Topic: 22 equal and Indian music

1 scales

Thread (4 messages)

From: Gene Ward Smith (2006-01-23)
Subject: 22 equal and Indian music

The Indian scheme has seven basic scale steps, sa, ri, ga, ma, pa,
dha, and ni. In terms of srutis, the interval struture is 4324432. I'm
stating this so definately because I've been reading the various
authors collected in S. M Tagore's "Hindu Music", and they all seem to
agree on this.

If the srutis are of the same size, then the above heptatonic scale
would be the famous Zarlino/Ptolemy scale, tempered by 22-equal.
However, the srutis are not of the same size. Some people seem to
think that the major tone, 9/8, should be divided into four equal
srutis, the minor tone, 10/9, into 3 equal srutis, and 16/15 into two
srutis. This in fact seems to be the plan behind
"indian-oldellis.scl", described as 
"Ellis Old Indian Chromatic, Helmholtz, p. 517. This is a 0.5 cent
appr. to #73". You will indeed find a #73 on that page. This scale is
extremely closely approximated by the following 494-edo scale:

scale: [21, 42, 63, 84, 109, 134, 159, 182, 205, 226, 247, 268, 289,
310, 331, 352, 373, 398, 423, 448, 471, 494]

steps: [21, 21, 21, 21, 25, 25, 25, 23, 23, 21, 21, 21, 21, 21, 21,
21, 21, 25, 25, 25, 23, 23]

The explanation for this scale is easily found. If we take the Zarlino
scale in 494-et, and chop the 9/8 up into four equal parts of 21
steps, the 10/9 into three equal parts of 25 steps, and the 16/15 into
two equal parts of 23 steps, then we have this scale. Since 494 is
such a good 13-limit system, it's temping to write this in terms of
375/364 for the 21 steps, 175/169 for the 25 steps, and 125/121 for
the 23 steps, and then temper. 

Below I give the Old Indian Chromatic in 494; this is so close to the
other version Scala calls them the same scale, but when analyzedby
Show Data, it gives more comprehensible results.

! indianold494.scl
Ellis Old Indian Chromatic in 494-edo
22
!
51.012146
102.024291
153.036437
204.048583
264.777328
325.506073
386.234818
442.105263
497.975709
548.987854
600.000000
651.012146
702.024291
753.036437
804.048583
855.060729
906.072874
966.801619
1027.530364
1088.259109
1144.129555
1200.000000

From: Gene Ward Smith (2006-01-23)
Subject: Re: 22 equal and Indian music

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> The explanation for this scale is easily found. If we take the Zarlino
> scale in 494-et, and chop the 9/8 up into four equal parts of 21
> steps, the 10/9 into three equal parts of 25 steps, and the 16/15 into
> two equal parts of 23 steps, then we have this scale. 

Sorry, that should be the Indian Sa-grama scale, 
9/8-5/4-4/3-3/2-27/16-15/8-2. In 22-et that becomes 4324432.

From: wallyesterpaulrus (2006-01-30)
Subject: Re: 22 equal and Indian music

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> The Indian scheme has seven basic scale steps, sa, ri, ga, ma, pa,
> dha, and ni. In terms of srutis, the interval struture is 4324432. 
I'm
> stating this so definately because I've been reading the various
> authors collected in S. M Tagore's "Hindu Music", and they all seem 
to
> agree on this.
> 
> If the srutis are of the same size, then the above heptatonic scale
> would be the famous Zarlino/Ptolemy scale, tempered by 22-equal.
> However, the srutis are not of the same size. Some people seem to
> think that the major tone, 9/8, should be divided into four equal
> srutis,

Never seen anyone claim these srutis should be equal. Where did you 
find this claim?

> the minor tone, 10/9, into 3 equal srutis,

Ditto.

From: Gene Ward Smith (2006-01-30)
Subject: Re: 22 equal and Indian music

--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> Never seen anyone claim these srutis should be equal. Where did you 
> find this claim?

Where I said, in Tagore's "Hindu Music." Tagore himself says this, in
fact.