lattice history (was: Essential reading about microtonal music)

Hi Paul,

> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 23, 2001 8:59 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > Hi Gene,
> >
> > ... <snip> ...
> >
> > I'm not totally clear on what you're asking there, but if
> > it's concerning the history of tonal lattices, I can offer
> > this: the big pre-Tuning-List names are Euler, Riemann,
> > Tanaka, Fokker, and Wilson.
> >
> > The 5-limit triangular lattice, under the name of Riemann's
> > "Tonnetz", was employed quite a bit in theoretical literature
> > (especially German) of the 1800s.
> >
> Don't forget the "Duodenarium" in Helmholtz-Ellis; Barbour's
> lattices, which did have the triangular arragement; and Donald Hall's
> nice hexagonal tuning lattices (also the triangular arrangement but
> allowing for the display of the error in each interval).

You're correct about Barbour, and of course his book was perhaps
the primary English resource on tuning information until
the advent of the Tuning List, so I suppose I could have
mentioned him. But his triangular arrangement is nothing more
than the Riemann Tonnetz, which as I said is already very familiar
from the German literature.

There's also the very-hard-to-find book by Tipple and Frye
(but I managed to get a copy!), which uses its own variants
of the Tonnetz.

Ellis's Duodenarium is a bit different because it uses the
rectangular format, so I guess he should have been included
in my original list.

And please post more info about Donald Hall! I've never
heard of him, and searching the web only turned up a poet
and a Hawaiian artist by that name.

REFERENCES
----------

Barbour, James Murray. 1951.
_Tuning and Temperament: A Historical Survey_.
Michigan State College Press, East Lansing.
Reprint Da Capo Press, New York, 1973.

Frye, Royal Merrill and Esther W. Tipple. 1942.
_A Graphic Introduction to the Harmon_.
and Data Supplement to a Graphic Introduction to the Harmon.
Self-published, Boston.
(L.o.C. #s: ML 3809 .T 56 G 7 and ML 3809 .T 557)

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:

> And please post more info about Donald Hall! I've never
> heard of him, and searching the web only turned up a poet
> and a Hawaiian artist by that name.

Donald E. Hall wrote a wonderful textbook, _Musical Acoustics_

http://www.windworld.com/emi/bookstore/hall.htm

which is the best single book on the subject if you're not already an
expert. The last few chapters cover psychoacoustics, tuning, and
musical harmony. Hall has also written a number of fine journal
articles on tuning, some of which I have copies of.