Adams K. A New Theory of Chromaticism from the Late Sixteenth to the Early Eighteenth Century

A New Theory of Chromaticism
from the Late Sixteenth to
the Early Eighteenth Century
Kyle Adams
Abstract This article is intended as a solution to a perceived problem with existing theories of pretonal chromatic music: Many modern theories of this repertoire have made anachronistic uses of models from major/
minor tonality, and contemporaneous theories were not broad enough to adequately represent the phenomena
that, to my own—and, I believe, many other modern listeners’—ears, gave chromatic music its unique sound.
Both groups of theories missed the mark by treating all chromatic events in this repertoire equally. This article
therefore begins by suggesting that, just as in tonal music, chromaticism in this period comprises many different
phenomena. I therefore provide a model for separating chromatic tones according to their structural function and
an analytical method for reducing chromatic works to their diatonic foundations. I present examples of each of
the chromatic techniques that I describe and give detailed criteria for identifying each technique. In doing so, I
provide a new vocabulary by which scholars and analysts can model the way in which they hear chromatic music
from this period.
Introduction
the theory presented in this article is best introduced by an analogy to
tonal music. I present the two progressions given in Example 1 in order to
explain their relevance to the present subject. Each example uses the same
chromatic sonority, the B≤ major chord in the second half of m. 2, in different
ways. In Example 1a, the chromatic sonority is folded into the overall D-major
tonality and is understood as a substitute for a diatonic sonority. An analyst
would therefore label it ≤VI, in order to indicate its origins in the diatonic vi
chord. In Example 1b, the same chord functions as a chromatic pivot to usher
in a new tonality and would likely receive two labels, ≤VI in D and IV in F, to
indicate its dual function. The point of this example is twofold: First, our perception of the function of the chromatic sonority is dependent on context.
This article is a condensed version of the theory presented in my dissertation (Adams 2006), which I
encourage readers to consult for a more comprehensive treatment of this topic, including a complete list
of the repertoire I examined in my research. I express my gratitude to William Rothstein, Ruth DeFord,
David Gagne, Nancy Nguyen-Adams, and Linda Pearse, as well as the anonymous readers, for their help
in developing and focusing this article.
Journal of Music Theory 53:2, Fall 2009
DOI 10.1215/00222909-2010-004 © 2010 by Yale University
255
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J ou r nal o f M usic T h eo r y
256
The listener understands the chord only in light of the following sonorities,
since both progressions begin the same way.1 Second, tonal music theorists are
comfortable with the same chromatic sonority having different functions in
different contexts, with the use of different labels for such sonorities, and with
JMT 53:2 A-R Job 149-8 Adams Example 1a-b
the existence of different varieties of chromaticism in general.
(a)
!
²
Š ² ‡ ðð ðð
Ý ²² ‡ ðð ð
ð
(b)
ð ð ð
ð ¦ð ð
ðð −ð −ð
−ð ð
ð
ð
ð
ð
Ð
Ð
ÐÐ
ð ð
ð ð
ðð ð
ð
ð ð ¦ð
ð ¦ð ¦ ð
ðð −ð ð
−ð ¦ ð
−ðð
Ð
¦Ð
ðð ¦ Ð
¦Ð
Example 1. Chromaticism in two tonal progressions, (a) and (b)
I bring up these two points because, while tonal theory seems to be
completely at ease with these concepts, pretonal theory does not seem to be.
Part of what has hindered theorists’ understanding of chromaticism in early
music is the insistence on a single conception of chromaticism, from theorists
both of this time period and of our own. Thus, the present article begins from
the premise that chromatic sonorities can have different functions in pretonal
music,2 just as they can in tonal music, and that context can help to determine
the type of chromaticism at play in a given passage.
Background
Analysts approaching chromatic music from this period have suffered from an
overreliance on a single theoretical model.3 Theorists from the period under
discussion subscribed to one of two views of the chromatic genus. Those
adhering to the relative conception considered the chromatic genus to reside
in the use of a given interval or intervallic progression, typically the chromatic
semitone.4 This has also been the conception put forth by modern “historicist”
1 In fact, the very existence of chromaticism in this passage
is contextual. Out of context, the B≤ major chord is diatonic,
unlike, for example, an augmented sixth chord, which cannot be taken from any diatonic scale and is therefore chromatic regardless of its context.
2 I am aware of the strong differences of opinion on the
appropriate term for music from this period. Some scholars
consider “pretonal” overly teleological, and others consider
“early music” overly vague. Since this article clearly delineates the historical period with which it deals, I use both
terms interchangeably to describe music from that period
and do not enter into the controversy over terminology.
3 What follows is a highly condensed version of my summary of earlier conceptions of chromaticism in Adams 2007,
15–25, and of my explication of modern conceptions of early
chromaticism, as well as problems with both conceptions,
in Adams 2006, 53–79. Space does not permit me to thoroughly explore those subjects here, but I direct readers to
those works for a much more comprehensive treatment.
4 These include Vicentino ([1555] 1996), Lusitano ([1561]
1989), Burmeister ([1606] 1993), and Printz (1679). Even
Rameau ([1737] 1966) describes the origin of “this new
genus of Harmony” in the semitone produced by the overtones of two notes a third apart (171).
Kyle Adams
A New Theory of Chromaticism
257
scholars,5 notably Margaret Bent and James Haar, both of whom emphasize the
melodic nature of chromaticism in early music, especially the use of melodies
involving the chromatic semitone.6 On the other hand, theorists subscribing
to the absolute conception of chromaticism define the chromatic genus by its
use of pitches outside of an established diatonic collection.7 In the sixteenth
century, this collection was typically the gamut of musica recta, but moving
into the eighteenth century, it was conceived of as whatever diatonic scale (in
the modern sense) was operational in a given passage. Since this conception
of chromaticism is basically the one used in tonal theory, it is not surprising
that the more “presentist” analyses of early chromaticism use it as a starting
point. Presentist approaches take various forms, and most have focused on a
single work, the Prologue to Orlando di Lasso’s Prophetiae Sibyllarum (1560).
Among the approaches to this work are William Mitchell’s (1970) Schenker­
ian analysis, and Karol Berger’s (1976) and William Eastman Lake’s (1991)
hierarchical arrangements of Roman numerals. All three attempt to explain
Lasso’s chromaticism much as one would in a tonal piece, by describing the
chromatic sonorities as they relate to diatonic sonorities.
In brief, no single one of these approaches proves satisfactory for modeling the wealth of works, passages, and techniques from this period that can
reasonably be called “chromatic.” Reliance on the chromatic semitone creates
two problems. First, itWed
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passages from this period. Example 2 is from Lasso’s Sibylla Cimmeria. Lasso’s
own text to the Prologue of this work tells us that it is intended to be chromatic, and yet this brief succession of chords, striking as it is, contains no
chromatic semitones.
Second, one also finds passages in which notated chromatic semitones
occur in completely diatonic progressions. The best known of these comes
JMT 53:2
Job 149-8
Adams
2
from
Luca A-R
Marenzio’s
madrigal
O Example
voi che sospirate
a miglior note (1581), in which
a dense jumble of notated chromatic semitones can be renotated to reveal a
simple chain of descending fifths.8
!
Š ‡ ²² þþ
Ý ‡ ² þþ ý
²Ð
²Ð
ð
ÐÐ
ð
þÐ
ðð
ý
Example 2. Lasso, Sibylla Cimmeria
5 For explanations of the historicist and presentist positions, see Christensen (1993).
6 Haar’s view (1977, 392) is more temperate than Bent’s,
who asserts that “for Zarlino, only melodic progressions
that sound chromatic because they use the chromatic semitone qualified as chromatic” (2002, 129).
7 These include Zarlino ([1558] 1968), Bottrigari ([1594]
1962), Morley ([1597] 1973), Mersenne ([1627] 2003), and
Werckmeister ([1707] 1970).
8 This passage is discussed in Fétis 1879.
258
J ou r nal o f M usic T h eo r y
The presentist, “absolute” conception of chromaticism likewise has its
weaknesses. Both the Schenkerian and Roman-numeral analyses suffer from
attempts to fit Lasso’s prologue into an overall “tonality” of G. Mitchell ignores
surface features of the music that contradict his Schenkerian approach, while
Berger uses Roman numerals without regard for the hierarchy of functional
relationships that such usage traditionally implies. Thus, in Berger’s chart of
Roman numerals, one finds progressions such as V–VI–I without any explanatory note.
The present theory does not pretend to solve every problem in the analysis
of early chromatic music. However, as I stated above, I begin from the premise
that chromatic sonorities in early music can have different functions in different
contexts and that “chromaticism” as applied to early music does not describe a
single technique any more than it does in tonal music. I assert that not all chromatic tones exist for the same reason or at the same level of structure and that
different levels of these tones can be separated from one another according to
their structural functions. On one hand, I approach the music from a present­
ist point of view by attempting to describe my own—and, I believe, the typical
modern listener’s—perception of chromatic music.9 I use historical texts as
informants but do not try to divine the composer’s conception of chromatic
music or to describe the sixteenth- or seventeenth-century listener’s perception
of it. On the other hand, I take a historicist point of view by approaching the
music without using the Procrustean bed of major/minor tonality. I attempt
to provide an accurate model for this repertoire by using principles derived
from the musical texts. My theory therefore tries to converge the presentist and
historicist positions by using both the concepts available to earlier theorists and
appropriate concepts from the present day to describe as accurately as possible
the objective phenomena that, to a modern listener, distinguish this repertoire
from other types of sixteenth- and seventeenth-century music.
Repertoire and time period
The theory that follows is based on a study of all available chromatic music
published roughly within the time period 1555–1737. This period is demarcated by the publication of Nicola Vicentino’s Ancient Music Adapted to Modern Practice and Jean-Philippe Rameau’s Génération harmonique, which were,
respectively, the first and last works after classical antiquity both to discuss the
chromatic as a separate genus and to apply its use to contemporary music.10
Works from this time period were included in the study if they fell into one or
more of the following classes:
9 I use the term “listener” to mean someone familiar with
the norms of Western art music.
10 Even the use of these fairly objective criteria to choose
a time period led to some absurdities: Can one really say
that Bach used a different variety of chromaticism after
1737 than he used before? Nevertheless, it was necessary
to have some boundary dates for the musical examples in
order to keep their numbers from becoming unmanageably
large.
Kyle Adams
•
•
•
•
A New Theory of Chromaticism
259
Pieces whose title or text contains the word chromatic, or some var­
iation of it. This category includes pieces identified as durezze, a
seventeenth-century keyboard genre characterized by a multitude of
harsh dissonances and unusually resolving suspensions.
