Consonance in Tonal Jazz

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“Consonance” in Tonal Jazz: A Critical

Survey of Its Semantic HistoryJames McGowan

Published online: 24 Apr 2008.

To cite this article: James McGowan (2008) “Consonance” in Tonal Jazz: A Critical Survey of Its

Semantic History, Jazz Perspectives, 2:1, 69-102, DOI: 10.1080/17494060801949059

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‘‘Consonance’’ in Tonal Jazz: A Critical

Survey of Its Semantic HistoryJames McGowan

The terms ‘‘consonance’’ and ‘‘dissonance’’ have been subjected to a greater number

of interpretations than virtually any others in the history of music theory. Although

in a general and inclusive sense, ‘‘consonance’’ means ‘‘agreement in sound,’’ many

specific and exclusive meanings of consonance have been employed in vastly different

contexts. For one such context in particular, the analysis of tonal music, modern

scholarship in music theory has used one meaning more than others. This normative,Schenkerian understanding dictates that major and minor triads and their

constituent intervals are the only consonances. For most common-practice tonal

music up to the late nineteenth century, this view often leads to fruitful analytic

results. However, when applying the same definition to the analysis of other music

that is entirely tonal in structure and syntax, the result is problematic as some pieces

may not be comprised of any consonant chords whatsoever. This is certainly the

problem with analyzing most tonal jazz1 that consistently and idiomatically features

chords with four or more notes as syntactic resolutions from dissonant harmonies.

The three sample cases of Example 1 present an inescapable harmonic issue: how does one account for the variety of chords that are employable at moments of

consonance? This problem is intensified because most tonal music seems to employ

only triads in this role. These examples, however, feature apparently consonant tonic

chords that include ‘‘upper structures’’ beyond the triad.2 The excerpts include both

major and minor keys, taken from the beginning, middle, and end of their

performances, and are intended to represent a cross-section of tonal-jazz pieces, at

least regarding small groups featuring piano. In each case, a dominant chord

implicates the arrival on the tonic and the resulting resolution provides a sense of

repose. However, beyond the triad, these apparently consonant tonic chords also

1Martin notes: ‘‘the various styles of tonal jazz [include] the New Orleans and Chicago styles, swing,

bop, hard bop, gospel jazz, and blues.’’ See Henry Martin, ‘‘Jazz Harmony: A Syntactic Background,’’

Annual Review of Jazz Studies 4 (1988): 9. This list is not exhaustive but it does provide a useful

framework to understand the term. For the purposes of this paper, tonal jazz does not include other

styles that have been associated with jazz, particularly traditional blues (without functional harmony),

rock, and other popular musics. A compatible definition is jazz that ‘‘seeks closure,’’ as put forward by

Ajay Heble in Landing on the Wrong Note: Jazz, Dissonance, and Critical Practice (New York: Routledge,

2000), 52–60.2Steven Schenkel notes that ‘‘when [upper structures are] added to triads they strengthen the non-

resolving quality of the chords—i.e., the ability of the chord to stand alone as a complete and interesting

musical sound.’’ See Steven M. Schenkel, The Tools of Jazz (Englewood Cliffs, NJ: Prentice-Hall, 1983),

40.

Jazz Perspectives Vol. 2, No. 1, May 2008, pp. 69–102

ISSN 1749-4060 print/1749-4079 online # 2008 Taylor & FrancisDOI: 10.1080/17494060801949059


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include a chord tone of an added (major) 6th, major 7th, and minor 7th above the

root, respectively. Further, Example 1c also includes an additional major 9th

extension.3

From the perspective of traditional theory, these arrival tonic harmonies are clearly

dissonant structures, and are sometimes identified as unresolved or ‘‘frozen’’

Example 1A ‘‘Tempus Fugit,’’ Bud Powell Trio, May 1949, beginning. Cadence in D

minor. Example 1B ‘‘Isn’t It Romantic?’’ Bill Evans Trio, May 30, 1963, mm. 16–17 (firstchorus). Cadence in E-flat major. Example 1C ‘‘Ahmad’s Blues,’’ Ahmad Jamal Trio,

September 6, 1958, ending. Cadence in C major. ‘‘Tempus Fugit,’’ by Earl Bud PowellCopyright # 1949 (renewed) by Embassy Music Corporation (BMI) and Music SalesCorporation (ASCAP). International copyright secured. All rights reserved. Reprinted

with permission.

3 In jazz terminology, added sixths, ninths, and thirteenths are assumed to be major unless otherwise

specified. Thirteenths appearing in tonic chords are generally referred to as sixths.

70 ‘‘Consonance’’ in Tonal Jazz


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dissonances. This is counterintuitive to many jazz musicians who consider them to be

both idiomatic and contextually stable in tonal jazz—consonances in their own right.

Referring to such harmony as ‘‘dissonances’’ obscures the analysis of jazz as tonal

music, for it assumes that standard jazz chords serving as syntactically stable

harmonies require further resolution (which they never receive). Other theorists

evade this problem by recognizing the stability of some of these harmonies, but

conscientiously avoid using the term ‘‘consonance’’ altogether. This apologist

approach devalues the potential for meaningful analytical insight yielded by these

categories, and refuses to accept tonal jazz on its own terms.

As a solution to problems such as these, scholarly discourse about tonal jazz needs

a new conception of consonance and dissonance. Such a conception should be in line

with the venerable history of the terms and with factors specific to the musical

language of tonal jazz. Accordingly, this paper surveys the complex semantic history

of ‘‘consonance’’ and ‘‘dissonance,’’4 specifically as it is applicable to understanding

what consonance is and how it is employed in tonal jazz. Distilled from this survey,this article argues that consonance and dissonance refer to stable/passive and unstable/

active harmonic entities within the musical grammar of a distinct cultural system, as

influenced by sonorous euphony. By ‘‘sonorous euphony’’ I mean simply what

sounds ‘‘pleasant’’ when accounting for its context. The definition reflects a number

of distinct traditions of conceptions of consonance and dissonance.5

Many of the compositional features that the historic meanings of ‘‘consonance’’

sought to explain remain relevant in more recent music, and pre-existing conceptions

are juxtaposed with newer ones. Though some confusion results from using the same

term to describe very different phenomena, the semantic breadth of ‘‘consonance’’

nonetheless reflects the distinctive structural features of music in specific historical

and cultural contexts. Such is the case of tonal jazz, where all the major conceptions

of consonance and dissonance throughout time continue to be relevant in some way

4No attempt is made here to provide an exhaustive history of ‘‘consonance’’ and ‘‘dissonance.’’ Rather,

only general trends of the history of ‘‘consonance’’ are surveyed as received in twentieth-century

discourse of jazz theory. For significant surveys of the semantic history of the terms, see: Claude Palisca

and Brian C. J. Moore, ‘‘Consonance,’’ in The New Grove Dictionary of Music and Musicians, 2d ed., ed.

Stanley Sadie (London: Macmillan, 2001), 325–328; Carl Dahlhaus, ‘‘Konsonanz-Dissonanz,’’ Die

Musik in Geschichte und Gegenwart , vol. 5 (Bärenreiter Kassel, 1994–99), 565–577; James Tenney, A

History of ‘‘Consonance’’ and ‘‘Dissonance’’ (New York: Excelsior Music Publishing, 1988); Norman

Cazden, ‘‘The Definition of Consonance and Dissonance,’’ International Review of the Aesthetics and Sociology of Music 11 (1980): 123–168; David E. Cohen, ‘‘Metaphysics, Ideology, Discipline:

Consonance, Dissonance, and the Foundations of Western Polyphony,’’ Theoria 7 (1993): 1–86; H. F.

Cohen, Quantifying Music (Dordrecht, Holland: D. Reidel Publishing Company, 1984); William A.

Sethares, Tuning Timbre Spectrum Scale, 2d ed. (London: Springer Verlag, 2005), especially chapter 5

‘‘Consonance and Dissonance of Harmonic Sounds’’; David Huron, ‘‘Consonance and Dissonance:

The Main Theories,’’ http://www.music-cog.ohio-state.edu/Music829B/main.theories.html (accessed

November 30, 2004); Geza Révész, ‘‘The Consonance Problem,’’ in Introduction to the Psychology of

Music, trans. G. I. C. de Courcy (Norman: University of Oklahoma Press, 1954; reprint, Mineola, NY:

Dover, 2001), 77–94; R. Plomp and W. J. M. Levelt, ‘‘Tonal Consonance and Critical Bandwidth,’’

Journal of the Acoustical Society of America, 38 (1965): 549–552.5A more thorough exploration of these conceptual traditions can be found in James McGowan,

‘‘Dynamic Consonance in Selected Piano Performances of Tonal Jazz’’ (Ph.D. diss., University of

Rochester, 2005).

Jazz Perspectives 71


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to the analysis of its tonal structure. But with at least one additional significant

feature—harmonic extensions in jazz—a new musical language is created that

necessitates an original, more relevant conception of consonance. The present paper

thus proposes that a systemic understanding of consonance and dissonance for tonal

jazz is needed, which includes a pluralism of meanings but is specific to the

contextual concerns of individual jazz practices. In this way, we can offer a resolution

to the semantic dissonance of the history of ‘‘consonance’’ in tonal jazz.

