Re: TD 846: Octave doublings in medieval European polyphony

Hello, there, and in response to a very interesting post by Alison
Monteith, I'd like to address a question raised about the use of octave
doublings in medieval polyphony -- and also in monophonic singing.

A quick response is that the _Musica enchiriadis_ and _Scholia
Enchiriadis_ (the latter sometimes called the _Scolica Enchiriadis_)
of around 850-900 discuss and approve octave doubling, treating this as a
standard way to expand a two-voice organum in fifths or fourths to a
texture for three or voices. Thus for an original organum at the fourth
(the middle two voices of the following example), we have something like
the following as one possibility for four voices (C4 is middle C, and
since the notation is very pitch relative, a monastic community of women
or men might have performed it at any convenient pitch):

Organal voice octave above C4 D4 E4 C4 C4 B3 C4 D4 D4 C4
Original chant F3 G3 A3 F3 G3 E3 F3 G3 G3 F3
Added organal voice C3 D3 E3 C3 D3 B2 C3 D3 D3 C3
Chant doubled octave below F2 G2 A2 F2 G2 E2 F2 G2 G2 F2

This is indeed a very beautiful and imposing sound, and interestingly the
range of around a twelfth is still noted as a usual practical limit for
the size of vertical intervals by Jacobus of Liege about four centuries
later.

Another source of this general era, in describing a concept like
consonance or concord, says that it is what happens "when men and boys
sing the same thing," or "in that which is called _organum_." The first
reference seems to refer to the practice of octave doubling.

Guido, in his _Micrologus_ (c. 1030?), likewise describes how simple
parallel organum or _diaphonia_ (literally "singing apart") at the fourth
can be expanded to three voices by adding a third voice at the octave
above the lower one, producing a series of outer octaves with the fourth
below and fifth above.

Around the 1280's, the theorist Elias Salamon (sp.?) likewise describes a
mode of improvising for voices spaced at the fifth, octave, and twelfth,
with a suggestion that there may have been some ornamentation (a possible
inference of his advice that it not be overdone).

Around 1325, Jacobus of Liege gives an example of three voices singing in
parallel octaves and fifteenths, referring to the wonderful unity of these
intervals. As I recall, a similar example occurs in one of the early
organum treatises.

In short, some of the same early treatises which describe polyphony in
fifths and fourths also endorse octave doubling of parts to expand the
texture. Other apparent references to the singing of people with different
ranges in octaves (known also as _magadizing_ or the like) suggest that
then, as now, this may have been a natural and common occurrence.

A quick comment about "limits." As an exponent of medieval and
neo-medieval polyphony based on a 3-limit of _stability_, I would
emphasize that more complex intervals play a vital and often prominent
role. Guido, for example, recommends the 9:8 major second as the best
cadential approach to a unison, and Jacobus describes this interval as an
"imperfect concord." It is unstable, of course, but by no means
unpleasant.

A 3-limit or Pythagorean tuning rapidly generates very complex ratios, and
that's one of the delights of historical Gothic as well as neo-Gothic
music.

The Renaissance not only shifts to stable 5-limit intervals but restricts
intervals such as major seconds or minor sevenths in many ways by
comparison with the 13th and 14th centuries. What we have is, in my view,
not "progress" but a change in taste.

Complex 3-limit polyphony is a special art, as is the 5-limit polyphony of
the Renaissance. As someone deeply drawn to both traditions, I would
emphasize the beauty of each.

Most respectfully,

Margo Schulter
mschulter@value.net