response to Nangaku re: Schoenberg

Nangaku (Tuning Digest 1389):
> Trying to understand the 12ET overtone Schoenberg
> discussion - Are we saying Schoenberg recognized that
> the tempered scale's ratios were a bit off, but if you pay
> attention to the overtones created by the tempered scale
> (which will reflect the natural harmonic series), you can
> include that aspect into your music? Was he trying to
> connect the equal tempered system to the pure intervals
> you would associate with just intonation? And would
> Partch's response be - that's nice, but why don't we just
> start off with the pure ratios?

Monzo:
Basically, yes to all of the above, sort of. You've got a pretty
good grasp of the general ideas.

The main point is that Schoenberg knew of the limitations
of the 12-eq scale (in the sense that most of us on the
Tuning List feel it is limited) and decided, mostly for
reasons of practicality on instruments and in notation,
that it suited his needs.

(By the way, he invented an interesting new notation
designed specifically for the 12-eq scale. See the
article "A New Twelve-Tone Notation" [1924], reprinted
in "Style and Idea", p. 354-362, with some examples
from "Pierrot Lunaire" in the notation.)

Partch insisted that practicality was not a good enough
reason to sacrifice the subtlety and "acoustical truth"
of just-intonation, and so he built a whole ensemble
of his own instruments which were accurately tuned
according to his 43-note-per-octave 11-Limit
just-intonation system. (See Partch's book
"Genesis of a Music", 2nd ed. [1974].)

I will re-quote what I feel is the most relevant part of
Schoenberg's letter to Yasser (quoted more completely
by Daniel Wolf in Tuning Digest 1386):

Schoenberg:
> ''I have presented the little tabulation of overtones
> not in a scientific fashion, not as a theory, but solely
> as a handy assertion that...even the chromatic
> scale appears to be justified through circumstances of
> a natural character.

> ...indeed whenever I have had occasion to take up intonation
> with string players, I have always insisted on its _tempered_
> form... To be musical, then, means to have an ear in the
> sense of music and not in the sense of nature. A musical
> ear must have assimilated the tempered scale. And a
> singer who produces natural pitches is unmusical..."

Monzo:
Schoenberg thought of the study and use of just intervals
as belonging to science, while art (composition) should
utilize the "defective", but infinitely more practical, tempered
scale, perhaps basing at least some of its technique upon
the _implied_ just ratios. Wolf very succinctly summed
up the whole subject with two sentences (especially the
second):

Wolf:
> Need I remind anyone of Partch's anguished plea for the
> 'truth of just intonation'? Sch�nberg here is not rejecting
> such a "truth" in itself but rather the compositional
> utility of such.


Joseph L. Monzo
monz@juno.com
4940 Rubicam St., Philadelphia, PA 19144-1809, USA
phone 215 849 6723

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Dear List:

I have been receiving mail from this list for a couple of months now and felt
it was time I leaped into the fray...

As someone who has been de-tuning digital synthesizers - Casios (CZ's&VZ's),
Yamahas (DX7II & TG77), and Kurzweil (K2000) - for twelve years, I am
constantly surprised by what is considered acceptable pitch resolution for
just tunings. Its been my experience that even the simplest of pitch arrays
can be frustratingly arbitrary on any of the above named instruments. Of
course, this would clearly be the case on the Casios and Yamahas which all had
resolutions larger than one cent, but what finally opened my eyes was my
initial experience with the k2000 which has a fine tuning resolution of one
cent. The Kurzweil had less pure intervals available than the others! Upon
reflection I realized that due to the larger than one cent tuning res. of the
Casios (CZ - 1.667 ct res./VZ - 1.5625 ct res.) & the Yamahas (1.171875 ct
res.), at least once in a while one could stumble upon a relationship that
came somewhat close to a purely tuned inverval. On the other hand, the K2000,
with its 1200 parts per octave was in essence a type of "equal temperament"
with no possiblity of even accidentally coming close to the decimals needed
for seriously just tunings.

Since this experience (in 1992) I had the realization that the only way to
achieve pure ratio derived tunings on a digital synth was to make my own
samples at the desired frequencies and import them into my K2000. Perhaps some
acceptable fudging can be done with the above instruments if one is composing
percussive/pianistic types of music, but make no mistake - one is still only
approximating just intonation when using ANY commercial hardware synth's
tuning table.

David First


> >> >(K2500): nTET and nCET scales can be
> >> >created at the program level by adjusting a few parameters
> >> Perhaps you can provide some insight for Bill Meadows here:
> >Achieving nTET and nCET scales of any degree on K2000/K2500s is explained
> >in detail at my web site:
> t

Steven Sauve writes:
==============
Greetings...I'm a rookie here, and my first interest is finding Alt
Scales for the Yamaha TX802...i've checked the Mills FTP site, but it
seems fairly void of anything...are there others out there?...


thanks,

steven in toronto
===============

If you have a Macintosh, you can download JICalc from the Mills FTP site
(ftp://mills.edu/ccm/tuning/software/mac/jicalc443.sea.hqx). This will let
you send tunings to a TX802 over MIDI. In the same directory are hundreds
of tunings compiled by John Chalmers in JICalc-readable form. (These are
actually compressed text files, so you don't absolutely need a Mac or
JICalc to read them, but it makes it a lot easier.)

JICalc 4.43 is a new version with one minor change: scales can now be
displayed in cents relative to the 1/1, or relative to the previous tone in
the scale. This feature should have been added long ago.

Carter

>As someone who has been de-tuning digital synthesizers - Casios (CZ's&VZ's),
>Yamahas (DX7II & TG77), and Kurzweil (K2000) - for twelve years, I am
>constantly surprised by what is considered acceptable pitch resolution for
>just tunings.

Hmmm... Perhaps I missed some recent postings, but I can't recall any
JI enthusiasts on this list expressing satisfaction with the
pitch-resolution of typical off-the-shelf synthesizers. (But maybe that's
not important.)