Yahoo Tuning Groups Ultimate Backup tuning-math To PGH.

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> You said that you were having trouble getting 22tet to work well etc
in
> tuning-math message 17301. The tuning group has message tuning 76214
> with seven melodic scales in 22tet. Tuning message 76155 has eight
> chords which can be turned into scales if you map each chord onto I-
IV-
> V relationships like this. Example for chord 0-327-655 on C. 545-873-
> 1200 on F and 655-982-109 on G. Thus we get an harmonic scale of 0-
109-
> 327-545-655-873-982-1200. The other chords in the message can also be
> turned into heptatonic scales. I hope this clears up some of your
> troubles.
>
Actually that is not what I meant at all, but I'll look at it those
messages. Actually 22-tET is terrible for diatonic music.
PGH

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > You said that you were having trouble getting 22tet to work well
etc
> in
> > tuning-math message 17301. The tuning group has message tuning
76214
> > with seven melodic scales in 22tet. Tuning message 76155 has
eight
> > chords which can be turned into scales if you map each chord onto
I-
> IV-
> > V relationships like this. Example for chord 0-327-655 on C. 545-
873-
> > 1200 on F and 655-982-109 on G. Thus we get an harmonic scale of
0-
> 109-
> > 327-545-655-873-982-1200. The other chords in the message can
also be
> > turned into heptatonic scales. I hope this clears up some of your
> > troubles.
> >
> Actually that is not what I meant at all, but I'll look at it those
> messages. Actually 22-tET is terrible for diatonic music.
> PGH
>
From Robert. The diatonic scale in 22tet is septimal major and is:
0-218-436-491-709-927-1145-1200. Is this the scale you are referring
to when you say diatonic music?

🔗Paul G Hjelmstad <phjelmstad@msn.com>

Exactly. Sounds terrible. Well, it is okay for some melodies, but
look at some of the triads, nicht-so-gut....

PGH

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

🔗hstraub64 <straub@datacomm.ch>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <phjelmstad@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > From Robert. The diatonic scale in 22tet is septimal major
> > > and is:
> > > 0-218-436-491-709-927-1145-1200. Is this the scale you are
> > > referring to when you say diatonic music?
> >
> > Exactly. Sounds terrible. Well, it is okay for some melodies, but
> > look at some of the triads, nicht-so-gut....
> >
> > PGH
> >
> From Robert. Perhaps you would prefer the more traditional way
> that septimal major is described as: 0-204-435-498-702-933-1137-
> 1200.
>

What exactly do you mean with "more traditional way"? Rational
interval ratios?

Anyway, one big problem with the scale labeled "diatonic scale in
22et" above is the major third which is too large - and that is not
substantially better in your "more traditional" one.

But 22tet has the much better major third with 382 cents - so there
is no need for that terrible 435, is there? It's just not "diatonic",
then...
--
Hans Straub

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > <phjelmstad@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > From Robert. The diatonic scale in 22tet is septimal major
> > > > and is:
> > > > 0-218-436-491-709-927-1145-1200. Is this the scale you are
> > > > referring to when you say diatonic music?
> > >
> > > Exactly. Sounds terrible. Well, it is okay for some melodies,
but
> > > look at some of the triads, nicht-so-gut....
> > >
> > > PGH
> > >
> > From Robert. Perhaps you would prefer the more traditional way
> > that septimal major is described as: 0-204-435-498-702-933-1137-
> > 1200.
> >
>
> What exactly do you mean with "more traditional way"? Rational
> interval ratios?
>
> Anyway, one big problem with the scale labeled "diatonic scale in
> 22et" above is the major third which is too large - and that is not
> substantially better in your "more traditional" one.
>
> But 22tet has the much better major third with 382 cents - so there
> is no need for that terrible 435, is there? It's just
not "diatonic",
> then...
> --
> Hans Straub
>
If you examine the scale data given by Alexander Ellis in his
Additions by the Translator of Hermann Helmholtz's On the Sensations
of Tone you will encounter lots of traditional information. Other
sources no doubt carry similar information. Lots of microtonal
musicians consider the interval of 0-435 as being beautiful. The
figures 267 and 435 are usually associated together because they add
up to 702. Similarly, 316+386=702 and 294+408=702 and 351+351=702;
and 63+435=498. Septimal major in 22tet "behaves" as a diatonic scale
because it cycles through 22 fifths(709) just like 12tet cycles
through 12 fifths(700). Its chords can also be expressed in I-IV-V
situations. The fact that you and a few others think that the
interval 0-435 sounds terrible does not mean very much when there is
a large body of both traditional and anecdotal evidence to support
it. Anything else?

