[pianotech] P12th Clarification, Jeff

[ricb at pianostemmer.no]

Hi Jeff

The error was that I tried (at first) to simply multiply my starting
pitch for D3's 3rd partial by the 19th root of 3 to get D#3. Then
multiply the resulting D#3 by the 19th root of 3 to get E3... and so
on and so forth until I got to A4. That results in a straight line
(graphed). Linear if you will.  And thats not really all that useable
for pianos. Ron K (or who ever it was) provided a graph of that which
made it quite evident to me what kind of mistake I was making in
doing that.

Cheers
RicB


On Mon, Mar 9, 2009 at 5:38 PM, Richard Brekne <ricb at
pianostemmer.no> wrote:
>
<Snip>
>
> I remember Ron Koval (I think it was)  immediately shot a hole in
my first
> attempt at a 12ths temperament region pointing out that I'd simply
taken the
> 19th root of 3 and increasing each successive note from and
including D3 to
> A4. The hole was obvious enough... it resulted in a straight line
instead of
> the familiar curve.  So I devised a way of using Tunelab 97's
tuning curve
> editor to address that.
>
<Snip>
>
> Cheers
> Richard Brekne
>

Ric:

I am hoping that you can educate me on this. I take it that the error
you mention is more than using the 19th root of 3 instead of the 19th
root of the 3rd partial of D3 divided by the 1st partial of D3. I have
no experience with ETDs, but I understand math.

Is it because the 3rd partial of A4 divided by the 1st partial of A4
does not equal the 3rd partial of D3 divided by the 1st partial of D3?
This would also brings into question the 4:5 beat ratio of contiguous
major thirds
.

If this is too complicated to explain on the list, could you recommend
any books? I would only be interested in ones that really explain the
math, not just another “how to tune” book.