New Member-Question about ratios

Hello , I am Alex Papadopoulos from Greece.

My mathematics knowledge is pretty low , so I wonder if this list is accepting amateur-ish mathematics questions related to tunings.
If not please tell me , so I will not bother you.

If yes , my question is:

In Helmholtz's book "the sensations of tone" in page 15 he states ,that since we know the ratios of the C ,E and G notes , we can find
the rest of the C scale notes , by associating this C triad with the F and G triad.
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.

I must have something very wrong in my mind!

Thanks for your patience.

--- In tuning-math@y..., Alexandros Papadopoulos <alexmoog@o...>
wrote:
> Hello , I am Alex Papadopoulos from Greece.
>
> My mathematics knowledge is pretty low , so I wonder if this list is
> accepting amateur-ish mathematics questions related to tunings.
> If not please tell me , so I will not bother you.

Hi Alex,

We accept any mathematics questions related to tunings.

> If yes , my question is:
>
> In Helmholtz's book "the sensations of tone" in page 15 he states
,that
> since we know the ratios of the C ,E and G notes , we can find
> the rest of the C scale notes , by associating this C triad with the
F
> and G triad.
> 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.
>
> I must have something very wrong in my mind!

[If you are reading this on Yahoo's web interface you will need to
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What is it that you find?

15/8 is the correct ratio for B in a _justly_intoned_ C major scale
whose lattice follows.

A---E---B
/ \ / \ / \
F---C---G---D

5/3-5/4-15/8
/ \ / \ / \
4/3-1/1-3/2-9/8

Of course this is not the same as its tuning in equal temperament (the
most common tuning today). There all the notes are mapped to the
nearest power of the twelfth root of two. In the case of B this is
2^(11/12) ~= 1.888, whereas 15/8 is 1.875.

-- Dave Keenan