Shrutar[22] as srutis

Magic is the 22&41 temperament; we can also concoct srutis out of
shrutar, the 22&46 temperament. We now make each 9/8 a 2222 in 46et,
and each 16/15 a 22. This leaves two 2 steps and a 3 step for 10/9,
where we can vary the pattern. This time we make it

1-(2222)-9/8-(322)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-2

This gives Shrutar[22].

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> Magic is the 22&41 temperament; we can also concoct srutis out of
> shrutar, the 22&46 temperament. We now make each 9/8 a 2222 in 46et,
> and each 16/15 a 22. This leaves two 2 steps and a 3 step for 10/9,
> where we can vary the pattern. This time we make it
>
> 1-(2222)-9/8-(322)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-
(22)-2
>
> This gives Shrutar[22].

For Indian music, you're better served using the omnitetrachordal,
rather than the distributionally even, Shrutar[22] scale. So it becomes:

1-(2222)-9/8-(223)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-
2

This captures the whole Modern Indian Gamut and not just Sa-grama.

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

> For Indian music, you're better served using the omnitetrachordal,
> rather than the distributionally even, Shrutar[22] scale. So it becomes:
>
> 1-(2222)-9/8-(223)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-
> 2
>
> This captures the whole Modern Indian Gamut and not just Sa-grama.

Another thing to like about this version is that the minor whole tones
in Sa-grama are always 223, so it has a more regular arragement from
that point of view. Shrutar in general seems a better fit to the idea
that srutis are fairly even as to size than most alternatives. In
particular better than magic, and much better than the comma-sized
steps of Pythagorean. Most of the steps are 2/46, with just a few 3/46.

Gene,

I'm wondering about two things you wrote.

#1: Would you mind explaining the meaning of the
sequence that goes 1-(2222)-9/8-(223)-5/4-(22), etc.
I'm not familiar with this (2222) (223) (22) style of
notation or numerical representation. What do you
call it? How does it work?

#2: What exactly do you mean by the word Shrutar?
Years ago Jacques Dudon built a guitar-like Just
Intonation instrument that he named the Shrutar, but I
doubt if that's what you're referring to here.

--Mark Rankin

--- Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > For Indian music, you're better served using the
> omnitetrachordal,
> > rather than the distributionally even, Shrutar[22]
> scale. So it becomes:
> >
> >
>
1-(2222)-9/8-(223)-5/4-(22)-4/3-(2222)-3/2-(2222)-27/16-(223)-15/8-(22)-
> > 2
> >
> > This captures the whole Modern Indian Gamut and
> not just Sa-grama.
>
> Another thing to like about this version is that the
> minor whole tones
> in Sa-grama are always 223, so it has a more regular
> arragement from
> that point of view. Shrutar in general seems a
> better fit to the idea
> that srutis are fairly even as to size than most
> alternatives. In
> particular better than magic, and much better than
> the comma-sized
> steps of Pythagorean. Most of the steps are 2/46,
> with just a few 3/46.
>
>
>
>
>

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--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...>
wrote:
>
> Gene,
>
> I'm wondering about two things you wrote.
>
> #1: Would you mind explaining the meaning of the
> sequence that goes 1-(2222)-9/8-(223)-5/4-(22), etc.
> I'm not familiar with this (2222) (223) (22) style of
> notation or numerical representation. What do you
> call it? How does it work?

They're steps of the scale measured in steps of 46-equal. The ratios
are merely approximate in 46-equal.

> #2: What exactly do you mean by the word Shrutar?
> Years ago Jacques Dudon built a guitar-like Just
> Intonation instrument that he named the Shrutar, but I
> doubt if that's what you're referring to here.
>
> --Mark Rankin

I had no idea that this word was already taken. Dave Keenan and I
designed a guitar fretting with several specific desiderata in mind,
including a particular but limited connection with the shruti system.
So we came up with the name "Shrutar" for it.

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...> wrote:

> #1: Would you mind explaining the meaning of the
> sequence that goes 1-(2222)-9/8-(223)-5/4-(22), etc.
> I'm not familiar with this (2222) (223) (22) style of
> notation or numerical representation. What do you
> call it? How does it work?

These are steps of 46 equal to between one interval of Sa-grama
tempered in 46 and another, if we assume the particular scale I called
Shrutar[46] is being used to define sruits. In other words, in 46-et
9/8 is represented by 8, and the scale steps from 0 to 8 inclusive are
0-2-4-6-8; the differences between them being 2, 2, 2 and 2. Hence,
(2222).

> #2: What exactly do you mean by the word Shrutar?
> Years ago Jacques Dudon built a guitar-like Just
> Intonation instrument that he named the Shrutar, but I
> doubt if that's what you're referring to here.

I'm not the one who came up with the name, so Paul Erlich could
explain that aspect better. By "shrutar" I mean the "rank two"
temperament which has a period of half an octave, and a generator
a flattened 11/8 interval. In terms of 46, that is 23/46 of an octave
for the period, and 21/46 for the generator, so you can also take the
generator to be an approximate quarter-tone of size 2/46. This is, of
course, close to 1/22, and 22-tone scales can be constructed in this
way which are fairly close to, but not actually, 22 equal tones to the
octave. One way to do this would be two equal chains of 11 notes with
2/46 quartertone steps, one starting from 0 cents and one starting
from 600 cents; Paul was suggesting another scale would be better for
concocting something sruti-like.

In terms of commas being tempered out, shrutar can be characterized as
the 11-limit temperament tempering out 121/120, 176/175 and 245/243.