Adams K. a New Theory of Chromaticism From the Late Sixteenth to the Early Eighteenth Century

8/20/2019 Adams K. a New Theory of Chromaticism From the Late Sixteenth to the Early Eighteenth Century

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255

Journal of Music Theory 53:2, Fall 2009

DOI 10.1215/00222909-2010-004 © 2010 by Yale University

A New Theory of Chromaticismfrom the Late Sixteenth tothe Early Eighteenth Century

Kyle Adams

Abstract This article is intended as a solution to a perceived problem with existing theories of pretonal chro-

matic 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 musicfrom this period.

Introduction

is best introduced by an analogy totonal music. I present the two progressions given in Example 1 in order toexplain their relevance to the present subject. Each example uses the samechromatic 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 vichord. In Example 1b, the same chord functions as a chromatic pivot to usherin a new tonality and would likely receive two labels, ≤ VI in D and IV in F, toindicate its dual function. The point of this example is twofold: First, our per-ception 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.


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256 J O U R N A L o f M U S I C T H E O R Y

The listener understands the chord only in light of the following sonorities,since both progressions begin the same way.1 Second, tonal music theorists arecomfortable with the same chromatic sonority having different functions in

different contexts, with the use of different labels for such sonorities, and withthe existence of different varieties of chromaticism in general.

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Example 1. Chromaticism in two tonal progressions, (a) and (b)

I bring up these two points because, while tonal theory seems to becompletely at ease with these concepts, pretonal theory does not seem to be.Part of what has hindered theorists’ understanding of chromaticism in earlymusic is the insistence on a single conception of chromaticism, from theoristsboth of this time period and of our own. Thus, the present article begins fromthe premise that chromatic sonorities can have different functions in pretonalmusic,2 just as they can in tonal music, and that context can help to determinethe type of chromaticism at play in a given passage.

Background

Analysts approaching chromatic music from this period have suffered from anoverreliance on a single theoretical model.3 Theorists from the period underdiscussion subscribed to one of two views of the chromatic genus. Thoseadhering to the relative conception considered the chromatic genus to residein the use of a given interval or intervallic progression, typically the chromaticsemitone.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 can-

not be taken from any diatonic scale and is therefore chro-

matic 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 delin-

eates 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 sum-

mary 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 thor-

oughly 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 over-

tones of two notes a third apart (171).


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257Kyle Adams A New Theory of Chromaticism

scholars,5 notably Margaret Bent and James Haar, both of whom emphasize themelodic nature of chromaticism in early music, especially the use of melodiesinvolving the chromatic semitone.6 On the other hand, theorists subscribing

to the absolute conception of chromaticism define the chromatic genus by itsuse of pitches outside of an established diatonic collection.7 In the sixteenthcentury, this collection was typically the gamut of musica recta , but movinginto the eighteenth century, it was conceived of as whatever diatonic scale (inthe modern sense) was operational in a given passage. Since this conceptionof chromaticism is basically the one used in tonal theory, it is not surprisingthat the more “presentist” analyses of early chromaticism use it as a startingpoint. Presentist approaches take various forms, and most have focused on asingle 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 explainLasso’s chromaticism much as one would in a tonal piece, by describing thechromatic sonorities as they relate to diatonic sonorities.

In brief, no single one of these approaches proves satisfactory for mod-eling the wealth of works, passages, and techniques from this period that canreasonably be called “chromatic.” Reliance on the chromatic semitone createstwo problems. First, it does not account for all of the intentionally chromaticpassages from this period. Example 2 is from Lasso’s Sibylla Cimmeria . Lasso’sown text to the Prologue of this work tells us that it is intended to be chro-

matic, and yet this brief succession of chords, striking as it is, contains nochromatic semitones.

Second, one also finds passages in which notated chromatic semitonesoccur in completely diatonic progressions. The best known of these comesfrom Luca Marenzio’s madrigal O voi che sospirate a miglior note (1581), in whicha dense jumble of notated chromatic semitones can be renotated to reveal asimple chain of descending fifths.8

5 For explanations of the historicist and presentist posi-

tions, 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 semi-

tone 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.

Š Ý ‡‡ þþþþ ý²²² ÐÐ²² ÐÐð ð ð ð Ðþý!Example 2. Lasso, Sibylla Cimmeria


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The presentist, “absolute” conception of chromaticism likewise has its weaknesses. Both the Schenkerian and Roman-numeral analyses suffer fromattempts to fit Lasso’s prologue into an overall “tonality” of G. Mitchell ignores

surface features of the music that contradict his Schenkerian approach, whileBerger uses Roman numerals without regard for the hierarchy of functionalrelationships that such usage traditionally implies. Thus, in Berger’s chart ofRoman numerals, one finds progressions such as V–VI–I without any explana-tory note.

