> From: monz <joemonz@yahoo.com>

> To: <tuning@yahoogroups.com>

> Sent: Saturday, July 14, 2001 2:25 PM

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

>

>

> 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

I was playing around with these Pythagorean srutis on an

Excel graph, trying to see what kind of proportions they

exhibit among themselves, and found something very interesting.

First, I noticed just by changing the scale of the y-axis to

a major unit of 22.5 cents that the approximate proportions

of the cents-values of these three srutis is 1:3:4.

I vaguely remember reading something about this somewhere,

in that the intervals between pitches of the Indian scale

were given in that book as 1, 3, or 4 srutis. The specific

type of sruti would thus have been the purana, tho not so

indicated in that book.

Then I went on and did the math, and look what I found:

90.22499567 / 23.46001038 = 3.845906042 = 3 & 3151/3725

66.76498529 / 23.46001038 = 2.845906042 = 2 & 3151/3725

Isn't it odd that these proportions both have *exactly*

the same fractional part? Or is it a property of Pythagorean

tuning that makes this so?

The denominator, 3725, is prime-factored into (5^2) * 149,

in case there's any significance in that.

Very curious,

-monz

http://www.monz.org

"All roads lead to n^0"

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monz wrote:

> First, I noticed just by changing the scale of the y-axis to

> a major unit of 22.5 cents that the approximate proportions

> of the cents-values of these three srutis is 1:3:4.

I think you've discovered 53 tone equal temperament.

> Then I went on and did the math, and look what I found:

>

> 90.22499567 / 23.46001038 = 3.845906042 = 3 & 3151/3725

> 66.76498529 / 23.46001038 = 2.845906042 = 2 & 3151/3725

>

> Isn't it odd that these proportions both have *exactly*

> the same fractional part? Or is it a property of Pythagorean

> tuning that makes this so?

The largest sruti is the sum of the other two.

90.22499567 / 23.46001038

= (66.76498529 + 23.46001038) / 23.46001038

= 66.76498529 / 23.46001038 + 1

Graham

> From: <graham@microtonal.co.uk>

> To: <tuning-math@yahoogroups.com>

> Sent: Sunday, July 15, 2001 1:56 AM

> Subject: [tuning-math] Re: interesting observation on sruti proportions

>

>

> monz wrote:

>

> > First, I noticed just by changing the scale of the y-axis to

> > a major unit of 22.5 cents that the approximate proportions

> > of the cents-values of these three srutis is 1:3:4.

>

> I think you've discovered 53 tone equal temperament.

Yup, I noticed that too! Thanks.

>

>

> > Then I went on and did the math, and look what I found:

> >

> > 90.22499567 / 23.46001038 = 3.845906042 = 3 & 3151/3725

> > 66.76498529 / 23.46001038 = 2.845906042 = 2 & 3151/3725

> >

> > Isn't it odd that these proportions both have *exactly*

> > the same fractional part? Or is it a property of Pythagorean

> > tuning that makes this so?

>

> The largest sruti is the sum of the other two.

>

> 90.22499567 / 23.46001038

>

> = (66.76498529 + 23.46001038) / 23.46001038

>

> = 66.76498529 / 23.46001038 + 1

Hmmm... thanks for explaining this, Graham. Could you go

into a little more detail as to why the fractions work

out the way they do? It's interesting to me, with my

numerology fetish.

-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

"The" "Monz" wrote:

> > The largest sruti is the sum of the other two.

> >

> > 90.22499567 / 23.46001038

> >

> > = (66.76498529 + 23.46001038) / 23.46001038

> >

> > = 66.76498529 / 23.46001038 + 1

>

>

> Hmmm... thanks for explaining this, Graham. Could you go

> into a little more detail as to why the fractions work

> out the way they do? It's interesting to me, with my

> numerology fetish.

Pythagorean tuning can be defined using two intervals. So you can never

have more than two Pythagorean intervals that are all independent. That's

the only mathematically interesting thing I see here.

Graham