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Tonal Function and Metrical Accent: A Historical Perspective
Author(s): William Caplin
Source: Music Theory Spectrum, Vol. 5 (Spring, 1983), pp. 1-14
Published by: University of California Press on behalf of the Society for Music Theory
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Tonal
A
Function
Historical
Metrical
and
Accent:
Perspective
WilliamCaplin
One of the most interesting and contentious issues in modern music theory concerns the way in which functional harmonic progressionsrelate to the metrical organizationof music. By functional harmonic progressions, I am referring
primarilyto the motion within a given tonal region between
tonic and dominant harmonies (and occasionally, even tonic
and subdominant).By metricalorganization,I mean the moreor-less regularlyalternatingsuccession of accented and unaccented beats (also termed strong and weak beats) at one or
more levels of musical structure.Now, at least one prominent
theorist maintainsthat there is absolutely no inherent relation
between a given harmonic progression and meter: Wallace
Berry, in his recent work Structural Functions in Music, argues
that "tonal function . . . is in and of itself metrically neutral."
For instance, the harmonic progression of Example la "is
not. . . more or less plausible" than that of Example lb.I
Example 1. Berry, StructuralFunctions in Music, p. 330
(b)
(a)
n
vt
I
I
I
11
Other theorists, however, believe that the innate stabilityof
tonic harmony naturally associates it with metrical strength.
Yet the analyticalconclusions that these theorists draw from
this harmonic-metricrelationship vary widely. Some writers
look to the progressionof dominant to tonic as a major criterion for establishingmetrical weight at higher levels of structure. For example, Carl Dahlhaus has argued that a theory of
"metrische Qualitat" (metrical quality) is based upon the
premise that "the weight of a measure is primarilyfounded in
its harmonicfunction. The tonic should be valued as 'strong'
and the dominantas 'weak.' "2Dahlhaus illustratesthis principle with the cadential progression tonic-subdominantdominant-tonic (Example 2). Inasmuch as the initial tonic
chordcan be viewed as a secondarydominantto the following
subdominantharmony, the complete progression represents
the metricalqualityof weak-strong-weak-strong.Dahlhausunderstandsthis correlationof harmonyand meter to be an analytical norm against which irregular, though not nonsensical,
passagescan be identified.3
I
lWallace Berry, StructuralFunctions in Music (Englewood Cliffs, N.J.,
1976), p. 330.
2" ...
das Gewicht eines Taktes [sei] primar in seiner harmonischen
Funktion begriindet. . . . Die Tonika soil als 'schwer,' die Dominante als
'leicht' gelten" ("Uber Symmetrie und Asymmetrie in Mozarts Instrumentalwerken,"Neue Zeitschriftfur Musik 124 [1963]:209).
3See also Carl Dahlhaus, "Zur Kritikdes RiemannschenSystems," in Studien zur Theorieund Geschichteder musikalischenRhythmikund Metrik, by
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2
MusicTheorySpectrum
Example2
A more cautious approachto the relationshipof tonal function and metricalorganizationis taken by Carl Schachter,who
admits that "downbeats and other important accents would
seem to correspondto stable tonal events." But after analyzing
what he considers some important differences between tonal
stabilityand metricaldownbeats, Schachterconcludesthat this
"analogy. . . ought not to be overdrawn,"and that "contradictions are so frequent that we can hardlyconsider them abnormalities."Indeed, Schachterpresentssome actualmusicalpassages in which "it is precisely from the conflict between accent
and tonal stability that the rhythmic effect of the excerpts
comes." (Example 3)4
An investigationinto the history of this controversialproblem reveals that a number of prominenttheorists in the eighteenth and nineteenth centuries also believed that tonal function and meter directly interrelate. Within the writings of
Jean-PhilippeRameau, Georg Joseph (Abbe) Vogler, Simon
Sechter, Moritz Hauptmann,and Hugo Riemann, we can find
importantstatements positing a definite connection between
tonic harmonyand metricalaccent. The attemptsof these theorists to describe and explain the complexities of this relationship form a fascinatingchapter in the history of music theory,
one whose contents I wish to outline here.