From variable understandings of ‘‘consonance,’’ to variable conceptions about

tonality in different jazz styles, to the variability of the object of analysis itself, there

are a plethora of issues that must be confronted in dealing with the problem of

consonance (and dissonance) in tonal jazz. But as David Cohen observes:

Consonance and dissonance must surely be counted among the concepts that haveexercised a particularly powerful, even a determining, influence on the theory andpractice of music in the Western world. They have always stood among the

foundational principles, the indispensable categorieses of discourse and practice, of European polyphony, from its historical origins in the ninth-century Enchiriadis theory of organum to the theories of Schenker and his followers, and the great tonalworks to which they apply.6

The opening section of this article critically examines different conceptual

dichotomies—contextual/universal, horizontal/vertical, sensory/musical, and fixed/

variable—which are found in the literature that addresses ‘‘consonance.’’ The use of

this paper’s pluralist meaning of consonance is then supported in a survey of both

successful and unsuccessful semantic precedents within the discourse of jazz theory,

especially pedagogical and Schenkerian-oriented jazz theory. The article concludes by

supplementing the technical meaning of consonance with metaphoric meaning,demonstrating that ‘‘consonance’’ and ‘‘dissonance’’ have both specialized and broad

implications for interpretation and possible analytical applications.

Conceptual Dichotomies in the History of ‘‘Consonance’’ and ‘‘Dissonance’’

Within ancient Greek music theory, there were significant differences of opinion

regarding the nature of consonance. The Pythagoreans (followers of Pythagoras in the

fifth century B.C.E.) believed that consonance was objectively based in simple ratios of

the numbers 1 through 4. Applied to acoustics, these ratios correspond to intervals of a

perfect fourth, fifth, octave, twelfth, and double octave, as found in the overtone series.They believed that this Natural Law theory 7—consonance arising from simple ratios—

was universally applicable to all music (as well as manifest in other disciplines, such as

astronomy), and this belief formed a core component of their spirituality.8 Aristoxenus

(third century B.C.E.) rejected the quasi-religious foundation of the Pythagorean

6Cohen, ‘‘Metaphysics,’’ 2.7Cazden, ‘‘Definition,’’ 146.8They also believed that the same ratios governed these intervals formed in any vibrating medium (e.g.,

solid bodies, stretched strings, vibrating air columns, and ‘‘the heavens’’), which, while not true, was not

disproven until the Renaissance critique of ancient science. See Claude V. Palisca, Humanism in Italian

Renaissance Musical Thought (New Haven: Yale University Press, 1985), 166–178.



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conception of consonance in favor of a conception grounded in human sensory

perception. He relied on ‘‘judgment of the ear’’ to distinguish between consonant and

dissonant intervals subjectively. This Aristoxenian theory of aesthetics is thus grounded

in the musical practice of his contemporary culture, though Aristoxenus never really

spells out that practice in detail, and it is therefore subject to variation within different

musical systems that existed at different times.9 Despite these conceptual dichotomies,

however, both ideologies are substantially in agreement over which specific intervals

are consonant.10

While Pythagorean and Aristoxenian understandings have continued in different

guises within the discourse of music theory up to the present time, so have differences

of opinion as to the viability of both.11 Accepting simple ratios as universal

determinants for consonance is untenable since there are some notable musical

contexts that contradict it.12 One example of an important criticism of Natural Law

theory demonstrates that the interval of a perfect fourth, a simple tuning ratio of 4:3,

is normally treated as a dissonance in triadic tonal music. Another common criticismof Natural Law theory is its ineffectiveness in accommodating the minor triad as

musically equal to the major triad. The Aristoxenian alternative, however, creates a

9 It is safe to say that Aristoxenus surely was unaware of how other musical traditions and cultures

functioned. Without too much of a stretch, however, one could assert the claim with the benefit of

present-day hindsight.10The consonance of the eleventh is one detail on which they did not agree. West provides a good

introduction to issues in ancient Greek music theory (and consonance and dissonance in particular)

M. L. West, Ancient Greek Music (Oxford: Clarendon Press, 1992), especially 218–253. For an overview

of the conceptual differences between the Pythagorean and Aristoxenian understandings of intervallic

consonance, see Lawrence M. Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analysis

(Oxford: Oxford University Press, 2002), 6–16.11Fred Lerdahl and Ray Jackendoff seem to argue for a Natural Psychological Law theory instead of a

Natural Law theory. They write: ‘‘the fact that certain trends appear among simpler tonal systems (for

example, the frequent use of small-ratio intervals as points of harmonic stability . . . ) suggests the

possibility of an innate system of preferences among tonal systems analogous to the principles of

markedness in phonological systems of language.’’ Fred Lerdahl and Ray Jackendoff, A Generative

Theory of Tonal Music (Cambridge: MIT Press, 1983), 296. Interesting examples of jazz theorists making

reference to Natural Law theory can be found with George Russell’s seminal work (in his preference for

the acoustically supported #4 in the Lydian tonic as opposed to the natural-4), as well as more recent

incarnations such as Norm Vincent’s exposition on Lydian-Dominant theory. George Russell, The

Lydian-Chromatic Concept of Tonal Organization: The Art and Science of Tonal Gravity, vol. 1, 4th ed.

(Brookline, MA: Concept Publishing, 2002); and Norm Vincent, ‘‘Lydian-Dominant Theory forImprovisation,’’ http://www.lydiandominant.com/theory/lydian-dominant_theory.html (accessed

February 26, 2006). Cazden counters the claim of ‘‘musical universals’’ by stressing that the perception

of consonance is solely the propriety of cultural practice and not linked to any psycho-acoustic

phenomena—a claim from which he backpedaled in later writing. Norman Cazden, ‘‘Musical

Consonance and Dissonance’’ (Ph.D. diss., Harvard University, 1947), 2; and Cazden, ‘‘The

Definition of Consonance and Dissonance.’’12Even the very notion of ‘‘simple ratios’’ is problematic because intervals have different ratios in

different tuning systems. The major third and minor third are 5:6 and 4:5 in just tuning, but 64:81 and

27:32 in Pythagorean tuning. These differences can partially account for why the thirds were classified as

dissonances in ancient Greek theory and consonant in Renaissance theory with just tuning. Gioseffo

Zarlino’s version of a single explanatory system for consonance was the senario, an extension of the

tetraktys, that allowed ratios of numbers up to 8, thus including just major and minor thirds. Tenney,

History, 50–52.



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different problem. Relegating the determination of consonance to the subjectivity of

one’s ear seriously undermines its use as a term with any substantive meaning.

Taking both the universality of simple ratios and context of culture into consideration

offers a more balanced approach to consonance. Further, some studies have shown that

there is some correspondence between subjective perception of consonance and simple

ratios.13 Norman Cazden asserts ‘‘consonance and dissonance in tonal music are

functional moments or dynamic configurations that operate on a systemic level,’’ but he

also acknowledges that ‘‘the striking evidence favoring the Natural Law theory’’ plays a

role in perceiving relative consonance and dissonance within historical and cultural

systems.14 This present study’s definition of consonance is a modification of Cazden’s

systemic approach, designed specifically for the musical characteristics of tonal jazz. The

need for a unique definition arises because the terminology and discourse of musical

consonance reflect the compositional priorities of specific musical languages. This

understanding thus needs to recognize the role of simple ratios as found in the core

harmony of tonal jazz, along with the tempered surrogates of the simple ratios, butallows for dynamic variation in the harmonic dialects of the musical language.

Another important dichotomy exists between consecutive and simultaneous

musical relationships. James Tenney offers five different conceptions of consonance

and dissonance (CDCs) that have existed in music-theoretical discourse from the

period of ancient Greece to the early twentieth century. Briefly, the conceptions

classify consonance and dissonance based the following criteria: CDC 1 – melodic

intervals; CDC 2 – simultaneous dyads; CDC 3 – contrapuntal treatment of intervals;

CDC 4 – harmonic triads; and CDC 5 – acoustical tonal color. Tenney’s CDC 1 (the

Ancient Greek conception) differs from CDCs 2–5 in that his first conception is theonly one that is exclusively melodic.15 As Western music developed into a primarily

polyphonic art, discourse about consonance and dissonance reflected this new

priority of vertical structures.16 By the common-practice period, a prevailing

conception of consonance was that of a note’s agreement with a chord (CDC 4). As

such, a note is shown either to be part of or distinct from a triad, which is conceived

13For an overview, see Palisca and Moore, ‘‘Consonance,’’ 326–327.14Cazden, ‘‘Definition,’’ respectively 162, 148. As discussed below, Cazden does not go far enough,

however, in accommodating sensory consonance to his systemic approach. Conversely, Lerdahl and

Jackendoff’s claim of innate musical universals, including the cognition of tonal hierarchy, do notsufficiently accommodate idiom specificity. Lerdahl and Jackendoff, Generative Theory, 278–301.15Tenney, History. Tenney’s definitions of CDCs 2 and 4 do not exclusively involve simultaneous

relationships, but unlike CDC 1, they can (and are most often used to) describe dyads and triads.