🔗hstraub64 <straub@datacomm.ch>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> The figures 267 and 435 are usually associated together because they
> add up to 702. Similarly, 316+386=702 and 294+408=702 and
> 351+351=702; and 63+435=498. Septimal major in 22tet "behaves" as a
> diatonic scale because it cycles through 22 fifths(709) just like
> 12tet cycles through 12 fifths(700). Its chords can also be expressed
> in I-IV-V situations.

Sure, this is all clear to me. But what was the exact reason for 435
(apart from lots of microtonal musicians considering it quite
beautiful)?

> The fact that you and a few others think that the interval 0-435
> sounds terrible does not mean very much when there is a large body of
> both traditional and anecdotal evidence to support it.

What I am saying is just that 382 is in any case a much better
approximation of the pure major third (5/4) than 435. That is one of
the major advantages of 22tet; another advantage is the good
approximation of the harmonic seventh (7/4). For this, there is a body
of traditional and anecdotal evidence, too. And both of these
properties are lost in the tuning you gave. Sure, if I like diatonic
scales created from the cycle of fifths and I-IV-V progressions, I can
use that - but then I do not see the connection with 22tet.
--
Hans Straub

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > The figures 267 and 435 are usually associated together because
they
> > add up to 702. Similarly, 316+386=702 and 294+408=702 and
> > 351+351=702; and 63+435=498. Septimal major in 22tet "behaves" as
a
> > diatonic scale because it cycles through 22 fifths(709) just like
> > 12tet cycles through 12 fifths(700). Its chords can also be
expressed
> > in I-IV-V situations.
>
> Sure, this is all clear to me. But what was the exact reason for
435
> (apart from lots of microtonal musicians considering it quite
> beautiful)?
>
> > The fact that you and a few others think that the interval 0-435
> > sounds terrible does not mean very much when there is a large
body of
> > both traditional and anecdotal evidence to support it.
>
> What I am saying is just that 382 is in any case a much better
> approximation of the pure major third (5/4) than 435. That is one
of
> the major advantages of 22tet; another advantage is the good
> approximation of the harmonic seventh (7/4). For this, there is a
body
> of traditional and anecdotal evidence, too. And both of these
> properties are lost in the tuning you gave. Sure, if I like
diatonic
> scales created from the cycle of fifths and I-IV-V progressions, I
can
> use that - but then I do not see the connection with 22tet.
> --
> Hans Straub
>
From Robert. See message 17322 for additional info. The just major
third is 386 and the septimal major third is 435 cents. 22tet is
constructed in such a way that the septimal major scale turns out to
be the diatonic scale. If you want the just major scale to be the
diatonic scale you should go for 31tet where the just major scale of
0-194-387-503-697-890-1084-1200 is the diatonic scale. What was the
exact reason for 435? Apart from being connected to 267 (which is
connected to 969) there might be a connection to 429 cents (41/32).
You really should see message 17322 so that you can design your own
conversions. Most of what I do is based on simple arithmetical
scaling procedures.

🔗hstraub64 <straub@datacomm.ch>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> From Robert. See message 17322 for additional info. The just major
> third is 386 and the septimal major third is 435 cents. 22tet is
> constructed in such a way that the septimal major scale turns out
to
> be the diatonic scale. If you want the just major scale to be the
> diatonic scale you should go for 31tet where the just major scale
of
> 0-194-387-503-697-890-1084-1200 is the diatonic scale. What was the
> exact reason for 435? Apart from being connected to 267 (which is
> connected to 969) there might be a connection to 429 cents (41/32).

Alright - complement of 7/4, doubled. All clear now.

> You really should see message 17322 so that you can design your own
> conversions.

