Ratio Math

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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