danielou's opinions, I would humbly suggest we should stick
> to the aesthetics and the related theory -- not mixing it with any
> other considerations, however interesting they may be.
>
> 5. Bharat Muni did not refer to ANY mathematical terms or ratios or
> fractions -- he refers only to three numerals: 9, 13 and 22. And if an
> anecdote or legend cannot be supported by the texts, it is to be
> discarded.
>
> 6. Sitar has a number of NOTES (20, 26 ...), not shruti-s.
>
> 7. As traditionally rendered, Hindustani music contains absolutely no
> modulation.
>
> 8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
> studied, using spectrograms. The shruti-s (perceived 'notes') reported
> include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat) 7/4, Ni 15/8,
> as also Ma 21/16, and Dha 27/16. These do not fully agree with the
> traditional Indian gamut tables.
>
> 9. In practice, the contemporary Indian music may be said to be based
> on 12 notes, JI, 5-limit, with shruti-s close to those 12 notes (the
> 12 notes themselves being shruti-s, of course). The singer does not
> 'stay' on the remaining 10 shruti-s usually, but tastefully touches
> and passes through them.
>
> Nevertheless, he DOES use all shruti-s, according to his sense of
> aesthetics, even if mostly unknowingly. That is the reason "meend"
> (glissando) is so very important in Indian music.
>
> Regards,
> Haresh.
>
>

Dear Ozan, thanks for your input.

With moorchchhana-s replaced by raga-s, and with the Tanpura now an
integral part in Hindustani music, even a semblance of modulation is
ruled out.

A fourth or a fifth above the fundamental certainly may become a kind
of tonal center around which raga patterns are woven for elaboration
and improvisation; but such activity, however intense, continues to
exist only in relation to the fundamental (streaming from the Tanpura).

However, the more important centers in a raga are its Sonant note
(vaadi) and Consonant note (samvaadi). During improvisation, note
patterns are woven around these two notes. Vaadi and Samvaadi do not
necessarily bear a fourth or fifth relationship with the fundamental.
But they do bear such relationship between themselves. Let me give an
example:

Take a raga, say, Yaman. Sa Re Ga Ma# Pa Dha Ni. Here Ga is the Sonant
and Ni is the Consonant. Neither has the fourth or fifth relationship
with Sa; but they have the fifth relationship between themselves.
For a modulation to take place, Ga or Ni should be treated as the new
fundamental (Sa). But this never happens. If this were to happen, the
intervallic relationship among the various notes would be changed, and
the raga would no more sound the same.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> Haresh, what about modulations of the tetrachord - however scarce -
a fourth
> or a fifth above the fundamental tone? That would be enough
information to
> deterimine the key.
>
> Cordially,
> Ozan
>

Dear Haresh, can you provide the cent values of the principal scale of the
Raga Yaman? I believe I may draw some parallels with Maqam Penchgah.

Still, we may not be referring to the same phenomenon when we speak of
modulation. There are many Maqams that modulate (repeat their tetrachordal
or pentachordal structure over the other degrees of their principal scale)
and I suspect that Ragas are not much different in that respect.

Cordially,
Ozan

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 01 �ubat 2006 �ar�amba 18:55
Subject: [tuning] Re: More on shruti-s

> Dear Ozan, thanks for your input.
>
> With moorchchhana-s replaced by raga-s, and with the Tanpura now an
> integral part in Hindustani music, even a semblance of modulation is
> ruled out.
>
> A fourth or a fifth above the fundamental certainly may become a kind
> of tonal center around which raga patterns are woven for elaboration
> and improvisation; but such activity, however intense, continues to
> exist only in relation to the fundamental (streaming from the Tanpura).
>
> However, the more important centers in a raga are its Sonant note
> (vaadi) and Consonant note (samvaadi). During improvisation, note
> patterns are woven around these two notes. Vaadi and Samvaadi do not
> necessarily bear a fourth or fifth relationship with the fundamental.
> But they do bear such relationship between themselves. Let me give an
> example:
>
> Take a raga, say, Yaman. Sa Re Ga Ma# Pa Dha Ni. Here Ga is the Sonant
> and Ni is the Consonant. Neither has the fourth or fifth relationship
> with Sa; but they have the fifth relationship between themselves.
> For a modulation to take place, Ga or Ni should be treated as the new
> fundamental (Sa). But this never happens. If this were to happen, the
> intervallic relationship among the various notes would be changed, and
> the raga would no more sound the same.
>
> Regards,
> Haresh.
>

Dear Ozan,

Raga Yaman
==========

Ascending scale and cent values:

Sa Re Ga Ma# Pa Dha Ni Sa'
0 204 408 612 702 906 1110 1200

Descending scale, of course, is the exact reverse.

[By the way, the improvisation of Yaman does not follow the
sequence indicated in the above scales.]

I do hope this dialogue paves the way for me to learn more about maqam
music. My Guru ji, Ustad Gulam Kader Khan, has often talked to me
about the striking similarities between raga-s and maqam-s.

Please let me know about what you mean by modulation in maqam singing.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> Dear Haresh, can you provide the cent values of the principal scale
of the
> Raga Yaman? I believe I may draw some parallels with Maqam Penchgah.
>
> Still, we may not be referring to the same phenomenon when we speak of
> modulation. There are many Maqams that modulate (repeat their
tetrachordal
> or pentachordal structure over the other degrees of their principal
scale)
> and I suspect that Ragas are not much different in that respect.
>
> Cordially,
> Ozan
>
> ----- Original Message -----
> From: "Haresh BAKSHI" <hareshbakshi@h...>
> To: <tuning@yahoogroups.com>
> Sent: 01 Þubat 2006 Çarþamba 18:55
> Subject: [tuning] Re: More on shruti-s
>
>
> > Dear Ozan, thanks for your input.
> >
> > With moorchchhana-s replaced by raga-s, and with the Tanpura now an
> > integral part in Hindustani music, even a semblance of modulation is
> > ruled out.
> >
> > A fourth or a fifth above the fundamental certainly may become a kind
> > of tonal center around which raga patterns are woven for elaboration
> > and improvisation; but such activity, however intense, continues to
> > exist only in relation to the fundamental (streaming from the
Tanpura).
> >
> > However, the more important centers in a raga are its Sonant note
> > (vaadi) and Consonant note (samvaadi). During improvisation, note
> > patterns are woven around these two notes. Vaadi and Samvaadi do not
> > necessarily bear a fourth or fifth relationship with the fundamental.
> > But they do bear such relationship between themselves. Let me give an
> > example:
> >
> > Take a raga, say, Yaman. Sa Re Ga Ma# Pa Dha Ni. Here Ga is the Sonant
> > and Ni is the Consonant. Neither has the fourth or fifth relationship
> > with Sa; but they have the fifth relationship between themselves.
> > For a modulation to take place, Ga or Ni should be treated as the new
> > fundamental (Sa). But this never happens. If this were to happen, the
> > intervallic relationship among the various notes would be changed, and
> > the raga would no more sound the same.
> >
> > Regards,
> > Haresh.
> >
>

Thank you Haresh, my comments are below...

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 01 �ubat 2006 �ar�amba 20:04
Subject: [tuning] Re: More on shruti-s

Dear Ozan,

Raga Yaman
==========

Ascending scale and cent values:

Sa Re Ga Ma# Pa Dha Ni Sa'
0 204 408 612 702 906 1110 1200

Descending scale, of course, is the exact reverse.

[By the way, the improvisation of Yaman does not follow the
sequence indicated in the above scales.]

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

[Oz]
As I suspected, this is the framework of Maqam Penchgah, which is defined as
Penchgah-i Zaid (Obsolete Penchgah) by Abdulbaki Nasir Dede (Mevlevi Sheik
during Selim III) and said to be confused with Maqam Selmek.

Here is Penchgah:

Ra Du Se Cha# Na Hu Ve Ra' (this solfege is proposed by Kemal Karaosmanoglu
and myself.)

with similar values expressed as ratios:

1
9/8
5/4 (81/64 in Selmek)
10/7 (or 729/512)
3/2
27/16
15/8 (243/128 in Selmek)
2/1

But surely, one can barrow the ratios of Selmek during improvisation, which
I suspect is unavoidable. Also, one can transpose the tritone over to 4/3,
effectively altering the augmented fourth in the process. This modulation, I
presume, should be pretty frequent, if not essential.

Other modulations would take place once the tonic is shifted to other
degrees of the scale during improvisation, which is surely inevitable!

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

I do hope this dialogue paves the way for me to learn more about maqam
music. My Guru ji, Ustad Gulam Kader Khan, has often talked to me
about the striking similarities between raga-s and maqam-s.

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

[Oz]
Indeed! The benefits are mutual, I'm sure.

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

Please let me know about what you mean by modulation in maqam singing.

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

[Oz]
Modulation is simply the shifting of the tonic degree - with or without
consequent alterations - of a melodic globule within a principal scale.
Chromatic Modulation in 12-tET is equivalent to Transposition. In a
diatonical framework, however, you can have few transpositions, but many
modulations. This is what happens in Maqam Music, and I'm sure it happens
with other genres too.

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

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

>>>>
Here is Penchgah:
1
9/8
5/4 (81/64 in Selmek)
10/7 (or 729/512)
3/2
27/16
15/8 (243/128 in Selmek)
2/1
>>>>

Dear Ozan,

This is different from Yaman only in 5/4 and 15/8. And Selmek is
identical with Yaman. 10/7 does not occur in Yaman.

>>>> But surely, one can barrow the ratios of Selmek during
improvisation, which I suspect is unavoidable. Also, one can transpose
the tritone over to 4/3, effectively altering the augmented fourth in
the process.
>>>>

Now, here is the most intriguing point:
We do have in Indian music a raga, very much like Yaman, called Yaman
Kalyan. And it does include shuddha Ma, 4/3 (say, F) in descending
scale. This shuddha Ma is permitted only as a part of a special
circular phrase. It is quite another issue that you call this
modulation, while we include shuddha Ma in Yaman Kalyan as a regular
note in descending scale (avaroha). Also, we do not find shuddha Ma
'unavoidable' -- you can omit it and simply sing Yaman.

Regards,
Haresh.

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 02 �ubat 2006 Per�embe 8:24
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> >>>>
> Here is Penchgah:
> 1
> 9/8
> 5/4 (81/64 in Selmek)
> 10/7 (or 729/512)
> 3/2
> 27/16
> 15/8 (243/128 in Selmek)
> 2/1
> >>>>
>
> Dear Ozan,
>
> This is different from Yaman only in 5/4 and 15/8. And Selmek is
> identical with Yaman. 10/7 does not occur in Yaman.
>

Alright then, in all likelihood, principal scale of Raga Yaman = principal
scale of Maqam Selmek.

> >>>> But surely, one can barrow the ratios of Selmek during
> improvisation, which I suspect is unavoidable. Also, one can transpose
> the tritone over to 4/3, effectively altering the augmented fourth in
> the process.
> >>>>
>
> Now, here is the most intriguing point:
> We do have in Indian music a raga, very much like Yaman, called Yaman
> Kalyan. And it does include shuddha Ma, 4/3 (say, F) in descending
> scale. This shuddha Ma is permitted only as a part of a special
> circular phrase. It is quite another issue that you call this
> modulation, while we include shuddha Ma in Yaman Kalyan as a regular
> note in descending scale (avaroha). Also, we do not find shuddha Ma
> 'unavoidable' -- you can omit it and simply sing Yaman.
>

This still leaves us with other modes that can be derived from the principal
scale of Yaman/Selmek. In fact, there are 7 modes (some very familiar, I'm
sure) that one can utilize during improvisation by shifting the tonic over
to another degree. This is the type of modulation which is surely an
integral part of every genre.

> Regards,
> Haresh.
>
>
>
>

Cordially,
Ozan

Dear Haresh, Carl, Osan, Gene, et al,

Years ago musicologist Siemen Terpstra pointed out to
me that if one were to divide the octave of 1200 cents
by 53, one would arrive at an irrational 'comma' of
about 22.64105009 cents. The 22 sruti tones can be
thought of as a 22-step subset of 53-step ET, with
each step comprising more than a Syntonic Comma, but
less than a Pythagorean Comma.

As all of you know, one way to visualize the 22 srutis
is to begin with the J.I. versions of the 12 tones of
the Chromatic Scale that is common to both India and
the West.

In India ten more ratios are then added, generating
the ten additional tones which bring the total to 22
Srutis, or 22 'tones heard'. Each of the 10
accompanying tones is placed a Syntonic Comma away
from one of the common Chromatic tones. The starting
tone, 1/1, Do or Sa, and the Perfect Fifth, 3/2, Sol
or Pa, do not receive accompanying tones.

Talk of the 22 srutis as comprising 22-ET has been
around for centuries, maybe millenia. It is as
ill-informed today as it was at the beginning. I have
a copy of Siem's paper on the 22 Srutis somewhere.
Some of his papers have been published in 1/1, the
Journal of the Just Intonation Network. Others have
been published on the Internet. Many haven't been
published. All are written in English. If anyone is
interested in his paper on the 22 Srutis I can unearth
it and get it to you somehow.

-- Mark Rankin

--- Haresh BAKSHI <hareshbakshi@hotmail.com> wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma"
> <clumma@y...> wrote:
> >>>>>
>
> > Hrm, I've never 'heard out' at 7/4 in Tanpura.
> Perhaps this
> > was showing up in the spectrogram because it is
> part of the
> > timbre of the instrument. Do you have a citation
> for this
> > study?
> >>>>>
>
> Thr reference:
>
http://www.tcs.tifr.res.in/~pandya/music/tanpura/papers/tanpura.pdf
>
>
>
>
>
>
>

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

On 2/2/06, Mark Rankin <markrankin95511@yahoo.com> wrote:
[snip]
> Talk of the 22 srutis as comprising 22-ET has been
> around for centuries, maybe millenia. It is as
> ill-informed today as it was at the beginning. I have
[snip]

In this case, "srutal" is a totally inappropriate name for the linear
temperament that is supported by both 12-edo and 22-edo and tempers
out 2048/2025. Srutis are not related to the "srutal" temperament but
rather to the "helmholtz" or "schismatic" temperament that tempers out
32805/32768.

Therefore I move that the name "srutal" be abolished and the 5-limit
temperament that tempers out 2048/2025 be forever known as
"diaschismatic".

Any objections?

Keenan

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:

> In this case, "srutal" is a totally inappropriate name for the linear
> temperament that is supported by both 12-edo and 22-edo and tempers
> out 2048/2025.

Lucky we call that one "pajara" in the 7-limit then. Paul is the only
one who seems to want to call the 5-limit temperament "srutal".

For the 7-limit, shrutar tempers out 2048/2025, but is not supported
by 12; rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
not supported by 22; rather 12, 34, 46 and 58. If you were to call the
5-limit temperament "diaschismic", would you want to call this one
something different?

Srutis are not related to the "srutal" temperament but
> rather to the "helmholtz" or "schismatic" temperament that tempers out
> 32805/32768.

I've seen that asserted, but not demonstrated. Some people's versions
of srutis are closely related to schismatic, but many other versions
are not. Who, if anyone, is right?

> Therefore I move that the name "srutal" be abolished and the 5-limit
> temperament that tempers out 2048/2025 be forever known as
> "diaschismatic".

The TOP tuning test does not strongly suggest this should have the
same name as 7-limit diaschismic, so if we called this diaschismic,
which I agree seems to make more sense than what Paul calls it, then
we may want another name for the 7-limit temperament.

On 2/3/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
> --- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:
>
> > In this case, "srutal" is a totally inappropriate name for the linear
> > temperament that is supported by both 12-edo and 22-edo and tempers
> > out 2048/2025.
>
> Lucky we call that one "pajara" in the 7-limit then. Paul is the only
> one who seems to want to call the 5-limit temperament "srutal".

Makes sense; I've been going by "A Middle Path". But if "srutal" is a
bad name for a temperament that includes 22-edo then "shrutar" is no
better.

> For the 7-limit, shrutar tempers out 2048/2025, but is not supported
> by 12; rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
> not supported by 22; rather 12, 34, 46 and 58. If you were to call the
> 5-limit temperament "diaschismic", would you want to call this one
> something different?

This confused me at first, but I looked at the wedgies from your site
and I think it makes sense to me now. "Shrutar" is supported, albeit
badly, by 24, right? Because its generator is half that of the 5-limit
temperament?

And although 22 is on the line of edos that support "diaschismic", you
say it doesn't support it because it gives the wrong number of steps
for intervals of 7? Would it make sense to say 22 is "incompatible"
with "diaschismic"?

> Srutis are not related to the "srutal" temperament but
> > rather to the "helmholtz" or "schismatic" temperament that tempers out
> > 32805/32768.
>
> I've seen that asserted, but not demonstrated. Some people's versions
> of srutis are closely related to schismatic, but many other versions
> are not. Who, if anyone, is right?

Well, that is the big question. I've been looking around FSU's music
library for anything on srutis, but no luck so far. My point was that
no one is still seriously arguing that srutis are equvalent to 22-edo,
so we should try to dispel this myth.

> > Therefore I move that the name "srutal" be abolished and the 5-limit
> > temperament that tempers out 2048/2025 be forever known as
> > "diaschismatic".
>
> The TOP tuning test does not strongly suggest this should have the
> same name as 7-limit diaschismic, so if we called this diaschismic,
> which I agree seems to make more sense than what Paul calls it, then
> we may want another name for the 7-limit temperament.

It's clear that there is one 5-limit temperament, which needs a name,
as well as at least three different 7-limit temperaments that descend
from it. I propose that the parent 5-limit temperament be called
"diaschismatic" (the proper Greek form of the adjective) because it
tempers out the 2048/2025 "diaschisma", although this name might clash
with the one people have been using for the obscure 7-limit
temperament "diaschismic" (has anyone actually written music in
"diaschismic" anyway?).

Keenan

Keenan Pepper wrote:
> On 2/3/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
>>For the 7-limit, shrutar tempers out 2048/2025, but is not supported
>>by 12; rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
>>not supported by 22; rather 12, 34, 46 and 58. If you were to call the
>>5-limit temperament "diaschismic", would you want to call this one
>>something different?
> > > This confused me at first, but I looked at the wedgies from your site
> and I think it makes sense to me now. "Shrutar" is supported, albeit
> badly, by 24, right? Because its generator is half that of the 5-limit
> temperament?
> > And although 22 is on the line of edos that support "diaschismic", you
> say it doesn't support it because it gives the wrong number of steps
> for intervals of 7? Would it make sense to say 22 is "incompatible"
> with "diaschismic"?

That confused me too at first, but then I realized he was continuing the sentence that began "For the 7-limit ... " and referring to the specific 7-limit temperament that's been referred to as "diaschismic" (as opposed to other 7-limit temperaments that also temper out 2048/2025).