To begin, let us then turn to the very founding of modern
harmonictheory and examine the views of Jean-PhilippeRameau, who in his treatiseNouveausystemede musiquetheorique
introduces an important discussion of how meter can help
define the tonal function of harmonicprogressions.5Rameau
opens his remarksby observingthat when we hear a single note
as a fundamentalbass, we also imagine at the same time its
thirdand fifth. Furthermore,he claimsthat a fundamentalbass
not only generates a consonanttriad, but also gives rise to a tonality.6In isolation, an individualsound naturallyfunctionsas a
ton principal or note tonique, and the triad that is built upon
that note represents the tonal center of a key. Rameau is so
convinced of the power of a single triad to express itself as a
tonic thathe extends this capabilityto the triadsbuilton the two
other fundamental tones of a key-the dominant and the
subdominant-and thus concludes that "each of the three fundamental sounds that constitute a key can, as soon as each is
heardas a fundamental,communicateto us, in its turn, the idea
of its own tonality, since each of the sounds bears a consonant
Ernst Apfel and Carl Dahlhaus, 2 vols. (Munich, 1974), 1: 185-87. The idea
that cadentialfunctionis related to higher-levelaccentuationalso findsexpression in the views of a numberof theoristsassociatedwith PrincetonUniversity:
see Roger Sessions, TheMusicalExperienceof Composer,Performer,Listener
(Princeton,N.J., 1950), pp. 13-14; EdwardT. Cone, MusicalFormand Musical Performance(New York, 1968), pp. 25-31; Arthur J. Komar, Theoryof
Suspensions(Princeton, N.J., 1971), pp. 155, 158; Robert P. Morgan, "The
Theory and Analysis of Tonal Rhythm," The Musical Quarterly64 (1978):
444-51.
4CarlSchachter,"Rhythmand LinearAnalysis," in TheMusicForum, vol.
4 (New York, 1976), pp. 319-20.
5Jean-PhilippeRameau, Nouveau systeme de musique theorique (Paris,
1726 ; reprinted. Jean-PhilippeRameau: Complete TheoreticalWritings,ed.
ErwinR. Jacobi, vol. 2 [Rome, 1967]).
6"Sinous ne pouvons entendre un Son, sans etre en meme tems frappezde
sa Quinte & de sa Tierce,nousne pouvons, par consequent, l'entendre, sans
que l'idee de sa Modulationne s'imprimeen meme tems en nous; ..." (ibid.,
p. 37). Rameau does not expressly refer to a tonalite, a term introduceda century later by Fetis; rather, he uses the expression modulation, which in
eighteenth-centurytheory covered a variety of theoretical concepts, ranging
from simple melodic motion to the modern sense of "change of key." In the
context of the passages considered here, the term clearly refers to a single key
or tonality.
T-S-D-T
(D-T)
weak-
strong- weak-
strong
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TonalFunctionand MetricalAccent
3
Example3. Schachter,"RhythmandLinearAnalysis,"p. 321
n
d5
(a)
t
I
I
[
PI
(b)
fi
H
....
..T
I))
.,1
II tk
I
II
r?1 i-&j:IF
M
y9 Of,'
Mozart,Symphonyno. 41, Trioof Menuetto
harmony."7But now Rameau is presentedwith a difficultsituation: how can the composer create a melody, accompaniedby a
progressionof triads, that remainsin one tonality?How can he
avoid the impression of a constant, if only fleeting, change of
key? For a solution to this dilemma, Rameau appealsto the effect of meter:
soundwhosetonalityone wishesto
Theharmonyof the fundamental
introduceis insertedinto the firstbeat of the measure,becausethis
firstbeatis the mostperceptibleof all. ... however,if I wantto go
intothekeyof one of the otherfundamental
sounds,I willpreferably
assignthatsoundto the firstbeatof the measure.8
Rameau illustrateshis point with a fundamentalbass line that
representsa successionof triads(Example 4). Accordingto his
7". .. chacundes trois Sons fondamentauxqui constituentun Mode, peut a
son tour imprimeren nous l'idee de sa Modulation, des qu'il se fait entendre
comme fondamental; puisque chacun d'eux porte une Harmonie egalement
parfaite(ibid.);translationsfrom Nouveau systemeare by the author, with reference to B. Glenn Chandler, "Rameau'sNouveau systemede musiquetheorique: An Annotated Translationwith Commentary,"Ph.D. diss., IndianaUniversity, 1975.
8". . . c'est d'insererdans le premier Temsde cette mesure,l'Harmoniedu
Son fondamentaldont on veut annoncer la Modulation;parce que ce premier
Temsest le plus sensible de tous: ... au lieu que si je veux entrerdans la Modulationde l'un des autresSons fondamentaux,je lui destinerayparpreferencece
premier Tempsde la Mesure"(Nouveau systeme, pp. 37-38).