Tenney proposes that CDC 1, as all the conceptions, continues to be used in modern times. This can be

evidenced in Paul Hindemith’s ‘‘Series 2’’ ranking of consonance and dissonance. Paul Hindemith, The

Craft of Musical Composition, bk. 1, trans. Arthur Mendel (New York: Associated Music Publishers,

1942).16One could postulate that the rise of each new conception of consonance was precipitated by a

significant change in musical practice. For example, CDC 2 developed as a result of the rise of dyadic

music, CDC 3 developed as a result of contrapuntal practice in polyphony, CDC 4 due to the

development of harmony, and CDC 5 due to the increased recognition of the contribution of tonal color.

The rise of tonal jazz thus necessitates a suitable revision of the concept of consonance. See Tenney,

History.



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either as a collection of consonant intervals or as a consonance itself. Understanding

the chord itself (originally, the triad) as a consonance ultimately originated in Jean-

Philippe Rameau, but its first incarnation as an explicit reference is found in the work

of Moritz Hauptmann.17 Hauptmann’s ‘‘directly intelligible intervals’’ point to an

understanding of the chord as consonance by Karl Mayrberger and, most completely

and influentially, by Hugo Riemann.18

However, even when consonance refers to simultaneous collections of notes in

tonal music, the horizontal dimension is still relevant. Rameau, for example,

conceived of ‘‘consonant progression’’19 as a fundamental bass progression by

consonant intervals, ultimately leading to the tonic. David Cohen notes:

Many modern theories of tonal harmony [including those by Schenker andRiemann] invoke the structural power of the tonic to explain the perceivedneed of even the consonant dominant triad to progress to tonic, exploiting amodern distinction between the merely acoustical consonance of major and

minor triads and the contextual consonance that ultimately belongs only to thetonic.20

Thus, this unusual aspect of CDC 1 has a relationship to the directed motion of

CDC 3. In CDC 3, intervals that are designated as dissonant require resolution to

consonant intervals, just as the Aristotelian philosophical axiom states ‘‘the imperfect

seeks its perfection.’’ But beyond the fact that dissonances being imperfect simply

‘‘tend toward’’ perfection (consonances), as Cohen notes, ‘‘the imperfect thing strives

by nature toward a particular , specific perfect thing; more precisely, it strives toward,

or seeks, the state of being that represents its own perfection with regard to some

specific imperfection’’ (emphasis in original).21

Thus, the horizontal dimension isdiscernible not only in chord progressions that lead specifically toward tonic, but also

in the proper resolution of dissonant verticals.

While little need exists for a theory to accommodate tonic chords greater than

triads in common-practice music, there is most certainly a need in the tonal-jazz

repertoire. Wolf Burbat writes:

In the European musical tradition, a fourth tone was added to the subdominantand dominant chords . . . These are called characteristic dissonances, since thefunction of each (in the context of classical music) is recognizable from the chord

17See Dale A. Jorgenson, ‘‘Moritz Hauptmann of Leipzig,’’ in Studies in the History and Interpretation of

Music, vol. 2 (Lewiston and Queenston: Edwin Mellen Press, 1986), 113 ff.18This is discussed in Robert Wason, Viennese Harmonic Theory from Albrechtsberger to Schenker and

Schoenberg (Rochester: University of Rochester Press, 1995; orig. pub. Ann Arbor: UMI Research Press,

1985), 100–101; Karl Mayrberger, Lehrbuch der musikalischen Harmonik (Pressburg and Leipzig: Gustav

Heckenast, 1878). For an overview of Riemann’s understanding, see Alexander Rheding, Hugo Riemann

and the Birth of Modern Musical Thought (Cambridge: Cambridge University Press, 2003), especially

52–5.19Tenney, History, 65.20David E. Cohen, ‘‘‘The Imperfection Seeks Its Perfection’: Harmonic Progression, Directed Motion,

and Aristotelian Physics,’’ Music Theory Spectrum 23 (2001): 140, see fn. 4 in particular.21Cohen, ‘‘The Imperfection Seeks Its Perfection,’’ 146.



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alone, independent of context. A major triad with added sixth was automatically asubdominant, one with added seventh a dominant. In jazz things are not so simple,since the sixth can be added to a tonic chord, and the seventh as ‘‘blue note’’ can beadded to any function.22

With the increased use of harmonic tensions in dissonances in both classical and

popular music at the end of the nineteenth century and into the beginning of the

twentieth, resolutions also moved beyond the basic triad. In a recent paper dealing

with the phenomenon of dissonant tonics, Daniel Harrison suggests:

consonance could be relativized without damaging the tonal-system environment.In other words, tonics could be made from chords that were more consonantrelative to non-tonics, but not necessarily triads. This accomplishment, of course,goes hand-in-glove with the well-known increase in dissonant chord formationsduring the nineteenth century; increasing levels of dissonance allow a higher settingof the consonance band to maintain the same rough absolute distance between‘‘imperfect,’’ non-tonic and perfect, ‘‘tonic’’ sonorities, the perfection of the latter,

in essence, being defined down.23

Although he did not write this specifically with jazz tonality in mind, it is nonetheless

very appropriate to tonal jazz. Jazz is, after all, a form of twentieth-century music. The

predictability of the jazz cadence, resulting from the use of common 12-bar blues

and 32-bar song forms, has encouraged harmonic developments to occur in the

vertical dimension more so than to the harmonic structure in the form of pieces. But

the ‘‘setting of the consonance band’’ does not occur in an ad hoc manner; rather

there is some sense that resolutions occur in appropriate balance to the degree of

tension.

Since Hermann Helmholtz’s groundbreaking work in psychoacoustics,24 a concep-

tion of sensory consonance was based upon the euphony of individual sonorities. This

conception is vastly different from musical consonance, since it does not consider

syntax. David Butler effectively defines these two meanings of consonance:

1. Sensory consonance, or euphony: the absence of acoustical interference in the

form of beats or roughness generated by two or more tones.

22

Wolf Burbat, Die Harmonik des Jazz, 4th ed. (Munich: DTV and Bärenreiter, 1994), trans. RobertWason (New York: Scarecrow Press, forthcoming), 10. The term ‘‘characteristic dissonance’’ originates

in Jean-Philippe Rameau, Treatise on Harmony, trans. Philip Gossett (New York: Dover Publications,

1971; originally published 1722). Burbat’s portrayal of characteristic dissonances in classical music

harmony is an oversimplification, particularly in the context of his analytical approach based in function

theory as influenced by Riemann. For more on Riemann’s use of the term ‘‘characteristic dissonance,’’

see Scott Burnham, ‘‘Method and Motivation in Hugo Riemann’s History of Harmonic Theory,’’ Music

Theory Spectrum 14 (Spring 1992): 5–7.23Daniel Harrison, ‘‘Dissonant Tonics and Post-Tonal Tonality,’’ a slightly modified version of a paper

read at the Music Theory Society of New York State, April 28, 2002, http://pantheon.yale.edu/,dh287/

research/DisTonic.pdf, p. 2 (accessed November 30, 2004).24Hermann Helmholtz, On the Sensations of Tone, trans. Alexander J. Ellis (New York: Dover

Publications, 1954). Note that acoustics and psychoacoustics differ in that the latter deals with the

perception of acoustics by the listener ‘‘in the ear.’’ Tenney calls this sense CDC 5.



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2. Musical consonance: the learned impression that a musical tone or chord serves

well as a stable point within a musical composition, based on tonal context. 25

Cazden criticizes the use of sensory consonance , claiming that it is not beneficial for

understanding how music functions, and is of use only in a pre-musical setting of

intonation. Tenney counters Cazden’s argument by noting that the ‘‘‘non-functional’

sense is supported by an enduring historical tradition—beginning in the ninth

century,’’26 to which Helmholtz’s work effectively belongs. The dichotomy between

these two very different understandings of consonance appears to be firmly entrenched.

Many scholars have tried to resolve the definitional ambiguity of consonance and

dissonance, believing that clarity may result if the concepts are assigned distinctive

names. Carl Stumpf 27 retained Konsonanz for its psycho-acoustic sense (where for

him it represents the purity of specific two-tone combinations) and designated

Konkordanz for its contextual sense of harmonic resolution (‘‘concordance and

discordance applied to the embodiments of chordal action that were perceived to

operate on the higher level of functional harmony’’).28 Shown in Table 1, Cazden lists

several other early proposals for terms corresponding to these distinctions.29 But

despite many attempts at new terminology, none have caught on. Excepting for the

occasional use of definitional modifiers to specify meaning, ‘‘consonance’’ continues

26Tenney, History, 99. He is referring to CDC 2, which characterizes consonance in terms tonal

blending and fusion.27Carl Stumpf, ‘‘Konsonanz und Konkordanz,’’ Beiträge zur Akustik und Musikwissenschaft 6 (1911):

116–50.28Cazden, ‘‘Definition,’’ 151.