5-limit diaschism(at)ic does include 22, as well as 56, in addition to the ones supported by 7-limit diaschism(at)ic, in the sense that the name has been used for a specific 7-limit temperament. This temperament also shows up in higher limit lists, as for instance a 13-limit version with this generator mapping:

<2, 3, 5, 7, 9, 10]
<0, 1, -2, -8, -12, -15]

which is supported by 46-ET and 58-ET. Whether all of these should be called "diaschism(at)ic" is a question that depends on your opinion of how related temperaments of different limits should be named in general (and I'd guess is the reason Paul decided to coin the name "srutal" for the 5-limit version to avoid potential confusion).

Herman Miller wrote:

> That confused me too at first, but then I realized he was continuing the > sentence that began "For the 7-limit ... " and referring to the specific > 7-limit temperament that's been referred to as "diaschismic" (as opposed > to other 7-limit temperaments that also temper out 2048/2025).

I've had a page about these temperaments for a long time:

http://x31eq.com/diaschis.htm

I avoid giving them a name most of the time (and originally it was called "The Third Way" or somesuch but I changed it because Blairism got to be less funny). Still, I have to take the blame for the spelling "diaschismic".

2048/2025 is the diaschisma, so diaschismatic has to refer to scales that temper out this interval, like schismatic scales temper out the schisma. There isn't one obvious 7-limit extension so you always have to qualify what kind of diaschismatic you're looking at. But 46&58 is the most obvious because it's best in the region where the optimal 5-limit tuning is likely to be (depending on how you optimize it).

A tuning around 46 is also a good fit for some justifications of the Indian shruti scale. We have to be careful about stealing names from another culture but "srutal" isn't such a bad choice.

The 22&46 "shrutar" temperament is qualitatively different. Although it tempers out the diaschisma, it does so with contorsion. The generator is half the size it would be in a diaschismatic temperament. So it isn't diaschismatic but it is related.

> 5-limit diaschism(at)ic does include 22, as well as 56, in addition to > the ones supported by 7-limit diaschism(at)ic, in the sense that the > name has been used for a specific 7-limit temperament. This temperament > also shows up in higher limit lists, as for instance a 13-limit version > with this generator mapping:
> > <2, 3, 5, 7, 9, 10]
> <0, 1, -2, -8, -12, -15]
> > which is supported by 46-ET and 58-ET. Whether all of these should be > called "diaschism(at)ic" is a question that depends on your opinion of > how related temperaments of different limits should be named in general > (and I'd guess is the reason Paul decided to coin the name "srutal" for > the 5-limit version to avoid potential confusion).

Fortunately or otherwise, it gets more complicated than that. I'm looking at the 19-limit, so here's an extension of that mapping:

<2, 3, 5, 7, 9, 10, 8, 13]
<0, 1, -2, -8, -12, -15, 1, -26]

It's good in the 13-limit, and can easily come top of the list in the 17-limit. I don't think there's any music to demonstrate how good it is in reality but Gene's worked on 46-equal in the 17-limit so that day may not be far off. It isn't so good in the 19-limit though. These diaschismatics come ahead of it in my relatively short list:

<2, 3, 5, 3, 5, 6, 8, 5]
<0, 1, -2, 15, 11, 8, 1, 20]

<4, 6, 10, 13, 17, 18, 16, 17]
<0, 1, -2, -5, -9, -9, 1, 0]

and this shrutar:

<2, 3, 5, 5, 7, 6, 8, 7]
<0, 2, -4, 7, -1, 16, 2, 17]

So in general it looks like an important bag of temperaments but no single, obvious mapping. I'm sure an enterprising composer can make use of more than one in a single piece.

Graham

I'm wondering now more than ever whether 100-tET is a possibility. What do
you think Gene? Are there better ets around this range? I remember that you
proposed 99, but that won't do for me. The generator fifth of 696 cents
gives the best Rast scale as default. 708 cent fifth isn't bad either.

Oz.

----- Original Message -----
From: "Mark Rankin" <markrankin95511@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 �ubat 2006 Cuma 3:45
Subject: Re: [tuning] Re: More on shruti-s

> Dear Haresh, Carl, Osan, Gene, et al,
>
> Years ago musicologist Siemen Terpstra pointed out to
> me that if one were to divide the octave of 1200 cents
> by 53, one would arrive at an irrational 'comma' of
> about 22.64105009 cents. The 22 sruti tones can be
> thought of as a 22-step subset of 53-step ET, with
> each step comprising more than a Syntonic Comma, but
> less than a Pythagorean Comma.
>
> As all of you know, one way to visualize the 22 srutis
> is to begin with the J.I. versions of the 12 tones of
> the Chromatic Scale that is common to both India and
> the West.
>
> In India ten more ratios are then added, generating
> the ten additional tones which bring the total to 22
> Srutis, or 22 'tones heard'. Each of the 10
> accompanying tones is placed a Syntonic Comma away
> from one of the common Chromatic tones. The starting
> tone, 1/1, Do or Sa, and the Perfect Fifth, 3/2, Sol
> or Pa, do not receive accompanying tones.
>
> Talk of the 22 srutis as comprising 22-ET has been
> around for centuries, maybe millenia. It is as
> ill-informed today as it was at the beginning. I have
> a copy of Siem's paper on the 22 Srutis somewhere.
> Some of his papers have been published in 1/1, the
> Journal of the Just Intonation Network. Others have
> been published on the Internet. Many haven't been
> published. All are written in English. If anyone is
> interested in his paper on the 22 Srutis I can unearth
> it and get it to you somehow.
>
>
> -- Mark Rankin
>
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> I'm wondering now more than ever whether 100-tET is a possibility.
What do
> you think Gene? Are there better ets around this range?

"Better" always raises the question, "better for what?"

I remember that you
> proposed 99, but that won't do for me.

Recently when I was looking at my music as a whole, it struck me that
99 would work nicely for most of it. But it won't, for example, work
very well as a miracle or meantone system. It's highly recommendable
for many purposes but not all of them.

From my point of view, 100 does not have a lot to offer that 50 isn't
already offering, but your point of view is different. Nearby which
might interest you there is 103, which *can* do both miracle (which
you havn't asked for) and meantone (which you have.) It has a fair
amount of flexibility.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> Recently when I was looking at my music as a whole, it struck me that
> 99 would work nicely for most of it.

And if 99 won't work, often 72 will. Sometimes they both work. I could
stagger on pretty well just using these two, I think.

> > Recently when I was looking at my music as a whole, it struck
> > me that 99 would work nicely for most of it.
>
> And if 99 won't work, often 72 will. Sometimes they both work.
> I could stagger on pretty well just using these two, I think.

Can these really replace 46?

I think 72 is over-rated.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Recently when I was looking at my music as a whole, it struck
> > > me that 99 would work nicely for most of it.
> >
> > And if 99 won't work, often 72 will. Sometimes they both work.
> > I could stagger on pretty well just using these two, I think.
>
> Can these really replace 46?

One of my early pieces was 46, then 27, then 46. 99 can't do that.
If I insisted on everything I've written in this millenium, without
insisting the tuning be exact, I'd need 27, 41, 53, 72 and 99 at minimum.

> I think 72 is over-rated.

It's a fine system, but there *is* no universal system. Is that why
you call it "over-rated"? How do you rate the usual suspects, anyway?

I looked into 81 and 88. For some reason I like 100 a lot better. Maybe it's
because of 1/4 P-comma meantone structure?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 06 �ubat 2006 Pazartesi 21:01
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
> wrote:
>
> > Recently when I was looking at my music as a whole, it struck me that
> > 99 would work nicely for most of it.
>
> And if 99 won't work, often 72 will. Sometimes they both work. I could
> stagger on pretty well just using these two, I think.
>
>
>

Good question. I wish I could answer in objective terms. Can you at least
compare 81, 88 and 100 for me?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 06 �ubat 2006 Pazartesi 20:55
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > I'm wondering now more than ever whether 100-tET is a possibility.
> What do
> > you think Gene? Are there better ets around this range?
>
> "Better" always raises the question, "better for what?"
>
> I remember that you
> > proposed 99, but that won't do for me.
>
> Recently when I was looking at my music as a whole, it struck me that
> 99 would work nicely for most of it. But it won't, for example, work
> very well as a miracle or meantone system. It's highly recommendable
> for many purposes but not all of them.
>
> >From my point of view, 100 does not have a lot to offer that 50 isn't
> already offering, but your point of view is different. Nearby which
> might interest you there is 103, which *can* do both miracle (which
> you havn't asked for) and meantone (which you have.) It has a fair
> amount of flexibility.
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Good question. I wish I could answer in objective terms. Can you at
least
> compare 81, 88 and 100 for me?

I could, but I would need to know, compare them using what criteria?
All of them can do a meantone, that's for starters.

I would like to figure out why a 696 cent fifth produces a better diatonic
major scale compared to others, and why a 709 cent fifth is just too wide a
bother compared to 708 cents.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
To: <tuning@yahoogroups.com>
Sent: 07 �ubat 2006 Sal� 3:00
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Good question. I wish I could answer in objective terms. Can you at
> least
> > compare 81, 88 and 100 for me?
>
> I could, but I would need to know, compare them using what criteria?
> All of them can do a meantone, that's for starters.
>
>
>

> > I think 72 is over-rated.
>
> It's a fine system, but there *is* no universal system. Is that
> why you call it "over-rated"? How do you rate the usual suspects,
> anyway?

I tend to like smaller ETs like 19 and 22 because they do so
much with so little. I also like simpler rank 2 temperaments
than you because of the wilder effects they make possible.
For me stuff like blackwood is slightly on the wrong side of
the accuracy line, unless adaptive timbres are used.

In near-JI land, I tend to prefer pure JI and don't like stopping
at 7. I like extended harmonic series stuff which doesn't lend
itself well to temperament.

By the way, considering they're arguably the single most useful
tuning systems out there, I think "rank 2" is a terrible name.
It has a space in it, a number (which causes consistency problems),
can be read to mean 'not as good as rank 1', and so on. They
deserve a special name and associating "linear" with "octave
period" is dumb.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> In near-JI land, I tend to prefer pure JI and don't like stopping
> at 7.

Hmmm. I like near-JI and often stop at 7. Which, of course, makes 99
look pretty good.

> They
> deserve a special name and associating "linear" with "octave
> period" is dumb.

R2 is probably not going to do it for you, then. Why not propose one?
Associating "linear" with octave period isn't dumb, and in any case
it's useful to have a name for that.

We should refine our terminology then. What do you suggest in place of the
octave to begin with?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 �ubat 2006 Sal� 5:06
Subject: [tuning] Re: More on shruti-s

> > > I think 72 is over-rated.
> >
> > It's a fine system, but there *is* no universal system. Is that
> > why you call it "over-rated"? How do you rate the usual suspects,
> > anyway?
>
> I tend to like smaller ETs like 19 and 22 because they do so
> much with so little. I also like simpler rank 2 temperaments
> than you because of the wilder effects they make possible.
> For me stuff like blackwood is slightly on the wrong side of
> the accuracy line, unless adaptive timbres are used.
>
> In near-JI land, I tend to prefer pure JI and don't like stopping
> at 7. I like extended harmonic series stuff which doesn't lend
> itself well to temperament.
>
> By the way, considering they're arguably the single most useful
> tuning systems out there, I think "rank 2" is a terrible name.
> It has a space in it, a number (which causes consistency problems),
> can be read to mean 'not as good as rank 1', and so on. They
> deserve a special name and associating "linear" with "octave
> period" is dumb.
>
> -Carl
>
>

> > They
> > deserve a special name and associating "linear" with "octave
> > period" is dumb.
>
> R2 is probably not going to do it for you, then.

It might, if we could agree to always use that shorthand.

> Why not propose one?

We used "linear" for a long time with no trouble.

> Associating "linear" with octave period isn't dumb,

What's linear about it?

> and in any case it's useful to have a name for that.

Perhaps. It'd be more useful to have a name for R2 temperaments
that DON'T have an octave period (since there are fewer of them
among good R2 temperaments).

-Carl

Oh, sorry Ozan, if this was a bit misleading. Gene and I are
sort of continuuing a discussion started on the tuning-math list.
It's not a name for "octave" we're hunting, but a name for
linear temperaments that do (or don't) have a generator mapping
that includes the octave as a single generator. Example:
the "augmented" temperament uses a chain of 3 major thirds to
map the octave.

-Carl

> We should refine our terminology then. What do you suggest in
> place of the octave to begin with?
>
> > By the way, considering they're arguably the single most useful
> > tuning systems out there, I think "rank 2" is a terrible name.
> > It has a space in it, a number (which causes consistency problems),
> > can be read to mean 'not as good as rank 1', and so on. They
> > deserve a special name and associating "linear" with "octave
> > period" is dumb.

How about octa-linear then?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 07 �ubat 2006 Sal� 5:35
Subject: [tuning] Re: More on shruti-s

> Oh, sorry Ozan, if this was a bit misleading. Gene and I are
> sort of continuuing a discussion started on the tuning-math list.
> It's not a name for "octave" we're hunting, but a name for
> linear temperaments that do (or don't) have a generator mapping
> that includes the octave as a single generator. Example:
> the "augmented" temperament uses a chain of 3 major thirds to
> map the octave.
>
> -Carl
>
> > We should refine our terminology then. What do you suggest in
> > place of the octave to begin with?
> >
> > > By the way, considering they're arguably the single most useful
> > > tuning systems out there, I think "rank 2" is a terrible name.
> > > It has a space in it, a number (which causes consistency problems),
> > > can be read to mean 'not as good as rank 1', and so on. They
> > > deserve a special name and associating "linear" with "octave
> > > period" is dumb.
>
>
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> > Associating "linear" with octave period isn't dumb,
>
> What's linear about it?

There's a single chain of generators which define the pitch-classes.
In other words, a linear modulatory space.

> > and in any case it's useful to have a name for that.
>
> Perhaps. It'd be more useful to have a name for R2 temperaments
> that DON'T have an octave period (since there are fewer of them
> among good R2 temperaments).

I've suggested "cylindrical temperament" for that, and Paul said
something which I think was that someone else thought that was good,
Erv already had that idea, or something like that.

On Thu, 2 Feb 2006 Mark Rankin wrote:
>
> Dear Haresh, Carl, Osan, Gene, et al,
>
> Years ago musicologist Siemen Terpstra pointed out to
> me that if one were to divide the octave of 1200 cents
> by 53, one would arrive at an irrational 'comma' of
> about 22.64105009 cents. The 22 sruti tones can be
> thought of as a 22-step subset of 53-step ET, with
> each step comprising more than a Syntonic Comma, but
> less than a Pythagorean Comma.
>
> As all of you know, one way to visualize the 22 srutis
> is to begin with the J.I. versions of the 12 tones of
> the Chromatic Scale that is common to both India and
> the West.
>
> In India ten more ratios are then added, generating
> the ten additional tones which bring the total to 22
> Srutis, or 22 'tones heard'. Each of the 10
> accompanying tones is placed a Syntonic Comma away
> from one of the common Chromatic tones. The starting
> tone, 1/1, Do or Sa, and the Perfect Fifth, 3/2, Sol
> or Pa, do not receive accompanying tones.
>
> Talk of the 22 srutis as comprising 22-ET has been
> around for centuries, maybe millenia. It is as
> ill-informed today as it was at the beginning. I have
> a copy of Siem's paper on the 22 Srutis somewhere.
> Some of his papers have been published in 1/1, the
> Journal of the Just Intonation Network. Others have
> been published on the Internet. Many haven't been
> published. All are written in English. If anyone is
> interested in his paper on the 22 Srutis I can unearth
> it and get it to you somehow.
>
>
> -- Mark Rankin

Mark,

Yes, please!

Regards,
Yahya

Just to clarify what Haresh is telling us:

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@...>
wrote:
>
> Hello ALL, I am thankful to all the Tuning Group members for their
> active interest in the quest for the meaning of shruti. I do not
think
> I can convey how much all this means to me.
>
> Let me try to make some points:
>
> 1. There was no Tanpura when jaati gaan and muoorchchhanaa were to
the
> fore -- until drupad and, later, khayal singing replaced jaati
gaan.
> According to one estimate, Tanpura may have been introduced around
the
> 12th-13th century.

The tanpura is the drone instrument.

> 7. As traditionally rendered, Hindustani music contains absolutely
no
> modulation.

Ozan, given this information, do you still consider Hindustani music
to be a form of Maqam music?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
>
> > 8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
> > studied, using spectrograms. The shruti-s (perceived 'notes')
reported
> > include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat) 7/4, Ni
15/8,
> > as also Ma 21/16, and Dha 27/16. These do not fully agree with the
> > traditional Indian gamut tables.
> >
> > 9. In practice, the contemporary Indian music may be said to be
based
> > on 12 notes, JI, 5-limit, with shruti-s close to those 12 notes
(the
> > 12 notes themselves being shruti-s, of course). The singer does
not
> > 'stay' on the remaining 10 shruti-s usually, but tastefully
touches
> > and passes through them.
>
> Even so, it doesn't look very 5-limit to me. If what you really have
> contains both 1-5/4-3/2-7/4 and 3/2-15/8-9/4-21/8, then the septimal
> nature of it all is evident.

What are you talking about? Haresh only mentioned some of the
harmonics of the tanpura drone; obviously 11-limit and higher
harmonics are present as well (and it's not too hard to hear them).
So? Most instruments have these harmonics in their sound. If I sing a
single note, am I singing 11-limit music? I would be by your logic.
More reasonable is to look at the *fundamentals* of the various notes
used in the music.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Haresh, thank you very much for you comments!
>
> > 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> > or fractions -- he refers only to three numerals: 9, 13 and 22.
>
> Hmm, suggests orwell?

Not at all, because the context here is a single scale of steps,
where the important intervals consist of 9, 13, and 22 steps in this
scale. The context is *not* different scales of steps, with 9, 13,
and 22 steps respectively all coming out to the same interval (an
octave).

> > 8. The harmonics of the Tanpura, tuned in G3 C4 C4 C3, have been
> > studied, using spectrograms. The shruti-s (perceived 'notes')
> > reported include: SA 1/1, Re 9/8, Ga 5/4, Pa 3/2, Ni komal (flat)
> > 7/4, Ni 15/8, as also Ma 21/16, and Dha 27/16. These do not fully
> > agree with the traditional Indian gamut tables.
>
> Hrm, I've never 'heard out' at 7/4 in Tanpura.

Really? I've heard all the overtones through the 13th, and many
higher ones as well, in the Hindustani drones I've heard.

> Perhaps this
> was showing up in the spectrogram because it is part of the
> timbre of the instrument.

What exactly do you mean? This seems patently obvious the way I'm
reading it, so I must be reading it wrong . . .