The present theory does not pretend to solve every problem in the analysisof early chromatic music. However, as I stated above, I begin from the premisethat chromatic sonorities in early music can have different functions in differentcontexts and that “chromaticism” as applied to early music does not describe asingle technique any more than it does in tonal music. I assert that not all chro-

matic tones exist for the same reason or at the same level of structure and thatdifferent levels of these tones can be separated from one another according totheir 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 typicalmodern listener’s—perception of chromatic music.9 I use historical texts asinformants but do not try to divine the composer’s conception of chromaticmusic or to describe the sixteenth- or seventeenth-century listener’s perceptionof it. On the other hand, I take a historicist point of view by approaching themusic without using the Procrustean bed of major/minor tonality. I attemptto provide an accurate model for this repertoire by using principles derived

from the musical texts. My theory therefore tries to converge the presentist andhistoricist positions by using both the concepts available to earlier theorists andappropriate concepts from the present day to describe as accurately as possiblethe objective phenomena that, to a modern listener, distinguish this repertoirefrom 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 musicpublished roughly within the time period 1555–1737. This period is demar-

cated by the publication of Nicola Vicentino’s Ancient Music Adapted to Mod- ern Practice and Jean-Philippe Rameau’s Génération harmonique , which were,respectively, the first and last works after classical antiquity both to discuss thechromatic 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 ormore 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.


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Pieces whose title or text contains the word• chromatic , or some var-iation of it. This category includes pieces identified as durezze , aseventeenth-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) conspicuoususes of the ancient Greek chromatic tetrachord (two semitones and aminor third);11 (b) widespread use of “black-key” (i.e., chromaticallyaltered) tones;12 and (c) employment of the chromatic fourth (i.e., sixconsecutive 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 con-•

tain the term “enharmonic” (as opposed to “chromatic”), and othersthat very clearly make use of enharmonic relationships to juxtaposedistantly related sonorities; and “labyrinth” or “circle” pieces that,through sequential repetition, travel to very distant tonalities andeventually 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 differ-

ent types of chromaticism and an analytical method that uses that modelto separate different types of chromatic tones according to their structuralfunctions.

Definitions. This theory uses the following definitions:

(1) Tonal system : A collection of pitch classes equivalent to the moderndiatonic scale but without any hierarchy among them. The tonalsystem is named for the number of accidentals it contains; thus,the one-sharp system would be equivalent to the modern G-majorscale 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 thepassage.14

(2) Diatonic : A diatonic tone is one that belongs to the governing tonalsystem. 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 pro-

gression, examples containing it are not treated in this

article.

14 See Appendix A for a further discussion of my concep-

tion of tonal system.


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(3) Chromatic : A chromatic tone is one that falls outside the governingtonal system. A chromatic sonority is one that contains any suchtones.

(4) Essential chromaticism : The use of chromatic alterations to correctan unacceptable sonority in a given repertoire. In the period underconsideration here, such alterations typically correct the intervalsexcluded 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 twotypes 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 Aalterations involve either cadential leading tones or Picardythirds (which themselves become less structurally importantthroughout this period);16 however, they may also be used topreserve strict imitation of a motive.17

(b) Type B : Alterations that serve only expressive purposes. Theymay exist for affective or text-painting reasons but do not cor-rect any type of incorrect sonority.

Figure 1. A continuum of chromaticism

The theoretical model: A continuum of chromaticism. Figure 1 presents a con-tinuum containing various categories of chromaticism. The techniques in Fig-ure 1 are listed in order of increasing chromaticism. The top of the continuum

is divided into three large categories. Diatonicism refers to passages governedby a single tonal system. Indirect chromaticism refers to passages in which anytwo successive sonorities belong to a single tonal system but the passage con-taining them does not. Direct chromaticism refers to passages containing twosuccessive sonorities that do not belong to the same tonal system. Underneaththe continuum are several smaller-scale techniques. At the two ends are pure

15 The status of chromatic alterations that correct cross-

relations 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 .

Indirect Direct

Diatonicism chromaticism chromaticism

Pure Nonessential Essential Juxtaposed Suspendeddiatonicism chromaticism chromaticism diatonicism diatonicism


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diatonicism , which refers to any passage that uses only diatonic sonorities, andsuspended diatonicism , which consists of any passage for which it is impossible todetermine the governing tonal system. The latter usually occurs because the

accumulation of semitones makes it impossible to arrive at a diatonic basis forthe passage. These endpoints are what Carl Dahlhaus, following Max Weber,refers to as ideal types;18 that is, they are categories that exist in principlebut 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 unnotatedmusica ficta is considered to be a given feature of the musical surface, as I argueit should (see Appendix B), then there is hardly a Renaissance work that doesnot exhibit chromaticism as I have defined it. Likewise, although many musi-cal examples verge on suspended diatonicism, this ideal type does not seem

to exist in practice. Every passage I have examined, no matter how denselychromatic, 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 generalcategory of diatonicism because nonessential chromatic tones are alterationsof 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 ofchromaticism along the continuum. Essential chromatic tones will nearlyalways 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 thatcame before. Juxtaposed diatonicism consists of the placement of two differenttonal systems alongside one another using direct chromaticism.