Table 1 Dualism of Terminology (from Cazden).

I [psychoacoustics] II [contextual / functional] [Source]

Euphonie Dynamie Choron, de la FageEufonia Dinamia Basevi

Consonance physique Consonance esthétique RenaudKonsonanz – Dissonanz Harmonie – Disharmonie WundtKonsonanz – Dissonanz,Konsonanzempfindung

Konkordanz – Diskordanz,Harmoniegefühl

Stumpf

Konsonanz Objectiv, Konsonanzgefühl Harmonie Subjektiv, Harmoniegefühl HennigDissonanz Auflösungbedürfnis Jonquièreakustischer Konsonanz – Dissonanz harmonischer Konsonanz – Dissonanz Louis, ThuilleDissonanzkonstatieren Dissonanzbehandlung Kurthconsonanza acustica consonanza armonica GentiliSensorial consonance Aesthetic consonance Guernsey Einfach – Kompliziert Harmonieführung Deutschakustische Konsonanz musikalische Konsonanz Nüll

29 Ibid., 152.

25David Butler, The Musician’s Guide to Perception and Cognition (New York: Schirmer, 1992), 224. This

study focuses on ‘‘chord’’ as opposed to ‘‘musical tone,’’ but otherwise concurs with these definitions.

The term ‘‘sensory consonance’’ was first employed by E. Terhardt and is equivalent to ‘‘tonal

consonance’’ used by Plomp and Levelt. E. Terhardt, ‘‘Pitch, Consonance, and Harmony,’’ Journal of

the Acoustical Society of America 55 (1974): 1061–9; and Plomp and Levelt, ‘‘Tonal Consonance.’’



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to be used today to account for everything from perfect intervals to tonic harmony,

and from ratios of small numbers to aesthetic beauty.

Despite this dichotomy, Claude Palisca and Brian Moore observe that the different

meanings commingle and create a dynamic understanding:

‘‘Musical consonance’’ is related to judgments of the pleasantness or unpleasant-ness of sounds presented in a musical context; it depends strongly on musicalexperience and training as well as on sensory consonance. These two aspects of consonance are difficult to separate, and in many situations judgments of consonance depend on an interaction of sensory processes and musicalexperience.30

Carl Dahlhaus reinforces this argument, declaring: ‘‘A consonance is an interval

determined by its fundamental nature and (not or) tradition.’’31 The systemic

conception of consonance advocated here embraces Dahlhaus’s pluralistic view, but

applies it to a sonorous collection of any cardinality of tones, not just intervals. I

believe that a useful understanding of tonal structure for tonal jazz recognizes that theeuphony of the individual sonority is directly connected with harmonic syntax in a

dynamic relationship between dissonant and consonant functions. As a result, the

perception of consonance is contingent upon the realization of harmonic expectation

as contextually appropriate in chordal membership, intervallic configuration, and

sonorous euphony. For example, a Herbie Hancock chord voicing will likely sound

out of place in a Fats Waller solo.

Over the centuries, Natural Law theory has been used to justify consonance both as

a fixed identity as well as a variable. Fixed identities are evident in the Pythagorean

sense (with ratios comprised of one through four), the contrapuntal sense (thedistinction among perfect consonances, imperfect consonances, and dissonances in

CDC 3), and the harmonic sense (only the triad is consonant). The latter case is

particularly evident among some proponents of Schenkerian theory.32 Others

disregard arguments for consonance based upon the ‘‘chord of nature,’’ but they

30Palisca and Moore, ‘‘Consonance,’’ 326.31Dahlhaus continues: ‘‘Fundamental nature, which constitutes a necessary (but not wholly sufficient)

condition of consonance, is the gradation of intervals according to degree of sonority that can be

measured in three ways. [These are: simplicity of ratios; fusion between pitches sounding together; and

coincidence of overtones.] Consonance is dictated by nature in that only higher degrees of sonority canbe consonances; but consonance is based on tradition and history in that the number of degrees of

sonority classified as consonances, as well as the reasons for their classification as such, are variable.’’

Excerpt from an unpublished translation by James McGowan and Elizabeth Sander of Dahlhaus,

‘‘Konsonanz-Dissonanz,’’ 566.32

Schenker writes: ‘‘The human ear can follow Nature as manifested to us in the overtone series only up

to the major third as the ultimate limit; in other words, up to that overtone which results from the fifth

division. This means that those overtones resulting from higher subdivisions are too complicated to be

perceived by our ear, . . . the overtones, 7, 11, 13, 14, etc., remain totally extraneous to our ear.’’

Heinrich Schenker, Harmony, ed. and annotated by Oswald Jonas, trans. Elisabeth Mann Borgese

(Cambridge: MIT Press, 1978), 25. Disciples of Schenker continued this line of thought, as seen , for

example, in Adele T. Katz, ‘‘Heinrich Schenker’s Method of Analysis,’’ The Musical Quarterly, 21 (July

1935): 311–29. For criticism on philosophical grounds, see Jamie C. Kassler, Music, Science, Philosophy:

Models in the Universe of Thought (Aldershot, UK: Ashgate Publishing, 2001), 225–40.



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agree that the major and minor triads (or their constituent intervals) are the only

consonances in common-practice tonality.33

Interestingly, tuning ratios have also been used to denote variable degrees of

consonance34 by theorists in the middle ages (such as John of Garland’s

categorization of dyads, evident in Tenney’s CDC 2), by Hindemith (his

categorization of intervals, especially his Series II), and by evolutionary theorists

such as Jacques Chailley (who recognized the expansion of the harmonic palette of

‘‘consonances’’ based on the overtone series throughout music history).35 These

traditions are connected with the sense of consonance as a sonic quality in the

complex harmonic tone, but there is also an element of subjectivity here in

determining the point in the continuum at which a sound is considered to be a

consonance or a dissonance.

The assertion of fixed values for consonance is only tenable when considering

examples from a closed and otherwise distinct system, such as the musical languages

of ancient Greek modality, Renaissance polyphony, and common-practice tonality.Without such a system, variable values for consonance are inevitable. This is

especially clear by analogy with spoken and written languages. When distinct

historical and regional linguistic groups are identified, aspects of their language can

be confidently identified as fixed values. But if the language under consideration is

actively undergoing linguistic change, fixed values cannot be asserted with

confidence; the accuracy of these values will still be changing and linguistic

differences may exist without a clearly defined boundary. Beyond this, spoken

language is particularly susceptible to variance even within a cultural group due to

the spontaneous nature of its use.Since jazz is often characterized by the fluid nature of its collective creation and

communication, the musical experience is already unpredictable. Fixed values can be

asserted for some aspects, since tonal jazz is in many ways a discrete musical

language; one could argue that after the mid 1960s, there was little innovation in

tonal jazz and explorations of tonal structure resulted in new musical languages (such

as modality, atonality, polytonality). But in other respects, the fluid cultural dynamics

of tonal jazz practice results in mutable values. Thus, the definition proposed in this

paper suggests that in tonal jazz there are inherently stable chord tones that form the

fixed triadic core of harmonic consonances, and there are also contextually stable

chord tones that appear as variable members of consonances. When these two

components are taken together, this results in a collection of chord types that serve a

common harmonic function. One could refer to these chordal varieties as harmonic

‘‘dialects,’’ continuing an analogy of the study of musical languages to the study of

33See, for example, Matthew Brown, ‘‘Rothstein’s Paradox and Neumeyer’s Fallacies,’’ Intégral 2

(1998): 95–132.34See the explanation of ‘‘consonance’’ in Dahlhaus, ‘‘Konsonanz-Dissonanz’’; cf. translation of article

in fn. 31, above.35See Tenney, History; Hindemith, Craft ; and Jacques Chailley, Historical Treatise of Harmonic Analysis,

trans. Sidney Kleinman (Paris: Alphonse Leduc, 1986).



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language.36 Determination of the contextually stable chord tones is therefore one of

the main analytical pursuits that can follow from this study.

Relativity and ‘‘Dissonance’’ in Jazz Parlance

In jazz parlance, an important facet of musical structure is relative stability. Both

consonance and dissonance are commonly qualified with an adjective that tries to

capture the degree to which it is stable or unstable. (Qualifiers can be attached to an

interval, a note in relation to a chord, or the chord itself.) A classic example of this

relativity, the triadic dialect is considered by many to be more stable than the major-

seventh dialect (which certainly has more tonal ‘‘roughness’’), even though it may be

less stylistically appropriate.