> > 9. In practice, the contemporary Indian music may be said to be
> > based on 12 notes, JI, 5-limit, with shruti-s close to those
> > 12 notes (the 12 notes themselves being shruti-s, of course).
> > The singer does not 'stay' on the remaining 10 shruti-s usually,
> > but tastefully touches and passes through them.
>
> Now this is the first theory of Indian music I've heard that
> I can really believe!

Why? I've described it (contemporary Indian music) this exact way
numerous times.

> > Nevertheless, he DOES use all shruti-s, according to his sense
> > of aesthetics, even if mostly unknowingly. That is the
> > reason "meend" (glissando) is so very important in Indian music.
>
> Yes, clearly there is a great degree of sensitivity and
> attention to intonation in this music. The glissandi are
> often profoundly beautiful.

Amen to that! (and pardon the poor choice of words :) )

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> >
> > Haresh, thank you very much for you comments!
> >
> > > 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> > > or fractions -- he refers only to three numerals: 9, 13 and 22.
> >
> > Hmm, suggests orwell?
>
> Orwell isn't very fifths-oriented; magic and shrutar both have lower
> complexity for fifths.
>
> > Hrm, I've never 'heard out' at 7/4 in Tanpura. Perhaps this
> > was showing up in the spectrogram because it is part of the
> > timbre of the instrument. Do you have a citation for this
> > study?
>
> That would be interesting. It's worth noting that the Modern Gamut
to
> Centaur via marvel gambit does produce these tetrads, separated by
> fifths relationships. They are in othr words already approximately
> present in the Modern Indian Gamut (MIG),

But are completely irrelevant to the music as the music is melody-
against-fixed drone, not 4-part polyphony.

> and the tuning can be made
> much better by smoothing it out via marvel.

Not when you consider what, in the music, actually gets smoothed or
roughened.

> > > 9. In practice, the contemporary Indian music may be said to be
> > > based on 12 notes, JI, 5-limit, with shruti-s close to those
> > > 12 notes (the 12 notes themselves being shruti-s, of course).
> > > The singer does not 'stay' on the remaining 10 shruti-s usually,
> > > but tastefully touches and passes through them.
> >
> > Now this is the first theory of Indian music I've heard that
> > I can really believe!
>
> Except it doesn't correspond to the data he just gave.

Sure it does. Overtones are overtones, 7th, 11th, and all, and occur
over each note regardless of what (if any) limit the actual tuning is
in.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Hi Gene.
> You wrote:
>
> > I guess you are thinking of MOS here, but I think the 9, 13, 22
refers
> > to mappings of fourths, fifths, and octaves. Hence, I think it is
> > saying that there is some connection to 22-et.
>
> But he said 13 shrutis was to be a third, didn't he?

No.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Sorry, I meant 9 shrutis.

9 shrutis subtends three steps in the diatonic scale. Maybe this was
your confusion. In the West, the interval that subtends three steps in
the diatonic scale is called a "fourth". Certainly "third" would be
mathematically more logical, but the Western terms were invented before
the wonderful zero (0) was imported from the East. So we have
the "unison" which is zero steps, the "second" which is one step,
the "third" which is two steps, the "fourth" which is three steps, etc.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> > I guess you are thinking of MOS here, but I think the 9, 13, 22
refers
> > to mappings of fourths, fifths, and octaves. Hence, I think it is
> > saying that there is some connection to 22-et.
>
> A) If 9|13|22 shrutis are to make a third|fifth|octave, respectively,
then
> they can't be equal.
> B) Whatever the truth is, I "vote" for unequal shrutis.

OK, so now I really *don't* know why you keep misreading "fourth"
as "third" . . .

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> This still leaves us with other modes that can be derived from the
principal
> scale of Yaman/Selmek. In fact, there are 7 modes (some very
familiar, I'm
> sure) that one can utilize during improvisation by shifting the tonic
over
> to another degree. This is the type of modulation which is surely an
> integral part of every genre.

Why do you say "every genre" when clearly Hindustani music is not such
a genre?

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:
>
> On 2/2/06, Mark Rankin <markrankin95511@...> wrote:
> [snip]
> > Talk of the 22 srutis as comprising 22-ET has been
> > around for centuries, maybe millenia. It is as
> > ill-informed today as it was at the beginning. I have
> [snip]
>
> In this case, "srutal" is a totally inappropriate name for the
linear
> temperament that is supported by both 12-edo and 22-edo and tempers
> out 2048/2025.

What does this have to do with the snip above?

> Srutis are not related to the "srutal" temperament but
> rather to the "helmholtz" or "schismatic" temperament that tempers
out
> 32805/32768.

On what basis do you make this claim?

> Therefore I move that the name "srutal" be abolished and the 5-limit
> temperament that tempers out 2048/2025 be forever known as
> "diaschismatic".
>
> Any objections?
>
> Keenan

Yes. Framjee and plenty of other authors have noticed that 2048:2025
is the simplest interval that arises as zero srutis, hence vanishes
in the srutal system. The most immediate practical example of this is
sruti #2 serving as both 135/128 and 16/15, depending on whether
you're in ma-grama or sa-grama. And, strikingly, the Modern Indian
Gamut and the 22-sruti scale are both basic, omnitetrachordal scales
in Srutal temperament, while in Helmholtz, they are far less
fundamental constructs. The basic scales in Helmholtz or Schismatic
are, instead, the 12-, 17-, and 29-note chains of fifths.

Reference:

Framjee, Firoze. Text book of Indian music (theory & practice):
useful alike to the scholars of both northern (Hindustani) as well as
southern (Carnatic) music. Sakhi Prakashan, Hathras (Aligarh), 1936,
Poona, 1938, 1986, 1991, 144 pages.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> For the 7-limit, shrutar tempers out 2048/2025, but is not supported
> by 12;

Huh?

> rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
> not supported by 22;

Double huh??

> > Therefore I move that the name "srutal" be abolished and the 5-
limit
> > temperament that tempers out 2048/2025 be forever known as
> > "diaschismatic".
>
> The TOP tuning test does not strongly suggest this should have the
> same name as 7-limit diaschismic, so if we called this diaschismic,
> which I agree seems to make more sense than what Paul calls it, then
> we may want another name for the 7-limit temperament.

First of all, Keenan said "diaschismatic", but you're
saying "diaschismic". Secondly, why do you assume that Keenan will
have any clue what you're talking about when you say "7-limit
diaschismic"?

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@...> wrote:

> My point was that
> no one is still seriously arguing that srutis are equvalent to 22-edo,
> so we should try to dispel this myth.

Calling the system where 2048:2025 vanishes 'srutal' does not
contribute to this myth in any way, shape, or from. Even the TOP tuning
for this temperament yields a 22-tone scale where the large step is
2.66 times the size of the small step!

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Whether all of these should be
> called "diaschism(at)ic" is a question that depends on your opinion
of
> how related temperaments of different limits should be named in
general
> (and I'd guess is the reason Paul decided to coin the name "srutal"
for
> the 5-limit version to avoid potential confusion).

Partly, but I actually think using "diaschismatic" or "diaschismic" as
a name for higher-limit 2D temperaments is about the worst thing you
can do in this area, since the diaschisma being referred to is only a 5-
limit "comma" (2048:2025), but additional "commas" have to be tempered
out to to get a 2D system that approximates the 7-limit or higher. Even
if one explicitly says "7-limit diaschismatic", that to me would mean a
3D temperament where only 2025:2048 is tempered out from 7-limit JI.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> I would like to figure out why a 696 cent fifth produces a better
diatonic
> major scale compared to others,

Just look at the three major thirds and four major sixths in the
diatonic scale. These intervals can't all get closer to 5-limit
consonances with any other size of generating fifth. Try it!

> and why a 709 cent fifth is just too wide a
> bother compared to 708 cents.

Who said so? Both are great for a number of 7-limit temperaments.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > They
> > > deserve a special name and associating "linear" with "octave
> > > period" is dumb.
> >
> > R2 is probably not going to do it for you, then.
>
> It might, if we could agree to always use that shorthand.
>
> > Why not propose one?
>
> We used "linear" for a long time with no trouble.

And with virtually no thought. Unlike Erv Wilson and George Secor.

> > Associating "linear" with octave period isn't dumb,
>
> What's linear about it?

When the period is an octave, the R2 tuning system can be described
as a linear chain of pitch classes. Otherwise, it can't. Haven't you
read Erv Wilson's papers?

> > and in any case it's useful to have a name for that.
>
> Perhaps. It'd be more useful to have a name for R2 temperaments
> that DON'T have an octave period (since there are fewer of them
> among good R2 temperaments).

Gene and George both suggested "cylindrical" as opposed to "linear"
for the ones where the octave is 2 or more periods.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
>
> > > Associating "linear" with octave period isn't dumb,
> >
> > What's linear about it?
>
> There's a single chain of generators which define the pitch-classes.
> In other words, a linear modulatory space.
>
> > > and in any case it's useful to have a name for that.
> >
> > Perhaps. It'd be more useful to have a name for R2 temperaments
> > that DON'T have an octave period (since there are fewer of them
> > among good R2 temperaments).
>
> I've suggested "cylindrical temperament" for that, and Paul said
> something which I think was that someone else thought that was good,

Yes, George Secor.

> Erv already had that idea, or something like that.

George sent a letter to Erv which asked him this specifically, and
included my entire paper in it. Erv's reply simply ignored both the
question and the paper.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:

> Yes. Framjee and plenty of other authors have noticed that 2048:2025
> is the simplest interval that arises as zero srutis, hence vanishes
> in the srutal system.

If you temper out both 2048/2025 and 32805/32768 you land in the
wonderful world of 12-et, so you could simplify everything by playing
all sruti music in 12 equal. Then again, 22 notes of 46&58 has a lot
to be said for it, especially if you favor high-limit interpretations
of it all.

The most immediate practical example of this is
> sruti #2 serving as both 135/128 and 16/15, depending on whether
> you're in ma-grama or sa-grama.

What are other pairs of numbers which share a single sruti?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:

> First of all, Keenan said "diaschismatic", but you're
> saying "diaschismic". Secondly, why do you assume that Keenan will
> have any clue what you're talking about when you say "7-limit
> diaschismic"?

I just said what I meant above when I said what it was supported by.
Plus, he can look up what I meant here:

http://www.xenharmony.org/sevnames.htm

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:

> > We used "linear" for a long time with no trouble.
>
> And with virtually no thought. Unlike Erv Wilson and George Secor.

I did object to the term.

> > 7. As traditionally rendered, Hindustani music contains absolutely
> > no modulation.
>
> Ozan, given this information, do you still consider Hindustani music
> to be a form of Maqam music?

I don't think Haresh was using the same meaning of the term
"modulation" as Ozan was.

-Carl

> > Haresh, thank you very much for you comments!
> >
> > > 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> > > or fractions -- he refers only to three numerals: 9, 13 and 22.
> >
> > Hmm, suggests orwell?
>
> Not at all, because the context here is a single scale of steps,
> where the important intervals consist of 9, 13, and 22 steps in
> this scale. The context is *not* different scales of steps, with
> 9, 13, and 22 steps respectively all coming out to the same
> interval (an octave).

Ah.

Nevertheless, don't various good intervals tend to fall on
smaller MOS in a larger MOS?

-Carl

> Why do you say "every genre" when clearly Hindustani music is not
> such a genre?

Why is it so clear?

-Carl

> > > Associating "linear" with octave period isn't dumb,
> >
> > What's linear about it?
>
> When the period is an octave, the R2 tuning system can be described
> as a linear chain of pitch classes. Otherwise, it can't.

It can always be described as linear with an equivalence interval
corresponding to the period.

> Haven't you read Erv Wilson's papers?

You know very well that I have.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

Gene:
> > > > Associating "linear" with octave period isn't dumb,

Carl:
> > > What's linear about it?

Gene:
> > When the period is an octave, the R2 tuning system can be
described
> > as a linear chain of pitch classes. Otherwise, it can't.

Carl:
> It can always be described as linear with an equivalence interval
> corresponding to the period.

Dave:
Carl, I'm sympathetic with your position (as I describe further
below) but I can't agree to calling a half-octave an "equivalence
interval" since nothing about it _sounds_ equivalent in the same way
that an octave does.

Gene:
> > Haven't you read Erv Wilson's papers?

Dave:
Gene, unfortunately, as Paul Erlich explained, it remains unclear
whether Erv intended "linear" to refer only to rank 2 temperaments
with an octave period or whether he simply wasn't interested in, or
aware of the existence of, rank 2 temperaments with half-octave, one-
third-octave etc. periods. Or whether he even thought in terms
equivalent to "rank 2".

I personally don't have a problem with calling all rank 2
temperaments "linear" (from an octave-equivalent perspective of
course) and within that differentiating "single-chain" and "multi-
chain".

However, I have adopted a compromise in the hope of minimising my
offence to the sensitivities of Paul Erlich, George Secor and others:

I use "linear" for single-chain only. And "multi-linear" for the
rest, with specific cases of "bi-linear", "tri-linear" etc. if
required.

When I want to include them all I write "(multi-)linear" with
parentheses.

I don't like the term "cylindrical". "Prismatic" would be more
accurate, but I don't like that either because cylinders and prisms
are of higher dimension or rank than lines, but multi-linear are of
the same rank or dimension as linear.

-- Dave Keenan

Hi Paul.

> OK, so now I really *don't* know why you keep misreading "fourth"
> as "third" . . .

Don't worry, I just thought it had something to do with the 4:5:6:8 chord.

Petr

> Gene:
> > > When the period is an octave, the R2 tuning system can be
> > > described as a linear chain of pitch classes. Otherwise, it
> > > can't.
>
> Carl:
> > It can always be described as linear with an equivalence interval
> > corresponding to the period.
>
> Dave:
> Carl, I'm sympathetic with your position (as I describe further
> below) but I can't agree to calling a half-octave an "equivalence
> interval" since nothing about it _sounds_ equivalent in the same
> way that an octave does.

I thought that was Paul. But anyway, though I do think there's
something special about the octave, I don't think it's necessary to
build it into the model this way. You never know when bizzaro
tritone partials might wind up evoking tritone-equivalence.

-Carl

I would have hoped that in the 7 or 8 times now this issue has come up on this list that it would no longer be an issue

I believe i have explained more than once than Erv is not locked into the octave at all. This is one of the reasons he uses logs as opposed to cents to define his series and/or structures. Especially with the Horograms he has shown me all type of non octave application. in particular cases he has pointed out where such patterns have surfaced in 12ET melodically

Likewise i have referenced even constant structures that did not repeat at the octave either which i have stated i learned from Erv. These were used in pieces that were recorded and released on CD possibly before this list existed.
The opening piece on the interiors CD is a good example of this. as well as my piece Crisis on my site

He is not particularly interested in the consonant /dissonant question which put Paul Erlich's application to different periodic intervals than the octave his own application to the problems Paul is concerned with. i would not interpret Erv's silence on this subject as anything outside of possibly having nothing to add that would be of useful.
>
> Message: 3 > Date: Sat, 18 Feb 2006 08:07:16 -0000
> From: "Dave Keenan" <d.keenan@bigpond.net.au>
> Subject: Re: More on shruti-s
>
> > Dave:
> Gene, unfortunately, as Paul Erlich explained, it remains unclear > whether Erv intended "linear" to refer only to rank 2 temperaments > with an octave period or whether he simply wasn't interested in, or > aware of the existence of, rank 2 temperaments with half-octave, one-
> third-octave etc. periods. Or whether he even thought in terms > equivalent to "rank 2".
>
>
> > -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> I would have hoped that in the 7 or 8 times now this issue has
come up
> on this list that it would no longer be an issue

Hi Kraig. Sadly, no. But good to hear from you.

I don't think anyone ever thought that Erv was locked into octaves.

However the "linear" scales we are are talking about here all have
octaves, i.e. they all repeat at the (possibly tempered) octave.
It's just that some of them also repeat at an aliquot part of the
octave (half, third, quarter etc.).

[An aside: Don't you love that term "aliquot part"? Look it up. I've
been wanting a term like that for years, to replace the
ambiguous "integer fraction". I came across it in a legal document.]

They all have a single generator that is chained within that
interval-of-repetition (or period), producing "Moments Of Symmetry"
at various stages.

I've put scare-quotes around "linear" and "MOS" because this usage
is the very thing we are having trouble agreeing on.

Erv's work is replete with examples where the minimum interval of
repetition is the whole octave (for which he uses the terms "linear"
and "MOS"), but those which also repeat at an aliquot part of the
octave are entirely absent, as far as I am aware.

We are not concerned with questions of priority here. We'd be quite
happy to learn that Erv discovered these too. We are actually
concerned with not using the terms "linear" and "MOS" in ways that
Erv would not approve of.

The one part of your response below, that makes the situation
clearer for me, is the last sentence. I agree that since Erv had a
chance to pronounce on the issue and declined, we should stop
worrying about what Erv might think, and just agree amongst
ourselves on whatever _we_ think best.

-- Dave Keenan

> I believe i have explained more than once than Erv is not locked
into
> the octave at all. This is one of the reasons he uses logs as
opposed to
> cents to define his series and/or structures. Especially with the
> Horograms he has shown me all type of non octave application. in
> particular cases he has pointed out where such patterns have
surfaced in
> 12ET melodically
>
> Likewise i have referenced even constant structures that did not
repeat
> at the octave either which i have stated i learned from Erv. These
were
> used in pieces that were recorded and released on CD possibly
before
> this list existed.
> The opening piece on the interiors CD is a good example of this.
as
> well as my piece Crisis on my site
>
> He is not particularly interested in the consonant /dissonant
question
> which put Paul Erlich's application to different periodic
intervals than
> the octave his own application to the problems Paul is concerned
with. i
> would not interpret Erv's silence on this subject as anything
outside of
> possibly having nothing to add that would be of useful.

Hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> [An aside: Don't you love that term "aliquot part"?
> Look it up. I've been wanting a term like that for years,
> to replace the ambiguous "integer fraction". I came across
> it in a legal document.]

Have you never read Partch's _Genesis of a Music_?
I'm sure you have, and just missed his use of it.
That's the first place i ever read it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

> > Gene, unfortunately, as Paul Erlich explained, it remains
> > unclear whether Erv intended "linear" to refer only to
> > rank 2 temperaments with an octave period or whether he
> > simply wasn't interested in, or aware of the existence of,
> > rank 2 temperaments with half-octave, one-third-octave etc.
> > periods. Or whether he even thought in terms equivalent
> > to "rank 2".

> i would not interpret Erv's silence on this subject as
> anything outside of possibly having nothing to add that
> would be of useful.

I would: Erv would not, if he could help it, contribute
to the prostration before terminology that often occurs
on these lists. Because our medium is strictly the
written word, we must be much more careful about terminology
than we normally would. But sometimes it certainly goes
overboard.

