P12 in Tunelab Pro / P12 theoretical basics

[Bernhard Stopper]

Ric wrote:

> so essentially the above two statements mean that
>
> (3/2)^12 = (3^12) / (2^12)
>
> which clearly cannot be.
>
> Please correct and then repost.


Ric,

(3/2)^12=1,5^12=129,746337890625

(3^12)/(2^12)=531441/4096=129,746337890625

so this is the same.

The thing that was not correct is that the pythagorean comma must be "added"
in mathematical form with a "multiplicator" placeholder like *

>Otherwise... I just have to say my own rendering was much more seat of
>the pants as it were.  I simply noticed that we tune using very  close
>to perfect 12ths in the tenor/treble/diskant registers as a rule... so I
>tried it out and used the previously mentioned procedure with Tune Lab
>97 to help assure a truly P 12th interval everywhere, and to divide the
<<temperament 12th>> into its associated curve.  I wanted at the time to
>see if the idea would sound good.  It did, and viola... the P 12ths
>tuning was <<born>> for me... which I related to others a couple years ago.

my P12 history was very similar in the beginning and also not a theoretical
approach....
i was some times impressed by the Cordier P5th tuning and after a while
practicing P5ths i experimented with the "natural fifth" in the
overtones.... the 12th (3rd harmonic)...
i tried it out and was shocked about its justness, so at this point i began
to search the theroetical base for it.

kind regards,

Bernhard