-
n) r I_
Beethoven,Sonata,op. 78
originalidea, each of these consonant chords could be considered a tonic. On account of the effect of meter, though, only
those triadson the firstbeat of the measureareperceivedas tonics, whereasthe chordson the upbeat of each measurefunction
as subdominantsor dominantswithin the keys defined by the
tonics.
Example 4. Rameau, Nouveau systeme, p. 38
[F.B.] \;J
XrJ
,J
| |
I
I
At this point in his argument, Rameau now formalizes the
notion that a tonic triadrepresentsa point of repose by terming
thismomenta "cadence."The cadentialchordis alwaysa tonic,
but the repose that it creates is made more-or-lesscomplete by
the harmony that precedes it. In the "perfect cadence," the
tonic is preceded by the dominant;the sense of conclusion, of
repose, is strongestbecause in descendinga fifth(fromthe dominantto the tonic) the fundamentalbass "returnsto its source."
In the "irregularcadences," the repose is less complete because
the tonic is now preceded by the subdominant,whose fundamental bass lies a fifth below. To exemplify these two kinds of
cadences and the significantrole that meter plays in defining
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4
MusicTheorySpectrum
them, Rameau presents another successionof triads(Example
5) along with an analysisof the cadences that are thus created.
Notice that the same series of four notes found at the beginning
of the passage-C, G, C, and F-is repeatedin the second half.
But as a resultof changingthe metricalplacementof the notes,
their respectivetonal functionschange as well. Each chord located on an accented beat becomes a tonic; indeed, Rameau
specificallystates that measures one through three are in C,
measure four is in G, and measure five, in F.9 The harmonic
analysisthat I have added below the example shows the changing harmonicfunctions.
Example5. Rameau,Nouveausysteme,p. 39
perfect
irregular irregular perfect
cadence Icadence ) cadence Icadence
[F.B.]r*
'
[C: I
| ".
V
I
IV
I G:IV
I
\
"I
I F:V
I]
Now what are we to make of Rameau's statements and examples? It is evident that he posits a definite relationshipbetween tonic harmonyand metricalaccent. And this relationship
is meant to have a genuine musicalsignificanceinsofaras meter
has the power to clarifywhich harmonyfunctionsas a tonic in
ambiguoussituationsinvolving consonant triads. But unfortunately, Rameau provides no explanationfor this effect outside
of a vague reference to a "greaterperceptibility"that a chord
acquireswhen it is placed on a metricallystrong position. Furthermore,he ultimatelymakeslittlepracticaluse of his appealto
meter in the resolutionof tonal ambiguity,for as soon as he introducesthe notion of dissonanceinto his harmonicsystem, the
need for meterto help definetonalityis largelyeliminated.Inas9Rameaudoes not clearly specify the point at which the change of key occurs, but he implies that the new key is confirmedat the downbeat of the measure and that the precedingchord is reinterpretedas either a dominant(in perfect cadences) or subdominant(in irregularcadences).
muchas a dissonantchordlacksthe necessarysense of repose to
be a tonic, the composer can mitigate the potential tonic function of a given triad by adding to it a dissonance. And indeed,
this structuralfunction of dissonance becomes such an importantpartof his theory that Rameau does not find it necessaryin
anyof his latertreatisesever againto invoke the idea that meter
can play a role in the expression of tonality. Nevertheless, despite Rameau's failure to provide any serious explanationfor
the phenomenon that he describes and the minimal
application-either compositionalor analytical-that he draws
fromhis observations,his brief remarkson the relationshipbetween tonal function and metrical accent in the Nouveau systemerepresenta significantfirstattemptin the historyof music
theory to confrontthis difficultissue of harmonic-metricinteraction. 0
Let us now examinehow, laterin the eighteenthcentury,the
rathereccentricGermantheorist Georg Joseph (Abbe) Vogler
goes much furtherthan Rameau in relatingharmonicprogressions to meter. In attemptingto discover the reason why a listener sometimes perceives a metrical interpretationthat conflictswith the notated meter, that is, the meter indicatedby the
'tHans Pischnersuggests that antecedents of Rameau's views on the relationship of tonal function and metrical accent are found in the writings of
Charles Masson and Michel de Saint-Lambert (Die HarmonielehreJeanPhilippeRameaus[2d. ed.; Leipzig, 1967], pp. 51, 124); it is difficultto verify
this claim, however, because Pischnerdoes not cite a single reference. To be
sure, Saint-Lambertdoes refer to situations that call for the accompanistto
bringa dominantseventh on a weak beat followed by a tonic on the downbeat
of the next measure, but he describes this completely in the language of thoroughbasstheory, that is, without any mentionof tonal function:"The tritoneis
accompanied by the octave and sixth when the following note descends a
fourth,being accompaniedby a perfect chordand fallingon the firstbeat of the
measure" ("Le Triton s'accompagne de l'Octave & de la Sixieme, quand la
note suivantedescend d'une quarte, 6tant accompagn6ed'un accordparfait, &
tombantsur le premiertems de la mesure.") (Michel de Saint-Lambert,Nouveau traitede l'accompagnementdu clavecin, de l'orgue, et des autres instruments[Paris, 1707;reprinted., Geneva, 1972], p. 14).