-Carl

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> > [An aside: Don't you love that term "aliquot part"?
> > Look it up. I've been wanting a term like that for years,
> > to replace the ambiguous "integer fraction". I came across
> > it in a legal document.]
>
> Have you never read Partch's _Genesis of a Music_?

I'm embarrassed to admit that I haven't.

> I'm sure you have, and just missed his use of it.
> That's the first place i ever read it.

Then why have I never seen it used on this list before?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:

> Then why have I never seen it used on this list before?

I've seen it more in connection to number theory than music.

On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
[...]
> Yes. Framjee and plenty of other authors have noticed that 2048:2025
> is the simplest interval that arises as zero srutis, hence vanishes
> in the srutal system. The most immediate practical example of this is
> sruti #2 serving as both 135/128 and 16/15, depending on whether
> you're in ma-grama or sa-grama. And, strikingly, the Modern Indian
> Gamut and the 22-sruti scale are both basic, omnitetrachordal scales
> in Srutal temperament, while in Helmholtz, they are far less
> fundamental constructs. The basic scales in Helmholtz or Schismatic
> are, instead, the 12-, 17-, and 29-note chains of fifths.

Are you sure 135/128 is sruti #2? It seems like it would be much
closer to sruti #1. What is sruti #1 used for, if not 135/128?

If the srutis are indeed based on tempering out 2048/2025 and not
32805/32768, then there must be two 13-sruti intervals that are not
perfect fifths. Which ones are they?

I really don't know much about srutis, so I probably shouldn't have
spoken so definitively, but I just hate to see something called by a
bad name.

> Reference:
>
> Framjee, Firoze. Text book of Indian music (theory & practice):
> useful alike to the scholars of both northern (Hindustani) as well as
> southern (Carnatic) music. Sakhi Prakashan, Hathras (Aligarh), 1936,
> Poona, 1938, 1986, 1991, 144 pages.

Unfortunately, none of FSU's libraries have this book (or any good
books on Indian music theory, for that matter). Any idea where I could
find a copy?

Keenan

On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
> > For the 7-limit, shrutar tempers out 2048/2025, but is not supported
> > by 12;
>
> Huh?

These statements confused me at first too, but they make sense.
"shrutar" (wedgie <<4 -8 14 -22 11 55||) divides the step of 5-limit
diaschismatic into two equal parts, so it is not supported by 12, but
by 24.

> > rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
> > not supported by 22;
>
> Double huh??

Here Gene refers to the 7-limit temperament with wedgie <<2 -4 -16 -11
-31 -26||, which has the wrong mapping for 7 in 22-edo.

[...]
> First of all, Keenan said "diaschismatic", but you're
> saying "diaschismic". Secondly, why do you assume that Keenan will
> have any clue what you're talking about when you say "7-limit
> diaschismic"?

"Diaschismic" is offensive to my ears because it's not a proper Greek
word. Not a big deal though.

Keenan

On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
[...]
> Partly, but I actually think using "diaschismatic" or "diaschismic" as
> a name for higher-limit 2D temperaments is about the worst thing you
> can do in this area, since the diaschisma being referred to is only a 5-
> limit "comma" (2048:2025), but additional "commas" have to be tempered
> out to to get a 2D system that approximates the 7-limit or higher. Even
> if one explicitly says "7-limit diaschismatic", that to me would mean a
> 3D temperament where only 2025:2048 is tempered out from 7-limit JI.

Well said. But now we have a problem that there are one or two good
7-limit temperaments that have no identifiers other than their
wedgies. Somebody hurry up and write some music in them, and give them
names while you're at it!

Keenan

Actually Erv has always used Aliquot in relations to flutes and especially the scales of Schlesinger
Beautiful word i agree

This is my understanding which might or might not be totally on the mark Erv would have no trouble recognizing any of these as scales. His question would be what makes them aesthetically viable and relate to how one hears
His concept of scale is rooted in both Yasser and Botany and the growth pattern of plants, as opposed to the Messiaen method of chop and slice. His investigations are what to him are along aesthetic lines.
For instance His paper on Rast uses to linear chains , the second one being any neutral third one likes ( he list a convergent series of these) for the most part though he says he is far more satisfied artistically by finding and exploring single series that achieves what he is looking for.

I guess the answer would be that he might feel he has better ways or for him more interesting ways of solving his problems than such methods.
But like the example with dual generators, there might be an instance where such a thing might explain something.
From: "Dave Keenan" <d.keenan@bigpond.net.au>

However the "linear" scales we are are talking about here all have octaves, i.e. they all repeat at the (possibly tempered) octave. It's just that some of them also repeat at an aliquot part of the octave (half, third, quarter etc.). [An aside: Don't you love that term "aliquot part"? Look it up. I've been wanting a term like that for years, to replace the ambiguous "integer fraction". I came across it in a legal document.]

They all have a single generator that is chained within that interval-of-repetition (or period), producing "Moments Of Symmetry" at various stages.

I've put scare-quotes around "linear" and "MOS" because this usage is the very thing we are having trouble agreeing on.

Erv's work is replete with examples where the minimum interval of repetition is the whole octave (for which he uses the terms "linear" and "MOS"), but those which also repeat at an aliquot part of the octave are entirely absent, as far as I am aware.

We are not concerned with questions of priority here. We'd be quite happy to learn that Erv discovered these too. We are actually concerned with not using the terms "linear" and "MOS" in ways that Erv would not approve of.

The one part of your response below, that makes the situation clearer for me, is the last sentence. I agree that since Erv had a chance to pronounce on the issue and declined, we should stop worrying about what Erv might think, and just agree amongst ourselves on whatever _we_ think best.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Haresh, thank you very much for you comments!
> > >
> > > > 5. Bharat Muni did not refer to ANY mathematical terms or ratios
> > > > or fractions -- he refers only to three numerals: 9, 13 and 22.
> > >
> > > Hmm, suggests orwell?
> >
> > Not at all, because the context here is a single scale of steps,
> > where the important intervals consist of 9, 13, and 22 steps in
> > this scale. The context is *not* different scales of steps, with
> > 9, 13, and 22 steps respectively all coming out to the same
> > interval (an octave).
>
> Ah.
>
> Nevertheless, don't various good intervals tend to fall on
> smaller MOS in a larger MOS?
>
> -Carl

Seems like a different issuen the way you put it. More comparable here are the numbers of steps of the fourth and fifth in 19-equal (8 and 11) and 31-equal (13 and 18). These numbers don't seem to support the contention I think you meant to make.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Associating "linear" with octave period isn't dumb,
> > >
> > > What's linear about it?
> >
> > When the period is an octave, the R2 tuning system can be described
> > as a linear chain of pitch classes. Otherwise, it can't.
>
> It can always be described as linear with an equivalence interval
> corresponding to the period.

What you get then aren't pitch classes but musically useless constructs that identify all the notes 1/N octave apart with one another. To treat "cylindrical" tunings in this way would be a huge mistake, in particular precluding the omnitetrachordal scales in tunings with a 1/2 octave period.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
>
> Gene:
> > > > > Associating "linear" with octave period isn't dumb,
>
> Carl:
> > > > What's linear about it?
>
> Gene:
> > > When the period is an octave, the R2 tuning system can be
> described
> > > as a linear chain of pitch classes. Otherwise, it can't.
>
> Carl:
> > It can always be described as linear with an equivalence interval
> > corresponding to the period.
>
> Dave:
> Carl, I'm sympathetic with your position (as I describe further
> below) but I can't agree to calling a half-octave an "equivalence
> interval" since nothing about it _sounds_ equivalent in the same way
> that an octave does.
>
> Gene:
> > > Haven't you read Erv Wilson's papers?
>
> Dave:
> Gene, unfortunately, as Paul Erlich explained, it remains unclear
> whether Erv intended "linear" to refer only to rank 2 temperaments
> with an octave period or whether he simply wasn't interested in, or
> aware of the existence of, rank 2 temperaments with half-octave, one-
> third-octave etc. periods. Or whether he even thought in terms
> equivalent to "rank 2".
>
> I personally don't have a problem with calling all rank 2
> temperaments "linear" (from an octave-equivalent perspective of
> course) and within that differentiating "single-chain" and "multi-
> chain".
>
> However, I have adopted a compromise in the hope of minimising my
> offence to the sensitivities of Paul Erlich, George Secor and others:
>
> I use "linear" for single-chain only. And "multi-linear" for the
> rest, with specific cases of "bi-linear", "tri-linear" etc. if
> required.
>
> When I want to include them all I write "(multi-)linear" with
> parentheses.
>
> I don't like the term "cylindrical". "Prismatic" would be more
> accurate, but I don't like that either because cylinders and prisms
> are of higher dimension or rank than lines, but multi-linear are of
> the same rank or dimension as linear.
>
> -- Dave Keenan

That very dimension or rank (2) is contradicted by the term 'linear'. Or, if we're talking about pitch classes, the dimensionalities are not the same, though the extra dimension in the "prismatic" or "cylindrical" case is a cyclic one.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Gene:
> > > > When the period is an octave, the R2 tuning system can be
> > > > described as a linear chain of pitch classes. Otherwise, it
> > > > can't.
> >
> > Carl:
> > > It can always be described as linear with an equivalence interval
> > > corresponding to the period.
> >
> > Dave:
> > Carl, I'm sympathetic with your position (as I describe further
> > below) but I can't agree to calling a half-octave an "equivalence
> > interval" since nothing about it _sounds_ equivalent in the same
> > way that an octave does.
>
> I thought that was Paul. But anyway, though I do think there's
> something special about the octave, I don't think it's necessary to
> build it into the model this way. You never know when bizzaro
> tritone partials might wind up evoking tritone-equivalence.
>
> -Carl

Timbres with all partials at tritones apart were used in a classic experiment by Pierce. They sound like dyads, not single notes. And besides, there's a model for temperaments, but then there's a model for the scales, instrument tunings, etc. drawn from these temperaments.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
>
> I would have hoped that in the 7 or 8 times now this issue has come up
> on this list that it would no longer be an issue

We've discussed "MOS", where the answer kept going back and forth, and we've discussed "constant structure", which no one ever had a problem applying to any of these systems. Here, rather, the question is "linear".

> I believe i have explained more than once than Erv is not locked into
> the octave at all. This is one of the reasons he uses logs as opposed to
> cents to define his series and/or structures.

I'm sure you're right, but his logs seem even more octave-centered than cents (which are also logarithmic), since the octave is 1 in his units (which you can verify by comparing with his frequency ratios)

Especially with the
> Horograms he has shown me all type of non octave application. in
> particular cases he has pointed out where such patterns have surfaced in
> 12ET melodically
>
> Likewise i have referenced even constant structures that did not repeat
> at the octave either which i have stated i learned from Erv. These were
> used in pieces that were recorded and released on CD possibly before
> this list existed.
> The opening piece on the interiors CD is a good example of this. as
> well as my piece Crisis on my site

Our question concerns systems that *do* repeat at the octave, so that it makes sense to use a set of note names that repeat every octave (which is how all of Erv's notation systems are set up), but where a "linear series" formed by a single generator doesn't manage to yield all the note names (or pitch classes).

> He is not particularly interested in the consonant /dissonant question
> which put Paul Erlich's application to different periodic intervals than
> the octave his own application to the problems Paul is concerned with.

I don't know what you're sayong here, but consonance/dissonance is completely irrelevant to this question.

> would not interpret Erv's silence on this subject as anything outside of
> possibly having nothing to add that would be of useful.

Then possibly he approves of the proposals George Secor made in his letter . . . (?)

>
> >
> > Message: 3
> > Date: Sat, 18 Feb 2006 08:07:16 -0000
> > From: "Dave Keenan" <d.keenan@...>
> > Subject: Re: More on shruti-s
> >
> >
> > Dave:
> > Gene, unfortunately, as Paul Erlich explained, it remains unclear
> > whether Erv intended "linear" to refer only to rank 2 temperaments
> > with an octave period or whether he simply wasn't interested in, or
> > aware of the existence of, rank 2 temperaments with half-octave, one-
> > third-octave etc. periods. Or whether he even thought in terms
> > equivalent to "rank 2".
> >
> >
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@...> wrote:
> [...]
> > Yes. Framjee and plenty of other authors have noticed that 2048:2025
> > is the simplest interval that arises as zero srutis, hence vanishes
> > in the srutal system. The most immediate practical example of this is
> > sruti #2 serving as both 135/128 and 16/15, depending on whether
> > you're in ma-grama or sa-grama. And, strikingly, the Modern Indian
> > Gamut and the 22-sruti scale are both basic, omnitetrachordal scales
> > in Srutal temperament, while in Helmholtz, they are far less
> > fundamental constructs. The basic scales in Helmholtz or Schismatic
> > are, instead, the 12-, 17-, and 29-note chains of fifths.
>
> Are you sure 135/128 is sruti #2? ?

Did you read my paper on 22?

> If the srutis are indeed based on tempering out 2048/2025 and not
> 32805/32768, then there must be two 13-sruti intervals that are not
> perfect fifths.

I think you mean three, not two.

> Which ones are they?

In sa-grama, sruti 10 to sruti 1, sruti 12 to sruti 3, and most importantly, sruti 11 to sruti 2. Trying to fix the latter yields 135/128 as the new ratio for sruti 2 but then of course we ruin the fifth from sruti 2 to sruti 15.

Sa-grama has become essentially the standard grama. But it seems that in ma-grama, the imperfect 13-sruti intervals are sruti 2 to sruti 15, sruti 1 to sruti 14, and sruti 3 to sruti 16.

> I really don't know much about srutis, so I probably shouldn't have
> spoken so definitively,

A key axiom expounded by a great many Hindu authors in modern times is that 16/15 is 2 srutis, 10/9 is 3 srutis, and 9/8 is 4 srutis. You may work out the consequences from there.

> Any idea where I could
> find a copy?

Someone on this list sent me a copy, but I'd only use it as one reference in conjunction with a number of others, as there are differences as well as similarities between the different sruti theories.

On 2/20/06, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
[...]
> > Are you sure 135/128 is sruti #2? ?
>
> Did you read my paper on 22?

Not thoroughly. Is the canonical version at lumma.org?

> > If the srutis are indeed based on tempering out 2048/2025 and not
> > 32805/32768, then there must be two 13-sruti intervals that are not
> > perfect fifths.
>
> I think you mean three, not two.

Well, if 2048/2025 being tempered out is the only condition, then the
minimum number of bad fifths is two, but of course it's possible for
more to be bad.

> > Which ones are they?
>
> In sa-grama, sruti 10 to sruti 1, sruti 12 to sruti 3, and most importantly, sruti 11
> to sruti 2. Trying to fix the latter yields 135/128 as the new ratio for sruti 2 but
> then of course we ruin the fifth from sruti 2 to sruti 15.

Aha! The interval from 11 to 2 differs from a 3/2 by exactly
2048/2025, so if that fifth is bad then 2048/2025 must not be tempered
out. Is there anything wrong with my reasoning?

> Sa-grama has become essentially the standard grama. But it seems that in
> ma-grama, the imperfect 13-sruti intervals are sruti 2 to sruti 15, sruti 1 to sruti
> 14, and sruti 3 to sruti 16.

Makes sense, but again, the interval from 2 to 15 differs from a 3/2
by 2048/2025.

[...]

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 2/17/06, wallyesterpaulrus <wallyesterpaulrus@...> wrote:
> > > For the 7-limit, shrutar tempers out 2048/2025, but is not supported
> > > by 12;
> >
> > Huh?
>
> These statements confused me at first too, but they make sense.
> "shrutar" (wedgie <<4 -8 14 -22 11 55||) divides the step of 5-limit
> diaschismatic into two equal parts, so it is not supported by 12, but
> by 24.

Only using a certain mapping, for the inconsistent 24-equal.

> > > rather 22, 46 and 68. Diaschismic tempers out 2048/2025, but is
> > > not supported by 22;
> >
> > Double huh??
>
> Here Gene refers to the 7-limit temperament with wedgie <<2 -4 -16 -11
> -31 -26||, which has the wrong mapping for 7 in 22-edo.
>
> [...]
> > First of all, Keenan said "diaschismatic", but you're
> > saying "diaschismic". Secondly, why do you assume that Keenan will
> > have any clue what you're talking about when you say "7-limit
> > diaschismic"?
>
> "Diaschismic" is offensive to my ears because it's not a proper Greek
> word. Not a big deal though.
>
> Keenan

But why use the name for this 7-limit temperament? Seems all wrong to me, by the arguments I laid out on Friday based on commas,

"Chop and slice" is a false impression given by the result of naturally tempering out certain commas, for example 2025:2048. I can't speak for Messaien, but one can see the period of the temperament where 2025:2048 vanishes as accomplishing a delicate balancing act between representing 45:32 and representing 64:45. All temperaments are about such balancing acts, but it's just an algebraic happenstance that here the representation of the octave can be expressed as a multiple of either of the two JI intervals above.

Two points I want to be loud and clear about, Kraig:

In my Middle Path paper, I deliberately omitted systems that result from a "chop and slice" approach even if they looked better than some of the systems in the paper according to the very complexity and error penalties used to select the latter. For example, a system like meantone, but with the generator split in half, would only be 2 times as complex as meantone, and have equal errors. But you can view the tuning as consisting of two meantone chains, and if one of the chains contains your 1/1, then no 5-limit ratios are ever going to map to the other chain. In the tunings in my paper, by contrast, every single note derives directly from ratios in the relevant JI lattice. So any "chopping and slicing" which introduces notes foreign to the JI foundation is ruled out in my approach. I'm not sure whether this has been clear to you or not; I suspect if I made generalized keyboard designs for each of the systems in my paper, with every button labeled with ratios, it might be clearer.

The second point is that knowing the generator of a tuning system is often one of the least important pieces of information for me as a musician. Scales like my decatonics are scales that you can play melodies in, find coherent sequences of harmonies in that don't divide the tuning into separate subsets, form a great basis for notation and key signatures, and certainly preserve the octave as the interval of equivalence. Since a single harmonic web connects all 10 notes (pitch classes) in the scale, it's barely significant to me that you can't lay out all 10 notes along a single chain of identical (or similar) generators. In my way of thinking, all the scales in my paper are about forming a single, coherent harmonic web that connects all of the notes. The representation in terms of period and generator is a mathematical convenience of these all being two-dimensional systems (when the octave is understood as a movement up or down in pitch), but doesn't hold any singificance in terms of the way they're initially conceived (as temperings of (sets of) commas out of JI) and doesn't have great significance in the musical realm either.

Hopefully that sums up why I think "chop and slice" is inappropriate if used in reference to the systems in my paper. More reponse inline, below.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Actually Erv has always used Aliquot in relations to flutes and especially the scales of Schlesinger

But in that context, subharmonic scales were meant.

