Re: Vertical and melodic dimensions (for Daniel Wolf)

Hello, there, and this is a message mainly to agree with some remarks
by Daniel Wolf and Paul Erlich about melodic and vertical elements in
medieval and Renaissance music, and at the same time to suggest some
fine points about possible agendas raised when people speak of
"harmonic" considerations.

First of all, please let me say that decisions on such points as
accidentals in medieval and Renaissance music -- either _musica recta_
(within the usual gamut, e.g. the choice between B-natural and Bb, or
in German nomenclature H/B), or _musica ficta_ (outside the usual
gamut, and therefore "feigned" or "invented," e.g. F#, C#, G#) --
are based on both vertical and melodic considerations, sometimes
subtly interwoven.

A major issue in such discussions, however, is that often the term
"harmonic" can imply for many readers not merely decisions oriented
around the vertical dimension (i.e. vertical sonorities and
progressions), but more specifically an 18th-century system of
verticality.

In fact, medieval theorists such as Marchettus of Padua (1318),
Prosdocimus of Beldemandis (e.g. 1413), and Ugolino of Orvieto around
the second quarter of the 15th century tell us that _musica ficta_ is
intended for "the perfection of some consonance." This is a vertical
perspective -- but a perspective in late medieval verticality, of
course, not 18th-century verticality ("harmony" to many modern
readers).

For example, a common rule of the 14th and 15th centuries calls for a
major third before a fifth and a major sixth before an octave. This
rule sometimes gives us a choice between two solutions in a cadence to
a given note, here shown in a notation where C4 is middle C and higher
note numbers show higher octaves:

C#4 D4 C4 D4
G#3 A3 G3 A3
E3 D3 Eb3 D3

(M6-8 + M3-5) (M6-8 + M3-5)

These progressions include accidentals which theorists of the time
explain in vertical terms, as do I. Of course, at the same time, the
narrow Pythagorean semitones have a very nice melodic effect also.
The important point is that often the two dimensions harmoniously
unite; but someone unfamiliar with the rule of M3-5, for example,
might attempt to describe the motivation for accidentals such as the
G# in the first example as "purely melodic."

As I have commented in other articles, the basic distinction between
medieval, Renaissance, and Manneristic verticality for three or more
voices (c. 1200-1640) and the era of c. 1670-1900 is one of
"combinative" vs. "chordal" verticality. In the first technique,
multivoice combinations and progressions are built from various
elementary two-voice intervals and progressions, which may be
superimposed or "stacked" (e.g. the M6-8 and M3-5 progressions in the
above example). In the second approach, chords (often derived at least
in theory from stacked thirds) are the "elementary" particles of
motion, with intervals often considered as fragments of such chords.

Generally, I might guess, in a combinative approach there is a
greater diversity of common vertical progressions than in a chordal
approach, and therefore a large range of musical choices which may
provide pleasing results in both dimensions. In a chordal approach,
the harmonic key structure tends to be a canalizing factor.

Thus I would say that decisions about unwritten accidentals in
medieval and Renaissance music (either _musica recta_ or _musica
ficta_) are often based on a consideration of both dimensions. In
practice, this might often mean that in ensemble music with one
performer per part, the performers (originally reading most often from
choirbooks or partbooks rather than from scores) on first reading
respond to cues from their own melodic lines. If vertical results
deemed "unpleasant" occur, then the performers make necessary
adjustments.

In 1529, Pietro Aron (the first known writer to describe the division
of a pure major third into four equally narrowed fifths, the basis for
1/4-comma meantone) added a fascinating supplement to his _Toscanello
in Musica_ focusing on these issues. He argues that while skilled
performers can recognize many places where unwritten accidentals are
called for, there is no performer so skillful as would not now and
then "be caught in a bit of dissonance" before figuring out that an
inflection was needed to avoid such an event.

In an excellent study on 16th-century intabulations which _do_ show
precisely the semitones required (e.g. on lute) for the arranger's
version of a piece, Robert Toft shows how vertical and horizontal
factors -- and the varying tastes of musicians -- can lead to
different solutions from different arrangers of the same motet by
Josquin des Prez, for example.

For more on Toft, and these topics generally, you might visit:

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

Anyway, while emphasizing the importance of both dimensions in early
European music, I'd like also to agree with Daniel Wolf's basic point
that melody is at least as basic as verticality in this mix. Writing
maybe around 1260, Franco of Cologne describes how to compose a
conductus for two, three, or four voices, and starts with this advice:
"Write as beautiful a melody as you can" to serve as the tenor or
foundation of the polyphonic composition. That isn't a bad starting
point.

Most appreciatively,

Margo Schulter
mschulter@value.net