What is certainly apparent among the jazz-pedagogical sources is that they

generally discuss ‘‘dissonance,’’ in its relative sense, much more than ‘‘consonance,’’

in any sense. For example, Kenneth Stanton writes: ‘‘The harmonic interval of theMajor Ninth . . . is not dissonant enough to warrant altering the 11th,’’ and he later

refers to intervals that are ‘‘significantly dissonant.’’37 Examples of Ted Pease and Ken

Pullig’s references to dissonance include ‘‘a mildly dissonant effect ,’’ ‘‘strong

dissonance,’’ ‘‘more dissonant,’’ and ‘‘maximum dissonance.’’38 Similarly, Bert

Ligon uses the phrase ‘‘absurdly dissonant’’ to describe a final chord in a big band

chart—an octatonic collection, stacked in thirds.39 Although not limited to discourse

in jazz theory,40 the use of adjective qualifiers is a common rhetorical strategy in such

discourse to address the consistent relativity of dissonance in the music. This strategy

is useful to describe sonorities in musics with a ‘‘higher setting of the consonanceband,’’ as noted earlier by Harrison.

The primarily pedagogical sources of jazz theory, such as those sampled above, use

‘‘dissonance’’ to refer to more than simply degrees of tension, but rather a variety of

phenomena. Some authors use more than one meaning of dissonance, usually

without explicit definition. Gordon Delamont defines dissonant ‘‘in the sense of

instability,’’ where ‘‘any chord that contains one or more (of these) dissonant

intervals will be a dissonant chord.’’41 Fifty-eight pages later, however, he allows the

36

For more on dialects as a possible application to the study of jazz harmony, see James McGowan,‘‘Understanding Jazz Styles through Sociolinguistic Models,’’ Discourses in Music 4 (Fall 2002),

http://www.discourses.ca/v4n1a1.html (accessed January 14, 2008).37Kenneth Stanton, Jazz Theory: A Creative Approach (New York: Taplinger Publishing, 1982), 64 and

68.38

Ted Pease and Ken Pullig, Modern Jazz Voicings: Arranging for Small and Medium Ensembles

(Milwaukee: Hal Leonard, 2001), 70, 70, 93, and 118.39Bert Ligon, Jazz Theory Resources: Tonal, Harmonic, Melodic and Rhythmic Organization of Jazz, vols. 1

and 2 (Milwaukee: Hal Leonard, 2001), 475.40See, for example, Edward T. Cone, ‘‘Sound and Syntax: An Introduction to Schoenberg’s Harmony,’’

Perspectives of New Music 13 (Autumn-Winter 1974): 26 and 35. Here, Cone employs phrases such as

‘‘mild dissonances’’ and ‘‘hyper-dissonant’’ in relation to dissonant (non-triadic) ‘‘normal’’ sonorities in

the early music of Schoenberg.41Gordon Delamont, Modern Harmonic Techniques, vol. 1 (Delevan, NY: Kendor Music, 1965), 58.



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other meaning of relative tension to appear when he comments on an especially spicy

example of jazz voicing: ‘‘A chord with only one ‘sharp dissonance’ in it will be more

biting than a chord containing only ‘mild dissonance,’ and the above voicing has

TWO sharp dissonances!’’42 Bert Ligon employs both fixed and variable meanings of

dissonance as well—first in the conventional sense as an unstable interval requiring

resolution and then as meaning a tense, colorful sonority; in one case he even does so

in the same sentence. In describing the motion of a ii7 to V#11, he writes: ‘‘If it [the

chordal 7th] resolves up, the dissonance is compounded by the unexpected ascension

and the resolution to the very dissonant #11.’’43 In an extreme case, Richard Lawn

and Jeffrey Hellmer use five different meanings for the terms creating significant

semantic ambiguity.44 In the studies of jazz by its pedagogues and practical theorists,

terminological specificity is generally not a concern. In most cases, however, the

context of the passage makes clear the particular meaning in use, even though the

terms are not specifically defined. For instance, Ligon uses consonance and

dissonance to refer to (1) the relationship between a given note and either a chordor another note (e.g., a ‘‘very dissonant’’ #11th over a minor triad, and a ‘‘relatively

consonant’’ 6th above a major triad); (2) the quality of a sonority (‘‘it can create a

vague and dissonant sonority’’); and (3) the functional identity of a harmony

(‘‘chords progress away from the tonic chords to other chords of relative dissonance

. . . [—i.e.,] to other diatonic chords or modulations to close or remote keys . . . —

and then return to re-establish the tonic at the end’’).45 Still, in this and other

sources, consonance and dissonance seem to be most consistently used in the sense of

a relative quality.

In its relative sense, the degrees of dissonance exist within a continuum—aharmony can be more or less tense. Therefore, this ‘‘dissonance’’ is partly the result of

the intervallic configuration of a particular chord, in which the presence of more

unstable intervals (in the sense of acoustic harshness) creates a more dissonant chord,

but which is qualified by cultural criteria. Two examples of how jazz theorists have

42 Ibid., 116.43Ligon, Jazz Theory Resources, 211.44Richard J. Lawn and Jeffrey L. Hellmer, Jazz Theory and Practice (Los Angeles: Alfred Publishing,

1993). The five uses include: (a) in introducing intervals, they categorize them into the standardized

binary distinction of consonant versus dissonant (p. 2); (b) they later use a different meaning of color whenthey comment that ‘‘the 6th provides no real added dissonance or tension to the major triad’’ (p. 24); (c)

in other parts of the book, they again use dissonance to describe an intervallic quality within a chord

(p. 28), but soon follow this in reference to chord quality (p. 30); (d) later still, they use the term

‘‘consonance’’ not to refer to intervals or a sonorous quality but rather to mean whether a note agrees

with a particular chord (p. 44); and, finally, (e) they burden the term ‘‘consonance’’ even further when

suggesting what notes to play in a given minor harmony in chord/scale theory: ‘‘The melodic minor scale

. . . is a good choice because it includes a major 6th and is, therefore, also consonant with the minor 6/9

chord ’’ (p. 52).45Ligon, Jazz Theory Resources, 212, 372, and 394, respectively. Although it is clear in what senses Ligon

uses the terms by context, in a broader sense all the meanings refer to one all-embracing view that

dissonance represents some form of relative tension and consonance represents some form of relative

stability. Different meanings thus interrelate with each other to create a deeper and more dynamic

understanding, as noted earlier in the citation of Palisca and Moore, ‘‘Consonance,’’ 326.



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rated the degree of dissonance are found in the works of William Russo and Henry

Martin.46 For his system of jazz arranging, Russo organizes dissonant intervals based

on an adaptation of Hindemith’s classification of intervals in his Series 2.47 Martin

creates relative values for intervallic dissonance when he subdivides dissonant

intervals into ‘‘modal’’ and ‘‘dissonant’’ intervals, designating major 2nds, minor

7ths, and the perfect 4th as modal and effectively ‘‘less dissonant.’’48 Martin’s

approach is clearly syntactic but moves away from the strict contrapuntal laws as

determined by the traditional fixed values. Both systems of categorization by Russo

and Martin seem to feign objectivity, despite being subjective interpretations of

musical aesthetics.49 Nonetheless, they can be used as general guidelines of one aspect

of musical style, as they do correspond to rough gradations of tension in harmonic

sonorities in the various jazz styles.

Just as dissonance can have degrees of tension, so can consonance, which is suggested

as early as the writings of the medieval theorist John of Garland. Martin has developed a

somewhat ad hoc method of rating consonance on a formalized ‘‘sliding scale’’ based onintervallic content. White also proposes a numeric consonance rating for any style of

music that is superficially objective. Despite its apparent potential, it does not offer a

systematic approach to assigning numeric values. Attempts such as these that grapple

with the issue of variable degrees of stability 50 are useful to identify the problem but offer

little or no real advantage to simply using adjective-qualifiers (which the theorists of the

middle ages did in CDC 2). Further, they can make the inherently subjective process of

musical analysis even more complicated than it already is.51

Since both dissonance and consonance are relative in the same manner, they can be

positioned at polar ends of the same scale. Palisca and Moore refer to thisphenomenon as the ‘‘consonance–dissonance dimension,’’ admitting degrees of both

within the same continuum.52 In this present understanding of relativity, dissonance

corresponds to tension and consonance to its release, such that a consonant chord

can be positioned between the poles yet remain mostly stable. In this interpretation,

consonant chords can have a range of unstable qualities and yet still be placed in the

consonant side of the spectrum of tension and stability. However, a chord that would

46William Russo, Jazz Composition and Orchestration (Chicago: University of Chicago Press, 1968), 32–

4; and Henry Martin, ‘‘Seven Steps to Heaven: A Species Approach to Twentieth-Century Analysis and

Composition,’’ Perspectives of New Music 38 (Winter 2000): 129–68.47See Hindemith, Craft .48Martin, ‘‘Seven Steps to Heaven,’’ 138.49Similarly, original counterpoint laws have been shown to have some basis in Natural Law but are not

entirely founded upon it. Cazden, ‘‘Definition,’’ 137–40.50

Martin, ‘‘Seven Steps to Heaven,’’ 148–51; and John D. White, The Analysis of Music (Metuchen, NJ:

Scarecrow Press, 1984), 15.51Measuring consonance and dissonance has had a modicum of success in the field of sensory

consonance, although this success has not taken musical consonance into context. See, for example,

Plomp and Levelt, ‘‘Tonal Consonance,’’ 556–7; and Akio Kameoka and Mamoru Kuriyagawa,

‘‘Consonance Theory, Part II: Consonance of Complex Tones and its Calculation Method,’’ Journal of

the Acoustical Society of America 45 (1969): 1460–9. The relevance of sensory consonance is addressed

below.52Palisca and Moore, ‘‘Consonance,’’ 325.



