Reply to Shaun Van Ault

Hi Shaun,

Here is a message I've posted with my recommendations for readings (for
lattices you might want to start with Graham Breed's page, the last entry
below):

I repost my message from TD 221 -- note that Graham has a new web page at
http://x31eq.com/:

Message: 4
Date: Wed, 16 Jun 1999 06:29:17 -0400
From: "Paul H. Erlich" <PErlich@xxxxxxxxxxxxx.xxxx
Subject: Re: Query

>Hello to all,
>I am new to your list and need your assistance. I am setting up a graduate
>level course for myself, and one of my areas of study will be harmonics and
>alternate tunings. Can anyone suggest text(s) knowing that I am at the
>beginning? Thank you very much.

>Most Sincerely,
>Azrael

My top recommendation is Helmholtz' _On the Sensations of Tone_, with notes
from the translator, Ellis. If you're at the graduate level this shouldn't
be too difficult for you. Just keep in mind when you read it that it's a
little out of date.

Partch's _Genesis of a Music_ is full of alternate tunings, including his
own. Just keep in mind that Partch is not trying to offer a balanced view of
the subject.

The rest of these overlap very little but taken together give a very wide
view of the subject:

"Pitch, consonance, and harmony" by Terhardt in _Journal of the Acoustical
Society of America_ Vol. 55 (1974). p. 1061 will give you a more
late-20th-century viewpoint on psychacoustics; if you made it through
Helmholtz and Partch then the ramifications of this should be clear.
For historical tunings, check out Barbour's _Tuning and Temperament_ or
Jorgenson's huge tome, _Tuning_;
for diatonic tunings, with both feet planted in history, Blackwood's
_Structure of Recognizable Diatonic Tunings_;
for an extension of historically-based considerations to some new
possibilities, Fokker's _New Music with 31 Notes_;
for experimental scales, the articles "Harmony and New Scales" by Mathews,
Pierce, and Roberts and "General Properties of Musical Pitch Systems" by
Krumhansl (both in _Harmony and Tonality_ edited by Sundberg), all issues of
_Xenharmonikon_, "Modes and Chord Progressions in Equal Tunings" by
Blackwood in _Perspectives of New Music_ Vol. 29 (1991) No.2 pp. 166-200,
"Six American Composers On Nonstandard Tunings" in _Perspectives of New
Music_ Vol. 29 (1991) No.1, "Tuning: At the Crossroads" by Wendy Carlos in
_Computer Music Journal_
for an experimental idea that strains credibility but is fantastically
presented, Yasser's _Theory of Evolving Tonality_;
a similar take but in just intonation is "On The Development of Musical
Systems" by Kraehenbuehl and Schmidt in _Journal of Music Theory_ Vol. 6
(1962) no. 1
for relationships between timbre (especially inharmonic timbres) and tuning,
Sethares' _Timbre, Tuning, Spectrum, Scale_;
one engineer's idiosyncratic take on the same theme: "An Electronically
Generated Complex Microtonal System of Horizontal and Vertical Harmony" by
Goldsmith in _Journal of the Audio Engineering Society_ Vol. 19 (1971) no.
10 pp. 851-858

for the complete citations see the vast bibliography at
ftp://ella.mills.edu/ccm/tuning/papers/bib.html. Many of us have web pages
with information that goes beyond the above; for example (and with stuff for
beginners), Graham Breed's page,
http://www.compulink.co.uk/~gbreed/tuning.htm.