More on Schoenberg

It certainly appears that, contrary to my suspicions, Schoenberg
would have been familiar with untempered music. His early stuff
was fairly conventional, though. Was he writing for, and being
performed by, string ensembles when making the progression towards
atonality?

As regards the possibilities of 11- or 13-equal, well, the style
would have been wholly different but beyond that we can only
speculate. Schoenberg and his disciples stuck with 12-equal
because it was the inheritance of the tradition they were working
in, and because that's what their pianos were tuned to.

I'm more concerned in the generalities of atonality and serialism
than the way they were realised in composition. As atonality
entails an avoidance of 5, or even 7-limit harmony in a scale with
no approximations to 11 or 13, it is really a prescription for the
avoidance of integer ratios altogether. Schoenberg and Brahms both
may have implied 13-limit ratios. What's particularly interesting
about Schoenberg, though, is his pioneering of atonality and
serialism. I don't see that you need higher overtones to explain
that.


To Patrick Ozzard-Low, and terminology:

> It seems reasonable that there are many different explanations of
> what serialism and atonality are. Rather than try to define these
> terms, try listening sometime to (not meaning to patronise):

> Schoenberg: Verklarte Nacht (Ensemble Intercontemporain, Sony)
> Berg: Piano Sonata (Barenboim on DG, maybe)
> Berg: Violin Concerto
> Schoenberg: Suite op 25 (Pollini on DG)
> Berg: Wozzeck
> Webern: Funf Satz fur Streich Quartette Op. 5

> Clearly, none of these works are 'serial' (Boulez came later) nor are
> any of them wholly 'atonal' - although the Op 25 Suite pushes that
> way. But I would say that a familiarity with some of these works
> would be the best introduction for getting any understanding of
> 'serialism' proper - although, apart from a short period of
> experimentalism in the 50's, it would seem there are extremely few
> _strictly_ serial works (Boulez Structures Book 1, for example).

My definition of atonality is:

1) avoid octaves, leaps or intervals.

2) Avoid major or minor triads and dominant sevenths, broken or
sounding together without some other note.

3) When a melodic phrase is greater than 1 octave in range, avoid
exposing equivalent pitches. Rarely use phrases of a smaller range.

4) Rarely use more than 3 notes in succession belonging to any 1 major
scale. Never compose a whole phrase with notes from 1 major scale.
After a series of notes from 1 major scale, avoid returning soon to
the same scale.

I think these instructions come from Schoenberg, although he
wouldn't have described the result as atonality. The first two
clearly imply a avoidance of 7-limit harmony. 5-limit _intervals_
are still used. A 12-note scale is assumed, of course. Two notes
an enharmonic diesis apart are "the same" note. Applying these
rules in 19-eq would give entirely different results, as it's
easier to avoid keys without using all