Re: [tuning] temperament ordinaire

bethisy.scl:
Bethisy tempérament ordinaire, see Pierre-Yves Asselin:
Musique et tempérament
A: 220.0000 Hertz
1: 233.4552 Hertz
2: 246.4542 Hertz
3: 263.1814 Hertz
4: 276.7138 Hertz
5: 294.2458 Hertz
6: 310.9515 Hertz
7: 328.9768 Hertz
8: 350.5455 Hertz
9: 369.3685 Hertz
10: 393.5479 Hertz
11: 414.6019 Hertz
12: 440.0000 Hertz

Manuel

--- In tuning@y..., <manuel.op.de.coul@e...> wrote:
>
> bethisy.scl:
> Bethisy tempérament ordinaire, see Pierre-Yves Asselin:
> Musique et tempérament
> A: 220.0000 Hertz
> 1: 233.4552 Hertz
> 2: 246.4542 Hertz
> 3: 263.1814 Hertz
> 4: 276.7138 Hertz
> 5: 294.2458 Hertz
> 6: 310.9515 Hertz
> 7: 328.9768 Hertz
> 8: 350.5455 Hertz
> 9: 369.3685 Hertz
> 10: 393.5479 Hertz
> 11: 414.6019 Hertz
> 12: 440.0000 Hertz
>
> Manuel

Hello, all. In examining the above frequency table, the following
appear to be true:

1) The 4 fifths C-G-D-A-E are each narrowed from their just value (~702
cents) by 1/4 syntonic comma.

2) The 4 fifths E-B-F#-C#-G# are each narrowed from their just value by
1/12 pythagorean comma.

3) The fifth G#-Eb is just.

4) The 3 fifths Eb-Bb-F-C are each equally narrowed from their just
value by an amount that is needed to close the circle of fifths
(distribute the pythagorean comma in some fashion over all 12 fifths).

I have no idea if the inventor(s) of French (Bethisy?) Temperament
Ordinaire meant this or not. Any comment is greatly appreciated.
Sincerely,

--- In tuning@y..., arl_123@h... wrote:
> --- In tuning@y..., <manuel.op.de.coul@e...> wrote:
> >
> > bethisy.scl:
> > Bethisy tempérament ordinaire, see Pierre-Yves Asselin:
> > Musique et tempérament
> > A: 220.0000 Hertz
> > 1: 233.4552 Hertz
> > 2: 246.4542 Hertz
> > 3: 263.1814 Hertz
> > 4: 276.7138 Hertz
> > 5: 294.2458 Hertz
> > 6: 310.9515 Hertz
> > 7: 328.9768 Hertz
> > 8: 350.5455 Hertz
> > 9: 369.3685 Hertz
> > 10: 393.5479 Hertz
> > 11: 414.6019 Hertz
> > 12: 440.0000 Hertz
> >
> > Manuel
>
> Hello, all. In examining the above frequency table, the following
> appear to be true:
>
> 1) The 4 fifths C-G-D-A-E are each narrowed from their just value
(~702
> cents) by 1/4 syntonic comma.
>
> 2) The 4 fifths E-B-F#-C#-G# are each narrowed from their just
value by
> 1/12 pythagorean comma.
>
> 3) The fifth G#-Eb is just.
>
> 4) The 3 fifths Eb-Bb-F-C are each equally narrowed from their just
> value by an amount that is needed to close the circle of fifths
> (distribute the pythagorean comma in some fashion over all 12
fifths).
>
> I have no idea if the inventor(s) of French (Bethisy?) Temperament
> Ordinaire meant this or not. Any comment is greatly
appreciated.
> Sincerely,

I thought that the fifths Eb-Bb-F-C were supposed to be _widened_,
not narrowed, in Ordinaire. And indeed, in the table above, they are.
So it looks like the frequencies given above do correspond to what
was intended.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> I thought that the fifths Eb-Bb-F-C were supposed to be _widened_,
> not narrowed, in Ordinaire. And indeed, in the table above, they are.
> So it looks like the frequencies given above do correspond to what
> was intended.

You're always catching my mistakes, Paul. I should have said widened
for these fifths. Sorry if this caused confusion. Sincerely,