Ditonic comma

[Niklas Eliasson]

More about the maths (and a try to make it simplier)

Paul N. Bailey wrote:
>
> Ditonic (not diatonic) comma:
>
>         the excess of twelve just fifths over seven just octaves.
>         Its ratio is 531441 to 524288, and it is 23.46 cents in
>         size. This is also known as the Pythagorean comma.
>
>         log10(frequency of interest / frequency of reference)*
>         3986.3137=

and 3986.3137 comes from 1200/log10(2)  (in case somenone wondered)

(Sorry for this, but with all these numbers without an explanation
 you even get more confused....)


>         interval size in cents.
>         (3/2)^12=129.746338
>
>         2^7=128
>
>         129.746338/128=1.01364326
>
>         log(1.01364326)=0.00588514
>
>         0.00588514*3986.3137=23.4600103 cents
>
>         23.4600103/12=1.95500086 cents
>


You can always get the cent right away from the expression:

    1200*(log(rel)/log(2))

where 'rel' is in this case 1.01364326...


Niklas E, Linkoping, Sweden