Pieces with features that conformed to contemporaneous or earlier
theoretical conceptions of chromaticism, including (a) conspicuous
uses of the ancient Greek chromatic tetrachord (two semitones and a
minor third);11 (b) widespread use of “black-key” (i.e., chromatically
altered) tones;12 and (c) employment of the chromatic fourth (i.e., six
consecutive semitones filling the interval of a perfect fourth).13
Pieces featuring widespread use of what a modern musician would
call chromatic figuration.
Pieces from two tangentially related categories: those whose titles contain the term “enharmonic” (as opposed to “chromatic”), and others
that very clearly make use of enharmonic relationships to juxtapose
distantly related sonorities; and “labyrinth” or “circle” pieces that,
through sequential repetition, travel to very distant tonalities and
eventually return to their starting tonalities.
I. Explanation of the theory
Components of the theory and definitions
This theory has two components: a theoretical model for classifying different types of chromaticism and an analytical method that uses that model
to separate different types of chromatic tones according to their structural
functions.
Definitions. This theory uses the following definitions:
(1) Tonal system: A collection of pitch classes equivalent to the modern
diatonic scale but without any hierarchy among them. The tonal
system is named for the number of accidentals it contains; thus,
the one-sharp system would be equivalent to the modern G-major
scale but without a center on G. When a passage of music uses only
tones from a single tonal system, that system is said to govern the
passage.14
(2) Diatonic: A diatonic tone is one that belongs to the governing tonal
system. A diatonic sonority is one that contains only such tones.
11 In this article, “chromatic tetrachord” always refers to
this melodic succession.
12 Bottrigari [1594] 1962 defines the chromatic genus as the
use of these tones (see 33–34).
13 In my research, I examined more than 1,400 examples
of the chromatic fourth. Since my dissertation devotes an
entire chapter to my analytical findings regarding this progression, examples containing it are not treated in this
article.
14 See Appendix A for a further discussion of my conception of tonal system.
260
J ou r nal o f M usic T h eo r y
(3) Chromatic: A chromatic tone is one that falls outside the governing
tonal system. A chromatic sonority is one that contains any such
tones.
(4) Essential chromaticism: The use of chromatic alterations to correct
an unacceptable sonority in a given repertoire. In the period under
consideration here, such alterations typically correct the intervals
excluded by the mi contra fa prohibition, that is, imperfect unisons,
fourths, fifths, and octaves, whether vertical or horizontal.15
(5) Nonessential chromaticism: The use of either of the following two
types of chromatic alterations:
(a) Type A: Alterations that serve to correct sonorities that are
contextually incorrect. For example, in the sixteenth century,
a minor sixth is by no means prohibited but can become so if
it progresses to an octave at a final cadence. Typically, type A
alterations involve either cadential leading tones or Picardy
thirds (which themselves become less structurally important
throughout this period);16 however, they may also be used to
preserve strict imitation of a motive.17
(b) Type B: Alterations that serve only expressive purposes. They
may exist for affective or text-painting reasons but do not correct any type of incorrect sonority.
Diatonicism
Indirect
chromaticism
Direct
chromaticism
Pure
diatonicism
Essential
chromaticism
Juxtaposed
diatonicism
Nonessential
chromaticism
Suspended
diatonicism
Figure 1. A continuum of chromaticism
The theoretical model: A continuum of chromaticism. Figure 1 presents a continuum containing various categories of chromaticism. The techniques in Figure 1 are listed in order of increasing chromaticism. The top of the continuum
is divided into three large categories. Diatonicism refers to passages governed
by a single tonal system. Indirect chromaticism refers to passages in which any
two successive sonorities belong to a single tonal system but the passage containing them does not. Direct chromaticism refers to passages containing two
successive sonorities that do not belong to the same tonal system. Underneath
the continuum are several smaller-scale techniques. At the two ends are pure
15 The status of chromatic alterations that correct crossrelations depends on the composer and time period, since
cross-relations generally became more acceptable as this
period went on.
16 Following the distinctions made in Berger 2004, 137, I
consider cadences to be more structurally significant than
other places in which a composer or performer might choose
to create directed motion via a chromatic inflection.
17 See Appendix B for further discussion of the terms
essential and nonessential.
Kyle Adams
A New Theory of Chromaticism
261
diatonicism, which refers to any passage that uses only diatonic sonorities, and
suspended diatonicism, which consists of any passage for which it is impossible to
determine the governing tonal system. The latter usually occurs because the
accumulation of semitones makes it impossible to arrive at a diatonic basis for
the passage. These endpoints are what Carl Dahlhaus, following Max Weber,
refers to as ideal types;18 that is, they are categories that exist in principle
but may have no occurrences in actual music. Pure diatonicism, for example,
rarely exists for long spans of time, despite the fact that a single Renaissance
work may be notated without accidentals from beginning to end. If unnotated
musica ficta is considered to be a given feature of the musical surface, as I argue
it should (see Appendix B), then there is hardly a Renaissance work that does
not exhibit chromaticism as I have defined it. Likewise, although many musical examples verge on suspended diatonicism, this ideal type does not seem
to exist in practice. Every passage I have examined, no matter how densely
chromatic, has features that give it some diatonic context.
Between pure diatonicism and suspended diatonicism are three other
chromatic techniques identifiable in music from this period. Nonessential chromaticism has already been defined. Note that it appears under the general
category of diatonicism because nonessential chromatic tones are alterations
of diatonic tones and can be removed to reveal a passage of pure diaton­icism.
Essential chromaticism has also already been defined, and it is the first type of
chromaticism along the continuum. Essential chromatic tones will nearly
always signal a move into a tonal system in which they are diatonic. Unlike
true diatonic tones, however, they are chromatic in relation to the system that
came before. Juxtaposed diatonicism consists of the placement of two different
tonal systems alongside one another using direct chromaticism.
Figure 1 is not a line in which every chromatic work has a position relative to every other and one can plot precisely the relative degree of chromaticism of any work. The categories and techniques of chromaticism represented
on it can coexist in the same work, or even in a single passage. Nor is the
continuum the most accurate possible graphic representation of the categories it contains; for example, nonessential chromaticism can exist within juxtaposed diatonicism. Nonetheless, it is a useful way to schematize chromatic
techniques in the repertoire under consideration.
The analytical method: Diatonic reduction
Diatonic reduction is a method of distinguishing among various levels of chromaticism in a given passage. It consists of the removal of nonessential chromatic alterations to reveal the tonal system(s) underlying a given passage.
18 Weber, as quoted in Gossett 1989, describes an “ideal
type” as follows: “An ideal type is formed . . . by the synthesis of a great many diffuse, discrete, more or less present
and occasionally absent concrete individual phenomena,
which are arranged according to those one-sidedly emphasized viewpoints into a unified analytical construct. In its
conceptual purity, this mental construct cannot be found
empirically anywhere in reality” (51).
262
J ou r nal o f M usic T h eo r y
I explain diatonic reduction through reference to an example. The guidelines
for creating a diatonic reduction are also given in list form in Appendix C.
Example 3 presents a diatonic reduction of the last eight measures of
Carlo Gesualdo’s Ma tu, cagion, the second part of Poichè l’avida sete, from the
fifth book of madrigals. Because my focus at this stage is on the meaning of the
analytical notation and not on the composition itself, I do not make extensive
arguments for the analytical choices the notation communicates.
A typical diatonic reduction, like the one in Example 3, has four components. The top system reproduces the score. The lowest staff, labeled “tonal
systems,” tracks the governing tonal system at each moment in the music. The
ways in which key signatures and barlines are used on this staff are explained
below. Between these two systems are two successive stages of reduction. Stage 1
of the reduction reproduces the score without any type B alterations (those
that exist only for expressive purposes). Stage 2 reduces stage 1 even further
by removing type A alterations (those that correct structurally incorrect sonorities). If a given passage contains only one type of nonessential alteration, or
none at all, either stage 1 or 2 or both may be omitted. The lowest system of
music in the reduction will always contain the diatonic framework upon which
a given chromatic passage is built, and the “tonal system” staff below that will
show its governing tonal system.
Example 3 may be read as follows: The passage begins in the two-sharp
system, as shown on the lowest staff. Tonal systems on this staff will always
be notated as modern key signatures,19 with two exceptions: Passages of suspended diatonicism will have no key signature, and passages in the natural system will be written with a signature of BΩ.20 The two-sharp signature means that
any tones in the original passage not belonging to the two-sharp system are
chromatic alterations and have been removed either in stage 1 or in stage 2
of the reduction. By comparing the score with the stages of reduction, readers
can see which types of chromatic alterations have been removed; thus, in the
first measure of the example, the soprano D≥ has been removed in stage 2 of
the reduction since it is a type A alteration, providing directed motion to the
following sonority.
On the “tonal system” staff, changes of system brought about by indirect
chromaticism are represented with dotted barlines, followed by whatever accidental has been added, or a natural sign in the position where an accidental
has been removed. Any accidentals before the dotted barline are assumed to
still be in effect after it. In the middle of m. 28, CΩ is introduced via indirect
chromaticism (the leaps from G to C in alto and tenor 1). The music therefore briefly moves into the one-sharp system. At the end of the bar, the passage returns to the two-sharp system, again via indirect chromaticism. (C≥ is
19 These signatures are not intended to be equivalent to
modern key signatures; they represent only the sharps or
flats used in the tonal system, which I notate in the traditional positions for clarity.
20 I chose BΩ mainly because of its position in the middle of
the staff and because of the special significance of the BΩ/
B≤ relationship in early music.
JMT 53:2 A-R Job 149-8 Adams Example 3 page 1 of 2
Kyle Adams
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263
Ł ²Ł Ł Ł ²Ł ¦ ð Ð þ
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27
S
A New Theory of Chromaticism
duol,
Ł ² Ł Ł Ł ² Łð (²) ð Ł Ð½
ðð
Ł ð
ð
ð Ł Ð
Ł ½ ²² ŁŁ ŁŁ ðð ½ ð
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ô
ô
ô
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²
Example 3. Diatonic reduction of Gesualdo, Ma tu, cagion, mm. 27–34
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Ł Ł ÐŁ Ł ² ð
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JMT
Example
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264 53:2 A-RJ Job
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Example 3 (continued) Diatonic reduction of Gesualdo, Ma tu, cagion, mm. 31–34
þ
þ
Kyle Adams
A New Theory of Chromaticism
reintroduced in the soprano to form a perfect fifth with the upcoming bass
F≥.) The two-sharp system governs the passage through the middle of m. 31,
within which one can see the removal of two type B alterations (CΩ and G≥ in
mm. 29–30) in stage 1, and two type A alterations (the tenor 2 D≥ in m. 30 and
the bass G≥ in m. 31) in stage 2.
