Re: TD 388: Reply to John Chalmers on Babylonian tuning

Hello, there, and in Tuning Digest 388, John Chalmers wrote:

> Dan: Granted the tuning tablets are silent on what kind of fifths
> are used to tune the harp, but what kind do you imagine were tuned
> on rather crude instruments in the 2nd millennium BCE? As for
> Pythagoreanism, I would define any tuning system by fifths (and/or
> fourths) and octaves as basically pythagorean in the absence of any
> data on tempering or tweaking to get better consonances.[...]

Here I would say that it is very tempting for me to overlook the fact
that we are indeed talking about Babylon in the 2nd millennium BCE,
not Western Europe in roughly the first four-tenths of the 2nd
millennium CE. In the latter context, I could eloquently advocate a
pure Pythagorean tuning, just as someone focusing on a different
context could advocate "tempering" toward 5-limit just intonation
(JI), or maybe "tweaking" toward Javanese _slendro_ (near 5-tone equal
temperament, or 5-tet).

Unless we have some idea of Babylonian music, it seems an exercise
either in guessing, or possibly in ethnocentricism of one's favorite
flavor.

Here are a few "ifs" which might reflect my own European medievalist
leanings.

If Babylonian music were mainly monophonic, then the Pythagorean
whole-tone of 9:8 (generously wide) and semitone of 256:253 (neatly
compact) might be fine without any reason for "tweaking."

If Babylonian music featured polyphony based mainly on fifths and
fourths, then vertical as well as melodic considerations might favor
Pythagorean, as in most recorded polyphony of medieval Europe. If
other vertical intervals are incidental, they may give little reason
for complicating the tuning. If such interval (including thirds and
sixths) are used in unstable sonorities contrasting with stable ones
featuring fifths and fourths, then their tension may be a positive
feature.

If Babylonian music sometimes used vertical thirds as restful
intervals, then either actual 5-limit intervals or Pythagorean schisma
thirds might serve such a music. Here the system of _srutis_ in India
might serve as a precedent, and some people suggest that this system
(including a 5:4) maybe have evolved from a Pythagorean tuning with
schisma intervals.

> Taken literally, the Babylonians seemed to check their tuning by
> listening to the thirds or sixths. I don't find it unbelievable that
> they considered the pythagorean intervals to the be the norm rather
> than the 5-limit ones we might prefer. (comments?, Margo)

As someone who prefers Pythagorean for most Gothic music but 5-limit
(or its keyboard approximation of meantone) for Renaissance music, my
first reaction might be, "it depends on the kind of music being
performed -- for me, at any rate, and possibly for the ancient
Babylonians also."

The idea of tuning a Pythagorean instrument by listening to thirds and
sixths could be maybe a bit analogous to tuning Renaisance meantone by
listening to the fifths or fourths. It's an intriguing idea, and I'd
be curious about the sources and translations; musically, why not?

Anyway, thank you for this discussion on a topic that raises lots of
questions both about history itself and about its possible
interpretations.

Most appreciatively,

Margo Schulter
mschulter@value.net