Re: Medieval JI, equisones, etc.

Hello, there, and to the topic of medieval European JI and concepts
such as unisonal and equisonal intervals, I might add a few words to
comments by Alison Monteith and the Monz, after first offering two
articles discussing 13th-century polyphony and Pythagorean JI tuning
at more length:

http://www.medieval.org/emfaq/harmony/13c.html
http://www.medieval.org/emfaq/harmony/pyth.html

Thanks to Todd McComb of the Medieval Music and Arts Foundation for
hosting these pages.

In medieval theory, with some Greek precedent, the term "equisonal"
seems to apply especially to the octave (2:1), and also as I recall
the fifteenth (4:1), although the latter interval goes beyond the
usual compass of medieval polyphony. In contrast, the unison (1:1) is
unisonal.

Jacobus of Liege discusses some of these terms in his _Speculum
musicae_ of around 1325 or so, so that they are still of interest to
him, although he mainly follows one variant of the usual kind of
13th-century scale of concord/discord with four, five, or six
categories with various degrees of "perfect" (pure) or "imperfect"
(partial) blending or tension.

In one standard kind of 13th-century ranking, the unison and octave
are indeed grouped together as "perfect concords," and the fifth and
fourth as "intermediate concords." This is rather analogous to the
earlier distinction between unisonal or equisonal intervals (unisons,
octaves) and other "consonances" or _symphoniae_, the fifth (3:2) and
fourth (4:3), which in medieval polyphony represent the point of
rich and saturated stable concord.

The idea of gradations of tension among the unstable intervals --
indeed collectively known as "dissonances" in Greek theory -- seems
implicitly presented by Guido (c. 1030), who in addition to unisons
and fourths endorses the use in _diaphonia_ or polyphony of minor
thirds (32:27), major thirds (81:64), and whole-tones (9:8), while
excluding minor seconds (256:243) and tritones (729:512).

In 13th-century terms, the intervals which Guido admits all have some
degree of "compatibility," while the minor second and tritone are
"perfect discords," that is, "perfectly" or thoroughly "incompatible."
This doesn't stop them from being used boldly and beautifully in
13th-century music, however!

One fine issue which Jacobus and other theorists address: is the
unison itself a "concord," or rather the beginning of concord. Jacobus
himself suggests, if I am reading him correctly, that a unison is not
a concord if produced by a single voice or instrument, but is if two
or more singers or instruments come together at a unison, since here
there is at once a plurality of sounds and a unity of ratio.

May I add that the _Musica enchiriadis_ and _Schola enchiriadis_ are
among my favorite musical treatises, a discovery of my secondary
school days when I found out my love of fifths and fourths and would
play them in parallel on the music room piano with rapt enjoyment. It
was amusing when I remarked that a note of the piano must be "out of
tune," and was quickly educated as to what a tritone is.

Most respectfully,

Margo Schulter
mschulter@value.net