The passage returns to the one-sharp system in the middle of m. 31,
again via indirect chromaticism, as indicated by the dotted barline and cancellation of C≥ by CΩ on the lowest staff. (The F≥ and C≥ at the beginning of
the lowest staff in m. 31 are courtesy accidentals and do not represent any
change.) Within this system, the leading tone G≥ in tenor 2 has been removed
in stage 2 of the reduction, since it is a type A alteration. At the end of m. 32
is a double barline, followed by a signature of three sharps. This signifies juxtaposed diatonicism, which is the juxtaposition of two tonal systems via direct
chromaticism.21 Here, the music abruptly moves into the three-sharp system
via the introduction of C≥ and G≥ on the downbeat of m. 33. Typically, as in this
example, the two tonal systems participating in juxtaposed diatonicism will
differ by more than one accidental. The only chromatic phenomenon from
Figure 1 not occurring in this passage is suspended diatonicism, which would
be indicated via a double barline followed by no signature.
Just as in the tonal progressions given in Example 1, this method allows
for the same phenomenon to be analyzed in different ways, depending on
context or function. Thus, in m. 32, the leading tone G≥ in tenor 2 has been
removed because it is chromatic within the governing one-sharp system. However, in the final measure, the alto leading tone G≥ remains in the reduction
because it is diatonic within the governing three-sharp system.
There are two guiding principles of diatonic reduction. The principle
of preferred diatonicism states that the governing tonal system of a passage will
always be the one in which the greatest possible number of sonorities are diatonic. Preference will be given to a tonal system in which the first sonority of
a passage is diatonic; however, as we shall see, many passages begin with chromatic sonorities. The principle of greater simplicity states that the stages of the
reduction must become successively more diatonic. The reduction may not
create chromaticism that was not present in the original passage. I illustrate
both of these principles in the examples that follow.
Diatonic reductions can be used in conjunction with the continuum of
Figure 1 to describe the types of chromaticism at play in a given passage. By
examining the single staff at the bottom of a reduction, a reader can determine whether a given passage is diatonic or uses indirect or direct chromaticism. If a given point on the lowest staff has no barline (which will be the
majority of the staff) and is preceded by a key signature, the passage above
21 This is an important distinction, to which I return further
below: Juxtaposed diatonicism requires the placement
alongside one another of two incompatible tonal systems,
not just two incompatible sonorities.
265
266
J ou r nal o f M usic T h eo r y
it is diatonic in the tonal system represented by the signature, and any chromatic tones appearing in the score at that point are nonessential alterations.
They will have been removed in either stage 1 or stage 2 of the reduction.
Rightward motions on the continuum are represented by barlines in the
reduction. Dotted barlines signal the use of indirect chromaticism, double
barlines followed by a key signature signify juxtaposed diatonicism, and double barlines followed by no key signature signify suspended diatonicism. In all
cases, the lowest system of music in the diatonic reduction will contain only
tones that are diatonic in the tonal system shown on the bottom staff.
II. Analyses
Essential and nonessential chromaticism
Nonessential chromaticism. Example 4 presents a diatonic reduction of
mm. 23–29 from Luzzasco Luzzaschi’s madrigal Lungi da te. All but two of the
semitones in the passage are type B nonessential alterations, since they do not
serve to correct any potential errors in part writing. These alterations have
therefore been removed to create the stage 1 reduction in the second system.
Notice that two penultimate G≥’s in the cantus remain, since they are type A
alterations: Both serve as leading tones to the following A, and the A between
them is only a decoration. The third system removes these alterations as well.
The single staff underneath the example has only a BΩ, indicating that the
entire passage is in the natural system.
One could argue that the distinction between type A and B alterations
is false. Almost every nonessential alteration involves raising a pitch, which
automatically creates directed motion to the following sonority, or at least
the expectation of it. In Example 4, all of the chromatic alterations in the
original create directed motion to the following sonority, and it may seem
arbitrary to single out the final alteration as more significant. However, raising the penultimate tone at the final cadence is a syntactical requirement, and
Luzzaschi’s notation of the alteration was more a reflection of contemporary
performance practice than an expressive chromatic gesture. By contrast, the
other chromatic alterations in the passage can be removed without creating
any violations of musical syntax. They do not belong to the fundamental voice
leading because, motivic considerations aside, the listener has no reason to
expect them. Rather, the continual raising of pitches by semitone and the successively higher statements of the chromatic tetrachord are probably intended
to portray the rising of the soul to heaven during the blessed death described
in the text.
The diatonic version of a tone does not always have to appear before
its corresponding chromatic version; frequently, a nonessential alteration will
appear before the tone that is altered. Example 5 presents a reduction of
mm. 25–30 from another of Luzzaschi’s madrigals, Se parti i’ moro.
JMT 53:2 A-R Job 14908 Adams Example 4 page 1 of 2
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Example 4. Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 23–27
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Example 4 (continued) Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 28–29
In a situation that is almost the exact reverse of Example 4, we find a
series of descending statements of the chromatic tetrachord.22 As indicated
on the lowest staff, this passage is governed by the natural system, which
means that in each statement of the chromatic tetrachord, the chromatic tone
22 Since this passage is based on the chromatic tetrachord,
one might argue that the “chromatic” tones are in fact
equivalent to diatonic tones. Vicentino, for example, viewed
the tones of the chromatic tetrachord as substitutes for the
tones of the diatonic tetrachord, so one might therefore say
that these tones are “diatonic” in the chromatic genus. This,
in turn, would imply that the tones I have reduced out as
“chromatic” were not, in fact, outside of the tonal system,
since those would be the only tones available in the tonal
system. There may be works for which this is true, but since
Se parti i’ moro contains passages that are clearly diatonic,
it seems fair to say that the chromatic tones in this passage
are not conceived of as structurally equivalent to diatonic
tones.
JMT 53:2 A-R Job 149-8 Adams Example 5 page 1 of 2
Kyle Adams
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Example 5. Reduction of Luzzaschi, Se parti i’ moro (1595), mm. 25–27
precedes the diatonic tone. Stage 1 of the reduction shows that nearly all of
the chromatic alterations are type B; only the G≥ in m. 25, which provides
directed motion to a cadence, and the Picardy thirds in mm. 26 and 30 are
type A alterations.
J ou r nal o f M usic T h eo r y
270
JMT 53:2 A-R Job 149-8 Adams Example 5 page 2 of 2
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Example 5 (continued) Reduction of Luzzaschi, Se parti i’ moro (1595), mm. 28–30
Essential chromaticism. Example 6 presents a reduction of the first six measures of Lasso’s madrigal Anna, mihi dilecta.23 This excerpt contains examples
of essential chromaticism. The E≤’s in the bass and tenor of m. 3 are essential
23 Note Lasso’s use of the chromatic tetrachord in the
soprano part of mm. 3–4.
JMT 53:2 A-R Job 149-8 Adams Example 6
Kyle Adams
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A New Theory of Chromaticism
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Example 6. Reduction of Lasso, Anna, mihi dilecta (1579), mm. 1–6
chromatic pitches, necessary to avoid a diminished fifth against the soprano
B≤. In m. 5, the A≤ in the bass is also an essential chromatic pitch, since it
avoids a melodic diminished fifth from the previous bass E≤.
The first stage of the reduction shows that the F≥ in m. 1 and the BΩ in
mm. 3 and 4 are the only nonessential chromatic pitches. It may seem counterintuitive to call the F≥ of the opening sonority chromatic, but the principle
of preferred diatonicism suggests this reading. After the opening sonority,
subsequent events make it clear that the F≥ was chromatic. More of the tones
in the first four measures belong to the one-flat system than to any system that
would contain the D-major sonority; also, this is a case in which we can claim
with near certainty to know what Lasso intended, since he wrote the one-flat
signature. Had he conceived the opening sonority as diatonic, he could have
notated the piece a whole step lower with no signature, making the opening
chord a “diatonic” C-major sonority, and the following one an A≤-major sonority, which would certainly appear chromatic.
Unlike Examples 2 and 3, however, the passage from Anna cannot be
explained in terms of a single governing tonal system, since the A≤ in m. 5
is incompatible with the AΩ of the opening sonority. This passage therefore
contains indirect chromaticism: Since the A≤-major sonority and the opening
D-major sonority cannot belong to the same tonal system, there must be a
change somewhere. But one cannot point to a single moment as signaling the
change, because any two adjacent sonorities in stage 1 are diatonic relative to
272
J ou r nal o f M usic T h eo r y
one another. One can only say that the passage begins in the one-flat system
and ends in the three-flat system. The lowest staff in the reduction tracks these
changes in tonal system with dotted barlines followed by the new flats. The dotted barlines indicate that the essential chromatic tones in stage 1 of the reduction bring about changes of tonal system without any direct chromaticism.
Most examples of essential chromaticism are created by descending-fifth
motion in the bass, as in m. 5 of the previous example. Although it is much
less common, essential chromatic tones can also be created by ascending-fifth
motion. Vicentino used this technique in several of his works. In the excerpt
from Anima mea presented as Example 7, he uses the technique quite beautifully to balance a previous descent by fifth.
As the reduction shows, the passage begins in the one-flat system, which
changes to the three-flat system through a series of descending-fifth motions,
only to cancel the newly added accidentals in the subsequent measures.
Although the chord progression in mm. 97–98 mirrors the progression from
mm. 94–95, the systems do not change accordingly because the sonorities in
mm. 97–98 still belong to the three-flat system, which has not yet been contradicted. Only with the reappearance of AΩ do the tonal systems begin to change
again. Also, because the passage contains only essential chromatic alterations,
both stages 1 and 2 of the reduction have been omitted, leaving only the single
staff to track the changes of tonal system.
Chromatic tones in the opening sonority. In Example 6, the opening sonority
of a piece contained a chromatic tone. There are many such cases, including
ones where it is quite difficult to distinguish chromatic from diatonic tones.
Example 8 is a reduction of the first four measures of Pomponio Nenna’s
motet Ecco, ò dolce, ò gradita. Even without the B≤ signature, the BΩ of the opening sonority would soon be revealed as a chromatic tone rather than a diatonic
tone. The soprano leap in m. 2 ensures for the listener that B≤ is at least an
essential chromatic tone,24 if not a diatonic tone, and the persistence of B≤
throughout the measure defines the BΩ at the end of the bar as a chromatic
alteration. Despite the one-flat signature in the music, I consider mm. 1–3 to
be in the two-flat system, since the E≤ in the bass and alto arise as essential chromatic tones, against the background of which the alto EΩ in m. 3 becomes a type
A alteration. (The one-flat system that governs most of the piece is not firmly
established until the cadence at the end of m. 4.) Analyzed this way, the striking
E≤ sonority under “dolce” becomes a sweetly relaxing move into the governing tonal system, rather than a striking chromatic event against the opening
G-major sonority, a reading that I find more consistent with the text.25
24 At this point in music history, with the innovations of
the secunda prattica, the distinction between essential and
nonessential pitches starts to blur. Nenna does use a vertical diminished fifth between the soprano and alto in m. 4.
