Reply to Joseph Monzo, mostly on Schoenberg

We seem to agree on priniples as regards temperament, once
differences of emphasis are accounted for.

I use "meantone" exclusively and unambiguously to mean scales with
no 81/80. This is a standard usage, at least on this list. At two
syllables, it's also the most efficient way of expressing that concept.

I assume an argument for meantone is also for 31-equal.

> Who's Gregg Gibson? I've been receiving the Tuning Digest since
> # 1314. (Email me something -- I'd like to see it).

He had "a strong presence" on the list between digests 1260 and
1278. The general argument was for 19-equal, and against everything
else. I don't know if he still subscribes or not, but he hasn't
posted since he left in a huff. The reason I mentioned him is that
he kept saying that scales with an 81/80 were unworkable, and yours
is the strongest contrary assertion I've seen.

What good points he made were swamped by noise and repetition. So,
that clutch of digests take up over 600Kb, and it isn't practicable
for me to forward them with the hardware I'm using at the moment.


>> Then again, perhaps Schoenberg had a piano.

> I took this as an attempt at humor. As I suggested, there are far
> more profound reasons why Schoenberg so enthusiastically
> embraced the 12-Eq scale. He intuitively understood much more
> about rational harmonic concepts than his limited mathematically
> ability demonstrates; and this is important because Schoenberg's
> compositions and theory have had a huge impact on a lot of
> this century's music, both academic and commercial.

I was making a serious point using humour. I didn't join in the
discussion as I don't know enough about the specific compositions.
As the following should make clear, that doesn't mean I don't
have an opinion.

The general innovations of the 2nd Viennese School look like a
direct response to 12-equal. And that's the realities of the
temperament, rather an idealised, transposable 5-limit scale.

Equal temperament is supposed to have become established in Europe
around 1850. Schoenberg was born in 1874, by which time it would
presumably have become ubiquitous on family pianos. As he was
self taught, he wouldn't have had experience of choral or orchestral
work. So, his primary experience of music would have been through
12-equal. He was, I think, the first composer to specify that a
string quartet should be played in 12-equal

One of Gregg Gibson's points was that 12-equal has a poor contrast
between consonance and dissonance. I'm sure Schoenberg, Webern and
the like spent a long time sitting at the piano saying "Why should
I play this chord, instead of this?" Try hitting random chords in
1/4 comma meantone, and then hitting some consonances. The contrast
is very strong, and there is a feeling of resolution. Then try the
same thing with 12-equal. The difference between consonance and
dissonance is still obvious, but the idea that dissonance should
resolve onto consonce less so. Rather, there are some spicy
dissonances that resolve onto boring old consonances. So, throw
away the consonance and keep the dissonance. This was the break
from tonality to atonality.

Schoenberg and Webern were also explicit that atonality and
utimately serialism arose from the practice af modulation.
Schoenberg preferred the term "pantonality" because it gave the
impression of playing in all keys at once. This shows the weaker
sense of 12-thinking: that all keys are the same. 12 tone serialism
obviously arises from the desire to place all 12 notes on an equal
footing. This wouldn't work even in a well temperament, because
there is a heirarchy inherent in the tuning.

The 2nd Viennese manner of constructing chords was to take an interval
and double it a major seventh above. The most common intervals in
Webern's atonal music, and I suspect Schoenberg's as well, are
major sevenths and tritones. These guarantee the avoidance of
5-limit harmony, but don't necessarily suggest approximations to any
higher limit. However he may have rationalised it, there is no
need to bring in any higher overtones. If you started from that
premise, you wouldn't arrive at 12-equal.

It may be possible to analyse Schoenberg's harmony in terms of
higher overtones. This may mean he was hearing them, or it may
be that randomly chosen chords could also be so interpreted. It
is a rare case where music theory requires statistical analysis. As
I said before, I don't know the details here. However, I see no
need to explain his general style as anything but an _avoidance_ of
integer ratios.

The quote I'm responding to is "there are far more profound reasons
why Schoenberg so enthusiastically embraced the 12-Eq scale." It
seems to me that the experience of 12-equal through pianos is the most
important reason for the direction his natural creativity took. Or,
at least, the most important one relevant to this list.

I don't think Schoenberg's mathematical ability is the problem here.
He seems to have been aware of the poor approximations to the
ratios he was implying. However, he probably lacked the instruments
to hear the ratios properly tuned. So, he persisted in the belief
that complex harmonies must come from higher primes, rather than being
an artefact of temperament.