Discussion on "Reply to Gary Morrison" (Bill Alves, Paule,

First of all: Greetings! I'm listening to the list now for several weeks, and I
find it exciting. My deep felt thanks to Enrique Moreno who introduced me
to it.

Secondly: There seems to be some emotion around the question whether
the diatonic scale is based on the major triad, and wonderful
expressions like "historico-geographic fallacy" are thrown into the ring. I
never had an opportunity to read what Mathews and Pierce have been
advocating in this regard. However, when I (some time in the early
seventies) was in the process of "discovering" what has been since
dubbed the Bohlen-Pierce-Scale, I tried to come to terms with this
question, too. And I guess I still see the answer as I have seen it at that
time: the diatonic scale is the result of the INVOLUNTARY attempt to fill
the framework of the octave with the major triad and its sub-intervals,
and finally inserting small intervals created in the process to achieve
equidistance. When trying to make harmonic music, and that was a
cumbersome process during the middleages, the triad must have been
present on the minds of the composers, whether it was "invented" at
that time, or not. Okay, here you got my personal opinion, now shoot at
me!

By the way: I am interested in everything that Pierce or Mathews or
others have been writing on the "Bohlen-Pierce-Scale", and I promise to
send a copy of my first publication on the subject (alas, in German, and
only as long as stock lasts) to everybody who can help me out regarding
this matter. My address:

Mail: Dale Ave. # 109 Fax: 415-852-9517
Mountain View, CA 94040

E-Mail: heinz.bohlen@mptp.cpii.com

Heinz Bohlen

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On Wed, 20 Nov 1996, Bill Alves wrote:
> 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.

The most obvious thing that comes to my mind is that six pitches is as
many as you can chain together along the circle of fifths without
encountering a tritone, that "diabolus in musica".

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."

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> 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.

Certainly in meantone tunings you don't want to use a D# in place of an Eb,
for example!

Brian's point, which seems to me at least to be largely correct, is that mass
producing keyboards with more than 12 tones per octave was not terribly feasible
in the times when meantone tunings were popular. The only realistic solution
was to stick with 12 and tune them to well-temperaments instead.

As for whether that would qualify as a "revolution", I guess you can decide.


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