However, this diminished fifth is between two upper voices,
both of which are consonant with the bass, and is not nearly
as harsh as a leap of a diminished fifth in the soprano of
m. 2 would be.
25 It is true that “dolce” was often used ironically by composers of this period and therefore was often set using
harsh-sounding sonorities. However, I do not believe that
Nenna intended such a setting here.
JMT 53:2 A-R Job 149-8 Adams Example 7
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A New Theory of Chromaticism
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Example 7. Reduction of Vicentino, Anima mea (1572), mm. 92–101
Nonessential chromatic tones with characteristics of essential chromatic tones.
Occasionally, a chromatic tone that is nonessential in origin may also serve to
correct an unallowable dissonance. Example 9 presents a reduction of mm.
44–47 from Heinrich Scheidemann’s Praembulum from the Anders von Düben
Tablature.
The Praembulum illustrates the frequent ambiguity between the natural
and one-flat systems in pieces with a D final: B≤ and BΩ will each be diatonic
at various times, depending on whether a particular voice moves upward or
downward, and most such pieces will shift frequently between the two systems.
This piece is in the natural system with a final on D, and BΩ is the primary form
¼
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JMT 53:2 A-R Job 149-8 Adams Example 8 page 1 of 2
274
J ou r nal o f M usic T h eo r y
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Example 8. Reduction of Nenna, Ecco, ò dolce, ò gradita (1607), mm. 1–2
of B throughout the piece. The measures in question contain a chromaticized
variant of an ascending 5–6 sequence, one that creates some significant analytical problems.
Consider the F≥ in the left hand of m. 44. Is this tone essential or nonessential? Given the context, it is clearly an alteration of a diatonic FΩ and is
perceived as such if one follows only the voice leading of the various parts.
However, it is a nonessential alteration that has the added effect of correcting
what would otherwise have been a diminished triad, a sonority that composers
still did not generally use in root position and that certainly would not have
had a place in this sequence. If we read the F≥ as an essential chromatic tone,
it should signal at least a temporary change of tonal system, according to the
principles of diatonic reduction outlined above. But I feel it most accurately
JMT 53:2 A-R Job 149-8 Adams
Example 8A New
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Kyle Adams
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Example 8 (continued) Reduction of Nenna, Ecco, ò dolce, ò gradita (1607), mm. 3–4
represents the listener’s perception of the music to say that, while the F≥ is an
essential chromatic pitch, it is a rare essential chromatic pitch that does not
signal a change of tonal system. The nonessential nature of the F≥ is clearly
defined by the motion F–F≥–G in the tenor voice and the sequential nature of
the passage. In this sequence, the chords on the second and fourth beats are
clearly subordinate to those on the first and third beats, since the former are
what we would call applied dominants. One might therefore say that while the
F≥ is “essential” in order to create a perfect fifth with the bass, it is nonessential
in the larger sense of being part of a nonessential sonority. Therefore, the
reduction shows the first measure being governed by the natural system.
JMT 53:2 A-R Job 149-8 Adams Example 9 page 1 of 2
276
J ou r nal o f M usic T h eo r y
!
�
� Łý
� Łý
� Łý
²
Ł
Š 00 Ł ý
²
Ł
Ł Ł Ł Ł
Ł Ł
¹ Ł Ł ² Ł Ł� Ł
�
�
−
Ł
Ý 0 ŁŁ ² ŁŁ ðŁ Ł
¦ ðŁ Ł Ł ¦ ŁŁ
0
!
�
� Łý
� Łý
� Łý
Ł
Š 00 Ł ý
Ł
Ł
Ł
Ł
Ł Ł Ł
¹ Ł Ł Ł Ł� Ł
�
�
−
Ł
ð
¦ Ł Ł Ł (¦) ŁŁ
Ý 0 ŁŁ ² ŁŁ ðŁ Ł
0
!
�
� Łý
� Łý
� Łý
Ł
Š 00 Ł ý
Ł
Ł
Ł
Ł
Ł Ł Ł
¹ Ł Ł Ł Ł� Ł
�
�
−
Ł
ðŁ Ł Ł ¦ ŁŁ
Ý 0 ŁŁ ² ŁŁ ðŁ Ł
0
44
Score
Stage 1
Stage 2
Tonal
Systems
Š¦
−
Example 9. Reduction of Scheidemann, Praembulum (early seventeenth century), mm. 44–45
As I have shown in the reduction, however, the music does change to
the one-flat system beginning with the G-minor sonority in m. 45. This sonority serves as the goal of directed motion rather than a sonority that provides
such motion. An analysis consistent with what has come before would read
the tones of this sonority as diatonic. Just as in the previous tenor progression F–F≥–G, the F≥ was a chromatic alteration, so, in this tenor progression
B≤–BΩ–C, the BΩ is read as a chromatic alteration, albeit another essential chromatic alteration that does not signal a change of system. The corresponding
change to the one-flat system also accounts for the B≤-major sonority in the
following bar. The final chromatic tone in the passage, C≥, remains in stage 1
of the reduction because it is syntactically required at the cadence.
Juxtaposed diatonicism
Juxtaposed diatonicism is perhaps the most difficult type of chromaticism to
identify, since its use is often independent of the chromatic semitone, and
JMT 53:2 A-R Job 149-8 AdamsKyle
Example
2 ofTheory
2
Adams9 page
A New
of Chromaticism
Score
Stage 1
Stage 2
Tonal
Systems
ŁŁ ý Ł Ł ² Ł� ŁŁ Ł Ł Ł Ł ² Ł Ł
� ¹ ¼
ðŁ Ł ² ðð
!
�
�
Š ŁŁ ý Ł Łý Ł −Ł ý Ł Ł ¦ Ł
�
ð
Ý ðŁ Ł − Ł Ł
!
�
�
�
Ł ŁŁ
Š ŁŁ ý Ł Łý Ł −Ł ý Ł Ł Ł ŁŁ ý Ł Ł ² Ł ŁŁ Ł¹ (²) Ł Ł¼
�
�
²
ð
ð
ð
ð
Ý ðŁ Ł − Ł Ł Ł Ł
!
�
�
Š ŁŁ ý Ł Łý Ł −Ł ý Ł Ł ¦ Ł
�
ð
Ý ðŁ Ł − Ł Ł
46
ŁŁ ý Ł Ł Ł� ŁŁ −Ł Ł Ł Ł Ł Ł
� ¹ ¼
ðŁ Ł ðð
Š−
Example 9 (continued) Reduction of Scheidemann, Praembulum (early seventeenth century),
mm. 46–47
since its identification often relies on subjective judgment. Unlike examples of
essential and nonessential chromaticism, it has little or no basis in sixteenthor seventeenth-century music theory.
Example 10 presents a diatonic reduction of the first nine bars of the
celebrated Prologue to Lasso’s Prophetiae Sibyllarum.26 The piece begins in the
natural system, which Lasso juxtaposes against the four-sharp system in m. 3.
This system remains in effect until the second chord of m. 6, whose DΩ signals
a change to the three-sharp system. The following series of bass motions down
by fifth carries a change of system with each chord change until the arrival of
the one-flat system, which is juxtaposed against the one-sharp system on the
downbeat of m. 8. Stage 2 has been omitted from the reduction because the
passage contains no type A alterations to remove. Even though the two final
26 As I noted above, the presentist /historicist debate
regarding early chromaticism has played out almost entirely
in reference to this piece; see Mitchell 1970, Berger 1976,
Lake 1991, and Bent 2002.
277
JMT 53:2 A-R Job 148-9 Adams Example 10
J ou r nal o f M usic T h eo r y
278
Score
Stage 1
!
!
ÿ
Š‡ ÿ
ÐÐ ýý
(Car
mi - na
Car
mi - na)
Chro
Ý ‡ Ðý Ðý ð þ
ÿ
ð Ð
ÿ
Š‡ ÿ
ÐÐ ýý
² þþ
² þþ
ðð ÐÐ
Ý ‡ Ðý Ðý ð þ
ÿ
ð Ð
² þþ
6
Score
Stage 1
Tonal
Systems
!
Š ²² ðð ðÐ Ð Ð ð Ðð Ð ð
!
Š ²² ðð ðÐ Ð Ð ð Ðð Ð ð
ðð Ð
ðð −Ð
Ý ² ÐÐ
Ð
−Ð
au - dis
au
-
Ý ² ÐÐ
Š
-
Ð ý ² ðð ² ÐÐ ² ÐÐ
²Ðý
²Ðý
²Ðý
ma
-
ti
ðð
-
co
quae
ÐÐ ² ÐÐ
Ð ý ² ðð ² ÐÐ ² ÐÐ
²Ðý
² Ð ý ð Ð ² ÐÐ
²Ðý ð Ð
²²²²
Š¦
Tonal
Systems
² þþ
ðð ÐÐ
mo dis
mo
ðð Ð
Ð
¦ ¦ ¦
du
-
la du - la
ta
ðð −Ð
−Ð
¦ −
² ðð ðð ŁÐ ² Ł Ł ² ð ÐÐ
te - no
ta
te - no
-
ðð −ðð ÐÐ
-
-
² ðð ðð ŁÐ ² Ł Ł ² ð
ðð ðð ÐÐ
re
re
ÐÐ
ÐÐ
ÐÐ
ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
²
Example 10. Reduction of Lasso, Prologue from Prophetiae Sibyllarum (1560), mm. 1–9
Kyle Adams
A New Theory of Chromaticism
F≥’s in the cantus serve to create directed motion to the following G, they are
diatonic tones rather than chromatic alterations, since the one-sharp system
governs this progression. In fact, the only nonessential alteration in the entire
passage is the type B alteration of EΩ to E≤ in the bass of m. 8.
Example 10 also
the
application
ofbonnie
the principles
of prems_11 (code) /home/jobs/journals/jmt/j8/4_adams
Weddemonstrates
May 5 12:13 2010
Rev.2.14
100% By:
Page 1 of 1 pages
ferred diatonicism and greater simplicity. The B-major sonority in m. 3 ushers in a new, four-sharp system according to the principle of preferred diatonicism. Without this principle, one is forced to somehow integrate the next
four sonorities into the natural system as chromatic alterations of underlying
diatonic sonorities. However, while Lasso’s triads on B, C≥, E, and F≥ are chromatic in relation to the G harmony that came immediately before, they are
certainly
chromatic
to one another.
In fact, if the entire passage
JMT
53:2 not
A-R
Job 148-9in relation
Adams Example
11
were transposed as in Example 11, the opening would appear chromatic while
mm. 3–5 would appear diatonic.
!
