Re: TD 738 -- Sevenths and tritones around 1600

Hello, there, and please let me begin by thanking Pierre Lamothe
(whose English and graciousness are alike impressive) for directing me
to a very interesting Web site. Before responding to questions about
this material, I would like to read it more carefully, and hope to
have a response within the next day or so.

In the meantone -- the "meantime," that is -- I might reply to some
comments from Paul Erlich about the use of bold seventh sonorities
around 1600, and the role of tritone tension.

As to the use seventh sonorities around 1600 with and without
tritones, I would view this practice in terms of the fluid modality
and bold "rhetorical" use of dissonance flourishing in this era,
rather than in terms of "defining a key." What these sonorities do is
typically at once to underscore a cadential progression and provide a
moment of drama and color, which in vocal music may be associated with
expressive or emotion-charged words.

Such gestures can occur on various degrees of a mode, and as Carl
Dahlhaus has noted, occur interspersed with progressions which would
not fit a key-based orientation. I might add that these latter
progressions, sometimes based on motion between 5-limit sonorities
guided by traditional 3-limit resolutions (e.g. M3-5 by contrary
motion), give the music much of its beauty, and distinguish it from
later major/minor styles.

From the standpoint of practice by the time of Corelli (c. 1680), and
of theory by the time of Rameau's treatise (1722), it is of course
true that many progressions of the 16th and early 17th centuries (such
as those involving tritone resolutions) have become "key-defining"
events. Another way of putting this is that composers and theorists of
the late 17th and 18th centuries have selected, adapted, and reshaped
elements of earlier styles in creating a new set of styles based on
major/minor tonality.

For Claudio Monteverdi and his brother Giulio Cesare, however, the
bold use of dissonance was one feature of a fluid modal style in which
a composition might combine various modes. Although the Monteverdi
brothers did not mention Nicola Vicentino in defending this style, in
fact Vicentino describes and approves of the mixing of modes both for
"architectural variety," so to speak, and for expressing the sometimes
shifting emotions of a text.

While the use of bold seventh sonorities around 1600, with and without
tritones, is an innovation which provoked controversy (most notably
Giovanni Maria Artusi's famous polemic of 1600 on _The Imperfections
of Modern Music_), the use of tritone resolutions is a standard
feature of 16th-century style as recognized by Vicentino (1555),
Zarlino (1558), Artusi himself, and others. It is the unprepared
seventh, used by Monteverdi with or without a tritone, which is a
dramatic innovation around the end of the 16th century.

From a Renaissance perspective, tritone resolutions such as a
diminished fifth contracting to a major third (d5-M3) might fit a more
general paradigm of two-voice progressions by stepwise contrary
motion. Other progressions of this kind, borrowed from earlier 3-limit
practice, are m3-1, M3-5, and M6-8, discussed for example by Zarlino.

In a Gothic 3-limit setting, the diminished fifth or augmented fourth
is curiously unique as the one variety of unstable diatonic interval
which cannot resolve to a stable interval (unison, octave, fifth, or
fourth) by stepwise contrary motion.

However, by the late 15th century, thirds and sixths have become
pervasive in the texture and are approaching stability; by around
1500, composers such as Josquin des Prez are using them in closing
sonorities.

Thus a tritone resolution such as d5-M3 or A4-m6 now fits the general
paradigm of "vertical tension resolved by directed contrary motion,"
the third or sixth now serving as a point of full concord and restful
resolution.

By the mid-16th century, there is a certain distinction in practice
and theory between the tritone (augmented fourth) or diminished fifth
and other intervals regarded as dissonances, specifically seconds and
sevenths, which normally occur either in ornamental contexts or as
suspensions and the like.

Zarlino notes that the diminished fifth, unlike other dissonances, can
be written "in a single percussion" -- without syncopation -- if it is
followed by a major third.

Often such a resolution is combined in a multi-voice cadence with the
traditional M6-8 or m3-1 resolution. I term this kind of process of
combining mutually-reinforcing resolutions as "cadence-stacking" or
"progression-stacking." Thus a very popular internal cadence which
might occur on various degrees of a mode is the following, with C4 as
middle C and higher notes showing higher octaves:

C5 B4
F#4 G4
C4 D4
A3 G3

(M6-8 + d5-M3)

Here the major sixth A3-F#4 expands to the octave in the usual manner,
while the diminished fifth F#4-C5 contracts to the major third G4-B4.

This kind of progression is routine 16th-century style; Zarlino
remarks that both "ancients" (maybe meaning the Josquin generation)
and "moderns" use it. For example, Antonio Cabezon has a beautiful
organ piece in which this kind of tritone resolution adds color to a
momentary "cadence" on D in the overall context of E Phrygian.

