More diatonicism (und Yasser ist auch dabei)

>I wrote,

>>14 notated pitches per octave in 1850?
>
PaulE wrote:

>At least.

I guess I misunderstood what was meant by "14 notated pitches." If you mean
enharmonics, then certainly they were common centuries before then.
However, the use of different spellings for enharmonics does not mean that
the composer requires (or even desires) a different tuning for the two. I
still fail to see any revolution coming from the mass production of the
12-pitch-per-octave piano keyboard in the 19th century.

John Chalmers wrote a good summary of some of the main points of the
history of the tuning of the diatonic scale, and then:

>It seems to me to be a coincidence that Ptolemy's Intense Diatonic
>in the Greek Lydian mode provides 4:5:6 triads on 1/1, 4/3 and 3/2.
>There is little evidence that the Greeks were aware of this fact
>and there were other diatonic tunings in favor without this property.

I'm not sure I would go so far as to call it coincidence, though clearly
triads and a theory of harmony in general were unknown to the Greeks.
Instead I would point out that Ptolemy's love of superparticulars
intersected with the European love of the major triad (or, more generally,
sweet-sounding thirds). Thus they arrived at the same scale for different
reasons.

Daniel Wolf wrote:

>Before we confirm tetrachords as the source of the diatonic scale, it is
>worthwhile to look closer at hexachords, which, unlike tetrachords, are
>able to sort out which Pythagorean collection is in play - the one with
>beginning with B (Bb) or the one going up to H (B natural) - thus keeping
>the augmented fourths/diminished fifths under control, along with an
>intonationally excellent solfege.

What I have been getting at is that there is a big difference between an
interpretation of a musical construct to help fit practice and provide a
convenient conceptual background for composition, and the actual reasons
that the construct appeared in the first place. Like other musical
constructs, the diatonic scale was reinterpreted (and sometimes "tweaked"
to use John Chalmers' term) to fit changing musical aesthetics. Thus it
could be thought of as interlocking triads, hexachords, or whatever.
However, it would be putting the cart before the horse to claim that the
diatonic scale was invented as a result of these insights.

Well, I don't think we CAN find a "theoretical basis" for the diatonic
scale, as I believe its origins in Europe lie in the dim period of
intersection of "barbarian" and Roman cultures in the first centuries of
the Current Era. This is not to say that such "folk" musics do not have a
theoretical underpinning, but only that I don't think we can say what it
was at that time.

Medieval hexachordal theory is a problem. I've heard several unconvincing
arguments as to why Guido chose 6 for his theory. Your explanation sounds
interesting, but perhaps I'm not following it. Why couldn't heptachords
(i.e. octave species) accomplish the same thing? It would certainly have
helped many a music history student who scratched their heads over this
hexachordal "basis" for heptatonic scales.

At any rate, I think the important thing to remember is that Guido's was a
pedagogical method, not an attempt to provide a theoretical basis for the
existence of the scale. The use of hexachordal solfege in early vocal music
is fascinating. Perhaps their experience could help explain Guido's
reasoning.

Dan also wrote:

>(3) Taking Yasser=A5s age and era into account, I find it terribly unfair t=
o
>characterize him as ethnocentric. In fact, I defy anyone to tell me exactly
>what ethnicity was central to Yasser. (He was a Russian-born scholar of
>Jewish Music).

At the risk of sounding like an apologist for McLarenesque hyperbole, let
me say that I meant to criticize the ideas not the man, whom I understand
lived in a different time with different ideas. Perhaps I should have
dubbed "Eurocentric" his interpretation of the music of other cultures, and
Chinese music in particular, always in reference to an ideal of European
common-practice harmony. Thus he sees Chinese music as centuries less
advanced as European music, a viewpoint that I think is blind to the
differences of intent, the differences of aesthetics, and the true beauties
of that music.

>His Darwinian streak, is, however, fair game, but can
>someone suggest a more P.C. term than _evolution_ to describe transitions
>towards more complex tonal systems?
>
I guess a theory of harmonic progression is more "complex" in 19TET in the
sense that there are more choices, but it does not follow that European
music is more complex than Chinese or that there is necessarily a
progression from one to the other. He's just looking at one theoretical
dimension (harmony/counterpoint) that happens to be very important in
certain European music and not in others. What would happen if I based my
analysis of music history on rhythmic complexity? Certainly Europe of the
same period would come off as a very "primitive" music culture.

Bill

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^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
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