ÿ
Š‡ ÿ
− ÐÐ ýý
− ðð − ÐÐ
Ý ‡ −Ð ý
−ð −þ
ÿ −Ð ý
−ð −Ð
þþ
þþ
Ðý
Ðý
Ðý
Ðý
ðð
ðð
ÐÐ
ÐÐ
Ð
Ð
ÐÐ
Example 11. Transposition of the first five bars of the Prologue
This suggests that Lasso’s chromaticism does not have a single diatonic
foundation, but rather stems from the side-by-side placement of two incompatible diatonic passages. The advantage of reading juxtaposed diatonicism in
this and other such examples is that it highlights the fact that many sonorities
belong to the same diatonic system, without attempting to create a functional
hierarchy between the sonorities or the systems.
One might argue that the B-major sonority in m. 3 is an alteration of an
underlying B-minor triad, and that the D≥ serves to create directed motion
to the next sonority in the manner of an evaded cadence. This would lead to
the diatonic reduction presented in Example 12. (I present only the first six
measures, since the remainder of the reduction would be the same.)
Here, the relevant juxtaposition would occur in m. 3 between the
one-sharp and three-sharp systems. But this reading ignores the very moment
that gives the passage its chromatic sound, namely, the change from the G-major
to the B-major harmony. (Recall that the principle of preferred diatonicism
gives preference to a tonal system in which the first sonority of a group is diatonic.) Example 10 is therefore a much simpler interpretation, and one that
corresponds more closely to the listener’s experience of the music.
279
JMT 53:2 A-R Job 149-8 Adams Example 12
J ou r nal o f M usic T h eo r y
280
Score
Stage 1
Tonal
Systems
!
!
ÿ
Š ‡ ÿ ÐÐ ýý
Car
² þþ
ðð ÐÐ
(Car
mi - na)
- mi - na
Chro
Ý ‡ Ðý Ðý ð þ
ÿ
ð Ð
² þþ
ÿ
Š ‡ ÿ ÐÐ ýý
ðð ÐÐ
Ý ‡ Ðý Ðý ð þ
ÿ
ð Ð
þþ
² þþ
Š¦
-
Ð ý ² ðð ² ÐÐ ² ÐÐ ²² ðð ðÐ Ð Ð
²Ðý
² Ð ý ð Ð ² ÐÐ
²Ðý ð Ð
ma - ti - co
Ðý
²Ðý
²Ðý
²Ðý
quae
² ðð ² ÐÐ ² ÐÐ
ðð ÐÐ ² ÐÐ
²²²
au-dis mo au - dis mo -
² ÐÐ
ðð Ð
Ð
ð
² ðð Ð Ð Ð
² ÐÐ ðð ÐÐ
¦ ¦
Example 12. Alternate reduction, first six bars of the Prologue
One final point about Example 10: The presence of only four pitchclasses in mm. 1–2 means that those measures could be interpreted in either
the natural or the one-sharp system. I have interpreted them in the natural
system in accordance with the absence of F≥ in the gamut. While this situation
does not arise often enough to warrant its inclusion as a principle, the reductions will show a preference for interpreting tones belonging to the gamut of
musica recta as diatonic.
Distinguishing juxtaposed diatonicism from nonessential chromaticism. One
defining characteristic of juxtaposed diatonicism is the placement of two
incompatible tonal systems alongside one another, not just two incompatible
sonorities. If Lasso’s Prologue continued as in Example 13, the soprano D≥
would simply be a type B nonessential alteration and could be removed to
reveal an underlying one-sharp system.
Instead, juxtaposed diatonicism is created by the continuation of a system in which the D≥ and its corresponding B-major triad become diatonic.
The reading given in Example 10 recognizes that, while the harmonies in
mm. 4–6 may be chromatic in relation to the harmonies in mm. 1–2, they are
diatonic in relation to each other; it is the system to which they belong that
is chromatic.
Notice that mm. 6–7 of the Prologue contain a chromatic circle-of-fifths
progression, one of the most common ways that composers—especially Lasso—
introduced chromaticism in this period. The different ways of analyzing such
progressions bear heavily on the concept of juxtaposed diatonicism because
JMT 53:2 A-R Job 149-8 Adams Example 13
Kyle Adams
!
ÿ
Š‡ ÿ
ÐÐ ýý
ðð ÐÐ
Ý ‡ Ðý Ðý ð þ
ð Ð
ÿ
² þþ
² þþ
A New Theory of Chromaticism
ðð
ðð
ðð
ð
ð
281
ŁÐ ² Ł Ł ð þþ
þ
ÐÐ
þ
Example 13. Prologue with alternate continuation
most examples of it are either preceded or followed by such progressions.
Often, a juxtaposition is followed by a descending circle-of-fifths progression
that returns to the original system. Klaus Hübler (1976), in his analysis of the
Prophetiae Sibyllarum, explained Lasso’s chromaticism in just this way, as consisting of a Sprung, or leap to a distant harmony, followed by motion around
the circle of fifths. Alternatively, a descending circle-of-fifths progression that
has “gone too far” and left the original system is followed by a juxtaposition
to bring the original system back. The following illustrates how this theory
accounts for such progressions.
Consider mm. 113–28 from Claudio Monteverdi’s well-known canzonetta Zefiro, torna, presented as Example 14. This passage could be read as a
series of nonessential chromatic alterations within the one-sharp system. In
such a reading, the chromatically altered tones in mm. 114–16 and parallel
passages could be seen as type B alterations creating directed motion to the
following sonorities. Nevertheless, the reduction shows this succession as a
true instance of juxtaposed diatonicism. The difference lies in context. The
fourth measure of the excerpt does indeed return to a sonority belonging
to the one-sharp system that has governed the piece so far, but, after m. 113,
there is never a sonority that belongs exclusively to the one-sharp system. If
the passage proceeded as in Example 15, the E-major and A-major sonorities
would be perceived in retrospect as chromatic alterations.
Not only does Monteverdi not return to the one-sharp system, but he
introduces a second juxtaposition to the four-sharp system. This time, the
succeeding circle-of-fifths progression returns to the one-sharp system, but
Monteverdi spends enough time in the new system that m. 117 is perceived in
retrospect as motion to a new tonal system rather than as a series of chromatic
alterations.27
This theory must allow for a certain amount of subjectivity in determining whether chromatic juxtapositions will be perceived as nonessential chromaticism or a move to an entirely new system. Factors other than harmony can
27 Example 14 would seem an ideal place to apply Hübler’s
concept of a Sprung to a distant harmony followed by motion
around the circle of fifths; one might wonder whether it is
appropriate to describe Monteverdi’s chromaticism in terms
of Sprünge. While the idea of a Sprung would accurately
describe the juxtapositions in mm. 113–14, 116–17, and
122–23 of this example, Hübler’s concept does not provide
a complete picture of a passage such as this one. In particular, it does not address the issue of the relationship of
the Sprünge to the underlying tonal systems. Sprünge, like
single chromatic tones, do not always exist for the same
reason or serve the same purpose.
JMT 53:2 A-R Job 149-8 Adams Example 14 page 1 of 2
J ou r nal o f M usic T h eo r y
282
$
113
Tenor 1
Š /- þ
+
to
+
to
Š /- Ð ÿ Ð
Tenor 2
Ý/
% - þý
(Basso
Continuo)
Š
Tonal
Systems
$
T2
²ð
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Systems
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dor
Ý
Ð
Sol
i - o
per
Ð
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sel - ve ab-ban-do-na - te
so - le
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ð ¼Ł
²ð
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l’ar -
²²²²
² Ł Ł Ł Ł Ł Łý Ł ² Ł Ł ¼ Ł ² ð Ł Ł Ł Ł
�� �� �� �� �
�� � �
per
sel - ve ab-ban-do-na - te so - le
l’ar - dor
di due be �
��� �
�
ÿ
Ł Ł Ł Ł ² Łý
Ł ²Ł ý Ł Ł Ł ½
Š
i - o
½ ¼Ł
ÿ
�� � �
‡ ² Ł Ł ¼ Ł ² Ł Ł� Ł� Ł� Ł� Łý Ł� ² Ł Ł ¼ Ł
²²²
²Ł Ł ¼ Ł
+
ÿ
‡
‡
Š
+
B.C.
Sol
²
117
T1
ÿ
di due be - glioc
-
ð
²²²²
Š
chiel mio tor - men - to
²ð
Ð
²
Ð
Example 14. Reduction of Monteverdi, Zefiro, torna (1632), mm. 113–20
influence one’s hearing of a passage; in Example 14, the change of meter and
the change from a dancelike character to a recitative reinforce the sense of
juxtaposed diatonicism.28 Nevertheless, from the preceding examples we can
induce some criteria that serve to separate examples of juxtaposed diaton­
icism from other types of chromaticism. First, the listener is much less likely
28 Gioseffo Zarlino himself emphasized that chromaticism
was as much a stylistic phenomenon as a structural one:
“There cannot be a difference in genus between compositions that do not sound different in melodic idiom. . . .
Conversely, a difference of genus may be assumed when
a notable divergence in melodic style is heard, with rhythm
and words suitably accommodated to it” ([1558] 1968, 277).
Dahlhaus (1967) makes a similar point, noting that chromaticism arises not only from the juxtaposition of unrelated
harmonies, but also from the rhythmic isolation, metrical
relationship, and position (i.e., inversion) of those harmonies (78–79).
JMT 53:2 A-R Job 149-8 AdamsKyle
Example
of 2
Adams14 page
A New2 Theory
of Chromaticism
$ ² Łý Ł Ł ý Ł
Ł Ł ¼ Ł
Š
�
�
+
121
T1
glioc - chiel mio
ÿ
½
Ý ð
²ð
Ð
Š
¦
Š
T2
+
B.C.
%
Tonal
Systems
$
125
T1
Tonal
Systems
Š
sol
%
sol
+
na - te
so - le
l’ar - dor
+
na - te
sol - le
la’r - dor
²²²
Š
ð
Ð
²
per
� � � �
Ł Ł Ł Ł
ve ab-ban-do -
sel
-
Ł Ł ¼ Ł
ð
Ð
Ð
Ł Ł Ł Ł
� � � �
- ve ab-ban-do -
i - o
²²²
¦
Łý Ł� ² Ł Ł ¼ ² Ł ð
Ý ²ð
i - o
¼ Ł
�
Š ² Łý Ł Ł Ł ¼ Ł ð
T2
B.C.
tor - men - to
²Ł Ł ¼ Ł ²ð
283
per
²
sel
�
� � � �
�
Ł ² Ł Ł Ł Łý Ł Ł ý Ł Ł Ł
de due be-gl’oc - chiel
mio
tor-men - to
ð
ð
� � � �
�
Ł Ł Ł Ł Łý Ł Ł ý Ł Ł Ł
�
de due be-gl’oc - chiel mio tor-men - to
Ð
¦
Example 14 (continued) Reduction of Monteverdi, Zefiro, torna (1632), mm. 121–28
to perceive a change in system if, following a potential juxtaposition, the composer introduces a sonority that was diatonic in the original system but would
not be in the new one. Such a sonority will probably not sound chromatic in
a new system but will serve as a reminder of the original tonal system, against
which previous chromatic events will stand out as nonessential alterations.