Figure 1 is not a line in which every chromatic work has a position rela-tive to every other and one can plot precisely the relative degree of chromati-cism of any work. The categories and techniques of chromaticism representedon it can coexist in the same work, or even in a single passage. Nor is thecontinuum the most accurate possible graphic representation of the catego-ries it contains; for example, nonessential chromaticism can exist within jux-taposed 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 chro-maticism in a given passage. It consists of the removal of nonessential chro-matic 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 synthe-

sis of a great many diffuse, discrete, more or less present

and occasionally absent concrete individual phenomena,

which are arranged according to those one-sidedly empha-

sized viewpoints into a unified analytical construct. In its

conceptual purity, this mental construct cannot be found

empirically anywhere in reality” (51).


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I explain diatonic reduction through reference to an example. The guidelinesfor 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 thefifth book of madrigals. Because my focus at this stage is on the meaning of theanalytical notation and not on the composition itself, I do not make extensivearguments for the analytical choices the notation communicates.

A typical diatonic reduction, like the one in Example 3, has four com-ponents. The top system reproduces the score. The lowest staff, labeled “tonalsystems,” 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 explainedbelow. Between these two systems are two successive stages of reduction. Stage 1of the reduction reproduces the score without any type B alterations (those

that exist only for expressive purposes). Stage 2 reduces stage 1 even furtherby removing type A alterations (those that correct structurally incorrect sonor-ities). If a given passage contains only one type of nonessential alteration, ornone at all, either stage 1 or 2 or both may be omitted. The lowest system ofmusic in the reduction will always contain the diatonic framework upon whicha given chromatic passage is built, and the “tonal system” staff below that willshow its governing tonal system.

Example 3 may be read as follows: The passage begins in the two-sharpsystem, as shown on the lowest staff. Tonal systems on this staff will alwaysbe notated as modern key signatures,19 with two exceptions: Passages of sus-

pended diatonicism will have no key signature, and passages in the natural sys-tem will be written with a signature of BΩ.20 The two-sharp signature means thatany tones in the original passage not belonging to the two-sharp system arechromatic alterations and have been removed either in stage 1 or in stage 2of the reduction. By comparing the score with the stages of reduction, readerscan see which types of chromatic alterations have been removed; thus, in thefirst measure of the example, the soprano D≥ has been removed in stage 2 ofthe reduction since it is a type A alteration, providing directed motion to thefollowing sonority.

On the “tonal system” staff, changes of system brought about by indirect

chromaticism are represented with dotted barlines, followed by whatever acci-dental has been added, or a natural sign in the position where an accidentalhas been removed. Any accidentals before the dotted barline are assumed tostill be in effect after it. In the middle of m. 28, CΩ is introduced via indirectchromaticism (the leaps from G to C in alto and tenor 1). The music there-fore briefly moves into the one-sharp system. At the end of the bar, the pas-sage 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 tradi-

tional 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.


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Example 3. Diatonic reduction of Gesualdo, Ma tu, cagion , mm. 27–34


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Example 3 (continued) Diatonic reduction of Gesualdo, Ma tu, cagion , mm. 31–34


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reintroduced in the soprano to form a perfect fifth with the upcoming bassF≥.) 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 andthe 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 can-cellation of C≥ by CΩ on the lowest staff. (The F≥ and C≥ at the beginning ofthe lowest staff in m. 31 are courtesy accidentals and do not represent anychange.) Within this system, the leading tone G≥ in tenor 2 has been removedin stage 2 of the reduction, since it is a type A alteration. At the end of m. 32is a double barline, followed by a signature of three sharps. This signifies jux-taposed 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 thisexample, the two tonal systems participating in juxtaposed diatonicism willdiffer by more than one accidental. The only chromatic phenomenon fromFigure 1 not occurring in this passage is suspended diatonicism, which wouldbe indicated via a double barline followed by no signature.

Just as in the tonal progressions given in Example 1, this method allowsfor the same phenomenon to be analyzed in different ways, depending oncontext or function. Thus, in m. 32, the leading tone G≥ in tenor 2 has beenremoved because it is chromatic within the governing one-sharp system. How-

ever, in the final measure, the alto leading tone G≥ remains in the reductionbecause it is diatonic within the governing three-sharp system.

There are two guiding principles of diatonic reduction. The principleof preferred diatonicism states that the governing tonal system of a passage willalways be the one in which the greatest possible number of sonorities are dia-tonic. Preference will be given to a tonal system in which the first sonority ofa passage is diatonic; however, as we shall see, many passages begin with chro-matic sonorities. The principle of greater simplicity states that the stages of thereduction must become successively more diatonic. The reduction may notcreate 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. Byexamining the single staff at the bottom of a reduction, a reader can deter-mine whether a given passage is diatonic or uses indirect or direct chromati-cism. If a given point on the lowest staff has no barline (which will be themajority 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.


