Re: Gregorian chant and Pythagorean intonation

Hello, there, Rami and everyone, and please let me briefly respond to
the question about Gregorian chant intonation and Pythgorean tuning.

First of all, I find it wise to note that human vocal intonation seems
inherently flexible, so that Pythagorean or any other model is
necessarily an approximate one.

Having said this, I would suggest that Pythagorean intonation for
Gregorian chant generally tends to fit both the theoretical
documentation of medieval Western European sources (e.g. Guido
d'Arezzo), and the character of this purely melodic music.

Various treatises document Pythagorean tuning for organs and
monochords, based on pure fifths or fourths at 3:2 and 4:3, and
scholars such as Easley Blackwood and Mark Lindley find it apt both
for this chant literature and for polyphonic or part-music of the
9th-14th centuries composed in Contintental Wester Europe.

Melodically, Pythagorean tuning provides major seconds at a full 9:8
(~203.91 cents), and compact diatonic semitones at 256:243 (~90.22
cents). Gregorian chant takes on a nice quality with this contrast
between whole-tones and semitones.

For much European polyphony of the era 850-1400 or so, Pythagorean
tuning additionally has vertical intervals fitting the sonorous
structure of the music, as I discuss in an article at the Early Music
FAQ Site edited by Todd McComb:

http://www.medieval.org/emfaq/harmony/pyth.html

This doesn't mean that vocal intonation anywhere was _exactly_
Pythagorean, nor that it might not have varied rather widely from
Pythagorean in some regions.

However, I find a Pythagorean model consistent with the theory of the
era, and with the nature of the music itself.

Most respectfully,

Margo Schulter
mschulter@value.net