> Beautiful word i agree
>
> This is my understanding which might or might not be totally on the mark
>
> Erv would have no trouble recognizing any of these as scales. His question would be what makes them aesthetically viable and relate to how one hears
> His concept of scale is rooted in both Yasser

Yasser makes a much bigger brouhaha about consonance and dissonance than anyone I know, insisting that all scales must have "seconds" (one-step intervals in the scale) as dissonances and "thirds" (two-step intervals in the scale) as dissonances. He even suggests suppressing the 3rd partial in all instrument timbres so that the perfect fifth in 19-equal can function as a dissonance in his 12-out-of-19 scale.

> and Botany and the growth pattern of plants,

Kraig, do you remember the pictures of cacti I posted? Phyllotaxis where the period is one-half a full revolution around the center is found in nature, where it serves a survival function . . .

> as opposed to the Messiaen method of chop and slice.

Any references?

> His investigations are what to him are along aesthetic lines.

True of both Wilson and Messaein I'm sure, and myself I might add.

> For instance His paper on Rast uses to linear chains , the second one being any neutral third one likes ( he list a convergent series of these) for the most part though he says he is far more satisfied artistically by finding and exploring single series that achieves what he is looking for.
>
> I guess the answer would be that he might feel he has better ways or for him more interesting ways of solving his problems than such methods.
> But like the example with dual generators, there might be an instance where such a thing might explain something.

Dual generators?

>
>
>
>
> From: "Dave Keenan" <d.keenan@...>
>
>
> However the "linear" scales we are are talking about here all have
> octaves, i.e. they all repeat at the (possibly tempered) octave.
> It's just that some of them also repeat at an aliquot part of the
> octave (half, third, quarter etc.).
>
>
>
> [An aside: Don't you love that term "aliquot part"? Look it up. I've
> been wanting a term like that for years, to replace the
> ambiguous "integer fraction". I came across it in a legal document.]
>
> They all have a single generator that is chained within that
> interval-of-repetition (or period), producing "Moments Of Symmetry"
> at various stages.
>
> I've put scare-quotes around "linear" and "MOS" because this usage
> is the very thing we are having trouble agreeing on.
>
> Erv's work is replete with examples where the minimum interval of
> repetition is the whole octave (for which he uses the terms "linear"
> and "MOS"), but those which also repeat at an aliquot part of the
> octave are entirely absent, as far as I am aware.
>
> We are not concerned with questions of priority here. We'd be quite
> happy to learn that Erv discovered these too. We are actually
> concerned with not using the terms "linear" and "MOS" in ways that
> Erv would not approve of.
>
> The one part of your response below, that makes the situation
> clearer for me, is the last sentence. I agree that since Erv had a
> chance to pronounce on the issue and declined, we should stop
> worrying about what Erv might think, and just agree amongst
> ourselves on whatever _we_ think best.
>
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
>

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:

> A key axiom expounded by a great many Hindu authors in modern times
is that 16/15 is 2 srutis, 10/9 is 3 srutis, and 9/8 is 4 srutis. You
may work out the consequences from there.

This gives three equations in three unknowns, the solution of which
gives <22 35 51|. Hence, there ought to be 22 srutis, and they may be
expected to define a constant structure scale, which would be
epimorphic if its a 5-limit scale.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:

> That very dimension or rank (2) is contradicted by the
term 'linear'. Or, if we're talking about pitch classes, the
dimensionalities are not the same, though the extra dimension in
the "prismatic" or "cylindrical" case is a cyclic one.
>

Hi Paul,

Well of course in using "equal" "linear" "planar" as they have been
used in the past (even when no aliquot parts of octaves are
involved) we are talking about pitch-classes. i.e. we knock off one
rank because we are thinking octave-equivalently.

You're not going to suggest we start calling equal
temperaments "circular" or "polygonal" are you?

-- Dave

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> On 2/20/06, wallyesterpaulrus <wallyesterpaulrus@...> wrote:
> [...]
> > > Are you sure 135/128 is sruti #2? ?
> >
> > Did you read my paper on 22?
>
> Not thoroughly. Is the canonical version at lumma.org?

Yup.

> > > If the srutis are indeed based on tempering out 2048/2025 and not
> > > 32805/32768, then there must be two 13-sruti intervals that are not
> > > perfect fifths.
> >
> > I think you mean three, not two.
>
> Well, if 2048/2025 being tempered out is the only condition, then the
> minimum number of bad fifths is two, but of course it's possible for
> more to be bad.
>
> > > Which ones are they?
> >
> > In sa-grama, sruti 10 to sruti 1, sruti 12 to sruti 3, and most importantly, sruti 11
> > to sruti 2. Trying to fix the latter yields 135/128 as the new ratio for sruti 2 but
> > then of course we ruin the fifth from sruti 2 to sruti 15.
>
> Aha! The interval from 11 to 2 differs from a 3/2 by exactly
> 2048/2025, so if that fifth is bad then 2048/2025 must not be tempered
> out. Is there anything wrong with my reasoning?

No one explicitly said there are bad fifths in the original treatises. But a set of diatonical modes were specified and any 13-sruti intervals occuring in these modes should be good. Some sa-grama modes contain #2 and #15, while it seems to me that some ma-grama modes (using #13 as tonic) must contain #2 and #11. So #2 "wants" to be tempered so that it can form a good fifth with either #11 or #15, and there seems to be some evidence that this is done (through the use of ratios such as 17/16 for sruti #2).

> > Sa-grama has become essentially the standard grama. But it seems that in
> > ma-grama, the imperfect 13-sruti intervals are sruti 2 to sruti 15, sruti 1 to sruti
> > 14, and sruti 3 to sruti 16.
>
> Makes sense, but again, the interval from 2 to 15 differs from a 3/2
> by 2048/2025.

Not "again", but for the first time.

>
> [...]
>
> Keenan
>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
>
> > That very dimension or rank (2) is contradicted by the
> term 'linear'. Or, if we're talking about pitch classes, the
> dimensionalities are not the same, though the extra dimension in
> the "prismatic" or "cylindrical" case is a cyclic one.
> >
>
> Hi Paul,
>
> Well of course in using "equal" "linear" "planar" as they have been
> used in the past (even when no aliquot parts of octaves are
> involved) we are talking about pitch-classes. i.e. we knock off one
> rank because we are thinking octave-equivalently.
>
> You're not going to suggest we start calling equal
> temperaments "circular" or "polygonal" are you?
>
> -- Dave
>
Actually, that's how they're often thought of, and when the tuning is slighly unequal, these terms are of course more appropriate than "equal". *You're* not suggesting that equal temperaments be considered "point" temperaments, are you? Because that's what seems to follow from your logic.

I ask the same thing myself. Has he sampled all the pieces of Hindustani
music to conclude as such?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 �ubat 2006 Cumartesi 8:27
Subject: [tuning] Re: More on shruti-s

> > Why do you say "every genre" when clearly Hindustani music is not
> > such a genre?
>
> Why is it so clear?
>
> -Carl
>
>

Clearly? By what authority do you speak as such?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 3:33
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > This still leaves us with other modes that can be derived from the
> principal
> > scale of Yaman/Selmek. In fact, there are 7 modes (some very
> familiar, I'm
> > sure) that one can utilize during improvisation by shifting the tonic
> over
> > to another degree. This is the type of modulation which is surely an
> > integral part of every genre.
>
> Why do you say "every genre" when clearly Hindustani music is not such
> a genre?
>

I do not know in which context Haresh uses the term modulation. I understand
modes to be octave species of any diatonical scale, and thus am sure that
every Rag contains improvisational modulations within its principal
scale(s).

Which modulation do you have in mind Paul?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 1:27
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

SNIP

>
> > 7. As traditionally rendered, Hindustani music contains absolutely
> no
> > modulation.
>
> Ozan, given this information, do you still consider Hindustani music
> to be a form of Maqam music?
>
>
>

For the love of Allah, will no one condone the usage of the term modulation as this poor soul imagines it to be?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 8:18
Subject: [tuning] No drone in Indian music before 12th century (was: Re: More on shruti-s)

> > > 7. As traditionally rendered, Hindustani music contains absolutely
> > > no modulation.
> >
> > Ozan, given this information, do you still consider Hindustani music
> > to be a form of Maqam music?
>
> I don't think Haresh was using the same meaning of the term
> "modulation" as Ozan was.
>
> -Carl
>
>

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 Şubat 2006 Cumartesi 5:14
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > I would like to figure out why a 696 cent fifth produces a better
> diatonic
> > major scale compared to others,
>
> Just look at the three major thirds and four major sixths in the
> diatonic scale. These intervals can't all get closer to 5-limit
> consonances with any other size of generating fifth. Try it!
>

I do not get it.

> > and why a 709 cent fifth is just too wide a
> > bother compared to 708 cents.
>
> Who said so? Both are great for a number of 7-limit temperaments.
>
>

709 cents is a little wide for my tastes. 708 is the ideal limit as far as I
am concerned.

Dear Ozan,

The way I understand modulation, it can be between different tonal
centres, and between different tonal types (major and minor tonalities).

An example: we can modulate from the major tonality of C to:
1. A different tonal centre, but the same tonal type, such as F major;
2. The same tonal centre, but a different tonal type, which is c minor;
3. A different tonal centre and a different tonal type, such as f minor.

And what I contend is that modulation in the above sense does not
exist in Indian music. I stand corrected if the term 'modulation' does
not mean what I think it means.

As Carl remarked, your interpretation of the usage of 'modulation' is
perhaps different from the above. Can you please tell me more about this?

Thanks and regards,
Haresh.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> For the love of Allah, will no one condone the usage of the term
modulation as this poor soul imagines it to be?
>
> ----- Original Message -----
> From: "Carl Lumma" <clumma@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 8:18
> Subject: [tuning] No drone in Indian music before 12th century (was:
Re: More on shruti-s)
>
>
> > > > 7. As traditionally rendered, Hindustani music contains absolutely
> > > > no modulation.
> > >
> > > Ozan, given this information, do you still consider Hindustani music
> > > to be a form of Maqam music?
> >
> > I don't think Haresh was using the same meaning of the term
> > "modulation" as Ozan was.
> >
> > -Carl
> >
> >
>

Dear Haresh, a question if you will: Since major and minor are names that
stand for the two modes which we call `Ionian` and `Aeolian`whose tonics are
different degrees of the famous natural diatonical scale on the white keys
of a Halberstadt keyboard design, and since modulation is simply changing
the tone centre/key during music, would you say that it is allowable to
`modulate` from Ionian to Dorian (still the same scale) within a basic
melodic framework without any chords?

If your answer to this question is yes, you have inadvertantly accepted the
fact that no genre we are aware of can evade `modulation`. One way or
another, even performing on a basic scale of 3 notes such as C F and G
(considering that only 3 notes exist in that particular musical universe)
has to modulate if music is to be made:

C F G
F G C
G C F

Here is a piece based on this 3-note universe at:

http://www.ozanyarman.com/anonymous/modulation-example.wav

See? There are three possible modulations here alone. Now imagine all the
modulations possible if you increase the number of tones to higher limit
consonances.

Cordially,
Ozan

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 21 �ubat 2006 Sal� 19:41
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

Dear Ozan,

The way I understand modulation, it can be between different tonal
centres, and between different tonal types (major and minor tonalities).

An example: we can modulate from the major tonality of C to:
1. A different tonal centre, but the same tonal type, such as F major;
2. The same tonal centre, but a different tonal type, which is c minor;
3. A different tonal centre and a different tonal type, such as f minor.

And what I contend is that modulation in the above sense does not
exist in Indian music. I stand corrected if the term 'modulation' does
not mean what I think it means.

As Carl remarked, your interpretation of the usage of 'modulation' is
perhaps different from the above. Can you please tell me more about this?

Thanks and regards,
Haresh.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > You're not going to suggest we start calling equal
> > temperaments "circular" or "polygonal" are you?
> >
> Actually, that's how they're often thought of, and when the tuning
is slighly unequal, these terms are of course more appropriate
than "equal". *You're* not suggesting that equal temperaments be
considered "point" temperaments, are you? Because that's what seems
to follow from your logic.
>

Hi Paul,

I guess you've got me there. :-) I wouldn't consider them "point"
temperaments, but I can certainly consider them "multi-point".

So I agree to stick to using "multi-linear". Or do you have concerns
about that too?

-- Dave Keenan

I'm with Haresh. In a given piece of Hindustani classical music, the drone establishes the tonic, the rag establishes the allowed pitches and ascending and descending melodic sequences, and neither of these change at any time in the performance -- hence, no modulation in this sense.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I do not know in which context Haresh uses the term modulation. I understand
> modes to be octave species of any diatonical scale, and thus am sure that
> every Rag contains improvisational modulations within its principal
> scale(s).
>
> Which modulation do you have in mind Paul?
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 1:27
> Subject: [tuning] No drone in Indian music before 12th century (was: Re:
> More on shruti-s)
>
>
> SNIP
>
> >
> > > 7. As traditionally rendered, Hindustani music contains absolutely
> > no
> > > modulation.
> >
> > Ozan, given this information, do you still consider Hindustani music
> > to be a form of Maqam music?
> >
> >
> >
>

I would in an instant, if you can better explicate the differences in our definitions, and provide a recoridng to listen to which
shows the phenomenon to which you're referring.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> For the love of Allah, will no one condone the usage of the term modulation as this poor soul imagines it to be?
>
> ----- Original Message -----
> From: "Carl Lumma" <clumma@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 8:18
> Subject: [tuning] No drone in Indian music before 12th century (was: Re: More on shruti-s)
>
>
> > > > 7. As traditionally rendered, Hindustani music contains absolutely
> > > > no modulation.
> > >
> > > Ozan, given this information, do you still consider Hindustani music
> > > to be a form of Maqam music?
> >
> > I don't think Haresh was using the same meaning of the term
> > "modulation" as Ozan was.
> >
> > -Carl
> >
> >
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 5:14
> Subject: [tuning] Re: More on shruti-s
>
>
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > > I would like to figure out why a 696 cent fifth produces a better
> > diatonic
> > > major scale compared to others,
> >
> > Just look at the three major thirds and four major sixths in the
> > diatonic scale. These intervals can't all get closer to 5-limit
> > consonances with any other size of generating fifth. Try it!
> >
>
>
> I do not get it.

With 7 notes in the scale, you can create a table showing the 49 intervals in the scale. The table will be antisymmtric about the diagonal. Anyway, all the thirds/sixths will be in there and you can see how well they approximate the ratios of 5 as a function of the size of the diatonic scale's generating fifth. Shall I create an Excel spreadsheet for you to demonstrate this?

>
> > > and why a 709 cent fifth is just too wide a
> > > bother compared to 708 cents.
> >
> > Who said so? Both are great for a number of 7-limit temperaments.
> >
> >
>
> 709 cents is a little wide for my tastes. 708 is the ideal limit as far as I
> am concerned.

OK. What's the lower limit for you? And how about octaves, fourths, etc.?

> Seems like a different issuen the way you put it. More comparable
> here are the numbers of steps of the fourth and fifth in 19-equal
> (8 and 11) and 31-equal (13 and 18). These numbers don't seem to
> support the contention I think you meant to make.

Perhaps not. Something's going on, though. The fifth is often
1 less step than the octave was in the smaller system, I've
noticed. 58 is the 7:4 in 72...

-Carl

> Timbres with all partials at tritones apart were used in a
> classic experiment by Pierce. They sound like dyads, not single
> notes.

Oh, I'm sure there's a way to get them sound like single tones.

>And besides, there's a model for temperaments, but then there's
>a model for the scales, instrument tunings, etc. drawn from these
temperaments.

Exactly. The model for scales is where equivalence intervals
come in, so the word for temperaments shouldn't employ them.

-Carl

And you would likewise be bold enough to say that the first 40 seconds of
the majestic opening of the St. Mattheus Passion by J.S. Bach (Otto
Klemperer rendition) - although based entirely on a glorious E drone (basso
ostinato) supported by organ and bassi - is devoid of any modulation?

Go figure.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 1:12
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

I'm with Haresh. In a given piece of Hindustani classical music, the drone
establishes the tonic, the rag establishes the allowed pitches and ascending
and descending melodic sequences, and neither of these change at any time in
the performance -- hence, no modulation in this sense.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I do not know in which context Haresh uses the term modulation. I
understand
> modes to be octave species of any diatonical scale, and thus am sure that
> every Rag contains improvisational modulations within its principal
> scale(s).
>
> Which modulation do you have in mind Paul?
>

> > A key axiom expounded by a great many Hindu authors in modern
> > times is that 16/15 is 2 srutis, 10/9 is 3 srutis, and 9/8 is
> > 4 srutis. You may work out the consequences from there.
>
> This gives three equations in three unknowns, the solution of which
> gives <22 35 51|. Hence, there ought to be 22 srutis, and they may
> be expected to define a constant structure scale, which would be
> epimorphic if its a 5-limit scale.

This seems significant.

-C.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> For the love of Allah, will no one condone the usage of the term
> modulation as this poor soul imagines it to be?

I think I will. But perhaps you can give us a short audio
or notated example. I'm curious about this file:

http://www.ozanyarman.com/anonymous/modulation-example.wav

-Carl

In that example, you can easily see that even 3 notes are sufficient to
establish a tone centre/key. That would still be the case if a C drone
persisted throughout. Try it and see for yourself.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 2:35
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > For the love of Allah, will no one condone the usage of the term
> > modulation as this poor soul imagines it to be?
>
> I think I will. But perhaps you can give us a short audio
> or notated example. I'm curious about this file:
>
> http://www.ozanyarman.com/anonymous/modulation-example.wav
>
> -Carl
>
>

> An example: we can modulate from the major tonality of C to:
> 1. A different tonal centre, but the same tonal type, such as
> F major;

What length of music is required to make such a modulation clear?
Must Bb be used to enforce the modulation? And can I ever use
Bb while remaining C Major (passing note?).

-Carl

Why don't you read my response to Carl and follow the link?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 1:17
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

I would in an instant, if you can better explicate the differences in our
definitions, and provide a recoridng to listen to which
shows the phenomenon to which you're referring.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> For the love of Allah, will no one condone the usage of the term
modulation as this poor soul imagines it to be?
>

[PA]
With 7 notes in the scale, you can create a table showing the 49 intervals
in the scale. The table will be antisymmtric about the diagonal. Anyway, all
the thirds/sixths will be in there and you can see how well they approximate
the ratios of 5 as a function of the size of the diatonic scale's generating
fifth. Shall I create an Excel spreadsheet for you to demonstrate this?

[OZ]
Indeed, I would be delighted to be enlightened!