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TonalFunctionand MetricalAccent
time signatureand the bar lines, Vogler concludes that such a
problemcan be traced back to an incorrectmetricalplacement
of the harmonies.He thus formulatesa single rule for harmonic
settingsthat a composer must alwaysfollow:
Justas ... thetonictakesprecedenceoveritsdominantinimpression
andstrengthon theear,so too is thefirsteighthnotestrongerthanthe
second,andthe firstquarternote strongerthanthe second,andthe
firsthalfnoteor wholemeasurestrongerthanthe secondhalfnoteor
wholemeasure.Thetonicmustthusbelongto thestrongbeatandthe
dominantto a weakbeat.11
Here then is a remarkablestatement:Vogler describesboth
tonic harmony and metrical accent as possessing "emphasis"
and "strength,"and these common attributesprovide the link
between the two musical dimensions. Harmonic strength and
weaknessshouldcorrespondrespectivelywith metricalstrength
and weakness; in passages where this relationshipis wanting,
"the ear must be offended."12
Needless to say, Vogler'srigidrule of compositioncan all too
easily be refuted by the overwhelmingevidence offered by actual practice, where composers are clearly not bound at all by
Vogler's restrictionon the placement of harmonies. But more
interestingthan this manifestweakness in Vogler's approachis
the fact that when he tries to explain specific questions of harmonic and metricaltheory or even to criticizepassagesfrom actual compositions,Vogler consistentlymisapplieshis own principle of harmonyand meter in some respect or another.
""Gleichwie . . . der Haupton an Eindruck und Gewalt auf das Gehor
seinem fiinften vorgeht: so ist auch das erste Achtel starkerals das zweite, das
erste Viertel starkerals das zweite, der erste halbe oder ganze Schlag starker
als der zweite halbe oder ganze. Der erste Ton muBalso auf den starkenTheil
. . .und der fiinfte Ton einem schwacherenzukommen" (Betrachtungender
MannheimerTonschule2 [April-May, 1780]: 368 [394]). (The page numberin
bracketsrefers to the reprintedition [4 vols.; Hildesheim, 1974].)
12"Wennman nun an dem Plaz des fiinften Tones den ersten; an den Plaz
des ersten Tones den fiinften leget, ... so muBdas Gehor beleidiget werden"
(Tonwissenschaftund Tonsezkunst[Mannheim,1776, reprinted., Hildesheim,
1970], p. 37).
5
To take just one example, he initiallyraises the question of
how tonal function and meter relate while attemptingto justify
the traditionalrule of setting the suspension dissonance on a
strong metrical position.13Comparing Examples 6a and 6b,
Vogler notes that the former case violates the rule because the
harmoniesare poorly distributedwithin the measures: in the
firstplace, the dominantarrivestoo earlyin measureone which,
because it is an odd-numbered,and hence accented, measure,
should contain only tonic harmony; in the second place, the
tonic is incorrectlyset on the second half of measure two, because this even-numbered,unaccented measure should be occupied only by dominantharmony. Moreover, the addition of
dissonances,which"makethe strongestimpressionon the ear,"
rendersthe poor effect of the misplacedharmoniesall the more
offensive.14
It can be questioned, however, whetherVogler has correctly
accountedfor the faulty placement of both the harmoniesand
the dissonancesin Example 6a. The difficultythat Vogler encountersconcernsthe question of hierarchicallevels, for it can
be observedthat whereasthe alternationof tonic and dominant
harmoniesoccursat the level of the full measure, the succession
of preparation,dissonance, and resolution occurs at the halfmeasure level. Any statement about the misplacement of
chordsat one level, however, will not necessarilypertainto the
location of the dissonances at a lower level. This point can be
seen by placingVogler's correctedversion, Example 6b, in the
context of (say) an eight-measurephrase, such as that shown in
Example 7.