12/50


it is diatonic in the tonal system represented by the signature, and any chro-matic 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 thereduction. Dotted barlines signal the use of indirect chromaticism, doublebarlines followed by a key signature signify juxtaposed diatonicism, and dou-ble barlines followed by no key signature signify suspended diatonicism. In allcases, the lowest system of music in the diatonic reduction will contain onlytones 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 ofmm. 23–29 from Luzzasco Luzzaschi’s madrigal Lungi da te . All but two of thesemitones in the passage are type B nonessential alterations, since they do notserve to correct any potential errors in part writing. These alterations havetherefore 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 Aalterations: Both serve as leading tones to the following A, and the A betweenthem is only a decoration. The third system removes these alterations as well.The single staff underneath the example has only a BΩ, indicating that theentire passage is in the natural system.

One could argue that the distinction between type A and B alterationsis false. Almost every nonessential alteration involves raising a pitch, whichautomatically creates directed motion to the following sonority, or at leastthe expectation of it. In Example 4, all of the chromatic alterations in theoriginal create directed motion to the following sonority, and it may seemarbitrary to single out the final alteration as more significant. However, rais-ing the penultimate tone at the final cadence is a syntactical requirement, andLuzzaschi’s notation of the alteration was more a reflection of contemporaryperformance practice than an expressive chromatic gesture. By contrast, theother chromatic alterations in the passage can be removed without creating

any violations of musical syntax. They do not belong to the fundamental voiceleading because, motivic considerations aside, the listener has no reason toexpect them. Rather, the continual raising of pitches by semitone and the suc-cessively higher statements of the chromatic tetrachord are probably intendedto portray the rising of the soul to heaven during the blessed death describedin the text.

The diatonic version of a tone does not always have to appear beforeits corresponding chromatic version; frequently, a nonessential alteration willappear before the tone that is altered. Example 5 presents a reduction ofmm. 25–30 from another of Luzzaschi’s madrigals, Se parti i’ moro .


13/50


+

+

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¼ð

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ð

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Š Š

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ð ð Ð

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ôÿÐð ð

ð Ł ²

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¼

¼ð Ð

Ł

ð

ð Ł

Ł

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ð Ł

Ł ð �

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ð ð Ł

ÿð

ÿð Ł ð ð

Ł

Ł

ð ¼

Ð

ð ²

Ðð ð ¼

ð

ð

ð

Ðð ý

Ðð

ð

ý

Ł �

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Ł ¼ð

ð Ł ¼

Ł Ł ²

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!

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¦

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Score

Stage 1

Tonal

Systems

Score

Stage 1

Tonal

Systems

e mo-ri - ro

e

be

mo-ri

- a

- ro

e

be

mo-ri - ro

- ta

- a

e

be

mo-ri-ro

- a

- ta,

e

be

mo-ri

-

-

-

a

ro

ta,

- ta,

be

e

- a

e

mo

(e

- ri - ro

mo - ri - ro

mo - ri

be

- ta,

- ro

be

- a

- a

be

(e

- ta

(e

- a

mo - ri - ro

- ta,

e

be

mo - ri

-

-

-

23

26

Example 4. Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 23–27


14/50


In a situation that is almost the exact reverse of Example 4, we find aseries of descending statements of the chromatic tetrachord.22 As indicatedon the lowest staff, this passage is governed by the natural system, whichmeans that in each statement of the chromatic tetrachord, the chromatic tone

+

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ð Ł

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þð ð Ł

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ð Ł

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ð

ð Ł �

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Ł Ł

þþ²þ

þþ

þþþþþ²

þþþþþ

$

%

!

!¦

Score

Stage 1

Stage 2

Tonal

Systems

a

ro

ta)

mo

(e

- r i - r o

- ta,)

be

e

mo - ri

be

mo

- ro)

- a

- a

- ri

be

- ro

- a

b e - a

- ta

- ta

- ta

- ta)

28

Example 4 (continued) Diatonic reduction of Luzzaschi, Lungi da te (1595), mm. 28–29

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 diatonictones.