> >
>
> 709 cents is a little wide for my tastes. 708 is the ideal limit as far as
I
> am concerned.

[PA]
OK. What's the lower limit for you? And how about octaves, fourths, etc.?

[OZ]
The fifth should be somewhere between 696-708, give or take a couple of
atoms. The octave should be pure, and thus the fourths derived thus.

Carl Lumma escreveu:
>>Timbres with all partials at tritones apart were used in a
>>classic experiment by Pierce. They sound like dyads, not single
>>notes.
> > > Oh, I'm sure there's a way to get them sound like single tones.

What is that "classical experiment"?

I recall a small Pierce's text published at JASA: "Attaining Consonance in Arbitray Scales". There, the consonance was given by intervals of 1/4 octave (or its multiples), between pitches taken from a 1/8 octave scale. The frequency ratios of the partials were:

1 (0 octave)
2.378 (1.25 oct)
4 (2 oct)
5.657 (2.5 oct)
6.726 (2.75 oct)
8 (3 oct)

This can really sound as a single tone.

--
'-------------------------------------------------------------------.
Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
*N�o deixe seu voto sumir! http://www.votoseguro.org/
*Ap�ie o Manifesto: http://www.votoseguro.com/alertaprofessores/

== THE WAR IN IRAQ COSTS ==
http://nationalpriorities.org/index.php?option=com_wrapper&Itemid=182
.-------------------------------------------------------------------'
--

_______________________________________________________
Yahoo! Acesso Gr�tis - Internet r�pida e gr�tis. Instale o discador agora!
http://br.acesso.yahoo.com

> > > For the love of Allah, will no one condone the usage of the term
> > > modulation as this poor soul imagines it to be?
> >
> > I think I will. But perhaps you can give us a short audio
> > or notated example. I'm curious about this file:
> >
> > http://www.ozanyarman.com/anonymous/modulation-example.wav
>
> In that example, you can easily see that even 3 notes are
> sufficient to establish a tone centre/key. That would still be
> the case if a C drone persisted throughout. Try it and see for
> yourself.

There's no doubt that a key is established. Where, in your
view, do(es) the modulation(s) occur?

-Carl

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear Haresh, a question if you will: Since major and minor are names that
> stand for the two modes which we call `Ionian` and `Aeolian`whose tonics are
> different degrees of the famous natural diatonical scale on the white keys
> of a Halberstadt keyboard design, and since modulation is simply changing
> the tone centre/key during music, would you say that it is allowable to
> `modulate` from Ionian to Dorian (still the same scale) within a basic
> melodic framework without any chords?
>
> If your answer to this question is yes, you have inadvertantly accepted the
> fact that no genre we are aware of can evade `modulation`.

There's something wrong with your logic. We are aware of a genre where the tone center/key does not change during the musicn because it is played continuoisly by the fixed drone.
Just because it may be very easy to change tone center in many genres by no means forces such a conclusion about every genre we are aware of.
>
> ----- Original Message -----
> From: "Haresh BAKSHI" <hareshbakshi@...>
> To: <tuning@yahoogroups.com>
> Sent: 21 Þubat 2006 Salý 19:41
> Subject: [tuning] No drone in Indian music before 12th century (was: Re:
> More on shruti-s)
>
>
> Dear Ozan,
>
> The way I understand modulation, it can be between different tonal
> centres, and between different tonal types (major and minor tonalities).
>
> An example: we can modulate from the major tonality of C to:
> 1. A different tonal centre, but the same tonal type, such as F major;
> 2. The same tonal centre, but a different tonal type, which is c minor;
> 3. A different tonal centre and a different tonal type, such as f minor.
>
> And what I contend is that modulation in the above sense does not
> exist in Indian music. I stand corrected if the term 'modulation' does
> not mean what I think it means.
>
> As Carl remarked, your interpretation of the usage of 'modulation' is
> perhaps different from the above. Can you please tell me more about this?
>
> Thanks and regards,
> Haresh.
>

With my statement, perhaps, with my logic, not in the least! Fixed drones do
not preclude modulation as seen in many passages of Western common music
practice reinforced with bassi ostinati.

How about if you can produce me a piece where no modulation takes place?

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 20:31
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Dear Haresh, a question if you will: Since major and minor are names that
> stand for the two modes which we call `Ionian` and `Aeolian`whose tonics
are
> different degrees of the famous natural diatonical scale on the white keys
> of a Halberstadt keyboard design, and since modulation is simply changing
> the tone centre/key during music, would you say that it is allowable to
> `modulate` from Ionian to Dorian (still the same scale) within a basic
> melodic framework without any chords?
>
> If your answer to this question is yes, you have inadvertantly accepted
the
> fact that no genre we are aware of can evade `modulation`.

There's something wrong with your logic. We are aware of a genre where the
tone center/key does not change during the musicn because it is played
continuoisly by the fixed drone.
Just because it may be very easy to change tone center in many genres by no
means forces such a conclusion about every genre we are aware of.

> There's something wrong with your logic.

Do statements like this add anything to your point?

> We are aware of a genre where the tone center/key does
> not change during the musicn because it is played
> continuoisly by the fixed drone.

How do you define "tone center" here?

-Carl

> Fixed drones do not preclude modulation as seen in many
> passages of Western common music practice reinforced with
> bassi ostinati

Also known as pedal point, and it does not preclude
modulation even in the Western sense. But Paul is
right that know Western-sense modulation occurs in
Hindustani music. However, it is clear that motifs
are repeated in different modes of the scale, which
qualifies as "modulation" in many texts I have read
on maqam music.

-Carl

Carl, if mode A is `do-fa-sol`, mode B is `fa-sol-do` and mode C is
`sol-do-fa`, the modulations occur at 11 seconds from A to B and back again
at 18 seconds... then, finally during the cadence from 24 seconds onward,
thru A to C to B to A.

Glad someone agrees with me at last about keys!
Cordially,
Ozan

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 6:09
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> > > > For the love of Allah, will no one condone the usage of the term
> > > > modulation as this poor soul imagines it to be?
> > >
> > > I think I will. But perhaps you can give us a short audio
> > > or notated example. I'm curious about this file:
> > >
> > > http://www.ozanyarman.com/anonymous/modulation-example.wav
> >
> > In that example, you can easily see that even 3 notes are
> > sufficient to establish a tone centre/key. That would still be
> > the case if a C drone persisted throughout. Try it and see for
> > yourself.
>
> There's no doubt that a key is established. Where, in your
> view, do(es) the modulation(s) occur?
>
> -Carl
>
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Fixed drones do not preclude modulation as seen in many
> > passages of Western common music practice reinforced with
> > bassi ostinati
>
> Also known as pedal point, and it does not preclude
> modulation even in the Western sense. But Paul is
> right that know Western-sense modulation occurs

D'oh! I meant "no". -C.

Exactly! You have received the light my colleague.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 21:15
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> > Fixed drones do not preclude modulation as seen in many
> > passages of Western common music practice reinforced with
> > bassi ostinati
>
> Also known as pedal point, and it does not preclude
> modulation even in the Western sense. But Paul is
> right that know Western-sense modulation occurs in
> Hindustani music. However, it is clear that motifs
> are repeated in different modes of the scale, which
> qualifies as "modulation" in many texts I have read
> on maqam music.
>
> -Carl
>
>

> > http://www.ozanyarman.com/anonymous/modulation-example.wav
> >
> > There's no doubt that a key is established. Where, in your
> > view, do(es) the modulation(s) occur?
>
> Carl, if mode A is 'do-fa-sol', mode B is 'fa-sol-do' and
> mode C is 'sol-do-fa', the modulations occur at 11 seconds
> from A to B and back again at 18 seconds... then, finally
> during the cadence from 24 seconds onward, thru
> A to C to B to A.

Great, as I thought. Just wanted to be clear on this.
Except I didn't catch the modulations from 24 seconds
onward (only the one at 11 seconds). To me, this final
phrase is so short that I wouldn't say it contains any
modulation.

> Glad someone agrees with me at last about keys!

Well, I suggest we keep the term "key" (as in "key change")
for use in the Western sense. But "modulation" seems fair
game. FWIW, I used the term "modal modulation" for years
on this list to clarify the two meanings of this overloaded
term.

-Carl

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 21:26
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> > > http://www.ozanyarman.com/anonymous/modulation-example.wav
> > >
> > > There's no doubt that a key is established. Where, in your
> > > view, do(es) the modulation(s) occur?
> >
> > Carl, if mode A is 'do-fa-sol', mode B is 'fa-sol-do' and
> > mode C is 'sol-do-fa', the modulations occur at 11 seconds
> > from A to B and back again at 18 seconds... then, finally
> > during the cadence from 24 seconds onward, thru
> > A to C to B to A.
>
> Great, as I thought. Just wanted to be clear on this.
> Except I didn't catch the modulations from 24 seconds
> onward (only the one at 11 seconds). To me, this final
> phrase is so short that I wouldn't say it contains any
> modulation.
>

Even a single note lasting as short as one fifth of a second makes the
entire difference of modulation. Surely there can be no argument against
that!

> > Glad someone agrees with me at last about keys!
>
> Well, I suggest we keep the term "key" (as in "key change")
> for use in the Western sense. But "modulation" seems fair
> game.

That is a paradoxical suggestion. Key is the prerequisite of modulation per
se. First of all you need to establish a default pitch-plane, then determine
the number of tones therefrom, and then acquire modes from a master-scale
thru which you can modulate. If the number of tones are sufficient,
transpositions too become feasible, and hence, you can change `keys` also
while modulating.

Alternatively, as in the example I have played on my piano, you can set a
key/tonal centre without `linear transpositions`. Instead, you substitute
that with `non-linear mapping`, which amounts to `modulation` once again.
Still, you and I do not desist from calling it a key.

In a 7-note diatonical major scale, no transpositions are possible, but
modulations are the order of the day.

In an historical 12-tone framework, you make a giant leap forward and
combine modulations with transpositions which yield `tonality`, hence `keys`
the way most of us Western oriented folks are used to say.

In contrast, Maqam Music pitches are much more numerous, which automatically
imply modulations and transpositions. Hence, Maqam Music is tonal and is
based on keys likewise. Here, I find it imperative to expand the term `key`
to accomodate Maqams, because the perdes are deeply connected with the way a
Maqam flows (as in Buselik using perde buselik, Hijaz using perde hijaz,
Mahur, using perde mahur, etc...).

While I'll admit to the fact that not all musical genres are based on
`tonality` in the Western sense, I am very certain that none exist that lack
`modulation`.

FWIW, I used the term "modal modulation" for years
> on this list to clarify the two meanings of this overloaded
> term.
>

I don't see the significance of such a discrimination. For all I know, it is
the "type of modulation based on harmonic tonality" which needs to be
explained aside from simple and generalized `modulation`.

> -Carl
>
>

Oz.

Dear Haresh, you can read my response to Carl on this matter.

Cordially,
Ozan

----- Original Message -----
From: "Haresh BAKSHI" <hareshbakshi@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 6:54
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> Dear Ozan, I have the same question that Carl has:
>
> The key is there; where is the modulation, or, where are the modulations?
>
> Regards,
> Haresh.
>
>

Again, one of my problems with "multi-linear" is that the word already has another meaning in close conceptual proximity for me: "multilinear algebra" is what we use in general in the theory of wedgies, vals, etc., which applied to all these types of temperament.

But for an ET, "multi-point" doesn't quite get across, as well as "circular" or "cyclic", the way that the points are all generated in a topologically regular way, just as "linear" does in its sphere of relevance. Linear temperaments have many points too . . .

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > > You're not going to suggest we start calling equal
> > > temperaments "circular" or "polygonal" are you?
> > >
> > Actually, that's how they're often thought of, and when the tuning
> is slighly unequal, these terms are of course more appropriate
> than "equal". *You're* not suggesting that equal temperaments be
> considered "point" temperaments, are you? Because that's what seems
> to follow from your logic.
> >
>
> Hi Paul,
>
> I guess you've got me there. :-) I wouldn't consider them "point"
> temperaments, but I can certainly consider them "multi-point".
>
> So I agree to stick to using "multi-linear". Or do you have concerns
> about that too?
>
> -- Dave Keenan
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Timbres with all partials at tritones apart were used in a
> > classic experiment by Pierce. They sound like dyads, not single
> > notes.
>
> Oh, I'm sure there's a way to get them sound like single tones.

Go ahead and try. You'll have to make some of those partials pretty
darn quiet!

> >And besides, there's a model for temperaments, but then there's
> >a model for the scales, instrument tunings, etc. drawn from these
> temperaments.
>
> Exactly. The model for scales is where equivalence intervals
> come in,

In my paper's approach, yes.

>so the word for temperaments shouldn't employ them.

This is why I use "2D temperaments" in my paper. In much of the
published literature, though, the equivalence intervals come in right
along with the temperaments, which is the context where "linear" has
been used.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> And you would likewise be bold enough to say that the first 40
seconds of
> the majestic opening of the St. Mattheus Passion by J.S. Bach (Otto
> Klemperer rendition) - although based entirely on a glorious E
drone (basso
> ostinato) supported by organ and bassi - is devoid of any
modulation?

Western tonality is quite different from Indian dronality (to use
Mathieu's word).

> Go figure.

I hope you treat Haresh with a bit more patience and open-mindedness.

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 1:12
> Subject: [tuning] No drone in Indian music before 12th century
(was: Re:
> More on shruti-s)
>
>
> I'm with Haresh. In a given piece of Hindustani classical music,
the drone
> establishes the tonic, the rag establishes the allowed pitches and
ascending
> and descending melodic sequences, and neither of these change at
any time in
> the performance -- hence, no modulation in this sense.
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > I do not know in which context Haresh uses the term modulation. I
> understand
> > modes to be octave species of any diatonical scale, and thus am
sure that
> > every Rag contains improvisational modulations within its
principal
> > scale(s).
> >
> > Which modulation do you have in mind Paul?
> >
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > A key axiom expounded by a great many Hindu authors in modern
> > > times is that 16/15 is 2 srutis, 10/9 is 3 srutis, and 9/8 is
> > > 4 srutis. You may work out the consequences from there.
> >
> > This gives three equations in three unknowns, the solution of which
> > gives <22 35 51|. Hence, there ought to be 22 srutis, and they may
> > be expected to define a constant structure scale, which would be
> > epimorphic if its a 5-limit scale.
>
> This seems significant.
>
> -C.

Indeed! It leads quite naturally to the sruti scale given by S.
Ramanathan, Erv Wilson, etc., as one of the JI possibilities.

I meant a recording of Hindustani music which shows the phenomenon to
which you're referring.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Why don't you read my response to Carl and follow the link?
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 1:17
> Subject: [tuning] No drone in Indian music before 12th century
(was: Re:
> More on shruti-s)
>
>
> I would in an instant, if you can better explicate the differences
in our
> definitions, and provide a recoridng to listen to which
> shows the phenomenon to which you're referring.
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > For the love of Allah, will no one condone the usage of the term
> modulation as this poor soul imagines it to be?
> >
>

> Even a single note lasting as short as one fifth of a second
> makes the entire difference of modulation. Surely there can be
> no argument against that!

I'm not even sure what it means.

> > Well, I suggest we keep the term "key" (as in "key change")
> > for use in the Western sense. But "modulation" seems fair
> > game.
>
> That is a paradoxical suggestion. Key is the prerequisite of
> modulation per se.

I disagree. In my view, "key" arises in tonal music, which
has preferred modes. In your earlier example, a change from
C ionian to D dorian is not a change of key since the same
pitches are involved. Those 7 pitches uniquely signal that
one of only two keys can be in effect (in Western practice,
at least).

However, my view is not based on any real understanding of
maqam music.

> For all I know, it is the "type of modulation based on
> harmonic tonality" which needs to be explained aside from
> simple and generalized `modulation`.

Maybe so, but the harmonic-tonality type is rather
synonymous with "modulation" in the West.

-Carl

Paul, your answer does not satisfy me in the least. Besides, I'm as patient
and open-minded as I ever am.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 23:41
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> And you would likewise be bold enough to say that the first 40
seconds of
> the majestic opening of the St. Mattheus Passion by J.S. Bach (Otto
> Klemperer rendition) - although based entirely on a glorious E
drone (basso
> ostinato) supported by organ and bassi - is devoid of any
modulation?

Western tonality is quite different from Indian dronality (to use
Mathieu's word).

> Go figure.

I hope you treat Haresh with a bit more patience and open-mindedness.

I am dying to hear from you a piece of Hindustani music that is devoid of
`modulation` to begin with.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 �ubat 2006 �ar�amba 23:47
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

I meant a recording of Hindustani music which shows the phenomenon to
which you're referring.

> > > <22 35 51|
> >
> > This seems significant.
> >
> > -C.
>
> Indeed! It leads quite naturally to the sruti scale given by S.
> Ramanathan, Erv Wilson, etc., as one of the JI possibilities.

Which scale is that?

-Carl

> > > Timbres with all partials at tritones apart were used in a
> > > classic experiment by Pierce. They sound like dyads, not
> > > single notes.
> >
> > Oh, I'm sure there's a way to get them sound like single tones.
>
> Go ahead and try. You'll have to make some of those partials
> pretty darn quiet!

Strong enough transients and fast enough decay should do it,
even with 1/n^2 amplitudes (which would be generous). Or,
just play a melody. Psychoacoustic experiments are notorious
for making much too strong generalizations about timbre.

> > >And besides, there's a model for temperaments, but then there's
> > >a model for the scales, instrument tunings, etc. drawn from
> > >these temperaments.
> >
> > Exactly. The model for scales is where equivalence intervals
> > come in,
>
> In my paper's approach, yes.

In any appropriately-generalized approach.

> >so the word for temperaments shouldn't employ them.
>
> This is why I use "2D temperaments" in my paper. In much of the
> published literature, though, the equivalence intervals come in
> right along with the temperaments, which is the context
> where "linear" has been used.

Bah.

-Carl

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
>
> [PA]
> With 7 notes in the scale, you can create a table showing the 49
intervals
> in the scale. The table will be antisymmtric about the diagonal.
Anyway, all
> the thirds/sixths will be in there and you can see how well they
approximate
> the ratios of 5 as a function of the size of the diatonic scale's
generating
> fifth. Shall I create an Excel spreadsheet for you to demonstrate
this?
>
> [OZ]
> Indeed, I would be delighted to be enlightened!

/tuning/files/Erlich/forozan.xls

You may put the size of generating fifth in the top row, overwriting
the 696 that's they're now. As you try different possibilities,
observe the sizes of the errors displayed at the bottom. What size of
fifth makes all these errors fairly small?

> > 709 cents is a little wide for my tastes. 708 is the ideal limit
as far as
> I
> > am concerned.
>
> [PA]
> OK. What's the lower limit for you? And how about octaves, fourths,
etc.?
>
> [OZ]
> The fifth should be somewhere between 696-708, give or take a
couple of
> atoms. The octave should be pure, and thus the fourths derived thus.

