"typical" sruti ratios [was: what a dope (user)]

----- Original Message -----
From: George Zelenz <ploo@mindspring.com>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 14, 2001 12:21 PM
Subject: Re: [tuning] what a dope (user)

> What would a typical sruti be as a just ratio?

Wow, George, what a question!...
I think I've come across several *dozen* answers to it!

The exact size of a sruti has been a matter of considerable
debate for a long time. It's almost certain that the original
Indian tuning was a Pythagorean cycle, and over the centuries
the ratios have been redefined again and again. For some ideas
on what might be a "typical just ratio" for a sruti, see:

5-Limit Implications of Ancient Indian Tuning
http://www.ixpres.com/interval/monzo/indian/indian.htm

The Indian sruti system as a periodicity-block
http://www.ixpres.com/interval/td/erlich/srutipblock.htm

You should be aware that the term "sruti" has been used
to refer to both pitches and the intervals between them.

As quoted on the latter webpage, Donald Lentz in his book
gives the following:

>> 1. 81/80. Pramana sruti (or comma diesus): equal to
>> 22 cents or 5.4 savarts. This is the difference between a
>> major and minor tone. (9/8 � 10/9 = 81/80.)
>>
>> 2. 25/24. Nyuna sruti: equal to 70 cents or 17.73 savarts.
>> This is the difference between a minor tone and a semitone.
>> (10/9 � 16/15 = 25/24.)
>>
>> 3. 256/243. Purana sruti (or limma): equal to 90 cents
>> or 22.65 savarts. This is the difference between a perfect fourth
>> two major tones.

But as I discuss on both pages, Indian tuning would have
originally been specified as a series of "perfect 4ths and 5ths".
This is a procedure which no doubt goes all the way back
to the Sumerians.

Here's a table which gives the original theoretical
specification for the sruti scale, a series of
octave-invariant pitches calculated as 3^(-10...11).

(The > does not mean "greater than". It is simply
a symbol to show that I'm measuring the "in between"
intervals.)

NOTE INTERVAL BETWEEN
3^x Semitones 3^x Semitones

0 12.00
> - 5 0.90 limma
5 11.10
> 12 0.23 Pythagorean comma
- 7 10.86
> -17 0.67 ? (does this interval have a name?)
10 10.20
> 12 0.23
- 2 9.96
> - 5 0.90
3 9.06
> 12 0.23
- 9 8.82
> -17 0.67
8 8.16
> 12 0.23
- 4 7.92
> - 5 0.90
1 7.02
> - 5 0.90
6 6.12
> 12 0.23
- 6 5.88
> -17 0.67
11 5.22
> 12 0.23
- 1 4.98
> -5 0.90
4 4.08
> 12 0.23
- 8 3.84
> -17 0.67
9 3.18
> 12 0.23
- 3 2.94
> - 5 0.90
2 2.04
> 12 0.23
-10 1.80
> -17 0.67
7 1.14
> 12 0.23
- 5 0.90
> - 5 0.90
0 0.00

You can see here the three Pythagorean equivalents for
the sruti names given by Lentz. The three types of
srutis have the following Pythagorean ratios and
interval sizes in approximate cents:

Ratio Lentz's 5-limit Indian
2^x * 3^y ~cents equivalent sruti name

| -19 12 | 23.46001038 81/80 pramana
| 27 -17 | 66.76498529 25/24 nyuna
| 8 - 5 | 90.22499567 -- purana

Hope that helps.

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Monzo-abandonzo!

Thanks mucho. What a reply!

I hope this is of some interest to other Indian neophytes.

GZ

monz wrote:

> ----- Original Message -----
> From: George Zelenz <ploo@mindspring.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, July 14, 2001 12:21 PM
> Subject: Re: [tuning] what a dope (user)
>
> > What would a typical sruti be as a just ratio?
>
> Wow, George, what a question!...
> I think I've come across several *dozen* answers to it!
>
> The exact size of a sruti has been a matter of considerable
> debate for a long time. It's almost certain that the original
> Indian tuning was a Pythagorean cycle, and over the centuries
> the ratios have been redefined again and again. For some ideas
> on what might be a "typical just ratio" for a sruti, see:
>
> 5-Limit Implications of Ancient Indian Tuning
> http://www.ixpres.com/interval/monzo/indian/indian.htm
>
> The Indian sruti system as a periodicity-block
> http://www.ixpres.com/interval/td/erlich/srutipblock.htm
>
> You should be aware that the term "sruti" has been used
> to refer to both pitches and the intervals between them.
>
> As quoted on the latter webpage, Donald Lentz in his book
> gives the following:
>
> >> 1. 81/80. Pramana sruti (or comma diesus): equal to
> >> 22 cents or 5.4 savarts. This is the difference between a
> >> major and minor tone. (9/8 � 10/9 = 81/80.)
> >>
> >> 2. 25/24. Nyuna sruti: equal to 70 cents or 17.73 savarts.
> >> This is the difference between a minor tone and a semitone.
> >> (10/9 � 16/15 = 25/24.)
> >>
> >> 3. 256/243. Purana sruti (or limma): equal to 90 cents
> >> or 22.65 savarts. This is the difference between a perfect fourth
> >> two major tones.
>
> But as I discuss on both pages, Indian tuning would have
> originally been specified as a series of "perfect 4ths and 5ths".
> This is a procedure which no doubt goes all the way back
> to the Sumerians.
>
> Here's a table which gives the original theoretical
> specification for the sruti scale, a series of
> octave-invariant pitches calculated as 3^(-10...11).
>
> (The > does not mean "greater than". It is simply
> a symbol to show that I'm measuring the "in between"
> intervals.)
>
> NOTE INTERVAL BETWEEN
> 3^x Semitones 3^x Semitones
>
> 0 12.00
> > - 5 0.90 limma
> 5 11.10
> > 12 0.23 Pythagorean comma
> - 7 10.86
> > -17 0.67 ? (does this interval have a name?)
> 10 10.20
> > 12 0.23
> - 2 9.96
> > - 5 0.90
> 3 9.06
> > 12 0.23
> - 9 8.82
> > -17 0.67
> 8 8.16
> > 12 0.23
> - 4 7.92
> > - 5 0.90
> 1 7.02
> > - 5 0.90
> 6 6.12
> > 12 0.23
> - 6 5.88
> > -17 0.67
> 11 5.22
> > 12 0.23
> - 1 4.98
> > -5 0.90
> 4 4.08
> > 12 0.23
> - 8 3.84
> > -17 0.67
> 9 3.18
> > 12 0.23
> - 3 2.94
> > - 5 0.90
> 2 2.04
> > 12 0.23
> -10 1.80
> > -17 0.67
> 7 1.14
> > 12 0.23
> - 5 0.90
> > - 5 0.90
> 0 0.00
>
> You can see here the three Pythagorean equivalents for
> the sruti names given by Lentz. The three types of
> srutis have the following Pythagorean ratios and
> interval sizes in approximate cents:
>
> Ratio Lentz's 5-limit Indian
> 2^x * 3^y ~cents equivalent sruti name
>
> | -19 12 | 23.46001038 81/80 pramana
> | 27 -17 | 66.76498529 25/24 nyuna
> | 8 - 5 | 90.22499567 -- purana
>
> Hope that helps.
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>
> _________________________________________________________
>
> Do You Yahoo!?
>
> Get your free @yahoo.com address at http://mail.yahoo.com
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/