15/50


Example 5. Reduction of Luzzaschi, Se parti i’ moro (1595), mm. 25–27

+

+

+

Š Š Š Š

Ý

Š

ÝŠ

Ý

Š

‡‡‡‡‡

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‡‡‡

ð

ð ð

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ð ð ð

ð ð

ð ð ð ð ð

Ł

Ł Ł

Ł Ł

Ł Ł Ł

Ł Ł

Ł Ł Ł Ł Ł

Ł Ł Ł

Ł

Ł

Ł Ł Ł Ł Ł

Ł Ł Ł Ł Ł

ð ý

ð ýð ý

ð ý²ð ý

ð ð ð

ð ð ýýý

ýý

²

ð ð ð ð ð ýýýýý

Ł

Ł Ł

Ł ²Ł

Ł Ł Ł Ł Ł

²

Ł Ł Ł Ł Ł

ð Ð²Ð

Ð

Ð

ÐÐÐ

Ðð ²

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ð

ð

ð

ð ý²

½ÿÿ

ÿ

ÿÿÿ½ð ý

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ð

ð

ð

Ł ¦

Ł

Ł

Ð

ð ý²½ÿ

ô

ÿ½Ðð ý

ôô

ð

ð

Ł ¦

Ł

ÐÐð ý²½

½ð ÐÐý

ð

ð

Ł ¦

Ł

$

%

!

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Score

Stage 1

Stage 2

Tonal

Systems

Quei

Quei

Quei

Quei

Quei

che

che

che

che

che

cor

cor

cor

cor

cor

-giun

-giun

-giun

-giun

-giun

- se A

- se A

- se A

- se A

- se A

- mor

- mor

- mor

- mor

- mor

per - che

per

di - vi

- che

per

di

- di,

- vi

- che

per

di

-

-

-

25

precedes the diatonic tone. Stage 1 of the reduction shows that nearly all ofthe chromatic alterations are type B; only the G≥ in m. 25, which providesdirected motion to a cadence, and the Picardy thirds in mm. 26 and 30 aretype A alterations.


16/50


+

+

+

Š Š Š Š

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ð ý²

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Ðð ý²

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½

ý

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ð ý²½

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ÐÐ½½ð ý

ôô

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¼

ð

ð ð ¼

ð ð

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ð

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ð

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ð Ł

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Ł Ð

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¼Ł

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Ł

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ð

ð ð

ð ð ð

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ÐÐ

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Score

Stage 1

Stage 2

Tonal

Systems

di,

vi

che

per

di

- di,

- vi

- che

per

di

- che

- di,

- vi

per

per

di

- che

- vi

- che

- di,

per

di

- di,

- che

di

- vi

di - vi

- vi

di

di

- vi

- vi

- di?

- di?

- di?

- di?

- di?

28

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 mea-sures of Lasso’s madrigal Anna, mihi dilecta .23 This excerpt contains examplesof 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 thesoprano part of mm. 3–4.


17/50


chromatic pitches, necessary to avoid a diminished fifth against the sopranoB≤. In m. 5, the A ≤ in the bass is also an essential chromatic pitch, since itavoids 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 inmm. 3 and 4 are the only nonessential chromatic pitches. It may seem coun-terintuitive to call the F≥ of the opening sonority chromatic, but the principleof preferred diatonicism suggests this reading. After the opening sonority,subsequent events make it clear that the F≥ was chromatic. More of the tonesin 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-flatsignature. Had he conceived the opening sonority as diatonic, he could havenotated the piece a whole step lower with no signature, making the openingchord a “diatonic” C-major sonority, and the following one an A ≤-major sonor-ity, which would certainly appear chromatic.

Unlike Examples 2 and 3, however, the passage from Anna cannot beexplained in terms of a single governing tonal system, since the A ≤ in m. 5is incompatible with the A Ω of the opening sonority. This passage thereforecontains indirect chromaticism: Since the A ≤-major sonority and the openingD-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 thechange, because any two adjacent sonorities in stage 1 are diatonic relative to

Example 6. Reduction of Lasso, Anna, mihi dilecta (1579), mm. 1–6

Š

Ý

Š

ÝŠ

−

−

−

−−

0.

0.

0.

0.

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( )

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Score

Stage 1

Tonal

Systems

An

(An

- na,

- na)

mi - hi di - le - cta,

(cta)

ve - ni, me -


18/50


one another. One can only say that the passage begins in the one-flat systemand ends in the three-flat system. The lowest staff in the reduction tracks thesechanges in tonal system with dotted barlines followed by the new flats. The dot-

ted barlines indicate that the essential chromatic tones in stage 1 of the reduc-tion 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 muchless common, essential chromatic tones can also be created by ascending-fifthmotion. Vicentino used this technique in several of his works. In the excerptfrom Anima mea presented as Example 7, he uses the technique quite beauti-fully to balance a previous descent by fifth.

As the reduction shows, the passage begins in the one-flat system, whichchanges 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 frommm. 94–95, the systems do not change accordingly because the sonorities inmm. 97–98 still belong to the three-flat system, which has not yet been contra-dicted. Only with the reappearance of A Ω do the tonal systems begin to changeagain. Also, because the passage contains only essential chromatic alterations,both stages 1 and 2 of the reduction have been omitted, leaving only the singlestaff to track the changes of tonal system.