Message 17322, I got to say, did not help me much since it is merely
a list of cent values without explanations. But message 17329 is
interesting!

> Most of what I do is based on simple arithmetical
> scaling procedures.
>

Yes. With the explanations, it's indeed quite simple.
--
Hans Straub

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > From Robert. See message 17322 for additional info. The just
major
> > third is 386 and the septimal major third is 435 cents. 22tet is
> > constructed in such a way that the septimal major scale turns out
> to
> > be the diatonic scale. If you want the just major scale to be the
> > diatonic scale you should go for 31tet where the just major scale
> of
> > 0-194-387-503-697-890-1084-1200 is the diatonic scale. What was
the
> > exact reason for 435? Apart from being connected to 267 (which is
> > connected to 969) there might be a connection to 429 cents
(41/32).
>
> Alright - complement of 7/4, doubled. All clear now.
>
> > You really should see message 17322 so that you can design your
own
> > conversions.
>
> Message 17322, I got to say, did not help me much since it is
merely
> a list of cent values without explanations. But message 17329 is
> interesting!
>
> > Most of what I do is based on simple arithmetical
> > scaling procedures.
> >
>
> Yes. With the explanations, it's indeed quite simple.
> --
> Hans Straub
>
From Robert. I'm glad things are more clear. Sometimes I assume
that things which are clear and obvious to me are clear and obvious
to the reader. For comparison purposes here is a list of the 22
Indian srutis as interpreted by some people: 182-884-386-1088-590-90-
792-294-996-498-1200-702-204-906-408-1110-612-112-814-316-1018-520.
It appears to be just intervals running into pythagorean intervals
running into just intervals. Or else an unbroken string of figures
from 53tet.

🔗Paul G Hjelmstad <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "hstraub64" <straub@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> > >
> > > From Robert. See message 17322 for additional info. The just
> major
> > > third is 386 and the septimal major third is 435 cents. 22tet
is
> > > constructed in such a way that the septimal major scale turns
out
> > to
> > > be the diatonic scale. If you want the just major scale to be
the
> > > diatonic scale you should go for 31tet where the just major
scale
> > of
> > > 0-194-387-503-697-890-1084-1200 is the diatonic scale. What was
> the
> > > exact reason for 435? Apart from being connected to 267 (which
is
> > > connected to 969) there might be a connection to 429 cents
> (41/32).
> >
> > Alright - complement of 7/4, doubled. All clear now.
> >
> > > You really should see message 17322 so that you can design your
> own
> > > conversions.
> >
> > Message 17322, I got to say, did not help me much since it is
> merely
> > a list of cent values without explanations. But message 17329 is
> > interesting!
> >
> > > Most of what I do is based on simple arithmetical
> > > scaling procedures.
> > >
> >
> > Yes. With the explanations, it's indeed quite simple.
> > --
> > Hans Straub
> >
> From Robert. I'm glad things are more clear. Sometimes I assume
> that things which are clear and obvious to me are clear and obvious
> to the reader. For comparison purposes here is a list of the 22
> Indian srutis as interpreted by some people: 182-884-386-1088-590-
90-
> 792-294-996-498-1200-702-204-906-408-1110-612-112-814-316-1018-520.
> It appears to be just intervals running into pythagorean intervals
> running into just intervals. Or else an unbroken string of figures
> from 53tet.
>
The Sruti scale I looked at has 81/80 almost half the time
and sqrt(2) as the middle, otherwise all just intervals.

22 = 1 + 21 (<=> 256/243 x 243/128 = 2)

= 2 + 20 (<=> 16/15 x 15/8 = 2)

= 3 + 19 (<=> 10/9 x 9/5 = 2)

= 4 + 18 (<=> 9/8 x 16/9 = 2)

= 5 + 17 (<=> 32/27 x 27/16 = 2)

= 6 + 16 (<=> 6/5 x 5/3 = 2)

= 7 + 15 (<=> 5/4 x 8/5 = 2)

= 8 + 14 (<=> 81/64 x 128/81 = 2)

= 9 + 13 (<=> 4/3 x 3/2 = 2).

= 10 + 12 (<=> 27/20 x 40/27 = 2)

= 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).