13Ibid.,pp. 35-38.
14SinceVogler does not use musicalnotation in Tonwissenschaft,Example
6 is a realizationof the tablaturesystem that he presents:
9
Example 6a:
c
Example6b:
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ggc
65985
7
CG
8
c
c
gg
43
C
G
C
6
Music Theory Spectrum
Example 6. After Vogler, Tonwissenschaftund Tonsezkunst, p. 36
(a)
(b)
I
d IJ
2
-
fJ
94 J
j4
'
J
I
j
ld
J
I
I
j_-;
'
4<
O
J-
.
r"7Jri
:
Example7
1o
3
2
I
I
d
-9
"
"
o0
(.
a'
a,
0
112
V6
C: I
4
5
,j
j
6
1
8
8
f8
13
I
After the initial tonic in measure one, all of the remaining tonic
chords fall on even-numbered, and hence unaccented, measures in violation of Vogler's principles. Yet, at the same time,
each of the dissonances is prepared on a weak beat, sounded on
a strong beat, and resolved on a weak beat, fully compliant with
the traditional rule. Therefore, Vogler's appeal to the tonal
function of harmonic progressions for explaining the metrical
location of the suspension dissonance is misdirected. The problem with the harmonic placement of Example 6a is not one that
involves whether the chords are tonics or dominants, but rather
it is the general syncopation of the individual chords, regardless
of their harmonic content, that causes the disturbance in the
passage.
The mistake of confusing hierarchical levels, as seen in this last
example, is repeated by Vogler on a number of other occasions
V
I
V
I
throughout his writings. Moreover, he often misapplies his rule
in other ways as well. For instance, in one passage he misinterprets the key in which the music is set; in another, he confuses
dominant harmony with the establishment of a dominant tonal
region. Even more interesting are several situations in which he
uses his rule (unsuccessfully, I believe) to explain the metrical
placement of chords within the circle of fifths sequence.15
Thus considering Vogler's failure to provide convincing applications of his one harmonic-metric principle, it is little wonder
that his dogmatic ideas on the relationship of tonal function and
'1Fora more complete examination of Vogler's difficultiesin applyinghis
rule of harmonyand meter, see William Earl Caplin, "Theories of HarmonicMetric Relationshipsfrom Rameau to Riemann" (Ph.D. diss., University of
Chicago, 1981), chap. 4.
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TonalFunctionand MetricalAccent
meter had little influence on succeeding theorists.16 In fact, I
have yet to discover any other theorist who goes so far as
Vogler in insistingthat tonic and dominantfunctionshave a determinatemetrical location; to do so, of course, would run directlycounter to the empiricalevidence offered by actualcompositions, where these harmonies are freely placed on any
metrical position. Nevertheless, the notion of an important
connection between tonic function and metrical accent persisted throughoutthe nineteenth century and found important
expression in the writings of three of its leading music
theorists-Simon Sechter, Moritz Hauptmann, and Hugo
Riemann. Thus, in the rest of this study, I wish to examine how
these thinkersapproachedthe problemthat had interested Rameau and so obsessed Vogler in the precedingcentury.
In his monumental treatise Die Grundsitze der musikalischen
Komposition, Simon Sechter, the foremost theorist of midnineteenth-century Austria, devotes a complete chapter to
"The Laws of Meter in Music," wherein he offers instructions
to the composer for insuringthat the downbeat of each measure is clearly articulated by the succession of harmonies.'7
Among his principles for the correct metrical placement of
chordsis one that touches upon the relationshipof tonal function and meter. In rankingthe metricaldecisiveness of various
fundamental-bassprogressions, Sechter notes, "Leaps of a
thirdare weak, but leaps of a fourth or fifth are decisive; how16Forexample, Gottfried Weber, who is highlyindebted to Vogler on many
issues, does not at all discuss any special principlesfor the metricalplacement
of tonic and dominantharmonies.
'7SimonSechter, Die Grundsatzeder musikalischenKomposition, 3 vols.
(Leipzig, 1853-54), vol. 2, chap. 1.
7
ever, leaps of an ascending fourth or descending fifth are the
most decisive."18Unfortunately, Sechter does not explain why
a descending fifth progression of the fundamentalbass is the
most powerful articulatorof metrical strength. So a complete
interpretationof his views must go beyond what he himself has
offered. Nevertheless, in one way Sechter does provide the basis for a likely explanation when he notes early in his treatise
that all descending fifths are "imitations"of the V-I cadential
progression(1:17) and specificallyshows that a dominant-tonic
relationshipis announced at each step in the circle of descending fifths(Example 8).