Chromatic tones in the opening sonority. In Example 6, the opening sonorityof 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 open-ing sonority would soon be revealed as a chromatic tone rather than a diatonictone. The soprano leap in m. 2 ensures for the listener that B≤ is at least anessential 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 chromaticalteration. Despite the one-flat signature in the music, I consider mm. 1–3 tobe in the two-flat system, since the E≤ in the bass and alto arise as essential chro-matic 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 firmlyestablished until the cadence at the end of m. 4.) Analyzed this way, the strikingE≤ sonority under “dolce” becomes a sweetly relaxing move into the govern-ing tonal system, rather than a striking chromatic event against the openingG-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 verti-

cal 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 nearlyas 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 com-

posers of this period and therefore was often set using

harsh-sounding sonorities. However, I do not believe that

Nenna intended such a setting here.


19/50


Nonessential chromatic tones with characteristics of essential chromatic tones.

Occasionally, a chromatic tone that is nonessential in origin may also serve tocorrect an unallowable dissonance. Example 9 presents a reduction of mm.44–47 from Heinrich Scheidemann’s Praembulum from the Anders von DübenTablature .

The Praembulum illustrates the frequent ambiguity between the naturaland one-flat systems in pieces with a D final: B≤ and BΩ will each be diatonicat various times, depending on whether a particular voice moves upward ordownward, 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

Š

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ð ð

ÿð

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ð ð Ł −

ð ð

Ð¼−

ð −

Ł −

ð −ð Ł

Ł

Ł −

Ł −Ł

−

ð Ł −ð ð ý−

−

ð Ł

−

ð −

ð

¼

ð −

ð −

Ł Ł −

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ð

¼

ð −

ð

Ł

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ð Ł

ð Ł −

ÿ¼

Ł ð

Ł

½¼

ð

ð

Ł

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−−

[ ]

( ) ( )

( )

( )

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( )

( )( )

( )( )

( )

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Score

Tonal

Systems

Score

Tonal

Systems

A - ni - ma me - a tur - ba - ta est tur - ba - ta

est val - de sed tu do - mi - ne

92

97

Example 7. Reduction of Vicentino, Anima mea (1572), mm. 92–101


20/50


of B throughout the piece. The measures in question contain a chromaticized

variant of an ascending 5–6 sequence, one that creates some significant ana-lytical problems.

Consider the F≥ in the left hand of m. 44. Is this tone essential or non-essential? Given the context, it is clearly an alteration of a diatonic FΩ and isperceived 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 composersstill did not generally use in root position and that certainly would not havehad 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 theprinciples of diatonic reduction outlined above. But I feel it most accurately

Š

Š Ý

Š Ý

Š

ÝŠ

−

−

−

−−

−

−−−

0.0.0.

0.0.

0.

0.

ÐÐ ý¦

Ð ýÐÐ ýý

ÐÐÐÐÐ ýýýý−

ô

ô

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Ð

ð ¦

ð ð ð

ð ð ð ð −

¼

¼

¼

¼¼

ô

ô

Ł Ł

Ł Ł Ł

Ł Ł Ł Ł Ł

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ð Ł

ð −ð Ł

ð ð Ł ð Ł

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$

%

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!( ) ( ) ( )

Score

Stage 1

Stage 2

Tonal

Systems

Ec

Ec

- co

- co

O

O

dol

dol

- ce, o

- ce,

gra -

Example 8. Reduction of Nenna, Ecco, ò dolce, ò gradita (1607), mm. 1–2


21/50


represents the listener’s perception of the music to say that, while the F≥ is anessential chromatic pitch, it is a rare essential chromatic pitch that does notsignal a change of tonal system. The nonessential nature of the F≥ is clearlydefined by the motion F–F≥–G in the tenor voice and the sequential nature ofthe passage. In this sequence, the chords on the second and fourth beats areclearly 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 theF≥ is “essential” in order to create a perfect fifth with the bass, it is nonessentialin the larger sense of being part of a nonessential sonority. Therefore, the

reduction shows the first measure being governed by the natural system.

Š

Š

Ý

Š Ý

Š Ý

Š

−

−

−

−−

−

−

−−

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ÐŁ Ł ÐŁ ¦

ÐŁ Ł

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Ł

ð Ł

ð Ł Ł

ð Ł Ł

ð

ð

ð ð

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ð ð

ð ð ð

ð ð ð ð ð

ð ð ð ð ð

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Ł Ł Ł Ł

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ð Ł Ł

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Ł �

Ł �

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ð ð

ð

ð ð ð

ð Ł ð ð

Ł ²

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ð ð ²

ð

ð

ð ð ð ð ²

ð ð

ð ð

Ł

Ł

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$

%

!