The most popular multi-voice final cadence of the era, as Zarlino notes,
involves a two-voice progression where an upper voice ascends by a
semitone while the bass falls a fifth or rises a fourth (e.g. M3-8 or
M3-1). In a composer such as Josquin, this progression is often combined
with a traditionan M6-8 or m3-1 resolution:

F#4 G4
D4 D4
A3 G3
D3 G2

(M6-8 + M3-8)

Here the tenor and soprano have a classic M6-8 resolution, while the
outer two parts move in an M3-8 (actually M10-15) resolution of the
kind described by Zarlino.

In a variation which becomes more and more common during the early
16th century, this kind of four-voice cadence is modified to permit
arrival at a full 5-limit sonority, Zarlino's _harmonia perfetta_ or
"complete harmony" featuring "the third-plus-fifth-or-sixth" above the
bass. This results in the following kind of progression:

F#4 G4
D4 D4
A3 B3
D3 G2

(M3-8)

Note that the tenor and soprano no longer have a standard M6-8
progression, but rather progress in parallel sixths, arriving at a
sonority including the 10th and 12th (octave extensions of the third
and fifth) above the bass. Here the M3-8 or M10-15 progression between
the outer voices seems to serve as the defining two-voice resolution.

While bold seventh sonorities with tritones may have come into vogue
during the era of 1590-1600 through a number of processes, including
suspensions and ornamented cadences, we can interestingly derive these
sonorities through a process of "cadence-stacking" which might have
easily occurred in improvised counterpoint. (Claude Palisca has
suggested a possible connecton between some of Monteverdi's bold
dissonances and such traditions of improvisation.)

As we have seen, the combination (M6-8 + d5-M3) produces a favorite
internal cadence of the 16th century, while (M6-8 + M3-8) produces a
favorite final cadence.

What happens, however, if we try combining alll three of these
elementary resolutions at once (M6-8 + M3-8 + d5-M3)? The result, to
be compard with the previous two examples of cadences on G, is
illustrated by the following five-voice cadence:

C5 B4
F#4 G4
A3 D4
A3 G3
D3 G2

(M6-8 + M3-8 + d5-M3)

This is actually the conclusion of the final cadence in Monteverdi's
madrigal _Anima mia perdona_. Note that, if we number the voices in
ascending order, with the bass as "1," then voices 2 and 4 form a
regular M6-8 resolution; voices 1 and 4 a regular M3-8 (or M10-15)
resolution; and the highest pair of voices a usual d5-M3 resolution.

However, this cadence-stacking permutation introduces the novel
element of the bold minor seventh or fourteenth, here present between
the outer voices (D3-C5).

From another perspective, we can also analyze this cadence as a
superimposition or "stacking" of two favorite three-voice cadences
similar to the four-voice cadences we have discussed above. Taken
alone, voices 1, 2, and 4 would form a standard (M6-8 + M3-8) formula
of a kind popular as a final three-voice close in the late 15th and
16th centuries. Voices 2, 4, and 5 would form a typical internal
three-voice cadence of our (M6-8 + d5-M3) variety.

From this point of view, the formula (M6-8 + M3-8 + d5-M3) -- or more
generally (M3-8 + d5-M3) -- could potentially have arisen at any point
in the 16th century. In practice, however, the usual conventions of
dissonance treatment evidently "selected against" permutations
involving a bold seventh -- until new tastes around 1600 selected in
favor of this musical "mutation," to borrow an evolutionary
metaphor.

In considering such evolutionary possibilities, it is very important
to recognize that the same vertical event may have different meanings
in different historical and stylistic settings.

Thus in the musical world of Western Europe around 1600, bold seventh
combinations either with or without tritones were part of a fluid
modal style featuring many "rhetorical figures" of chromaticism and
dissonance, etc.

By 1700, however, some of these same progressions had been
incorporated into a different scheme of music based on major and minor
keys, codified by Rameau starting in 1722.

Through these changes, some interesting evolutionary ties may
remain. Thus a 20th-century theorist such as Leonard Ratner explains a
simple three-voice version of a tritonic seventh resolution, e.g.

F4 E4
B3 C4
G3 C3

as combining two events: the d5-M3 resolution between the upper parts,
and the descent of the bass by a fifth (in this key-based context,
from dominant to tonic or "5-1").

Interestingly, these two events (separately) are also features of
favorite 16th-century cadences in theory and practice. Vicentino (1555)
observes that the bass, especially, defines the principal fifths or
fourths of a mode in polyphonic music, likely alluding at least in
part to its typical cadential leaps by a fifth or fourth. Thus the
diverse momentary cadential centers of 16th-century modal style may be
somewhat analogous to later key centers, also reinforced by this kind
of bass motion, although the two systems remain distinct.

Most respectfully,

Margo Schulter
mschulter@value.net