Ptolemy's accuracy & history of diatonic music

[me, monz]
>> ...Ptolemy (c. 150 AD)...made accurate measurements of the
>> intervals in all types of scales *actually in use*

[Paul Erlich, TD 204.16]
>
> Accurate measurements? Actually, I think the original Pentium
> chip came out in 150 AD, so his measurements may have been
> afflicted by that chip's division bug.
>
> Come on, Joe, what kind of accurate measurements could Ptolemy
> have made?

He used a monochord and a variant instrument of his own invention
based on monochord design.

Of course, 'accurate' is a relative term, and certainly,
objectively speaking, Ptolemy's methods were far less accurate
than some techniques we have available today. But I can
certify, from my own experience, that careful listening and
comparison on a monochord can give an accuracy within a few
cents - say, plus or minus 10 cents (I'm guessing and giving
the benefit of the doubt - the error may be less).

What I meant was that Ptolemy measured the intervals in a wide
variety of scales, and came up with a correspondingly wide variety
of ratios. Certainly, part of his desiderata was to accomodate
both the Aristoxenean and Pythagorean views on music theory,
which wasn't easy, the one being based on musical observation
by ear and the other by an avowed sovereignty of numerical
relationship regardless of acoustical observation.

> P.S. Didn't Johnny Reinhard tell you that diatonic music in
> Europe derived not from the Greeks but from another source
> (related to the Huns)? According to him, there was a definite
> discontinuity between the civilizations of classical antiquity
> and Christian Europe. Only later did scholars try to tie
> the two together, and apparently they were so succesful that
> many today suppose that one civilzation grew out of the other.

I wouldn't doubt that discontinuity one bit. Indeed, one of the
points I was trying emphasize in the post you quoted was that
*German* influence in the development of early medieval music has
been widely overlooked.

Their reputation as the most barbaric barbarians notwithstanding,
the Huns apparently had quite a cozy relationship with the
German Goths (I'll have to go to the library to get the reference
if anyone's interested).

So I wouldn't be at all surprised if aspects of Hunnish music
entered the European mainstream via the Goths, especially since
the earliest and one of the most 'civilized' of the German kindgoms
was the Ostrogothic Kingdom in Italy in the late 400s and early 500s
during Boethius's lifetime. ('Civilized' is also a relative
concept here: Boethius himself was cruelly tortured before his
execution for treason.)

However, all that said, there is still no question that the
ancient Greek theorists described a scale which they called
'diatonic', and whose ratios were virtually always the same
(i.e., did not vary from one theorist to another as did the
other genera), that is, Pythagorean (except for the different
'shades' described by Aristoxenus and Ptolemy), and which
largely agreed with what we think of today as diatonic.

Dante Rosati just recently mentioned, quoting the same post of
mine, that the Greeks got the diatonic scale from Babylon,
which I also have no reason to doubt.

So apparently the diatonic scale has been around since at
least ancient Greece or Babylon. And it doesn't seem to have
gone out of use at any time since then. Even tho there are
a few breaks in the production of theory treatises from about
200 to 900 AD, those in existence from either end of that period,
and the few from within it, indicate that the diatonic scale was
the one predominantly in use.

Of course, as far as actual *music* goes, the few scraps of
ancient Greek compositions must be treated with extreme caution,
as I have found much reason to be wary of the modern transcriptions
of these pieces which I have seen; and the earliest manuscripts
we have of real pieces in the 'modern' European tradition, with a
notation that indicates pitch, come from around the 900s. So
for any music composed before that, all we really have to go on
is the descriptions by the theorists.

-monz

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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