I'll try to keep this in mind, but I still wonder why the 694.2-cent
fifths in your tuning are not a problem for you.

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> Carl Lumma escreveu:
> >>Timbres with all partials at tritones apart were used in a
> >>classic experiment by Pierce. They sound like dyads, not single
> >>notes.
> >
> >
> > Oh, I'm sure there's a way to get them sound like single tones.
>
> What is that "classical experiment"?
>
> I recall a small Pierce's text published at JASA: "Attaining
Consonance
> in Arbitray Scales". There, the consonance was given by intervals
of 1/4
> octave (or its multiples), between pitches taken from a 1/8 octave
> scale. The frequency ratios of the partials were:
>
> 1 (0 octave)
> 2.378 (1.25 oct)
> 4 (2 oct)
> 5.657 (2.5 oct)
> 6.726 (2.75 oct)
> 8 (3 oct)
>
> This can really sound as a single tone.

I may have been thinking of a different Pierce (or someone else's)
experiment, where the partials occur *every* 1/2 octave above the
fundamental. Clearly, that would sound quite different.

> > Even a single note lasting as short as one fifth of a second
> > makes the entire difference of modulation. Surely there can be
> > no argument against that!
>
> I'm not even sure what it means.
>

It means, a single note in passing is sufficient to trigger `modulation`.

> > > Well, I suggest we keep the term "key" (as in "key change")
> > > for use in the Western sense. But "modulation" seems fair
> > > game.
> >
> > That is a paradoxical suggestion. Key is the prerequisite of
> > modulation per se.
>
> I disagree. In my view, "key" arises in tonal music, which
> has preferred modes. In your earlier example, a change from
> C ionian to D dorian is not a change of key since the same
> pitches are involved. Those 7 pitches uniquely signal that
> one of only two keys can be in effect (in Western practice,
> at least).
>

Let me guess, C and G. One may also conceive of F though.

> However, my view is not based on any real understanding of
> maqam music.
>

Ok, here is some examples and questions for you:

C Db E F G Ab B C >>> F G Ab B C Db E F >>> G Ab B C Db B C

1. Is this a modulation or not?

F G Ab B C Db C B >>> C D Eb F# G Ab G >>> C B Ab G F.

2. Is a key established above or not?

3. Are any of these sequences enough to establish tonality?

> > For all I know, it is the "type of modulation based on
> > harmonic tonality" which needs to be explained aside from
> > simple and generalized `modulation`.
>
> Maybe so, but the harmonic-tonality type is rather
> synonymous with "modulation" in the West.
>
> -Carl
>

I've truly had enough of this Westernist monopolization. Modulation is
simply changing the tone centre of a scale or scales during the flow of
music... as much in C major to A minor, or C major to F major, or even B
dorian to F# major (demonstrated in Praeludium XXIV in Wohltemperiertes
Klavier I for gosh sakes!) as in the several examples I underlined. Why
should any one of us Easterners consent to a European oriented
non-generalized definition of modulation or tonality?

Oz.

I could burn a copy of every Indian music CD and DVD in my collection
for you. Would you like that?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> With my statement, perhaps, with my logic, not in the least! Fixed
drones do
> not preclude modulation as seen in many passages of Western common
music
> practice reinforced with bassi ostinati.
>
> How about if you can produce me a piece where no modulation takes
place?
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 20:31
> Subject: [tuning] No drone in Indian music before 12th century
(was: Re:
> More on shruti-s)
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Dear Haresh, a question if you will: Since major and minor are
names that
> > stand for the two modes which we call `Ionian` and `Aeolian`whose
tonics
> are
> > different degrees of the famous natural diatonical scale on the
white keys
> > of a Halberstadt keyboard design, and since modulation is simply
changing
> > the tone centre/key during music, would you say that it is
allowable to
> > `modulate` from Ionian to Dorian (still the same scale) within a
basic
> > melodic framework without any chords?
> >
> > If your answer to this question is yes, you have inadvertantly
accepted
> the
> > fact that no genre we are aware of can evade `modulation`.
>
> There's something wrong with your logic. We are aware of a genre
where the
> tone center/key does not change during the musicn because it is
played
> continuoisly by the fixed drone.
> Just because it may be very easy to change tone center in many
genres by no
> means forces such a conclusion about every genre we are aware of.
>

You make it sound like you have hundreds in your possession. Just one
example without any instance of `modulation` will be enough, thank you.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 0:53
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

I could burn a copy of every Indian music CD and DVD in my collection
for you. Would you like that?

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> I could burn a copy of every Indian music CD and DVD in my collection
> for you. Would you like that?

Lots of us would like that. :)

I'm in the office and have nothing handy; perhaps Haresh can comply
with your request.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I am dying to hear from you a piece of Hindustani music that is
devoid of
> `modulation` to begin with.
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 22 Þubat 2006 Çarþamba 23:47
> Subject: [tuning] No drone in Indian music before 12th century
(was: Re:
> More on shruti-s)
>
>
> I meant a recording of Hindustani music which shows the phenomenon
to
> which you're referring.
>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > <22 35 51|
> > >
> > > This seems significant.
> > >
> > > -C.
> >
> > Indeed! It leads quite naturally to the sruti scale given by S.
> > Ramanathan, Erv Wilson, etc., as one of the JI possibilities.
>
> Which scale is that?
>
> -Carl

See, for example, http://www.rit.edu/~pnveme/raga/Sruti.html -- but
where two ratios are given (for Chyuta Panchama Madhyama), use only
the first: 729/512. This choice, but not the other, preserves the
constant structure / epimorphic property Gene was referring to. Kraig
says the distinction between this note and the "wrong" one a schisma
away is of aesthetic significance and can be heard by at least some
Indian masters . . .

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Timbres with all partials at tritones apart were used in a
> > > > classic experiment by Pierce. They sound like dyads, not
> > > > single notes.
> > >
> > > Oh, I'm sure there's a way to get them sound like single tones.
> >
> > Go ahead and try. You'll have to make some of those partials
> > pretty darn quiet!
>
> Strong enough transients and fast enough decay should do it,
> even with 1/n^2 amplitudes (which would be generous). Or,
> just play a melody. Psychoacoustic experiments are notorious
> for making much too strong generalizations about timbre.

They are? Well, I just use my ears. Church bells never sound like
single tones to me.

> > > >And besides, there's a model for temperaments, but then there's
> > > >a model for the scales, instrument tunings, etc. drawn from
> > > >these temperaments.
> > >
> > > Exactly. The model for scales is where equivalence intervals
> > > come in,
> >
> > In my paper's approach, yes.
>
> In any appropriately-generalized approach.

Huh?

> > >so the word for temperaments shouldn't employ them.
> >
> > This is why I use "2D temperaments" in my paper. In much of the
> > published literature, though, the equivalence intervals come in
> > right along with the temperaments, which is the context
> > where "linear" has been used.
>
> Bah.

Bah?

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> I've truly had enough of this Westernist monopolization.

Are you accusing Haresh of this too?

> Modulation is
> simply changing the tone centre of a scale or scales during the
flow of
> music... as much in C major to A minor, or C major to F major, or
even B
> dorian to F# major (demonstrated in Praeludium XXIV in
Wohltemperiertes
> Klavier I for gosh sakes!) as in the several examples I underlined.

Haresh's definition of modulation contained 3 possibilities, which
cover all of these examples and more.

> Why
> should any one of us Easterners consent to a European oriented
> non-generalized definition of modulation or tonality?

Is Haresh an Easterner in your view?

> > > Even a single note lasting as short as one fifth of a second
> > > makes the entire difference of modulation. Surely there can be
> > > no argument against that!
> >
> > I'm not even sure what it means.
>
> It means, a single note in passing is sufficient to trigger
> `modulation`.

Then I don't agree. The very definition of passing tones
precludes this.

> > > > Well, I suggest we keep the term "key" (as in "key change")
> > > > for use in the Western sense. But "modulation" seems fair
> > > > game.
> > >
> > > That is a paradoxical suggestion. Key is the prerequisite of
> > > modulation per se.
> >
> > I disagree. In my view, "key" arises in tonal music, which
> > has preferred modes. In your earlier example, a change from
> > C ionian to D dorian is not a change of key since the same
> > pitches are involved. Those 7 pitches uniquely signal that
> > one of only two keys can be in effect (in Western practice,
> > at least).
>
> Let me guess, C and G. One may also conceive of F though.

No, C and Amin.

> > However, my view is not based on any real understanding of
> > maqam music.
>
> Ok, here is some examples and questions for you:
>
> C Db E F G Ab B C >> F G Ab B C Db E F >> G Ab B C Db B C
>
> 1. Is this a modulation or not?

I don't think most Western musicians would call it that,
but there's something worth calling something there.

> F G Ab B C Db C B >> C D Eb F# G Ab G >> C B Ab G F.
>
> 2. Is a key established above or not?

Brahms might call that F gypsy minor or some such.

> > > For all I know, it is the "type of modulation based on
> > > harmonic tonality" which needs to be explained aside from
> > > simple and generalized `modulation`.
> >
> > Maybe so, but the harmonic-tonality type is rather
> > synonymous with "modulation" in the West.
>
> I've truly had enough of this Westernist monopolization.

Remember that you're translating into English.

> Why should any one of us Easterners consent to a European
> oriented non-generalized definition of modulation or tonality?

Is there a Turkish word for "modulation"?

-Carl

> > > > > <22 35 51|
> > > >
> > > > This seems significant.
> > >
> > > Indeed! It leads quite naturally to the sruti scale given by S.
> > > Ramanathan, Erv Wilson, etc., as one of the JI possibilities.
> >
> > Which scale is that?
>
> See, for example, http://www.rit.edu/~pnveme/raga/Sruti.html -- but
> where two ratios are given (for Chyuta Panchama Madhyama), use only
> the first: 729/512. This choice, but not the other, preserves the
> constant structure / epimorphic property Gene was referring to.
> Kraig says the distinction between this note and the "wrong" one a
> schisma away is of aesthetic significance and can be heard by at
> least some Indian masters . . .

Kyool. Manuel, is this in the Scala archive?

-Carl

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 0:13
Subject: [tuning] Re: More on shruti-s

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> >
> > [PA]
> > With 7 notes in the scale, you can create a table showing the 49
> intervals
> > in the scale. The table will be antisymmtric about the diagonal.
> Anyway, all
> > the thirds/sixths will be in there and you can see how well they
> approximate
> > the ratios of 5 as a function of the size of the diatonic scale's
> generating
> > fifth. Shall I create an Excel spreadsheet for you to demonstrate
> this?
> >
> > [OZ]
> > Indeed, I would be delighted to be enlightened!
>
> /tuning/files/Erlich/forozan.xls
>

Thanks. It looks swell.

> You may put the size of generating fifth in the top row, overwriting
> the 696 that's they're now. As you try different possibilities,
> observe the sizes of the errors displayed at the bottom. What size of
> fifth makes all these errors fairly small?
>

Well, I'll be! A 695.81 cent fifth equalizes the errors. Are there other
`magical` properties for this generator?

> > > 709 cents is a little wide for my tastes. 708 is the ideal limit
> as far as
> > I
> > > am concerned.
> >
> > [PA]
> > OK. What's the lower limit for you? And how about octaves, fourths,
> etc.?
> >
> > [OZ]
> > The fifth should be somewhere between 696-708, give or take a
> couple of
> > atoms. The octave should be pure, and thus the fourths derived thus.
>
> I'll try to keep this in mind, but I still wonder why the 694.2-cent
> fifths in your tuning are not a problem for you.
>
>

The bad effects are cancelled to a great extent by the pure fifths in the
system during modulations.

Hi Ozan.

> Well, I'll be! A 695.81 cent fifth equalizes the errors. Are there other
> `magical` properties for this generator?

I'm not sure if I caught your idea 100% correctly, but this makes a lot of
sense to me.
If you're looking for a generating fifth which, when combined with octaves,
makes major and minor thirds equally detuned, that means you wish to find
such a tuning in which the chroma (i.e. the difference of a major third from
a minor third) is tuned to 25/24 (i.e. the difference of 5/4 from 6/5). As
the chroma can be expressed as a distance of 7 fifths (not counting the
octave inversions, of course), in fact, our point is to find a fifth which,
when stacked 7 times, makes 50/3 (i.e. the 5-limit chroma + 4 octaves). When
you divide the size of the 50/3 into 7 equal parts (and you can try this out
on your own by doing "Calculate 50/3 \ 7" in Scala), you get a fifth which I
think is just the one you found. If you try "Equal 7 50/3 11" and then
"Normalize", you actually get a chain of 11 fifths upwards (i.e. from C to
E#) in 2/7-comma meantone.

Petr

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 2:07
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > I've truly had enough of this Westernist monopolization.
>
> Are you accusing Haresh of this too?
>

How should I know if Haresh is Westernized or not? I pass no judgements nor
make any remarks against the innocent.

> > Modulation is
> > simply changing the tone centre of a scale or scales during the
> flow of
> > music... as much in C major to A minor, or C major to F major, or
> even B
> > dorian to F# major (demonstrated in Praeludium XXIV in
> Wohltemperiertes
> > Klavier I for gosh sakes!) as in the several examples I underlined.
>
> Haresh's definition of modulation contained 3 possibilities, which
> cover all of these examples and more.
>

It is only a matter of three things:

1. Switch mode, preserve key (C major>c minor).
2. No switch, transpose mode (C major>G major).
3. Switch mode & transpose (C major>A minor).

By this definition, can you any longer refuse the fact that modulation
applies to Hindustani/Carnatic Sangeets as much as any `tonal` music no
matter the `drone` (which is little more than basso ostinato)?

> > Why
> > should any one of us Easterners consent to a European oriented
> > non-generalized definition of modulation or tonality?
>
> Is Haresh an Easterner in your view?
>
>

How am I supposed to know if he adheres to the traditions of the East?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 2:31
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> > > > Even a single note lasting as short as one fifth of a second
> > > > makes the entire difference of modulation. Surely there can be
> > > > no argument against that!
> > >
> > > I'm not even sure what it means.
> >
> > It means, a single note in passing is sufficient to trigger
> > `modulation`.
>
> Then I don't agree. The very definition of passing tones
> precludes this.
>

What? How about:

Ex. 1
E-----F-E-----D--C#
G==========G# A
C==========B- A

Ex. 2
E-----F-E-----D--C#
G=============A
C=============A

> > > > > Well, I suggest we keep the term "key" (as in "key change")
> > > > > for use in the Western sense. But "modulation" seems fair
> > > > > game.
> > > >
> > > > That is a paradoxical suggestion. Key is the prerequisite of
> > > > modulation per se.
> > >
> > > I disagree. In my view, "key" arises in tonal music, which
> > > has preferred modes. In your earlier example, a change from
> > > C ionian to D dorian is not a change of key since the same
> > > pitches are involved. Those 7 pitches uniquely signal that
> > > one of only two keys can be in effect (in Western practice,
> > > at least).
> >
> > Let me guess, C and G. One may also conceive of F though.
>
> No, C and Amin.
>

One may also think in terms of chords and say that it is possible to
modulate from C major to E minor to A minor to D minor to F major to G major
to C major using only 7 notes:

E=G=A=F=A=G=E
C=E=C=D=C=B=G
G===A===F=D=C
C=B=A=D=F=G=C

> > > However, my view is not based on any real understanding of
> > > maqam music.
> >
> > Ok, here is some examples and questions for you:
> >
> > C Db E F G Ab B C >> F G Ab B C Db E F >> G Ab B C Db B C
> >
> > 1. Is this a modulation or not?
>
> I don't think most Western musicians would call it that,
> but there's something worth calling something there.
>

And what else would you call it?

> > F G Ab B C Db C B >> C D Eb F# G Ab G >> C B Ab G F.
> >
> > 2. Is a key established above or not?
>
> Brahms might call that F gypsy minor or some such.
>

So you admit that there is a key?

> > > > For all I know, it is the "type of modulation based on
> > > > harmonic tonality" which needs to be explained aside from
> > > > simple and generalized `modulation`.
> > >
> > > Maybe so, but the harmonic-tonality type is rather
> > > synonymous with "modulation" in the West.
> >
> > I've truly had enough of this Westernist monopolization.
>
> Remember that you're translating into English.
>

Yes, I no speak well English, you me help understand? LOL

> > Why should any one of us Easterners consent to a European
> > oriented non-generalized definition of modulation or tonality?
>
> Is there a Turkish word for "modulation"?
>

It's called `cheshni`, or `recipe` if you will.

> -Carl
>
>
>

Oz.

Petr,

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 23 �ubat 2006 Per�embe 16:44
Subject: Re: [tuning] Re: More on shruti-s

> Hi Ozan.
>
> > Well, I'll be! A 695.81 cent fifth equalizes the errors. Are there other
> > `magical` properties for this generator?
>
> I'm not sure if I caught your idea 100% correctly, but this makes a lot of
> sense to me.

Shucks. I made sense for the first time in weeks!

> If you're looking for a generating fifth which, when combined with
octaves,
> makes major and minor thirds equally detuned, that means you wish to find
> such a tuning in which the chroma (i.e. the difference of a major third
from
> a minor third) is tuned to 25/24 (i.e. the difference of 5/4 from 6/5). As
> the chroma can be expressed as a distance of 7 fifths (not counting the
> octave inversions, of course), in fact, our point is to find a fifth
which,
> when stacked 7 times, makes 50/3 (i.e. the 5-limit chroma + 4 octaves).

Very interesting!

When
> you divide the size of the 50/3 into 7 equal parts (and you can try this
out
> on your own by doing "Calculate 50/3 \ 7" in Scala), you get a fifth which
I
> think is just the one you found. If you try "Equal 7 50/3 11" and then
> "Normalize", you actually get a chain of 11 fifths upwards (i.e. from C to
> E#) in 2/7-comma meantone.
>

Yes, I noticed how close 2/7 comma meantone comes to equalizing the errors.
Carrying this generator fifth to 119 tones produces a terrific
meantone-superpythagorean hybrid.

> Petr
>
>
>

Ozan

Hi Ozan.

> Yes, I noticed how close 2/7 comma meantone comes to equalizing the
errors.

Close to equalizing? Which errors do you mean? I thought you were trying to
equalize the errors of major and minor thirds -- and 2/7-comma meantone
equalizes these exactly.

> Carrying this generator fifth to 119 tones produces a terrific
> meantone-superpythagorean hybrid.