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otherwise be consonant may have significant characteristics that add tension and

bring about its reinterpretation as a dissonant chord.53

Most of the sources cited above emphasize the discussion of dissonance, in its

many semantic contexts, as opposed to consonance. In some studies, including those

by Kenneth Stanton, and Pease and Pullig cited earlier, the word ‘‘consonance’’ is not

even mentioned. The avoidance of the term may result from an unwillingness to

define it or an unstated assumption that chords are consonant unless asserted

otherwise. Still, the bias towards ‘‘dissonance’’ seems to arise from the preference jazz

musicians have for colorful, complex harmony of all functions over simple triads, and

their continuing attempts to describe these phenomena.

It is interesting the way many of these authors emphasize how ‘‘dissonance’’ (in its

qualitative sense) is a good and desirable thing. Mark Levine writes: ‘‘Dissonance is not a

pejorative term; it’s a musical device you can use when appropriate.’’54 Andrew Jaffe adds:

‘‘We should not assume that music that seems unduly dissonant to us is bad, but rather

approach it with an appreciation for the fact that it reflects a different system of musicalvalues in which a higherdegreeof . . . dissonancemay bea part.’’55Scott Reeves emphasizes

this embrace of dissonance when, discussing improvisation choices, he writes: ‘‘The tonic

(or first note) is so consonant that it lacks tension and color.’’56Whilepartlyunderstoodin

terms of its functional need for resolution, acoustic dissonance in jazz sonorities is a

desirable quality in itself, something to seek out as more musically interesting than

consonance. Many writers in jazz theory freely use both understandings. These

conceptions are borne out of jazz musicians’ unequivocal reliance on sound color for

personal expression, balanced by the tension and release that moves music forward. In this

realm, ideas of sonorous ‘‘dissonance’’ may even be necessary ingredients to consonance.

When considering the semantic history of consonance and dissonance in classical

music and the history of theory, this preference for tension or ‘‘dissonance’’ is quite

unique.57 The perception of the role and even value of ‘‘dissonance’’ epitomizes a

57David Cohen writes that ‘‘Boethius clearly associates dissonance with those sounds that are explicitly

non-musical.’’ Cohen further notes that it is not the word dissonance that is rejected, but he says that ‘‘it is

the very idea that there could be any legitimately musical phenomenon that is not also consonant.’’ While

this semantic and philosophical stance is quite extreme within the history of the terms, the root of this

bias against dissonance is part of an ideology that has flourished until recently. Cohen also writes that our

current ‘‘normal view’’ of the relationship of dissonance to consonance is based on the work of Schenker,

‘‘for whom the ‘organic unity’ of the musical masterwork consists precisely in the dialectical interplay by

which the ‘unity’ of consonance is activated and actualized via its temporal prolongation through

dissonance.’’ This so-called ‘‘normal view’’ realizes the accidental nature and ‘‘‘intrinsically’ secondary

status of dissonance with respect to consonance.’’ Cohen, ‘‘Metaphysics,’’ 68, 7. Yet Rameau suggests

that the role of dissonance is not discounted as insignificant, only imperfect, as he writes: ‘‘far from

dissonance being an embarrassment in composition, it facilitates its course.’’ Rameau, Treatise, 217.

56Scott D. Reeves, Creative Jazz Improvisation (Englewood Cliffs, NJ: Prentice Hall, 1989), 1.

55Andrew Jaffe, Jazz Theory (Dubuque, IA: Wm. C. Brown Company, 1983), 14. This comment also

anticipates dialects of consonance as a means to explain the differing complexity allowed in consonant

chords in different musical contexts.

54Mark Levine, The Jazz Theory Book (Petaluma, CA: Sher Music, 1995), 41.

53By analogy in the discipline of sociolinguistics, this is similar to issues with the classification of

linguistic varieties within a dialect continuum; when recognizable deviation occurs, varieties are typically

classified differently. Although determination of language or dialect types is grounded in observable data,

decisions of classification are ultimately based in interpretation.



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dichotomy between classical and jazz concepts. The use of the term in its positive

application for the jazz perspective provides contrast to the often negative connotation in

the classical perspective. Lubet writes: ‘‘The critical difference [in harmony] is, however,

not in the root progressions, but in the jazz tendency to extend virtually every chord,

including the tonic, to at least the seventh, while the ultimate goal of tonal [European]

harmonic progression must always be the absolutely stable pure major or minor triad.’’58

That ‘‘dissonance’’ or tension can be desirable, existing within a spectrum of instability

and harmonic expressiveness, is clearly evident in jazz musical thought. For example, the

works of Duke Ellington and the pianism of Thelonious Monk often contain a great deal

of dissonance, by any definition. Continuation of this line of thought reveals that a very

stable consonance is typically less desirable than a chord that is more ‘‘colorful.’’

Pedagogical Discourse about Consonance in Jazz Theory

Pedagogical (and speculative) publications in jazz theory 59

provide ample discussion of idiomatic jazz chords, and these rarely include simple triads. While their use of the word

‘‘consonance’’ is often ad hoc and semantically inconsistent (as discussed above), there are

enough examples for us to garner a general understanding of how each author interprets it.

The best way to determine what a consonance is in these sources is to examine their often

plentiful musical examples, even when these are contrived excerpts. In this way, these

publications tend to emphasize the major-seventh sonority as the most suitable consonant

chord.Withinmajor-keycontexts,60thesechordsareassociatedwithtonicandsubdominant

harmony, and the more thorough sources highlight the stability of the M7th on tonic

harmony in particular—consonance via syntax and sonority. Lawn and Hellmer write:

The Ima7 chord, or tonic chord, is, of course, the harmonic resting place for thecomposition, or in the case of a ii–V7–I progression of chords, the final destinationfor the cadence. The I chord typically signifies the end of a cadence; once this chordis reached, there is no momentum to move to another chord, particularly since thequality of the chord is a major 7th.61

Without explicitly saying that major sevenths are consonant harmonies, their

implication is that the chordal 7th is a requirement of the sonority in order for it to

be suitable for the functional status of tonic, and thereby providing proper tonal closure.

Pease and Pullig hold the view that notes a M7th above the root are chord tones, and

58Lubet, ‘‘Body and Soul,’’ 173.59Henry Martin uses these terms in reference to practical approaches to jazz theory designed to improve

performance and/or composition (including improvisation and arranging) of the lay musician.

Pedagogical writings generally address basic questions like ‘‘what notes, in addition to the ones of the

chord, are melodically compatible with that chord and are stylistically appropriate?’’ By contrast,

speculative jazz theory presents the student with a system or method so that, ideally, they could

eventually determine on their own what notes to play. See Henry Martin, ‘‘Jazz Theory: An Overview,’’

Annual Review of Jazz Studies 8 (1996): 7–8.60More discussion in the jazz pedagogy texts is given to major-key harmony with the good reason that

the majority of tunes in the tonal jazz repertoire are in major keys. Some texts also treat minor-key

harmony as transformed from the process of modal mixture.61Lawn and Hellmer, Jazz Theory and Practice, 89.



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they support this claim by referring to ‘‘tensions’’ (9ths, 11ths, and 13ths)62 as: ‘‘the

upper structure extensions of seventh chords. They are called tensions because they

create intervallic dissonance.’’63 If the seventh chord is the true consonance in jazz, then

it would have a status comparable to the role(s) of the triad in common-practice theory.

The reliance on the 7th chord, as seen in Lawn and Hellmer, is generally not the

only harmonic option for tonic chords cited in these books. The following passages

are useful in recognizing other options for the tonic, as well as their status as

compared with the 7th chord:

Another sonority that functions as a tonic chord is the 6/9 chord. This chord’sstructure often does not contain a 7th. Although the chord is fundamentally of major quality, its identity and function are somewhat obscured due to the absenceof a major or minor 7th. Identity is established through function, and, in mostcases, the 6/9 chord functions as a variation of the tonic.64

In most cases, major seventh chords are interchangeable with major sixth chords.

65

Chords shown on lead sheets as ‘‘major 7th’’ chords don’t necessarily have to havea major 7th. Quite often a pianist or guitarist will voice what’s shown as CD on themusic as C6, C9/6, or C #4.66

In each of these passages, Lawn and Hellmer accept the added 6th as a chordal

substitute for the major 7th but they still prefer the latter chord, mostly irrespective of

melodic content. Both chords are accepted in these sources as relatively stable entities

that can function as tonic.

A few, admittedly older books reverse their preference for the ideal harmonic

consonance in favor of the added 6th.67 For example, Stanton writes: ‘‘In jazz, thesixth will be added to the tonic chord to create a modern Major sound’’68 (underlined

64Lawn and Hellmer, Jazz Theory and Practice, 89-–90. 9/6 chords are often referred to as 6/9 chords in

jazz theory. But to maintain a logical system of nomenclature in this study, all higher numbers are placed

first and/or above other Arabic numbers (6/9 is the only common signature that does not already

conform to this convention).65Lawn and Hellmer, Jazz Theory and Practice, 13.66Levine, Jazz Theory Book, 289. The indication #4 is generally less common than #11, used to

describe the same phenomenon.

