Pythagorean tuning

[Barbaro:]
> Wasn't Pythagorean tuning the standard tuning for
> Western music from before 900 through about 1450 A.D.,

uh . . . in theory.

Actually it was the 'standard' for the diatonic genus
from about 500 BC until about 1500 AD - IN THEORY.

As I have speculated in several papers, musicians
seem to have been using 5-, 7-, and possibly even
11-limit ratios, or Pythagorean approximations of them,
for centuries (millenia?) since the time of the
ancient Greeks.

Ptolemy (c. 150 AD) used a prime/odd-limit of 23
in his detailed system outlining the ratios used in
the music of his day (in Alexandria, in Roman Egypt).

Apparently he was trying to reconcile what he heard
with the ancient rational theories, and as Partch said,
(I'm paraphrasing) to "use the smallest integer ratio
compatible with a given musical aesthetic effect".

I'm working on a new webpage exploring the Greek
notation described by Boethius (c. 505 AD) which,
altho he says it is a Pythagorean diatonic genus,
seems to me to indicate (implied) 5-limit.

It was Boethius's book which 'established' Pythagorean
tuning as the standard for the period you describe,
because the Franks (who were Germans) understood
only a little Latin and far less Greek, so Boethius's
book (apparently mostly a Latin translation of Nicomachus
and Ptolemy) was the one which transmitted the ancient
musical knowledge to them, and our music-theory derives
ultimately from theirs in an unbroken continuity.

Boethius also used much higher primes in describing
the chromatic and enharmonic genera, but these were
totally ignored by the Franks, who based their theory
firmly on the chants of the church, which apparently
were mainly diatonic - altho I dispute that too.

So I think that's what Marion meant with:

> Not that such scales are of much practical use, any more
> than the Pythagorean scales based on only 2 and 3 have ever
> been really used.

Thru-out musical history in any culture, musicians have
rarely stuck with *only* what is described by theory.
Indeed, my research into tuning theory shows me that
theory is almost *always* playing catch-up to explain
innovations arrived at by ear/intuition by great
composers/performers.

Only occasionally has it happened that a theoretical
treatise which is totally original (an example might
be Yasser's) has captured the attention of the musical
world in a serious way, if it's ever happened at all.

-monzo

|\=/|.-"""-. Joseph L. Monzo....................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\
_U//_/-/__/// |"...I had broken thru the lattice barrier..."|
/monz\ ((jgs; | - Erv Wilson |

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