PGH

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "hstraub64" <straub@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > <robertthomasmartin@> wrote:
> > > >
> > > > From Robert. See message 17322 for additional info. The just
> > major
> > > > third is 386 and the septimal major third is 435 cents. 22tet
> is
> > > > constructed in such a way that the septimal major scale turns
> out
> > > to
> > > > be the diatonic scale. If you want the just major scale to be
> the
> > > > diatonic scale you should go for 31tet where the just major
> scale
> > > of
> > > > 0-194-387-503-697-890-1084-1200 is the diatonic scale. What
was
> > the
> > > > exact reason for 435? Apart from being connected to 267
(which
> is
> > > > connected to 969) there might be a connection to 429 cents
> > (41/32).
> > >
> > > Alright - complement of 7/4, doubled. All clear now.
> > >
> > > > You really should see message 17322 so that you can design
your
> > own
> > > > conversions.
> > >
> > > Message 17322, I got to say, did not help me much since it is
> > merely
> > > a list of cent values without explanations. But message 17329
is
> > > interesting!
> > >
> > > > Most of what I do is based on simple arithmetical
> > > > scaling procedures.
> > > >
> > >
> > > Yes. With the explanations, it's indeed quite simple.
> > > --
> > > Hans Straub
> > >
> > From Robert. I'm glad things are more clear. Sometimes I assume
> > that things which are clear and obvious to me are clear and
obvious
> > to the reader. For comparison purposes here is a list of the 22
> > Indian srutis as interpreted by some people: 182-884-386-1088-590-
> 90-
> > 792-294-996-498-1200-702-204-906-408-1110-612-112-814-316-1018-
520.
> > It appears to be just intervals running into pythagorean
intervals
> > running into just intervals. Or else an unbroken string of
figures
> > from 53tet.
> >
> The Sruti scale I looked at has 81/80 almost half the time
> and sqrt(2) as the middle, otherwise all just intervals.
>
> 22 = 1 + 21 (<=> 256/243 x 243/128 = 2)
>
> = 2 + 20 (<=> 16/15 x 15/8 = 2)
>
> = 3 + 19 (<=> 10/9 x 9/5 = 2)
>
> = 4 + 18 (<=> 9/8 x 16/9 = 2)
>
> = 5 + 17 (<=> 32/27 x 27/16 = 2)
>
> = 6 + 16 (<=> 6/5 x 5/3 = 2)
>
> = 7 + 15 (<=> 5/4 x 8/5 = 2)
>
> = 8 + 14 (<=> 81/64 x 128/81 = 2)
>
> = 9 + 13 (<=> 4/3 x 3/2 = 2).
>
> = 10 + 12 (<=> 27/20 x 40/27 = 2)
>
> = 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).
>
>
> PGH
>
As far as I am aware the original Sanskrit (or whatever) is not
clear about whether the 22 srutis are in equal temperament or not. So
they seem to be open to creative interpretation. But I don't read
Sanskrit (or whatever).