AlthoughSechterstopsshortof connectingsuchdominant-totonic motion directlyto meter, it is not difficultto presumethat
a notion of tonal function as an expression of metrical accent
lies at the heart of his observations. Unlike Vogler, Sechter
does not insist that all tonic harmoniesbe placed on metrically
accentedpositions. Rather, he takes a more subtle approachby
characterizingthe descending-fifthmotion of the fundamental
bass as the most metricallydecisive harmonicprogressionand
uses this observationas a guide for the composer, not as a strict
requirementof compositionalpractice.
Writingat aboutthe sametime as Sechter,butfroman entirely
differenttheoreticalorientation, MoritzHauptmannalso finds
an importantrelationshipbetween tonal function and metrical
accent. But the nature of this relationshipis difficultto interpret because of the very abstractmode of Hauptmann'sargumentation. Hauptmannformulates his theory of music from a
18"MattsindTerzenspriinge,entscheidendaber die Quarten-und Quintenspriinge;der Quartsprungaufwartsund der Quintsprungabwartssind aber am
entscheidendsten"(ibid., 2:19).
Example 8. Sechter, Grundsdtze der musikalischen Komposition,
2:26
:( rrF F
Tonic, Dominant,
I-
I F Ir -I
Ton., Dom., Ton., Dom.,
Ton., Dom.,
r
r
Ton., Dom.,
i
>
I
r
11
I
I
Ton., Dom.,
Ton., Dom.,
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Tonic, etc.
8
Music Theory Spectrum
dialectical point of view, wherein every stage in the development of a harmonic and metrical system begins from a state of
unity [thesis], to which an element of opposition [antithesis] appears; a third element [synthesis] then emerges to reconcile the
opposition and to bring into being a new state of unity at the
next stage of the system. Thus, in the case of harmony, Hauptmann finds the interval of an octave to represent unity; the fifth
creates an opposition to this unity and the third unifies this opposition, creating at the same time a new unity, the major
triad.19The metrical manifestation of the same dialectical development involves the duple meter as a unity, the triple meter
as an opposition, and the quadruple meter as a reconciliation of
this opposition (pp. 223-29).
With the statement "Meter only repeats what harmony has
already set forth," Hauptmann makes it clear that relationships
between harmony and meter are not merely incidental, but
rather, fundamental to his theory of music.20 But needless to
say, the relationship between intervals and meters that Hauptmann thus establishes is entirely abstract and devoid of any specifically musical meaning. Indeed, he expressly denies that "in
a triple meter we ought to perceive the interval of a fifth, . . .
and in a duple meter to perceive an octave, . . . and in a quadruple meter, a third.'"2 Rather, these harmonic and metric
phenomena are associated with each other by virtue of their
mutual expression of the same dialectical concept.
In addition to these three logical components of unity, opposition, and unified opposition, Hauptmann also differenti-
ates between entities that express a positive or negative unity.
For example, within his theory of harmony, a major triad is
considered to be positive, whereas a minor triad is negative (p.
34); likewise, within meter, a metrical unit made up of an
accent followed by an unaccent is positive; however, the reverse sequence, that is, an upbeat motive, is negative (pp. 24849). Like the previous relationship between harmonic intervals
and metrical quantities, this new connection of major-minor
modality with metrical accentuation is also purely conceptual,
for a meaningful musical relationship here is inconceivable:
Hauptmann is in no way suggesting that downbeat metrical motives naturally occur in a major mode or that upbeat motives
are more appropriately used in a minor mode.
When Hauptmann addresses the question of how harmonic
progressions relate to metrical organization, he once again invokes the contrasting concepts of positive and negative, the latter of which he now terms a "relative":
19MoritzHauptmann, Die Natur der Harmonik und der Metrik(Leipzig,
1853), pp. 22-23.
20"Eswiederholtsich in der Metriknur, was die Harmonikschon dargelegt
hat: . . . " (ibid., p. 291). Englishtranslationsare by the author,with reference
to Moritz Hauptmann, The Nature of Harmony and Metre, trans. W. E.
Heathcote (London, 1893).