62Strunk defines a tension as ‘‘a pitch related to a structurally superior pitch (usually a chord tone) by

step, such that the tension represents and substitutes for the structurally superior pitch, called its

resolution, in the register in which it occurs.’’ See Steven Strunk, ‘‘Bebop Melodic Lines: Tonal

Characteristics,’’ Annual Review of Jazz Studies 3 (1985): 97–98. However, this definition is far from

universally accepted. Jaffe, for example, refers to tensions and extensions as synonyms, where extensions

are simply successive thirds stacked over a triad, without judgment as to their structural function. See

Jaffe, Jazz Theory, 49. Although there is general agreement about ninths and higher, there is some

dispute regarding whether scale degrees 6 and 7 are tensions, largely due to one’s definition of the‘‘tension,’’ not aesthetic judgment.63Pease and Pullig, Modern Jazz Voicings, 11.

67Delamont, Modern Harmonic Techniques, vol. 1, 52 and 62, addresses the subject of harmonic functions

with strict adherence to traditional (triadic) theory, although he recognizes added 6ths and 7ths, and

prefers the 6th for jazz usage. He also includes a few examples that present added-sixth chords.68Stanton, Jazz Theory, 21.



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emphasis in the original). He continues, ‘‘sixth chords will be applied only when the

use of a Tonic [I] chord is needed.’’69 (He employs sixth chords in minor in the same

way.) Stanton allows sevenths and other extended harmonies to be used (‘‘In

performance, when the jazz player reads the chord symbol for a Major Sixth chord, it

is traditionally understood that the Major 7th and 9th may be added’’70), but calls

7ths, 9ths, 11ths, and 13ths (so called when a sixth appears in a 7th chord) unresolved

tensions . Unlike the previous books cited, Stanton’s book identifies these tensions as

‘‘color’’ tones that ‘‘want to resolve.’’71

Some sources demonstrate by example that relatively stable harmony can be found asanything from simple triads to 11th chords, as seen in Pease and Pullig.72 Daniel

Ricigliano explains why different sonorities are available to serve as tonic harmony:

a) The major sixth or seventh is added to the major triad when more color is desired. . . .The major sixth chord is a somewhat more relaxed sound while the major seventh chordcreates more tension . b) The melody often may determine which tone is chosen.73

While he whets our appetite with insights, he leaves some significant questions

unanswered. Are these sonorities truly equivalent if one ‘‘color’’ is more tense than

another, despite being of the same function? Why are sonority choices limited to the

three illustrated in Example 1 and not others? Certainly germane to his discussion of theformer question is the issue of voicing and voice leading, which Ricigliano does not

address satisfactorily.74 Most importantly, like so many other authors of method books,

he does not provide any rationale for membership in the set of stable sonorities.

George Russell not only provides additional sonority possibilities for tonic, as

illustrated in Example 2, but also provides ample, if questionable, justification for

their acceptance.75 He allows six members of the tonic or ‘‘Lydian Mode I’’ chord

family: the major triad, added 6th, major 7th, major 9/7, and major #11/9/7 (he

also puts forward a Major 7/b5 which is just a subset of the previous complex

Example 2 George Russell’s relative Major Chord Family for Lydian Mode I.

69 Ibid., 22.70 Ibid., 62.71 Ibid., 61.72Pease and Pullig, Modern Jazz Voicings, 12–13.73Emphasis added. Ricigliano, Popular and Jazz Harmony, 125.74The topics of voicing and voice leading will be discussed with regard to the present definition of

‘‘consonance’’ in articles currently in preparation. See also McGowan, ‘‘Dynamic Consonance,’’

especially chapters 3 and 4.75See Darius Brubeck, ‘‘1959: The Beginning of Beyond,’’ in The Cambridge Companion to Jazz, eds.

Mervyn Cooke and David Horn (Cambridge: Cambridge University Press, 2002), 191–3; and two

articles by Mark Haywood, ‘‘The Harmonic Role of Melody in Vertical and Horizontal Jazz,’’ Annual

Review of Jazz Studies 5 (1991): 109–20, and ‘‘Exploring the Ramifications of George Russell’s Lydian

Chromatic Concept,’’ unpublished manuscript.



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chord).76 He states: ‘‘The major scale resolves to its tonic major chord. The Lydian scale

is the sound of its tonic major chord.’’77 Russell argues for the inclusion of #11, since

his model scale is the Lydian mode, not the major mode. Limitations for inclusion in

the collection of possible chords are due to factors of style and voicing.78

The #11 chord, and to a lesser degree chords with added 9ths, are typically

referred to as those adding ‘‘color.’’ For example, Ligon suggests that ‘‘extending the

Cmaj7 chord to the #11 brightens the sound beyond a normal resolution to

major.’’79 In some cases, the terms ‘‘tension’’ and ‘‘dissonance’’ also enter the

characterization, such as Reeves’s comment that ‘‘each additional chord tone adds

color and tension to the harmony,’’80 and Ricigliano’s statement that ‘‘the tones

presented in this chapter (especially 9ths and 11ths) may be added whenever the

reader desires more color, tension, or a thicker texture than is provided by the use of

triads, sixth, or seventh chords.’’81 Through musical example and indirect comments,

#11 is supported by some as being at least possible as a choice for a stable tonic if not

truly a consonance. Levine writes: ‘‘You can change a major chord (as in CD) to aLydian chord (CD#4) virtually any time. . . . Playing the #4 on a major chord is like

adding ice cream; it’s a cool sound.’’82 Note that in minor, chords with the natural

11th are also permitted because the potent minor-9th clash with the natural 3rd

found in major keys does not occur.

The final possibility for a tonic harmony that is cited in some sources is that of the major

triad with minor 7th(major-minor 7th). In fact, in jazz notation all7th chords are assumed

to have the minor seventh unless indicated otherwise. While most texts rightly observe that

such harmonies generally function as dominants, they can also serve as tonics within a

prevailing blues sonic environment. Burbat writes: ‘‘It is interesting that [in blues] not only the dominant is played with minor 7th (as usual), but also the tonic and subdominant.’’83

In discussing the development of blues progressions, Lawn and Hellmer note:

It was not long before the somewhat limiting V7-IV7-I7 cadence in the final fourmeasures [of a traditional blues progression] was replaced by the basic buildingblock of jazz and popular harmony, the ii7-V7-I progression. The tonic quality remained a dominant 7th as was the case in the first measure of the progression.84

78These factors of style and voicing are addressed in numerous sources in jazz theory pedagogy. Two

classic sources for jazz piano include John Mehegan, Jazz Improvisation, vols. 1–4 (New York: Watson-

Guptill Publications, 1959–65); and Bill Dobbins, The Contemporary Jazz Pianist , vols. 1–4 (Jamestown,

RI: GAMT Music Press, 1978).79Ligon, Jazz Theory Resources, 379.80Scott D. Reeves, Creative Beginnings (Upper Saddle River, NJ: Prentice Hall, 1997), 295.81Ricigliano, Popular and Jazz Harmony, 149.82Levine, Jazz Theory Book, 289.83Burbat, Harmonik des Jazz, 15.

76Emphasis in original. Burbat, in his Table 1, also enumerates possible chord choices for tonic,

including the same options as well as other combinations. See Burbat, Harmonik des Jazz, 8.77

George Russell, The Lydian-Chromatic Concept of Tonal Organization for Improvisation (New York:Concept Publishing Corp, 1959; reprint 1964), iv.

84Lawn and Hellmer, Jazz Theory and Practice, 170. This is echoed by Mark Levine who adds an

historical generalization that other harmonic qualities are possible (as tonic) in the blues from the bebop

period on. Levine, Jazz Theory Book, 220.



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Some writers acknowledge (while others only imply) that a prevailing blues idiom

will allow a tonic to be played with a minor 7th and still be conclusive.85 A few often

earlier sources, however, determinedly adhere to a view that such blues tonics are not

stable or consonant, nor do these harmonies provide effective endings. For example,

Avril Dankworth writes: ‘‘Instead of finishing on the tonic chord, the added blue note

gives the inconclusive effect of ending on a chord of the seventh.’’86 Comments like

this from the 1960s demonstrate an unwillingness to recognize blues dialects as

participating as consonant tonics within a tonal jazz language.

Examples 3A and B, presented by Burbat as his Examples 5-1B and 5-13,

demonstrate that a tonic sonority in the blues may be either a major-minor 7th or the

more conventional jazz harmony of the added 6th or major 7th. Example 3A

specifically features major-minor 7th chords that function as stable tonic harmonies.

