You should multiply ratios in order to add the intervals they represent:

3/2 = "fifth"

5/4 = "major third"

fifth + major third = 3/2 x 5/4 = 15/8

or

3 5 3 x 5 15

--- x --- = ----- = ----

2 4 2 x 4 8

Another quick example: (one for JI enthusiasts)

major second + major second does not equal a major third

9/8 x 9/8 = 81/64 = Pythagorean Major Third

Major second + small just second

9/8 x 10/9 = 90/72 cancelling down the fraction we get 5/4.

The difference between two intervals = divide the ratios

interval between pythagorean third and just third

81 . 5 81 4 81 81

-- --- - = -- x - = ------ = --

64 . 4 64 5 16 x 5 80

This is the comma of Didymus or the syntonic comma.

> From: tuning-math@yahoogroups.com

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

> Date: 6 Apr 2002 23:46:31 -0000

> To: tuning-math@yahoogroups.com

> Subject: [tuning-math] Digest Number 340

>

> So I thought that since G to B is a Major 3rd , I can add 5/4(Major 3rd)

> to G which has a ratio of 3/2.

> The B ratio is 15/8 , which is not what I find.

Thanks to the people who replied .

I am not very useful in this list due to my low level in mathematics , I

have only questions!

But , I can explain anything Greek which is very common in the tuning

technical language as far as I have seen.

On Sunday, April 7, 2002, at 11:58 AM, Mark Gould wrote:

> You should multiply ratios in order to add the intervals they represent:

>

> 3/2 = "fifth"

> 5/4 = "major third"

>

> fifth + major third = 3/2 x 5/4 = 15/8

>

> or

>

> 3 5 3 x 5 15

> --- x --- = ----- = ----

> 2 4 2 x 4 8

>

> Another quick example: (one for JI enthusiasts)

>

> major second + major second does not equal a major third

>

> 9/8 x 9/8 = 81/64 = Pythagorean Major Third

>

> Major second + small just second

> 9/8 x 10/9 = 90/72 cancelling down the fraction we get 5/4.

>

> The difference between two intervals = divide the ratios

>

> interval between pythagorean third and just third

>

> 81 . 5 81 4 81 81

> -- --- - = -- x - = ------ = --

> 64 . 4 64 5 16 x 5 80

>

> This is the comma of Didymus or the syntonic comma.

>

> > From: tuning-math@yahoogroups.com

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

> > Date: 6 Apr 2002 23:46:31 -0000

> > To: tuning-math@yahoogroups.com

> > Subject: [tuning-math] Digest Number 340

> >

> > So I thought that since G to B is a Major 3rd , I can add 5/4(Major

> 3rd)

> > to G which has a ratio of 3/2.

> > The B ratio is 15/8 , which is not what I find.

>

>

>

>

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