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <phjelmstad@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "hstraub64" <straub@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > <robertthomasmartin@> wrote:
> > > > >
> > > > > From Robert. See message 17322 for additional info. The
just
> > > major
> > > > > third is 386 and the septimal major third is 435 cents.
22tet
> > is
> > > > > constructed in such a way that the septimal major scale
turns
> > out
> > > > to
> > > > > be the diatonic scale. If you want the just major scale to
be
> > the
> > > > > diatonic scale you should go for 31tet where the just major
> > scale
> > > > of
> > > > > 0-194-387-503-697-890-1084-1200 is the diatonic scale. What
> was
> > > the
> > > > > exact reason for 435? Apart from being connected to 267
> (which
> > is
> > > > > connected to 969) there might be a connection to 429 cents
> > > (41/32).
> > > >
> > > > Alright - complement of 7/4, doubled. All clear now.
> > > >
> > > > > You really should see message 17322 so that you can design
> your
> > > own
> > > > > conversions.
> > > >
> > > > Message 17322, I got to say, did not help me much since it is
> > > merely
> > > > a list of cent values without explanations. But message 17329
> is
> > > > interesting!
> > > >
> > > > > Most of what I do is based on simple arithmetical
> > > > > scaling procedures.
> > > > >
> > > >
> > > > Yes. With the explanations, it's indeed quite simple.
> > > > --
> > > > Hans Straub
> > > >
> > > From Robert. I'm glad things are more clear. Sometimes I
assume
> > > that things which are clear and obvious to me are clear and
> obvious
> > > to the reader. For comparison purposes here is a list of the 22
> > > Indian srutis as interpreted by some people: 182-884-386-1088-
590-
> > 90-
> > > 792-294-996-498-1200-702-204-906-408-1110-612-112-814-316-1018-
> 520.
> > > It appears to be just intervals running into pythagorean
> intervals
> > > running into just intervals. Or else an unbroken string of
> figures
> > > from 53tet.
> > >
> > The Sruti scale I looked at has 81/80 almost half the time
> > and sqrt(2) as the middle, otherwise all just intervals.
> >
> > 22 = 1 + 21 (<=> 256/243 x 243/128 = 2)
> >
> > = 2 + 20 (<=> 16/15 x 15/8 = 2)
> >
> > = 3 + 19 (<=> 10/9 x 9/5 = 2)
> >
> > = 4 + 18 (<=> 9/8 x 16/9 = 2)
> >
> > = 5 + 17 (<=> 32/27 x 27/16 = 2)
> >
> > = 6 + 16 (<=> 6/5 x 5/3 = 2)
> >
> > = 7 + 15 (<=> 5/4 x 8/5 = 2)
> >
> > = 8 + 14 (<=> 81/64 x 128/81 = 2)
> >
> > = 9 + 13 (<=> 4/3 x 3/2 = 2).
> >
> > = 10 + 12 (<=> 27/20 x 40/27 = 2)
> >
> > = 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).
> >
> >
> > PGH
> >
> As far as I am aware the original Sanskrit (or whatever) is not
> clear about whether the 22 srutis are in equal temperament or not.
So
> they seem to be open to creative interpretation. But I don't read
> Sanskrit (or whatever).
>
More from Robert. My list of srutis is exactly the same as yours
except for 729/512 substituting for 40/27 and 45/32 for 590.22 cents.
Perhaps the last line of your maths means 600cents but I'm not sure.
If it is then your list of srutis is quite elegant from a graphical
point of view.