Second, the likelihood that the listener will perceive a change to a different
tonal system increases with the number and duration of sonorities that belong
to that system and not the previous one.
Juxtaposed diatonicism arising from nonessential chromaticism. Example 16,
mm. 20–26 from Henry Purcell’s Gloria Patri, illustrates how a chromatic tone
¦
JMT 53:2 A-R Job 149-8 Adams Example 15
J ou r nal o f M usic T h eo r y
284
$
Tenor 1
+
+
(Basso
Continuo)
to
Š ²ð
T2
+
B.C.
i - o
%
dor
Ý Ð
²
ÿ
Sol
i - o
per
²
Ł
per
½
¼ Ł
Sol
�� � �
‡ ² Ł Ł ¼ Ł ² Ł Ł� Ł� Ł� Ł� Łý Ł� ² Ł Ł ¼ Ł
‡Ð
Š Ł Ł ¼
+
ÿ
‡
Ð
Ý/
% - þý
5
T1
ÿ
Š /- Ð
Tenor 2
$
ÿ
Š /- þ
sel - ve ab-ban-do-na - te
so - le
ð
Ð
²ð
Ł Ł Ł Ł Ł Łý Ł Ð
�� �� �� ��
�
sel - ve ab-ban-do-na - te
� � � �
Ł Ł Ł Ł ²ð
di due be - glioc
-
ð
chiel
Ð
so
-
ð
le
l’ar -
½
ð ý ²Ł
Ł Ł ½
Ð
ð
mio
tor - men - to
½
Example 15. Alternate version of Zefiro, torna
that was originally nonessential can introduce a juxtaposition to a new tonal
system. The passage begins in the three-flat system that governs most of the
piece, as indicated by Purcell’s signature. Within this system, the soprano BΩ
in m. 22 is a type A alteration that, along with the alto F, creates expectation of directed motion to a C-minor sonority. (It is a type A rather than a
type B alteration since coming to rest on a minor seventh chord would have
been syntactically incorrect in this repertoire.) Nothing from m. 22 resolves
as expected: The F, a chordal seventh, leaps to D and then G before resolving, and when it does resolve, it moves to EΩ instead of E≤.29 Moreover, the
BΩ remains in the chord instead of resolving to C.30 The harmonies that follow are diatonic in relation to the E-minor sonority, creating the juxtaposition of the three-flat and natural systems shown in the reduction. The BΩ has
therefore changed from a nonessential chromatic pitch into a diatonic pitch.
29 I consider the motion to E in m. 23 a resolution of the F
from m. 22, albeit a highly decorated one.
30 None of the voice parts in m. 23 contains a literal carryover of BΩ from one sonority to the next. However, I
have included the editorial realization of the figured bass
by Anthony Lewis and Nigel Fortune, which shows that the
retention of BΩ is part of the underlying voice leading. The
claim that BΩ “remains” in the chord is not invalidated by
the fact that this voice leading is not literally expressed by
any one part.
JMT 53:2 A-R Job 149-8 Adams Example 16 page 1 of 3
Kyle Adams
20
Score
(Continuo)
Stage 1
Stage 2
Tonal
Systems
Si
$ − Łý
Š − − 00
Ł
�
�
Ý −− 0 ŁŁ
−0 �
−
Š − − 00 ðð
-
Ł
�
ŁŁ
�
Ý −− 0 ð
% −0
!
!
− Łý
Š − − 00
Ł
�
�
Ý −− 0 ŁŁ
−0 �
−
Š − − 00
Ý −− 0
−0
Ł
ŁŁ�
�
285
e - rat in prin - ci - pi - o
et nunc,
�
�Ł Ł� Ł� � � Ł� �
Ł
¹
Ł
Ł Ł (−) ŁŁ ŁŁ
Ł Ł
¹ � � Ł Ł Łý
¼
�
� �
�
� � �
Ł
Ł
�
�
Ł
�
¹
�
ŁŁ ŁŁ Ł Ł ŁŁ ŁŁ ¦ Ł Ł Ł Ł¹ Ł Ł� Ł Ł
� �
� � � � � � �
cut
Ł�
Ł
�
Ł
Ł
A New Theory of Chromaticism
Ł�
Ł
�
ðŁ
Ł
Ł
Ł�
Ł
�
ŁŁ�
�
ÿ
Ł
ðð
ð
Ł Ł Ł
¦Ł Ł
ð
Ł
Ł
�
Ł�
Ł
¹
Ł
�
Ł�
¹
ŁŁ
ðŁ
Ł
�
Ł� Ł� Ł� Ł� Ł ŁŁ�
Ł
¹ �
¼
Ł�
�
¹
�
Ł
Ł
Ł Ł Ł� Ł ŁŁ Ł
� � �
� �
ÿ
Ł
�
Ł�
ÿ
ÿ
−
Š−−
Example 16. Reduction of Purcell, Gloria Patri (late seventeenth century), mm. 20–21
The reduction appears to violate the principle of greater simplicity by introducing a cross-relation B≤ to EΩ in m. 23 that was not present before, but the reduction is intended to track the listener’s expectations and perceptions, according
to which B≤ would still be the expected diatonic tone in the three-flat system of
m. 22 and would only be supplanted by BΩ with the E-minor sonority in m. 23.
Ł� Ł
Łý
Ł�
Ł Ł� Ł Ł
� �
ou r149-8
nal o Adams
f M usic
T h eo r
286 53:2 A-RJ Job
JMT
Example
16y page 2 of 3
$ − ¹
Š−− ¼
Ł�
Ý −− Ł
−
�
− Ł
Š − − ŁŁ ýý
22
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Stage 1
Stage 2
Tonal
Systems
!
!
− ¹
Š−− ¼
Ł�
Ý −− Ł
−
�
− ¹
Š−− ¼
Ł�
Ý −− Ł
−
�
−
Š−−
�Ł nunc�
Ł
Ł
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Example 16 (continued) Reduction of Purcell, Gloria Patri (late seventeenth century), mm. 22–24
Suspended diatonicism
Pretonal music always contains diatonic features, although in some instances
one is unable to arrive at a definite governing tonal system for a passage. Situations that approach suspended diatonicism are rare; this section examines a
few types and the criteria by which one can identify them.
Suspended diatonicism arising from simultaneous chromatic tones. Suspended
diatonicism can be created by the use of several tones simultaneously that
JMT 53:2 A-R Job 149-8 Adams Example 16 page 3 of 3
Kyle Adams
A New Theory of Chromaticism
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Example 16 (continued) Reduction of Purcell, Gloria Patri (late seventeenth century), mm. 25–26
cannot belong to the same system. Example 17 presents mm. 49–53 from Bernardo Storace’s Passagagli [sic].
This is a very brief moment of suspended diatonicism in an otherwise clear passage. The natural system has governed the piece thus far and
is strengthened with each repetition of the ground bass pattern A–G–F–E.
Within this system, the sonority on the second beat of m. 50 is seemingly easy
to explain: The B≤ and the G≥ are both type B alterations. But the striking dissonance of the chord—it contains a diminished third, a diminished fifth, and
JMT 53:2 A-R Job 149-8 Adams Example 17
288
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Example 17. Reduction of Storace, Passagagli (1664), mm. 49–53
an augmented octave, as well as a leap of an augmented second to the next
chord—makes it extremely difficult for the listener to distinguish chromatic
tones from diatonic tones in real time and therefore creates a situation in
which the music could continue in one of several different tonal systems.31
For example, the passage could proceed as in Example 18, with a change to
the three-sharp system.
In this case, there would be no single moment of juxtaposition between
systems, only a passage in the natural system, followed by an ambiguous
sonority—the moment of suspended diatonicism—and a continuation in the
three-sharp system. The passage’s continuation in the same system in which it
began does not change the moment of suspended diatonicism.
31 This sonority is analogous to the sonority that FrançoisJoseph Fétis (1879) used to illustrate the omnitonic order,
a sonority that did not belong clearly to any one key and
therefore could resolve to virtually any key.
JMT 53:2 A-R Job 149-8 Adams Example 18
Kyle Adams
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A New Theory of Chromaticism
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Example 18. Alternate version of Passagagli
Suspended diatonicism arising from consecutive semitones. The most frequent
case of suspended diatonicism occurs when there is a buildup of consecutive
semitones in more than one voice, which can blur the distinction between
diatonic and chromatic semitones and make the identification of a single
tonal system impossible. As with juxtaposed diatonicism, the perception of
suspended diatonicism depends largely on context. Example 19, from Cuore
che reprime alle lingua di manifestare il nome della sua cara by Barbara Strozzi, is
not an example of suspended diatonicism, although it contains consecutive
semitones in both voices.
The bass progression in mm. 175–77, which chromatically fills in a perfect fifth, has an audible distinction between diatonic and chromatic tones
because the preceding passages have been governed exclusively by the natural system. The D≥, C≥, and B≤ are therefore type B alterations, and, having
been perceived as type B alterations in the bass, they will also be perceived as
such in the soprano in m. 176ff. The cadence on A in the natural system in
mm. 178–79 contextualizes the chromatic tones in the bass of the following
bars as type B alterations, and, having been chromatic in the bass, they are
chromatic in the soprano.
In Example 20, on the other hand, suspended diatonicism does occur
because there have not been enough tones sounding to establish a single tonal
system. The example gives a reduction of the first ten measures of the Fantasie
ex D by Claudio de Monteforte.
Stages 1 and 2 of the reduction have been omitted for the first four
measures. This is because the nature of suspended diatonicism is a lack of an
audible distinction between diatonic and chromatic tones; it is impossible in
such circumstances to distinguish among different types of chromatic tones.
Instead, the single staff below the score carries no signature at all until m. 5,
when the analysis proceeds as usual.
In the first four bars, only the tones D and A can be perceived as diatonic, and this is only because they each have twice the value of the other
tones. D begins the piece, and A is the first important metrical point of arrival.