2"So wenig uns nun zugemuthet werden soil, im dreitheilig-gegliederten
Metrum eine Klangquint . . . zu vernehmen, ebenso . . . im zweigliedrigen
Metrumeine Octav, . . und im viergliedrigenMetrumeine Terz; .. "(Harmonik und Metrik,p. 240).
22"Dieerste metrischeBestimmungist aber die der Folge eines Ersten und
Zweiten, eines Positivenund Relativen, des Accentuirtenund Nichtaccentuirten: ..
Auch die Harmoniehat im Begriffe der Folge ihr Positivesund Relatives. .
Ober- oder
.als die Beziehung eines Dominantaccords,-des
Unterdominant-dreiklang,-zu seinem tonischen Dreiklang . . ." (ibid., pp.
371-72). "Einem tonischen Accorde . . . entspricht direct das metrischPositive . . .; dem Accorde der Ober- oder Unterquint . . das metrischRelative . . ." (ibid., p. 376). Although Hauptmannsimply asserts here that
the tonic triadexpresses a positive and that the upper and lower dominantsex-
The firstmetricaldeterminationis the successionof a firstand second,
a positive and relative, an accented and unaccented .... Harmony
also has in the notion of succession its positive and relative, . . .
namely, the relation of a dominant or subdominanttriad to its tonic
triad.... The metrically positive corresponds directly to a tonic
chord, and the metricallyrelative correspondsto the upper and lower
dominants.22
Unlike the fully abstract harmonic-metric connections discussed before, the relationship of triads and accentuation that
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TonalFunctionand MetricalAccent
Hauptmannnow drawscan have a true musicalrealization,inasmuchas it is possible to associate these two musicalphenomena directlywith each other in a compositionalcontext: a tonic
harmonycan be an accented event, and a dominant, an unaccented one. But as he continues with his discussion, Hauptmann insists that all combinations of triads and metrical positions are usable in a musical work. It is not "contradictoryto
rational meaning" if a harmonic relative is combined with a
metricalpositive, or vice versa (p. 372).
Clearly, Hauptmannrealizes that an approachsuch as that
taken by Vogler is false, because tonic harmonies are not
confined to metrically strong positions. And Hauptmann is
ever carefulthroughouthis writingsto avoid makingclaimsthat
contradictmusicalpractice;indeed, he is so cautiousin this respect that it becomes difficult to assess the actual musical
significanceof the relationshipthat he findsbetween tonal function and meter. On the one hand, Hauptmannmay understand
this relationshipto be merely conceptual and thus implyingno
musicalrealizationwhatsoever;on the other hand, he mightbe
hinting that the varying metrical placements of harmony and
melody produce a perceived aesthetic effect based upon a normative connection of tonic harmony and accent. This idea is
suggestedwhen he notes that whereas the metrical placement
of triadsmay be unrestricted,the effect that they have in relation to meter is not merely neutral:
press a relative, he provides no additional justificationor explanation for his
claim. Indeed, he does not once refer to this meaningof the triadsin the entire
firstpartof his treatise devoted to harmony. Rather, in a chapteron "The Major Key," he shows how an individualtriad representsunity, how the relationship of this triad to its upper and lower dominantsrepresentsopposition, and
how the emergence of this triad as a tonic of a key representsunity of opposition (pp. 25-30). Furthermore,in chapters on the progressionsof chords and
on the cadence, Hauptmann discusses the dialectical meanings of individual
notes within the chords but makes no reference to the meanings of triads as a
whole. Consequently, Hauptmann'sassertionthat the tonic harmonyis a positive, to which the upper and lower dominantsare relative, comes as an entirely
new idea, one that he does not integrate into his general theory of harmony.
9
The same series of consonant chords may assume metricallythe most
variedforms and, thereby, can also be most manifoldlydifferentwith
respect to their inner meaning. . . . And if we continue with further
triadsin more advancedmetricalformations ... we may be led to the
greatestdiversityof harmonic-metricmeaning.23
Unfortunately,Hauptmanndoes not spell out whatsuch an "inner meaning" of harmony and meter might be. Again, this
meaningmay be purelyconceptual,in the sense of the common
meaningsharedby an octave and duple meter or that by a major
triadand a downbeatmotive. But it is also possible that Hauptmannhas in mind a more specificallymusicalmeaning, one that
informsa harmonicprogressionat the time that it obtainsa metricalinterpretation.In other words, Hauptmannmay very well
be suggestingthat we perceive varyingaesthetic effects arising
out of the many metrical arrangementsof triads. And thus by
specificallyrelating metrical accent with tonic harmony as expressinga "positive unity," the placement of this harmonyon
that metricalposition can be regarded as a kind of harmonicmetric norm against which other combinations, ones that are
nonethelessmusicallyintelligibleand aestheticallypleasing,can
be distinguished.Unfortunately,Hauptmann'sremarksremain
at such a high level of abstractionthat a definite conclusion
about the true musicalsignificanceof his ideas cannot be made
on the sole evidence of his text.
