Groven and Helmholtz schismatic tunings (was:Digest Number 2225)

hi John,

> From: "John Chalmers" <JHCHALMERS@UCSD.EDU>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, September 29, 2002 9:24 AM
> Subject: Re: [tuning] Digest Number 2225
>
>
> Joe et al. I believe Groven's tuning the same as the 1/8-th Skhisma
> tuning discoverd by Helmholtz. See Ellis's appendices in "On the
> Sensations of Tone."

right you are -- except that Helmholtz's version was 24 tones
rather than Groven's 36. from my webpage:

/tuning/files/monzo/groven/groven.htm

"Note that Helmholtz's schismatic temperament was a 24-note tuning
which made use of two alternates for the 12 keys of the usual
Halberstadt keyboard. Groven's tuning is simply an expansion of
this, allowing one more alternate for each of the 12 keys.
Helmholtz's Pythagorean chain was 3^(-16...+7), and so that subset
of the information given here also describes Helmholtz's tuning."

Groven's 36-tone schismatic temperament, described as a tempered
Pythagorean chain, is 3^(-19...+16).

but yes, the idea and the method of tempering is exactly the same.
my suspicion is that Groven got the idea from Helmholtz's book
and simply expanded on it.

> One might also compare this tuning to Sabat-Garibaldi's 1/9-skhisma
> tuning which makes the 6/5 and 5/3 just rather than the 5/4 and 8/5. See
> S-B Dinarra web pages for details and the Dinarra itself, a guitar
> fretted to 53 tone of the 1/9 skhisma tuning.

i've been meaning for some time to make a webpage about Sabat-Garibaldi's
Dinarra tuning, and in fact almost did it right after i created
the Groven page ... but i was tired of thinking about schismatic
temperaments after all the work i put into that. ;-)

PS -- John, i plan to create another Yahoo group for the rest
of the Sonic Arts pages, including yours and Ivor's.

-monz
"all roads lead to n^0"