It is safe to assume, therefore, that the listener would perceive these tones as
diatonic, or at least more stable than the others. But two diatonic tones do not
constitute a tonal system. True, the listener will most likely perceive the D as a
289
JMT 53:2 A-R Job 149-8 Adams Example 19 page 1 of 2
J ou r nal o f M usic T h eo r y
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Example 19. Reduction of Strozzi, Cuore che reprime alle lingua di manifestare il nome della
sua cara (1654)
final and the A as its fifth, but that does not necessarily determine the status of
the other tones. In particular, it is still uncertain whether FΩ or F≥ is diatonic.32
By m. 5, however, the diatonic context becomes much clearer: EΩ is another
point of arrival and thus diatonic for the same reasons as D and A, and the
four sixteenth notes at the end of the bar establish GΩ and FΩ as diatonic tones
as well. Only the tone B is left undecided, and, here, the principle of preferred
diatonicism, which would take the B≤ as diatonic since it appears first, is superseded by motivic considerations.33 Since EΩ has become clearly established as
diatonic on the downbeat of m. 5, the listener becomes aware that the E≤ at the
32 Although the FΩ falls on a downbeat and might therefore
be more easily perceived as diatonic, the meter does not
become clear until at least m. 3, so for the listener the metrical status of both FΩ and F≥ remains ambiguous. Nothing
in the first two bars indicates that the piece is not in triple
meter, with the EΩ falling on the second downbeat.
33 This piece, like Example 9, illustrates the difficulty of
determining tonal systems in pieces with a D final.
Kyle Adams
A New Theory of Chromaticism
291
JMT 53:2 A-R Job 149-8 Adams Example 19 page 2 of 2
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Example 19 (continued) Reduction of Strozzi, Cuore che reprime alle lingua di manifestare il
nome della sua cara (1654)
beginning of the subject was a chromatic tone, in accordance with which the
parallel B≤ in m. 5 is also chromatic. In m. 7, where either B≤ or BΩ would satisfy
the grammatical and syntactical requirements of the group of four sixteenth
notes, the composer opts for BΩ, allowing for a consistent reading with the
four sixteenths at the end of m. 5. BΩ turns out to be the dominant form of B
throughout the piece; Monteforte uses it consistently instead of B≤ whenever
either tone would be satisfactory. Its use establishes the natural system as the
governing tonal system for the piece.
Again, the difference between Examples 19 and 20 is one of context.
Although the bass of Example 19 is almost the exact reverse of the opening
subject from Example 20, it does not represent suspended diatonicism. In
Example 20 from Monteforte, no context had been established against which
chromatic alterations would stand out as such, whereas in Example 19 from
Strozzi, several cadences have strongly established the natural system. Furthermore, in mm. 179–82 of Strozzi’s work, the bass chromatically fills in an
JMT 53:2 A-R Job 149-8 Adams Example 20
J ou r nal o f M usic T h eo r y
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Example 20. Reduction of Monteforte, Fantasie ex D (1689–1700), m. 1–10
ŁŁ
JMT 53:2 A-R Job 149-8 Adams Example 21 page 1 of 3
Kyle Adams
A New Theory of Chromaticism
293
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JMT
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Example 21 (continued) Reduction of Rossi, Toccata VII (1657), mm. 75–83
JMT 53:2 A-R Job 149-8 AdamsKyle
Example
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A New3 Theory
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Example 21 (continued) Reduction of Rossi, Toccata VII (1657), mm. 84–87
octave (albeit with a change of register), with a durational accent on the fifth
step down, which will be the final of the piece. This gives Strozzi’s passage a
much stronger diatonic context than Monteforte’s, which chromatically filled
in the space of a ninth.
An even more striking example of suspended diatonicism occurs in
Example 21, mm. 69–87 of Michelangelo Rossi’s Toccata VII. Beginning in the
sixth measure, the accretion of chromatic semitones in all of the voices and
the lack of clear cadences, or even the expectation of them, makes discerning
a governing system impossible.34 This lack of a single discernible tonal system
is the primary feature that distinguishes suspended diatonicism from all of
the other chromatic phenomena discussed here. For instance, consider again
Example 10, the first nine bars of Lasso’s Prologue. In mm. 6–7, the reduction
34 Note that the example does begin in the natural system,
despite the one-flat signature.
295
296
J ou r nal o f M usic T h eo r y
shows the tonal systems changing with each sonority, beginning in the foursharp system and ending in the one-flat system. This, too, could be seen as an
instance of suspended diatonicism, since the tonal systems change so rapidly
and come to rest on a system so far removed from the one in which the passage started. But the crucial difference between Lasso’s passage and Rossi’s is
that in the Prologue, the music could come to rest on any of the sonorities in
mm. 5–7, and the governing diatonic system at that point would be clear. In
Rossi’s passage, on the other hand, if the music were to stop on any of the
sonorities from m. 74 to m. 81—even if the sonority were a major or minor
triad—there would not be a clear enough context to determine the governing
tonal system or the status (diatonic or chromatic) of the chord in question.
There are features that make certain tones stand out as more stable, if
not diatonic. Most of the chromatic ascents and descents fill in the interval
from G to D or from D to A, both of which are significant intervals within the
natural or one-flat systems. Note, in Example 21, the soprano’s ascent in m. 72,
the bass’s ascent from m. 73 to m. 75, and the soprano’s ascent beginning in
m. 77. Furthermore, all of the quarter notes and most of the repeated eighth
notes in the passage belong to the one-flat system, and many stand out as the
goals of chromatic ascents or descents (especially the soprano AΩ in m. 74 and
DΩ in m. 75). Certain progressions may also be interpreted as cadential: The
motion from E major to F major (mm. 73–74) can be interpreted as an evaded
cadence to A minor. In m. 75, the soprano and bass move quite forcefully from
an augmented sixth, E≤–C≥,35 to an octave D, although an actual cadence to
D minor is evaded by the middle voice’s motion to B≤. Finally, the motion from
m. 79 to m. 80 could be seen as a plagal-type cadence to D major, anticipating
the final cadence.
Nevertheless, overall the passage remains an example of suspended diatonicism. Of all the potential cadences, very few fall on strong beats, and most
are evaded, which weakens their ability to define a tonal system. There are
many situations where the use of several chromatic tones in succession in
multiple voices creates ambiguous sonorities and progressions. One of the
most common ways Rossi creates these situations is by having two voices move
by consecutive semitone in parallel motion, therefore maintaining the same
interval size.36 The complex of tones created by this type of motion can never
belong to a single tonal system, at least not by the third consecutive interval.
Nearly all of the music from the middle of m. 73 to m. 80 contains this type
of motion between at least two of the voices. On the second half of the third
beat of m. 73, the soprano and bass rise in parallel major thirds from D–F≥ to
35 This augmented sixth actually has two conflicting effects:
On the one hand, it intensifies motion to the octave D,
which could highlight the status of D as a diatonic tone, and
on the other hand, it destabilizes any sense of diatonicism
by virtue of the fact that E≤ and C≥ cannot belong to the
same tonal system.
36 Strozzi also used this technique in Example 19, but the
governing tonal systems were clear for the reasons outlined
above.
Kyle Adams
A New Theory of Chromaticism
F–A. (The fact that the bass continues moving up by semitone is the main factor that destabilizes the sense of evaded cadence on the downbeat of m. 74.)
Immediately after the downbeat of m. 74, the bass and middle voices begin to
move in parallel minor thirds, continuing until the second half of the third
beat. At this point comes the most tonally destabilizing event of all—the consecutive augmented triads from the third to the fourth beat of m. 74, leading
to another augmented triad on the downbeat of m. 75. The augmented triad
is already an ambiguous sonority; one augmented triad cannot belong to a
single tonal system, and two of them in a row completely negate any sense of
diatonicism. In mm. 76, 77, and 78, the middle voice and soprano move in
parallel perfect fourths, creating the sonority C–B–E on the second half of the
third beat of m. 77, a sonority difficult to explain by the voice-leading principles of tonal or pretonal music. Many more instances of this type of motion
occur between mm. 79 and 81.
The passage in Example 21 also contains many successions of sonorities that do not follow any kind of standard voice-leading pattern in either
the soprano or the bass (e.g., a descending-fifth pattern), much less exist in
any kind of functional relationship to one another. Consider the succession
of chords beginning on beat 3 of m. 77 and continuing to the downbeat of
m. 78. This is not a succession of sonorities that creates a predictable set of
expectations. Since it is not sequential, it does not even create the expectation that it will continue in the same fashion. Until the arrival of the bass G in
m. 82, it is difficult to distinguish stable from unstable tones and therefore to
differentiate tones belonging to the governing system from chromatic alter­
ations of those tones.
Conclusion
Concerning sixteenth-century music, James Haar has written: “There appears
to have been no regularly used term for music full of sharps and flats, but without direct melodic chromaticism. Pieces to which this description applies may
nonetheless sound quite chromatic, at least in the sense of being harmonically
colorful, to our ears” (1977, 393). This article was intended to address precisely this phenomenon. This theory recognizes, as Haar seems to, that “chromatic” had many different meanings to earlier musicians, not all of which are
accounted for by either contemporaneous or modern theories. It also serves
to blur the distinction between diatonic and chromatic by showing that sonorities are not always one or the other. Rather, there are shades of chromatic
tones, some of which exist at much deeper levels of structure than do others.
Some represent surface expressive devices, while others represent fundamental shifts in diatonic collections. The methodology presented here aims to give
analysts concrete criteria for differentiating among these types of tones and,
in doing so, to provide a vocabulary with which theorists can discuss the ways
in which they perceive different chromatic phenomena from this period.
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J ou r nal o f M usic T h eo r y
Reading an earlier draft of this article, one scholar pointed out that
some of the criteria I present for making analytical judgments run the risk of
opening the door to counterarguments. I view this as a strength, rather than a
weakness, of this theory. In none of the examples for this article do I intend to
assert that I have uncovered objective truths about the music. Rather, for each
example, my argument runs as follows: (1) This passage can legitimately be
called chromatic. (2) Chromaticism, in this period, consists of some combination of the techniques presented in Figure 1. (3) The observations made in my
discussion of the example represent the best way of applying my methodology
to this passage, that is, of using the vocabulary presented herein to model my
own hearing of the piece. Without a doubt, other analysts will hear many of
these examples differently, and, fortunately, the boundaries between each of
the chromatic techniques I discuss here are blurry enough that the theory
allows each analyst to account for his or her own hearing. In that sense, every
category I have presented here is an “ideal type.” None of them is a category
with fixed boundaries, such that a passage must be placed either inside or
outside the category.
Of the many aspects of this theory that are ripe for expansion, two are
worth mentioning here: its intersection with genre, and its relationship to the
crystallization of major/minor tonality. Concerning genre, it would be worth
studying the degree to which the various techniques I describe are used in
various genres. Both examples of suspended diatonicism, for example, are
from seventeenth-century keyboard works, no doubt because such tortuously
chromatic passages would be much more difficult to sing than to play. The
amount of chromaticism in sacred and secular genres would likewise be worth
exploring. To the best of my knowledge, juxtaposed diatonicism appears
rarely, if ever, in scared music. Such a striking degree of chromaticism seems
usually to be reserved for secular music, where it can more effectively mirror
the changes in textual affect. Nevertheless, it would be interesting to see if,
and how, the more highly charged chromatic techniques that I have described
are used in sacred music from this period.