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > <phjelmstad@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > <robertthomasmartin@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "hstraub64" <straub@>
wrote:
> > > > >
> > > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > > <robertthomasmartin@> wrote:
> > > > > >
> > > > > > From Robert. See message 17322 for additional info. The
> just
> > > > major
> > > > > > third is 386 and the septimal major third is 435 cents.
> 22tet
> > > is
> > > > > > constructed in such a way that the septimal major scale
> turns
> > > out
> > > > > to
> > > > > > be the diatonic scale. If you want the just major scale
to
> be
> > > the
> > > > > > diatonic scale you should go for 31tet where the just
major
> > > scale
> > > > > of
> > > > > > 0-194-387-503-697-890-1084-1200 is the diatonic scale.
What
> > was
> > > > the
> > > > > > exact reason for 435? Apart from being connected to 267
> > (which
> > > is
> > > > > > connected to 969) there might be a connection to 429
cents
> > > > (41/32).
> > > > >
> > > > > Alright - complement of 7/4, doubled. All clear now.
> > > > >
> > > > > > You really should see message 17322 so that you can
design
> > your
> > > > own
> > > > > > conversions.
> > > > >
> > > > > Message 17322, I got to say, did not help me much since it
is
> > > > merely
> > > > > a list of cent values without explanations. But message
17329
> > is
> > > > > interesting!
> > > > >
> > > > > > Most of what I do is based on simple arithmetical
> > > > > > scaling procedures.
> > > > > >
> > > > >
> > > > > Yes. With the explanations, it's indeed quite simple.
> > > > > --
> > > > > Hans Straub
> > > > >
> > > > From Robert. I'm glad things are more clear. Sometimes I
> assume
> > > > that things which are clear and obvious to me are clear and
> > obvious
> > > > to the reader. For comparison purposes here is a list of the
22
> > > > Indian srutis as interpreted by some people: 182-884-386-1088-
> 590-
> > > 90-
> > > > 792-294-996-498-1200-702-204-906-408-1110-612-112-814-316-
1018-
> > 520.
> > > > It appears to be just intervals running into pythagorean
> > intervals
> > > > running into just intervals. Or else an unbroken string of
> > figures
> > > > from 53tet.
> > > >
> > > The Sruti scale I looked at has 81/80 almost half the time
> > > and sqrt(2) as the middle, otherwise all just intervals.
> > >
> > > 22 = 1 + 21 (<=> 256/243 x 243/128 = 2)
> > >
> > > = 2 + 20 (<=> 16/15 x 15/8 = 2)
> > >
> > > = 3 + 19 (<=> 10/9 x 9/5 = 2)
> > >
> > > = 4 + 18 (<=> 9/8 x 16/9 = 2)
> > >
> > > = 5 + 17 (<=> 32/27 x 27/16 = 2)
> > >
> > > = 6 + 16 (<=> 6/5 x 5/3 = 2)
> > >
> > > = 7 + 15 (<=> 5/4 x 8/5 = 2)
> > >
> > > = 8 + 14 (<=> 81/64 x 128/81 = 2)
> > >
> > > = 9 + 13 (<=> 4/3 x 3/2 = 2).
> > >
> > > = 10 + 12 (<=> 27/20 x 40/27 = 2)
> > >
> > > = 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).
> > >
> > >
> > > PGH
> > >
> > As far as I am aware the original Sanskrit (or whatever) is
not
> > clear about whether the 22 srutis are in equal temperament or
not.
> So
> > they seem to be open to creative interpretation. But I don't read
> > Sanskrit (or whatever).
> >
> More from Robert. My list of srutis is exactly the same as yours
> except for 729/512 substituting for 40/27 and 45/32 for 590.22
cents.
> Perhaps the last line of your maths means 600cents but I'm not
sure.
> If it is then your list of srutis is quite elegant from a graphical
> point of view.
>
From Robert. I've gone over your figures more closely and they seem
to be transpositionally eqivalent (in whole cents) but I'm not 100%
sure without seeing your cent figures.

🔗Carl Lumma <carl@lumma.org>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> > As far as I am aware the original Sanskrit (or whatever) is not
> >clear about whether the 22 srutis are in equal temperament or not.
So
> >they seem to be open to creative interpretation. But I don't read
> >Sanskrit (or whatever).
>
> As far as I know, it's well-established that Indian music
> theory prescribes a 5-limit periodicity block of 22 tones.
> The musical practice doesn't necessarily correspond to it,
> though. -Carl
>
From Robert. Greetings Carl. I don't know how to insert internet
sites into emails but there is a relevant article called "The Idea of
22 Srutis" written by Subhash Kak in pdf form which members might
google. It seems to be very scholarly.

🔗hstraub64 <straub@datacomm.ch>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> More from Robert. My list of srutis is exactly the same as yours
> except for 729/512 substituting for 40/27 and 45/32 for 590.22 cents.
> Perhaps the last line of your maths means 600cents but I'm not sure.
> If it is then your list of srutis is quite elegant from a graphical
> point of view.
>

Your list of srutis coincides with the list once given by Marc Savage -
except that he gave 3 omore values. See tuning message 72704
(/tuning/topicId_63593.html#72704).

We have also collected some informations about srutis in the
xenharmonic wiki: see http://xenharmonic.wikispaces.com/Indian
--
Hans Straub

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > More from Robert. My list of srutis is exactly the same as yours
> > except for 729/512 substituting for 40/27 and 45/32 for 590.22
cents.
> > Perhaps the last line of your maths means 600cents but I'm not
sure.
> > If it is then your list of srutis is quite elegant from a
graphical
> > point of view.
> >
>
> Your list of srutis coincides with the list once given by Marc
Savage -
> except that he gave 3 omore values. See tuning message 72704
> (/tuning/topicId_63593.html#72704).
>
> We have also collected some informations about srutis in the
> xenharmonic wiki: see http://xenharmonic.wikispaces.com/Indian
> --
> Hans Straub
>
From Robert. Thankyou Hans. I'll have a close look at these links.