! ( ) ( )

Score

Stage 1

Stage 2

Tonal

Systems

di

o gra - di

- ta

- ta

Vi

Vi

- ta

- ta

del

del

- la

- la mia

mia

vi

vi - ta

- ta

3

Example 8 (continued) Reduction of Nenna, Ecco, ò dolce, ò gradita (1607), mm. 3–4


22/50


As I have shown in the reduction, however, the music does change tothe one-flat system beginning with the G-minor sonority in m. 45. This sonor-ity serves as the goal of directed motion rather than a sonority that providessuch motion. An analysis consistent with what has come before would readthe tones of this sonority as diatonic. Just as in the previous tenor progres-sion F–F≥–G, the F≥ was a chromatic alteration, so, in this tenor progressionB≤–BΩ–C, the BΩ is read as a chromatic alteration, albeit another essential chro-matic alteration that does not signal a change of system. The correspondingchange to the one-flat system also accounts for the B≤-major sonority in thefollowing bar. The final chromatic tone in the passage, C≥, remains in stage 1of the reduction because it is syntactically required at the cadence.

Juxtaposed diatonicism

Juxtaposed diatonicism is perhaps the most difficult type of chromaticism toidentify, since its use is often independent of the chromatic semitone, and

Š Ý

Š Ý

Š Ý

Š

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44

Example 9. Reduction of Scheidemann, Praembulum (early seventeenth century), mm. 44–45


23/50


since its identification often relies on subjective judgment. Unlike examples ofessential and nonessential chromaticism, it has little or no basis in sixteenth-or 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 thenatural 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 signalsa change to the three-sharp system. The following series of bass motions downby fifth carries a change of system with each chord change until the arrival ofthe one-flat system, which is juxtaposed against the one-sharp system on thedownbeat of m. 8. Stage 2 has been omitted from the reduction because thepassage contains no type A alterations to remove. Even though the two final

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46

Example 9 (continued) Reduction of Scheidemann, Praembulum (early seventeenth century),

mm. 46–47

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.


24/50


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6

Example 10. Reduction of Lasso, Prologue from Prophetiae Sibyllarum (1560), mm. 1–9


25/50


F≥’s in the cantus serve to create directed motion to the following G, they arediatonic tones rather than chromatic alterations, since the one-sharp systemgoverns 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 demonstrates the application of the principles of pre-

ferred diatonicism and greater simplicity. The B-major sonority in m. 3 ush-ers in a new, four-sharp system according to the principle of preferred dia-tonicism. Without this principle, one is forced to somehow integrate the nextfour sonorities into the natural system as chromatic alterations of underlyingdiatonic sonorities. However, while Lasso’s triads on B, C≥, E, and F≥ are chro-matic in relation to the G harmony that came immediately before, they arecertainly not chromatic in relation to one another. In fact, if the entire passage were transposed as in Example 11, the opening would appear chromatic while

mm. 3–5 would appear diatonic.

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Example 11. Transposition of the first five bars of the Prologue

This suggests that Lasso’s chromaticism does not have a single diatonicfoundation, but rather stems from the side-by-side placement of two incom-patible diatonic passages. The advantage of reading juxtaposed diatonicism inthis and other such examples is that it highlights the fact that many sonoritiesbelong to the same diatonic system, without attempting to create a functionalhierarchy between the sonorities or the systems.

One might argue that the B-major sonority in m. 3 is an alteration of anunderlying B-minor triad, and that the D≥ serves to create directed motionto the next sonority in the manner of an evaded cadence. This would lead tothe diatonic reduction presented in Example 12. (I present only the first sixmeasures, since the remainder of the reduction would be the same.)

Here, the relevant juxtaposition would occur in m. 3 between theone-sharp and three-sharp systems. But this reading ignores the very momentthat gives the passage its chromatic sound, namely, the change from the G-majorto the B-major harmony. (Recall that the principle of preferred diatonicismgives preference to a tonal system in which the first sonority of a group is dia-tonic.) Example 10 is therefore a much simpler interpretation, and one thatcorresponds more closely to the listener’s experience of the music.


26/50


One final point about Example 10: The presence of only four pitch-

classes in mm. 1–2 means that those measures could be interpreted in eitherthe natural or the one-sharp system. I have interpreted them in the naturalsystem in accordance with the absence of F≥ in the gamut. While this situationdoes not arise often enough to warrant its inclusion as a principle, the reduc-tions will show a preference for interpreting tones belonging to the gamut ofmusica recta as diatonic.

Distinguishing juxtaposed diatonicism from nonessential chromaticism. Onedefining characteristic of juxtaposed diatonicism is the placement of twoincompatible tonal systems alongside one another, not just two incompatiblesonorities. If Lasso’s Prologue continued as in Example 13, the soprano D≥ would simply be a type B nonessential alteration and could be removed toreveal an underlying one-sharp system.

Instead, juxtaposed diatonicism is created by the continuation of a sys-tem in which the D≥ and its corresponding B-major triad become diatonic.The reading given in Example 10 recognizes that, while the harmonies inmm. 4–6 may be chromatic in relation to the harmonies in mm. 1–2, they arediatonic in relation to each other; it is the system to which they belong thatis chromatic.

