It's the 15th!

That means the new issue of Perspectives of New Music should be out,
according to their website <http://www.perspectivesofnewmusic.org/>. Note
Mark Gould's article "Balzano and Zweifel: Another Look at Generalized
Diatonic Scales" (in <http://www.perspectivesofnewmusic.org/TOC382.pdf>).
He did e-mail me a while back mentioning this. Something about lattices
and whatever Balzano does being essentially the same thing. If anybody
has access to a copy, I'd be interested in a summary.

Graham

--- In tuning-math@y..., graham@m... wrote:
> That means the new issue of Perspectives of New Music should be
out,
> according to their website
<http://www.perspectivesofnewmusic.org/>. Note
> Mark Gould's article "Balzano and Zweifel: Another Look at
Generalized
> Diatonic Scales" (in
<http://www.perspectivesofnewmusic.org/TOC382.pdf>).
> He did e-mail me a while back mentioning this. Something about
lattices
> and whatever Balzano does being essentially the same thing. If
anybody
> has access to a copy, I'd be interested in a summary.

Graham, have you seen Balzano's older papers? He does use square
lattices of major thirds and minor thirds, but makes a mistake (I
feel) in identifying the importance of major thirds and minor thirds
in their ability to generate the tuning, i.e., C(3)*C(4)=C(12),
rather than in their acoustical consonance. He ignores the fact that
19- and 31-tone systems were actually used by a few early musicians,
sounded wonderful, but 12-tone simply proved more economical. When he
moves on to 20-equal, and constructs triads from 4/20-oct. and 5/20-
oct. intervals (since C(4)*C(5)=C(20)), all vestiges of acoustical
foundation are lost.

In-Reply-To: <9qfmh5+hos3@eGroups.com>
Paul wrote:

> Graham, have you seen Balzano's older papers?

No, I know very little about Balzano. And even less about Zweifel.

> He does use square
> lattices of major thirds and minor thirds, but makes a mistake (I
> feel) in identifying the importance of major thirds and minor thirds
> in their ability to generate the tuning, i.e., C(3)*C(4)=C(12),
> rather than in their acoustical consonance. He ignores the fact that
> 19- and 31-tone systems were actually used by a few early musicians,
> sounded wonderful, but 12-tone simply proved more economical. When he
> moves on to 20-equal, and constructs triads from 4/20-oct. and 5/20-
> oct. intervals (since C(4)*C(5)=C(20)), all vestiges of acoustical
> foundation are lost.

That doesn't sound very interesting to me. Perhaps it's better to go on
not knowing much about it.

Graham

In-Reply-To: <001e01c156cb$216b1420$2258d63f@stearns>
Dan Stearns wrote:

> I haven't read any Balzano or any of the related generalized diatonic
> scale articles, but do any of these even try to argue or hint at an
> acoustical foundation for any of this... if not, then why bother
> criticizing or expecting in a direction that doesn't really apply?

The impression I got from the e-mails he sent me was that Mark Gould's
article does cover JI lattices, similar to those on my website (which is
how he found me). But I don't have access to a library that has this
stuff, and I don't know if it's worth ordering a copy.

If there's no (psycho)acoustical foundation, I'm much less likely to be
interested in it.

Graham