Example 3B rightly interprets most major-minor 7th chords as dominants or as

applied dominants in a prevailing context of added 6/9 chords (aside from the F7 IV

chords). The examples also demonstrate the idiomatic use of extensions of a 9th andhigher, and feature Riemannian function-theory labels (T5Tonic; S5Subdominant;

D5Dominant; Sp5Subdominant-parallel; and [D]5secondary Dominant).

Other possibilities for tonic are discussed in some books. One often cited possibility

features a #5 in the chord, usually with the major 7th. In such examples, however, it is

clear that this tonic variant is not used as a stable harmonic arrival, but subsequently leads

either to a subdominant chord or stable tonic by resolving the #5 to another chord tone.

Referring to the latter situation, Levine writes: ‘‘Jazz musicians often resolve Lydian

augmented chords (that is, major #5 chords) to the unaltered major 7th chord by

lowering the #5 back to a natural 5th . . . [or raising it] upward to the 6th,’’ as shown in

Example 4.87 Perhaps because of its ambiguous symmetrical structure, a chord with an

augmented triad is not used as a stable arrival harmony in tonal jazz (this also holds true

for fully diminished seventh chords).88 Inversionally symmetric structures can

85Addressing the evolution of consonance in classical music, Chailley writes: ‘‘Finally, we may note a

recent phenomenon, widely put to use in jazz around 1920, by virtue of which the [interval of a] minor

7th, with certain precautions (notably its remoteness from the final chord), comes to lose its sense of

dominant 7th and is integrated into the tonic chord without leading it toward a modulation to the

subdominant.’’ Chailley, Historical Treatise, 46.

87Levine, Jazz Theory Book, 291.

86Avril Dankworth, Jazz: An Introduction to its Musical Basis (London: Oxford University Press, 1968),

31. This belief is also expressed in Ricigliano via musical examples in his book published one year earlier.

Ricigliano, Popular and Jazz Harmony, 87.

88This paper assumes that there is a scale-degree limitation on #5 and that it does not appear in a

consonance. The #5 (and its enharmonic equivalent b6) will not likely appear as a chord tone when the

#5th is present in the chord; the root, 3rd, and 5th are inherently stable chord tones in tonal music and

thus appear (or are implied) in all consonant harmonies. Some influential jazz pedagogues are emphatic

that the resultant minor 9th is prohibited as too harsh an interval in most jazz. See Coker, Improvising

Jazz (Englewood Cliffs, NJ: Prentice Hall, 1964; Touchstone, 1986), 24. This belief is echoed in more

recent sources, including Levine, Jazz Theory Book. Also relevant when consonances are added-sixth

chords, the effect of #5 in the chord (assuming the real or imagined presence of #5) would create two

simultaneous consecutive semitones. For discussions of this constraint, see James Kurzdofer,

‘‘Outrageous Clusters: Dissonant Semitonal Cells in the Music of Thelonious Monk,’’ Annual Review

of Jazz Studies 8 (1996): 184–185; and Dmitri Tymoczko, ‘‘The Consecutive–Semitone Constraint on

Scalar Structure: A Link between Impressionism and Jazz,’’ Intégral 11 (1997): 135–179.



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conceivably be interpreted as relatively stable in more recent, less tonally conceived

examples of jazz harmony. With this in mind, one could speculate that hearing #5 as

contextually stable acknowledges the evolutionary limit to tonal jazz. Extended tonality

ceases to be controlled by functional harmony when the perfect fifth of the triadic core inany stable chord is altered.

Jazz-pedagogical sources typically associate stability with tonic function, although

each source presents its own possibilities for allowable chord choices, undoubtedly

because of changing styles over the years.89 That harmonic stability and consonance

are interconnected becomes very clear in the writings of two very influential jazz

theorists, Andrew Jaffe and David Liebman. Jaffe states: ‘‘Two terms [consonance and

dissonance ] are used to refer to the extremes of harmonic stability and instability

Example 3A Wolf Burbat’s Example 5-1B, using major-minor (Mm) 7ths.Example 3B Wolf Burbat’sExample 5-13, where major-minor 7ths are dominant functioned.

89 In this paper, it is assumed that consonant harmony is usually tonic, though not necessarily vice versa.



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within an individual chord or a chord progression .’’90 Liebman agrees: ‘‘Contextually,

cadence means the use of a relative consonance, called a tonal anchor, to offset the

more dissonant chromaticism [of the dominant].’’91 Harmonic interest is often

drawn to complex harmonies (typically extended dominants), which ultimately need

to resolve to a harmonically stable tonal center. What is not clear, however, is what

harmonic entity can constitute a suitably stable harmony, or ‘‘relative consonance,’’in a given musical context. Many sources cite more than one harmonic possibility for

tonic, but generally provide little explanation as to why or how one is selected. For

example, Ricigliano states that ‘‘these [tonic] chords may be extended with additional

color tones without destroying the function of the original chord.’’92 This remark

suggests that different possibilities for consonant sonorities exist but no contextual

framework is offered to explain.

This article’s emphasis on tonic harmony in the discussion of consonance is

consistent with existing jazz pedagogy for the most part. Still, a functional context of

harmony is rarely prominently featured in discussions of consonance and dissonance

or comparable semantic pairings, such as stability and instability.93 The word‘‘consonance’’ in many jazz-pedagogical publications generally implies the harmonic

presentation of a collectional bias towards Ionian mode (with an ‘‘avoid tone’’), or

Lydian mode in the case of Russell and his followers. Chord/scale theory, now

commonly included in pedagogical texts, dictates that different modal collections are

used for different harmonic contexts, for example, Dorian mode for ii chords.94 This

approach is less effective for musical situations where chords other than major-

sevenths are used on tonic, such as a blues major-minor 7th, because tonic is

normally associated with Ionian or Lydian modes, not the Mixolydian mode. It also

does not provide a distinction for functional differences between I7 and IV7, whichtypically share the same collection (when both use the Lydian mode). Chord/scale

90Emphasis added. Jaffe, Jazz Theory, 14.91

David Liebman, A Chromatic Approach to Jazz Harmony and Melody (Rottenburg, Germany: Advance

Music, 1991), 13.92Ricigliano, Popular and Jazz Harmony, 145.93This topic will be addressed by this author in an article currently in preparation, with a working title of

‘‘Hierarchic Harmonic Function in Tonal Jazz.’’94Gonda sums up the value of chord/scale theory by expressing that ‘‘it is not really the single chords

which are important, but the functional movement embodied in the progression.’’ Janos Gonda,

‘‘Problems of Tonality and Function in Modern Jazz Improvisation,’’ Jazzforschung/Jazz Research 3/4

(1971–1972): 204.

Example 4 Mark Levine’s example of Lydian augmented chords as tonic.



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theory is helpful, however, in providing a framework for distinguishing between

playing ‘‘inside’’ and playing ‘‘outside,’’ the latter creating an additional level of

dissonance. Beyond this, chord/scale theory has little impact upon consonance in its

syntactic sense, where a tonic arrival of any chord creates a sense of stability and

repose when presented in a cadence.

With the possible exception of dominant-functioned sonorities (because of their

inherent need for tonal resolution), any chord can create a brief moment of

consonance at a surface level of structure. This is achievable by sonorous analogy to

stable chords (i.e., similar chord structures to tonic chords), by local tonicizations

(e.g., secondary dominants of ii instead of a vi chord), or both. Chords other than

tonic can be experienced as relatively consonant, particularly subdominant chords.95

(It is also important to note that many tonic chords do not, in fact, function

syntactically as consonances.) Additionally, consonant chords can have a variety of

voicings—in seconds (clusters), thirds (common tertian), fourths (quartal), or

combinations of these—or chromatic variants such as #4 and b7, as in the acousticcollection (e.g., C-D-E-F#-G-A-Bb).96 Despite such an array of choices, an audience

will be able to perceive moments of consonance with a wide range of chords, if and

when the performer projects syntactic resolution. This point is suggested, but not

made explicit, in most pedagogical texts.

What is especially ambiguous in these pedagogical books, and in jazz theory as a

whole, are the specific roles played by chordal extensions. Gary Campbell asks his

students to explore combining root-position major triads with triadic extensions to

‘‘encounter varying degrees of consonance and dissonance.’’97 In another example,

Trent Kynaston and Robert Ricci comment: ‘‘A plain C7 chord has the samedirectional potential as a C7 (#11/9), although the latter contains more tones of

activity and tonal embellishment.’’98 Situations abound in which some extensions, as

tensions, need to resolve; others are relatively stable but are functionally extraneous

color tones; and still others are stable and seem to function as members of the

underlying chords. How does one distinguish among these situations? Are there

95 In my dissertation, I argue that the functional mixture of tonic and subdominant harmony in some

closing chord towers can also serve as consonant sonorities, albeit complex ones and only in certain

contexts. McGowan, ‘‘Dynamic Consonance,’’ 198–207.96

The acoustic collection is obviously rooted in the overtone or harmonic series. Stable yet complex jazzchords often evoke the overtone series in both pitch collection and voicing (wide intervals in the lower

register, smaller intervals in the upper). However, I do not believe that a strict observance of the overtone

series is particularly ben

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Consonance in Tonal Jazz