Notice that mm. 6–7 of the Prologue contain a chromatic circle-of-fifthsprogression, one of the most common ways that composers—especially Lasso—introduced chromaticism in this period. The different ways of analyzing suchprogressions bear heavily on the concept of juxtaposed diatonicism because

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Car (Car- mi - na- mi - na) Chro - ma - ti - co quae auau-dis- dismo mo- -

Example 12. Alternate reduct ion, first six bars of the Prologue


27/50


most examples of it are either preceded or followed by such progressions.Often, a juxtaposition is followed by a descending circle-of-fifths progressionthat returns to the original system. Klaus Hübler (1976), in his analysis of theProphetiae Sibyllarum , explained Lasso’s chromaticism in just this way, as con-sisting of a Sprung , or leap to a distant harmony, followed by motion aroundthe circle of fifths. Alternatively, a descending circle-of-fifths progression thathas “gone too far” and left the original system is followed by a juxtapositionto bring the original system back. The following illustrates how this theoryaccounts for such progressions.

Consider mm. 113–28 from Claudio Monteverdi’s well-known canzo-netta Zefiro, torna , presented as Example 14. This passage could be read as aseries of nonessential chromatic alterations within the one-sharp system. Insuch a reading, the chromatically altered tones in mm. 114–16 and parallelpassages could be seen as type B alterations creating directed motion to thefollowing sonorities. Nevertheless, the reduction shows this succession as atrue instance of juxtaposed diatonicism. The difference lies in context. Thefourth measure of the excerpt does indeed return to a sonority belongingto 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. Ifthe 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 heintroduces a second juxtaposition to the four-sharp system. This time, the

succeeding circle-of-fifths progression returns to the one-sharp system, butMonteverdi spends enough time in the new system that m. 117 is perceived inretrospect as motion to a new tonal system rather than as a series of chromaticalterations.27

This theory must allow for a certain amount of subjectivity in determin-ing whether chromatic juxtapositions will be perceived as nonessential chro-maticism or a move to an entirely new system. Factors other than harmony can

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!Example 13. Prologue with alternate continuation

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 termsof 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 par-

ticular, it does not address the issue of the relationship of

the Sprünge to the underlying tonal systems. Sprünge , likesingle chromatic tones, do not always exist for the same

reason or serve the same purpose.


28/50


influence one’s hearing of a passage; in Example 14, the change of meter andthe change from a dancelike character to a recitative reinforce the sense of juxtaposed diatonicism.28 Nevertheless, from the preceding examples we caninduce some criteria that serve to separate examples of juxtaposed diaton-icism from other types of chromaticism. First, the listener is much less likely

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to Sol i - o per sel - ve ab-ban-do-na - te so - le

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117

Example 14. Reduction of Monteverdi, Zefiro, torna (1632), mm. 113–20

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 compo-

sitions that do not sound different in melodic idiom. . . .

Conversely, a difference of genus may be assumed whena 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 chro-

maticism arises not only from the juxtaposition of unrelated

harmonies, but also from the rhythmic isolation, metrical

relationship, and position (i.e., inversion) of those harmo-nies (78–79).


29/50


to perceive a change in system if, following a potential juxtaposition, the com-poser introduces a sonority that was diatonic in the original system but wouldnot be in the new one. Such a sonority will probably not sound chromatic ina 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 differenttonal system increases with the number and duration of sonorities that belongto 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

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121

125

Example 14 (continued) Reduction of Monteverdi, Zefiro, torna (1632), mm. 121–28


30/50


that was originally nonessential can introduce a juxtaposition to a new tonalsystem. The passage begins in the three-flat system that governs most of thepiece, 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 expecta-tion of directed motion to a C-minor sonority. (It is a type A rather than atype B alteration since coming to rest on a minor seventh chord would havebeen syntactically incorrect in this repertoire.) Nothing from m. 22 resolves

as expected: The F, a chordal seventh, leaps to D and then G before resolv-ing, and when it does resolve, it moves to EΩ instead of E≤.29 Moreover, theBΩ remains in the chord instead of resolving to C.30 The harmonies that fol-low are diatonic in relation to the E-minor sonority, creating the juxtaposi-tion of the three-flat and natural systems shown in the reduction. The BΩ hastherefore changed from a nonessential chromatic pitch into a diatonic pitch.

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to Sol i - o per sel - ve ab-ban-do-na - te so - le

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mio tor

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- men - to

5

Example 15. Alternate version of Zefiro, torna

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 car-

ryover 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.


31/50


The reduction appears to violate the principle of greater simplicity by introduc-ing a cross-relation B≤ to EΩ in m. 23 that was not present before, but the reduc-tion is intended to track the listener’s expectations and perceptions, accordingto which B≤ would still be the expected diatonic tone in the three-flat system ofm. 22 and would only be supplanted by BΩ with the E-minor sonority in m. 23.

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Documents

Adams K. a New Theory of Chromaticism From the Late Sixteenth to the Early Eighteenth Century