The question of chromaticism as it relates to the development of major/
minor tonality is more difficult. I present here a single analytical model that
attempts to account for all of the chromatic music written in a period for
which scholars still disagree on the best way to model diatonic music. As of
this writing, there is no universally accepted model for diatonicism in pretonal
music, and perhaps this is appropriate, since the meaning of “diatonic” at
the end of this period is so far removed from its meaning at the beginning.
It seems unlikely, then, that a single theory or analytical method could fully
account for chromaticism in early music either. The change from pretonal
to tonal music undoubtedly affected chromaticism in subtler, more intricate
ways than are, or can be, dealt with here. The change from pretonal to tonal
music is at best incompletely understood. Nevertheless, a fascinating and useful study could be made of the difference between the structural function of
Kyle Adams
A New Theory of Chromaticism
chromaticism in tonal and pretonal music, using traditional music theories as
models for the former and the theory presented here as a model for the latter.
Further study would no doubt lead to welcome changes and refinements in
the present theory. These, in turn, could expand my theory so that it might
better address the tremendous changes in tonality throughout the sixteenth,
seventeenth, and eighteenth centuries. Whether or not this comes to pass, it is
my hope that the term “chromatic” will be applied differently to music of this
period than it has been previously, to describe not a single narrowly defined
technique, but a rich source of compositional procedures and possibilities.
Appendix A: Further discussion of tonal systems
My conception of tonal systems was originally based on the hexachordal models of Dahlhaus (1990) and Eric Chafe (1992). Chafe defines tonal system as
“the aggregate of pitches (excluding accidentals) that may occur” (23), in
other words, the set of pitches that the listener would perceive as belonging
together at any given point in a piece, usually based on some previously established context. It is like a key in that it describes the unordered pitch-class
content of all the voices in a polyphonic texture—not just the ordered set of
pitches in a particular voice—and yet differs from a key in that no one pitch
necessarily serves as a tonal center to which all the others are subordinate.
Dahlhaus’s model of a tonal system consists of a single hexachord, either
on B≤, F, C, or G, and the triads that can be built upon its tones, with the proviso that minor triads can be altered to major for purposes of creating directed
motion. The tonal system is independent of the final of the piece. The lowest
tone of the hexachord on which the system is based will not necessarily be
the final; rather, the final can be any of the tones of the hexachord. Chafe
expands his tonal systems to include three hexachords and their corresponding triads. Chafe’s natural system consists of hexachords built on F, C, and G;
his one-flat system consists of hexachords on B≤, F, and C. (Chafe uses only
these two systems since Monteverdi’s music uses only these two signatures.)
Each of his tonal systems therefore corresponds to the modern diatonic scale
plus the raised fourth scale degree.
I have used Dahlhaus’s single-hexachord model as a starting point, but
mine differs from his in several respects. First, I allow for the existence, in
theory, of hexachords to be built on any tone. Thus, as stated in the article, the
tonal system can comprise any transposition of the tones of the modern diatonic scale. Allowing tonal systems to be built on tones other than B≤, F, C, and
G enables me to accurately describe all of the different diatonic progressions
in a given passage or work. Second, I do not necessarily allow minor triads to
be altered without a change of system, as Dahlhaus does. I prefer to treat such
alterations on a case-by-case basis since I believe that not all of them exist for
the same reason or at the same level of structure.
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Third, and most important, I have divorced my conception of tonal system from its hexachordal origins, since the concept of hexachord does not
ultimately play a role in my theory. Thus, although the pitches of the tonal
system were originally generated by a single hexachord, that generation does
not factor in to how the tonal systems are used. The hexachordal origins of
the tonal systems used in this theory are only important insofar as they point
to the reasons for the inclusion of certain accidentals at the expense of others. Each tonal system was generated from the triads that could be built using
only the tones of a given hexachord and the tone a perfect fifth above the
third hexachordal step. Thus, the one-sharp system includes F≥ (instead of,
e.g., C≥ or G≥) because it was generated from the triads built on the tones of
the G hexachord.
Appendix B: Further discussion of the terms essential and nonessential
Many scholars will undoubtedly take exception both to my use of these terms
and to the way in which I apply them. The following discussion sheds some
light on the specific ways in which I propose to use them. Clearly, the terms
have been adopted from Johann Kirnberger, but that does not mean that they
should be construed to have any relationship to his terms. Rather, they should
be taken as literally as possible: “Nonessential” chromatic alterations either
are unnecessary given the compositional style or could become so in a different context, and “essential” chromatic alterations are those that are necessary
no matter what the context. Readers of earlier versions of this article have
pointed me to many possible problems stemming from the use of these terms,
and I address the three most significant of these.
First, and perhaps most significant, is the objection that accidentals that
serve to create cadential leading tones should not be called chromatic at all.
Margaret Bent has amply elaborated on this point of view in “Diatonic Ficta”
and elsewhere, and it is necessary for me to clarify my position with respect
to this point. I do not deny that the progressions by which these accidentals
arise are, in many cases, entirely diatonic, in that they can be understood
and solmized entirely within the extended gamut. However, I consider these
accidentals chromatic, in a sense closer to the modern one, in that the pitches
arising from their use lie outside the governing tonal system (see my definitions on p. 260).37
Note the underlying assumption, in this article, that the ear will expect
the continuation of the governing tonal system unless explicitly directed otherwise. Thus, whether a chromatically altered cadential leading tone arises
from diatonic or chromatic melodic successions, it will be marked as a different form of a given letter name than that which one would expect.38 This is the
sense of the term “chromatic” that modern musicians use, and the one that I
37 This view is, in fact, consistent with that of many latesixteenth-century theorists; see Adams 2007.
38 Berger (2004, 45–46) makes a similar point.
Kyle Adams
A New Theory of Chromaticism
use here. In fact, although I would anticipate strong objections from Bent and
others in my use of “chromatic” to describe these tones, I can only imagine
that the same scholars would agree with my conclusions: that once such tones
are reduced out of the musical surface, a passage containing them is revealed
to be exclusively diatonic.
ms_B1 (code) /home/jobs/journals/jmt/j8/4_adams
Wed May 5 12:13 2010 Rev.2.14 100% By: bonnie Page 1 of 1 pages
The second objection is that cadential leading tones and Picardy thirds,
even if they can legitimately be called chromatic according to my definitions,
are hardly “nonessential,” especially in the sixteenth century. I do not wish to
imply here that the use of these tones was in some way optional, but rather
that the music could, in principle, continue in the same tonal system without
them. While cadential leading tones and Picardy thirds may be essential in
terms
of the
style,
circumstances
that B1
give rise to them are not. To illusJMT 53:2
A-R
Job the
149-8
Adams Example
trate, I will borrow two examples from Pietro Aron’s Aggiunta to the Toscanello
in musica.
!
Š ÐÐ ðð
Ý ÐÐ ðð
ðð
ð
ð
Ð ð ² þþ
ð
ÐÐ þþ
ÐÐ
Ð
Ð
Ððý Ł Ł ðð
ðð
ÐÐ
ð
¼
ðð
ð Ð Ł Ł ð ² þþ
þþ
ÐÐ
Example B1. Two examples from Aron, Aggiunta to the Toscanello in musica ([1529] 1970, 22)
Aron’s examples are intended to illustrate the sorts of circumstances
under which a composer should notate accidentals, rather than leaving them
to the discretion of the performer. However, they also illustrate rather nicely
my reasons for calling Picardy thirds “nonessential.” The first sonority of the
example shown on the right is intended to substitute for the third sonority
of the example shown on the left. Aron’s point is that the composer should
notate the soprano G≥ shown on the left in Example B1, because if the music
continued as on the right, the G would better be left unaltered. My reasons
for calling such a G≥ nonessential are similar. Of course the Picardy third in
the left example is an “essential” aspect of the style, but the fact that the music
happens to end there is not. If the music continued as on the right, there
would be no need for a G≥; in fact, it would be incorrect to add one. Thus,
the Picardy third G≥ on the left is nonessential, insofar as a different musical
context could render it unnecessary. One can easily imagine similar situations
with cadential leading tones, including the familiar “inganno” cadence.
Finally, the theory makes no distinction between accidentals included
by the composer in the score and those implied by the proper application
of musica ficta. Here, I would agree with Berger (2004) that accidentals
stemming from the proper application of musica ficta are as much a part of the
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J ou r nal o f M usic T h eo r y
musical text as those specifically notated by the composer (see 170ff.). In fact,
Example B1 illustrates this point as well. In the progression on the right, Aron
has not indicated a cadential C≥ in the alto, even though any performer of his
day surely would have included one. Thus, any analysis of this passage would
have to treat the alto voice as though it contained a notated C≥. While I would
still consider this a chromatic pitch, for the reasons given above, I would consider it “essential” to my analysis, if not to the musical surface. Thus, all of
my analyses treat implicit but necessary accidentals as equivalent to notated
accidentals.
Appendix C: Guidelines for diatonic reduction
The following is a more succinct presentation of the principles of diatonic
reduction given in Section I.
(1) The top system reproduces the score.
(2) Underneath the top system, and aligned with it, stage 1 of the reduction copies the score without any type B alterations. I have taken
out these alterations first because they are the furthest removed
from the underlying voice leading; they exist for expressive purposes rather than for reasons of musical syntax or grammar. Stage
1 therefore contains diatonic tones, essential chromatic tones, and
type A chromatic alterations.
(3) Underneath the second system, and aligned with the others, stage 2
reproduces stage 1 without any type A alterations. Stage 2 therefore
contains only diatonic tones and essential chromatic tones.
(4) Underneath the third system, a single staff tracks the tonal system(s)
governing the passage by notating each new tonal system underneath the point in stage 2 at which it appears. The tonal systems are
shown as key signatures. For example, a signature of F≥ would represent the one-sharp system. There are two exceptions: Passages
containing suspended diatonicism are given no signature at all,
and passages in the natural system are given a signature of BΩ to
distinguish them from suspended diatonicism. Changes of system
brought about by direct chromaticism are represented by double
barlines, followed by the signature of the new system.
(5) The principle of preferred diatonicism states that the governing tonal
system of a passage will always be the one in which the greatest possible number of sonorities are diatonic. Preference will be given to
a tonal system in which the first sonority of a passage is diatonic;
however, many passages do begin with chromatic sonorities.
(6) The principle of greater simplicity states that the stages of the reduction
must become successively more diatonic. The reduction may not
create chromaticism that was not present in the original passage.
Kyle Adams
A New Theory of Chromaticism
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Kyle Adams is assistant professor of music theory and aural skills coordinator at Indiana University. In
2009, he presented work on sixteenth-century music at the Society for Music Theory annual meeting
and was invited to speak on the analysis of rap music at the biannual Stop.Spot! festival in Linz, Austria.