Actually amazingly close to 119-EDO, don't you think? :-)

Petr

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 24 �ubat 2006 Cuma 1:24
Subject: Re: [tuning] Re: More on shruti-s

> Hi Ozan.
>
> > Yes, I noticed how close 2/7 comma meantone comes to equalizing the
> errors.
>
> Close to equalizing? Which errors do you mean? I thought you were trying
to
> equalize the errors of major and minor thirds -- and 2/7-comma meantone
> equalizes these exactly.
>

Then the problem is solved. This is the meantone that makes all the
difference.

> > Carrying this generator fifth to 119 tones produces a terrific
> > meantone-superpythagorean hybrid.
>
> Actually amazingly close to 119-EDO, don't you think? :-)
>

1.4 cent highest absolute difference. I wouldn't say amazingly, but yes,
pretty much.

> Petr
>
>

Oz.

> > > > In my view, "key" arises in tonal music, which has
> > > > preferred modes. In your earlier example, a change from
> > > > C ionian to D dorian is not a change of key since the same
> > > > pitches are involved. Those 7 pitches uniquely signal that
> > > > one of only two keys can be in effect (in Western practice,
> > > > at least).
> > >
> > > Let me guess, C and G. One may also conceive of F though.
> >
> > No, C and Amin.
>
> One may also think in terms of chords and say that it is possible
> to modulate from C major to E minor to A minor to D minor to F
> major to G major to C major using only 7 notes:
>
> E=G=A=F=A=G=E
> C=E=C=D=C=B=G
> G===A===F=D=C
> C=B=A=D=F=G=C

Chord changes are not key changes. (Though the issue is not
clearly delimited, and chord changes are like micro- key changes
in a way.) Music textbooks will say that the above example
is entirely in the key of C.

> > > C Db E F G Ab B C >> F G Ab B C Db E F >> G Ab B C Db B C
> > >
> > > 1. Is this a modulation or not?
> >
> > I don't think most Western musicians would call it that,
> > but there's something worth calling something there.
>
> And what else would you call it?
//
> > Is there a Turkish word for "modulation"?
>
> It's called `cheshni`, or `recipe` if you will.

Howabout "cheshni"?

> > > > Maybe so, but the harmonic-tonality type is rather
> > > > synonymous with "modulation" in the West.
> > >
> > > I've truly had enough of this Westernist monopolization.
> >
> > Remember that you're translating into English.
>
> Yes, I no speak well English, you me help understand? LOL

Your English is fantastic. But if you want an accurate
translation of the maqam concept of mode changes, an
unqualified "modulation" is not your best bet.

-Carl

Hi all,

I'm WAY behind on my reading, but simply couldn't resist
responding to this! ;-)

On Wed, 22 Feb 2006 Carl Lumma wrote:
>
> > > http://www.ozanyarman.com/anonymous/modulation-example.wav
> > >
> > > There's no doubt that a key is established. Where, in your
> > > view, do(es) the modulation(s) occur?
> >
> > Carl, if mode A is 'do-fa-sol', mode B is 'fa-sol-do' and
> > mode C is 'sol-do-fa', the modulations occur at 11 seconds
> > from A to B and back again at 18 seconds... then, finally
> > during the cadence from 24 seconds onward, thru
> > A to C to B to A.
>
> Great, as I thought. Just wanted to be clear on this.
> Except I didn't catch the modulations from 24 seconds
> onward (only the one at 11 seconds). To me, this final
> phrase is so short that I wouldn't say it contains any
> modulation.
>
> > Glad someone agrees with me at last about keys!
>
> Well, I suggest we keep the term "key" (as in "key change")
> for use in the Western sense. But "modulation" seems fair
> game. FWIW, I used the term "modal modulation" for years
> on this list to clarify the two meanings of this overloaded
> term.

Carl and Ozan,

I have no doubt that using "modulation" in this sense
simply muddies the waters.

If we simply move a motif up or down by a number of
scale degrees, we already have a perfectly clear term
for that, and its usage goes back way before I first
heard it as a lad. That term is "tonal transposition".
The adjective "tonal" distinguishes it from a purely
chromatic or "exact" transposition.

The term "modulation", on the other hand, means a
change of key centre or tonic.

Examples:
1. C F G C F G | C F G C : : | F Bb c F Bb c | F Bb c F : :
is a pair of phrases in which every note of the second
is an exact fourth higher than the corresponding note
in the first. The second phrase is an exact transposition
of the first.

2. C F G C F G | C F G C : : | F B c F B c | F B c F : :
is a pair of phrases in which every note of the second
is a diatonic fourth higher than the corresponding note
in the first. The second phrase is a tonal transposition
of the first.

If the music in Example 1, having been previously
centred on C, now continues with the new tone centre
F, we say it has modulated from C to F.

If however, it returns to the tonic C, few would agree
that repetition of the first phrase in a closely related
key constitutes a "modulation". Rather, we would say
that the _harmony_ is in C in the first phrase, and in F
in the second phrase.

These usages are not just my fancy - they have been part
of the common vocabulary of Western music for centuries.
And I see no compelling resaon to change them.

BTW, I think it a nonsense to suggest that Hindustani
music "modulates" in the accepted Western sense. Of
course it uses motivic transposition! But it does NOT
modulate!

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 268.1.1/270 - Release Date: 27/2/06

> Carl and Ozan,

Hi Yahya, thanks for chiming in.

> I have no doubt that using "modulation" in this sense
> simply muddies the waters.

Well, to be fair to Ozan, there are several web sites
on maqam music that use the term.

> If we simply move a motif up or down by a number of
> scale degrees, we already have a perfectly clear term
> for that, and its usage goes back way before I first
> heard it as a lad. That term is "tonal transposition".

I didn't know that. I have used "modal transpostion"
on this list in the past.

-Carl

Centuries of wrongs do not make a right my dear brother in Islam. I have
demonstrated all too clearly how modulation per se is utilized threefold in
not just Western practice, but Eastern as well.

What muddies the waters is inventing words to divide musical terminology
into cultural borders IMNSHO. Tonal transposition? Never heard of it, nor
found the need to use such an awkward concept. Here is what the Harvard
Dictionary of Music 4th edition has to say on transposition:

"The rewriting of performance of music at a pitch other than the original
one. This entails raising or lowering each pitch of the original music by
precisely the same interval. In tonal music, it results in changing the key
of the original. Works are often transposed to accomodate the ranges of
singers. The player of an instrument at one pitch will be required to
transpose in order to perform a part written at another pitch; e.g. the
player of a trumpet in Bb will be required to transpose in order to perform
a part for trumpet in C or D, in the first case by raising every pitch a
whole tone, in the second by raising every pitch a major third. See also
Transposing Instruments."

There is no mention of anything such as `tonal transposition` here, nor
anywhere else I could readily reach.

Modulation in the Western sense! Now that is something to be explained aside
from modulation in an intercontinental/universal sense.

Why be instrumental in propagating the nonsense of `motivic transposition`
just to avoid the beautifully suitable term `modulation`?

Cordially,
Ozan

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 5:12
Subject: [tuning] RE: No drone in Indian music before 12th century (was: Re:
More on shruti-s)

>
> Hi all,
>
> I'm WAY behind on my reading, but simply couldn't resist
> responding to this! ;-)
>
>
> On Wed, 22 Feb 2006 Carl Lumma wrote:
> >
> > > > http://www.ozanyarman.com/anonymous/modulation-example.wav
> > > >
> > > > There's no doubt that a key is established. Where, in your
> > > > view, do(es) the modulation(s) occur?
> > >
> > > Carl, if mode A is 'do-fa-sol', mode B is 'fa-sol-do' and
> > > mode C is 'sol-do-fa', the modulations occur at 11 seconds
> > > from A to B and back again at 18 seconds... then, finally
> > > during the cadence from 24 seconds onward, thru
> > > A to C to B to A.
> >
> > Great, as I thought. Just wanted to be clear on this.
> > Except I didn't catch the modulations from 24 seconds
> > onward (only the one at 11 seconds). To me, this final
> > phrase is so short that I wouldn't say it contains any
> > modulation.
> >
> > > Glad someone agrees with me at last about keys!
> >
> > Well, I suggest we keep the term "key" (as in "key change")
> > for use in the Western sense. But "modulation" seems fair
> > game. FWIW, I used the term "modal modulation" for years
> > on this list to clarify the two meanings of this overloaded
> > term.
>
>
> Carl and Ozan,
>
> I have no doubt that using "modulation" in this sense
> simply muddies the waters.
>
> If we simply move a motif up or down by a number of
> scale degrees, we already have a perfectly clear term
> for that, and its usage goes back way before I first
> heard it as a lad. That term is "tonal transposition".
> The adjective "tonal" distinguishes it from a purely
> chromatic or "exact" transposition.
>
> The term "modulation", on the other hand, means a
> change of key centre or tonic.
>
> Examples:
> 1. C F G C F G | C F G C : : | F Bb c F Bb c | F Bb c F : :
> is a pair of phrases in which every note of the second
> is an exact fourth higher than the corresponding note
> in the first. The second phrase is an exact transposition
> of the first.
>
> 2. C F G C F G | C F G C : : | F B c F B c | F B c F : :
> is a pair of phrases in which every note of the second
> is a diatonic fourth higher than the corresponding note
> in the first. The second phrase is a tonal transposition
> of the first.
>
> If the music in Example 1, having been previously
> centred on C, now continues with the new tone centre
> F, we say it has modulated from C to F.
>
> If however, it returns to the tonic C, few would agree
> that repetition of the first phrase in a closely related
> key constitutes a "modulation". Rather, we would say
> that the _harmony_ is in C in the first phrase, and in F
> in the second phrase.
>
> These usages are not just my fancy - they have been part
> of the common vocabulary of Western music for centuries.
> And I see no compelling resaon to change them.
>
> BTW, I think it a nonsense to suggest that Hindustani
> music "modulates" in the accepted Western sense. Of
> course it uses motivic transposition! But it does NOT
> modulate!
>
> Regards,
> Yahya
>

Carl, it appears to be a term invented in the absence or avoidance of
`modulation`.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 28 �ubat 2006 Sal� 11:26
Subject: [tuning] No drone in Indian music before 12th century (was: Re:
More on shruti-s)

> > Carl and Ozan,
>
> Hi Yahya, thanks for chiming in.
>
> > I have no doubt that using "modulation" in this sense
> > simply muddies the waters.
>
> Well, to be fair to Ozan, there are several web sites
> on maqam music that use the term.
>
> > If we simply move a motif up or down by a number of
> > scale degrees, we already have a perfectly clear term
> > for that, and its usage goes back way before I first
> > heard it as a lad. That term is "tonal transposition".
>
> I didn't know that. I have used "modal transpostion"
> on this list in the past.
>
> -Carl
>
>
>

Carl,

> > One may also think in terms of chords and say that it is possible
> > to modulate from C major to E minor to A minor to D minor to F
> > major to G major to C major using only 7 notes:
> >
> > E=G=A=F=A=G=E
> > C=E=C=D=C=B=G
> > G===A===F=D=C
> > C=B=A=D=F=G=C
>
> Chord changes are not key changes. (Though the issue is not
> clearly delimited, and chord changes are like micro- key changes
> in a way.) Music textbooks will say that the above example
> is entirely in the key of C.
>

If it will please you, I could just as well have modulated to another mode
of that same scale using only 7 pitches that would correspond to a key
changes, even in monophony:

C...D.E...F.GFAGF....

D...E.F...A.G..FED....

E...C.BAG...A........

Admit it, there is modulation (momentary key changes+tonicizations) all over
the place, even when I remain in the same key.

> > > Is there a Turkish word for "modulation"?
> >
> > It's called `cheshni`, or `recipe` if you will.
>
> Howabout "cheshni"?
>

So thou sayest. It is `modulation`, not some lousy `tonal transposition`
fetched up by Allah knows who.

> >
> > Yes, I no speak well English, you me help understand? LOL
>
> Your English is fantastic. But if you want an accurate
> translation of the maqam concept of mode changes, an
> unqualified "modulation" is not your best bet.
>

Unqualified?? I already defined it very congruently so much so that the term
perfectly matches not only Western common practice of harmony and polyphony,
but Eastern common practice of heterophony as well.

> -Carl
>
>
>
>

Oz.

Ozan Yarman wrote:

> What muddies the waters is inventing words to divide musical terminology
> into cultural borders IMNSHO.

I think this is perfectly OK, and the best way to go, when there are different cultural practices.

Tonal transposition? Never heard of it, nor
> found the need to use such an awkward concept. Here is what the Harvard
> Dictionary of Music 4th edition has to say on transposition:
> ...
> > There is no mention of anything such as `tonal transposition` here, nor
> anywhere else I could readily reach.

More often than with transposition, it is used with more specific instances like imitations, sequences and fugue subjects. They are either real transpositions, interval for interval, which constitute a new tonality, or tonal. These latter ones stay inside the established tonality for the price of exchanging major and minor intervals, fifths and fourths.

> > Modulation in the Western sense! Now that is something to be explained aside
> from modulation in an intercontinental/universal sense.

Western modulation means establishing a key, and the only Western way to establish a key is with IV-V-I or II-V-I cadence, and then establishing a different key by the same means. Hackneyed example:

Take a march in, say, F. There is an introduction, a high register melodic strain (repeated), a strain of broken chords in the low register (repeated), and then it's time for the trio, which will normally be in Bb. Instead of simply continuing in the other key ("gear shift" I think it's called in English) there are two extra bars where the tuba goes F-Eb-D-C. The F (plus five other tones) is common to F and Bb major and is ambiguous. The Eb is foreign to F and tells you that a modulation may be going on. As it happens, the next 1, first chord in the trio, is Bb; there really was a modulation. Without the two bars of preparation, you have a key change, but no modulation (this is not supposed to happen in classical music). Without the concluding Bb, your tonality is not established and you have to wait for the modulation to be completed (which, post-Satie, may never happen).

In Gregorian chant, modulation occurs (1) when a piece exceeds the octave (going from authentic to plagal or the other way around), (2) starts in D, but suddenly ends a number of phrases in E, or (3) uses an unusual repercussa (tenor, dominant), but (not 4) not when the authentic D-mode switches between B and Bb to avoid a mi-contra-fa (it is not known if this happened in monophonic music; it does in early polyphony). There may be more possibilities to use that term.

These two kinds of modulations have nothing to do with each other, and it is probably common to refer to the chant kind of modulation by an original latin term like modulatio or modus mixtus.

It is conceivable that a piece in a D-mode introduces an Eb o an F#. Your kanun sample had a lot of this, but I am not aware that it happens in Gregorian chant. Now if you want to talk about Western polyphony and Gregorian chant, you can refer to "molation" and "modulatio". If you want to talk about makam music and Western polyphony, you can use "modulation" and "mixed modes". What if you want to compare the moddal concepts of makam and Gregorian chant? Best to use, and teach us, the term used within the makam tradition, all along, and nothing universal, please.

didn't want to join in again.
klaus

Hallo all,

On Wed, 22 Feb 2006, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >
> > > > > <22 35 51|
> > > >
> > > > This seems significant.
> > > >
> > > > -C.
> > >
> > > Indeed! It leads quite naturally to the sruti scale given by S.
> > > Ramanathan, Erv Wilson, etc., as one of the JI possibilities.
> >
> > Which scale is that?
> >
> > -Carl
>
> See, for example, http://www.rit.edu/~pnveme/raga/Sruti.html

Paul, thank you for an excellent link! The site has many
other useful links on the subject of Indian (primarily
Carnatic) music. Whilst exploring the meaning of the
term "pallavi", I also came across another valuable
reference site, www.pallavi.org, with many useful links.

One of those links bears directly on the original issue
in this thread, namely: exactly how did Bharata (and
early practitioners) arrive at and tune their 22 sruti
per octave? Here is the article on the derivation of
the 22 sruti:
http://www.carnaticcorner.com/articles/22_srutis.htm

I recommend that anyone who thinks that the 22 sruti
were 22-EDO read this article. It makes some cogent
arguments that the classical tuning of both north and
south Indian was a 5-prime-limit just intonation system.
It goes beyond this, to elaborate what that system was.
Its only really weak point is, I think, in its arguments
for discarding some possible ratios for the fourth, Ma.
If anyone finds the terminology too terribly unfamiliar
or confusing, please let me know and I will try to
explain.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 268.1.1/271 - Release Date: 28/2/06

On Wed, 22 Feb 2006, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
[snip]
> > > >so the word for temperaments shouldn't employ them.
> > >
> > > This is why I use "2D temperaments" in my paper. In much of the
> > > published literature, though, the equivalence intervals come in
> > > right along with the temperaments, which is the context
> > > where "linear" has been used.
> >
> > Bah.
>
> Bah?

Black sheep ...

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 268.1.1/271 - Release Date: 28/2/06

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:

> Here is the article on the derivation of
> the 22 sruti:
> http://www.carnaticcorner.com/articles/22_srutis.htm
>
> I recommend that anyone who thinks that the 22 sruti
> were 22-EDO read this article.

Who since Bosanquet thinks that? The problem is not what they aren't,
but what they are.

> It makes some cogent
> arguments that the classical tuning of both north and
> south Indian was a 5-prime-limit just intonation system.
> It goes beyond this, to elaborate what that system was.

It seems to me it was like everything else I've read on this, very
iffy. However, one can certainly take 5-limit JI, organized by the
22-et val h22 = <22 35 51| as a postulate. If we do that, it occurred
to me that a concept one might call a "possible sruti" might prove useful.

Define a 5-limit ratio q as a "possible struti" for the ith strui
step, starting from 0, if

|22 log2(q) - h22(q)| < 1/2

A possible sruti is mapped to the ith sruti step, and is closer to the
ith 22edo step than it is to any other 22edo step. Presumably we
exclude the 0th step from this, as we want the unison. However, if we
suitably restrict the complexity of q, we don't have to. Below I list
sruti steps from 0 to 21, and a list of all the possible srutis with a
"Kees height" less than 1000. By that I mean we remove all factors of
2 from numberator and denominator, and choose the largest of the
resulting numbers. Note that not only do we get only one choice for
the unison, but 10/9 and 9/5 are also forced on us this way. A number
of other notes likewise have an obvious choice, such as 3/2 vs 1024/675.

0: [1]
1: [128/125, 25/24]
2: [135/128, 16/15]
3: [10/9]
4: [9/8, 256/225]
5: [75/64, 32/27]
6: [6/5, 625/512]
7: [768/625, 5/4, 512/405]
8: [32/25, 125/96]
9: [675/512, 4/3]
10: [27/20, 512/375, 25/18]
11: [45/32, 64/45]
12: [36/25, 375/256, 40/27]
13: [3/2, 1024/675]
14: [192/125, 25/16]
15: [405/256, 8/5, 625/384]
16: [1024/625, 5/3]
17: [27/16, 128/75]
18: [225/128, 16/9]
19: [9/5]
20: [15/8, 256/135]
21: [48/25, 125/64]