One thing is certain though: Hauptmannhimself may have
been reluctantto drawmusicalconclusionsfrom the logical relationshipthat he had established, but his most importantsuccessor, Hugo Riemann, had no such hesitation. Indeed,
Riemannlauncheshis career as a music theoristby reformulating Hauptmann's abstract conceptions into more specifically
23"DieselbeconsonanteAccordreihekann metrischverschiedensteGestalt
annehmen und wird dadurch auch ihrer inneren Bedeutung nach aufs Mannigfaltigste verschieden sein konnen. ... so wird eine fernere Dreiklangsfortsetzungin weiterer metrischerFormation. . . zu grossterVerschiedenheit
harmonisch-metrischer
Bedeutung fiihren konnen" (ibid., p. 373).
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10
MusicTheorySpectrum
musical principlesof harmonic-metricinteraction. In his very
firstpublication,a fascinatingarticleentitled "MusikalischeLogik," Riemannproclaimsthat he "will seek to carryon [Hauptmann's]theoryby beginningwhere he leaves off, namelyby applied harmony and meter."24 According to Riemann,
Hauptmanndeveloped theories of absoluteharmonyand absolute meter and, in so doing, created a gap between theory and
practicethat can be correctedonly by realizingthat "harmony
and meter go hand in hand; one requires the other."25Thus
Riemann proceeds to describe a metrical system at once in
terms of a harmoniccontext, and he establishes a relationship
between the tonic harmony of the cadential progression and
metricalaccentuationas expressions of the dialecticalconcept
of thesis. (Riemann also discussesthe harmonic-metricexpressions of antithesisand synthesis,but these remarksdo not pertainto the issue at hand.) Thus, in connectionwith the emphasis
associatedwith the firstbeat of a measure, he notes that,
Strictly speaking . . . this is not an emphasis [Hervorhebung]but
ratheronlya steppingforth[Hervortreten]....
Thusin the caseof peacefulandfullyemotionlessprogressions
of
chords,the thesis,the firsttonic,is thatwhichchieflyimalternating
pressesitselfuponus andof whichwe thereforebecomefondanddesire a return. ... I would like to call the accent of the beginningtime
elementthe theticaccent,whichis especiallywidespreadin the strict
churchstyle,butwhichcannotfreeitselffroma certainmonotony.26
24"AufMoritzHauptmannsHarmonikfussend . ., werde ich suchen, eine
Fortfuhrungseiner Theorie zu geben, indem ich da anfange, wo er aufhort,
namlichbei der angewandtenHarmonikund Metrik"("MusikalischeLogik,"
reprintedin Hugo Riemann, Praludien und Studien [3 vols.; Leipzig, 18951901],3:1).
25"Harmonikund Metrikgehen Hand in Hand, eins bedingt das andere .
"(ibid., p. 11).
ist das aber keine Hervorhebung,sondernnurein Her26"Strengenommen
vortreten;...
Bei ruhigemund vollig leidenschaftslosemFortgangedes Akkordwechsels
ist also die These, die erste Tonika das uns sich zunachstEinpragende,welches
deshalbvon uns lieb gewonnen und zuriickverlangtwird .... Ich mochte den
As Riemanndevelops this idea of thetic accent in the course
of his essay, there are some indicationsthat this logicalrelationship between tonic and accent may be purely abstract in a
Hauptmanniansense.27But a closer examinationof Riemann's
descriptionsuggests that he might also be referringto a genuinely musical connection of harmonyand meter. By mentioning the "peacefuland fully emotionless"progressionsof chords
most appropriateto a "strictchurchstyle," Riemann seems to
be describinga performancesituation that avoids any kind of
outside accentuationthat might be impartedby the performer.
Under such circumstances, the tonic chord "impresses itself
upon us," and we "desireits return."In other words, Riemann
specifiesthe appropriateconditions underwhich the tonic harmony itself would create, so to speak, its own metricalaccentuation. This idea is furtherimpliedby Riemann'sexplicit preference for the term Hervortreten over Hervorhebung: the former
carriesan associationof emphasis arisingfrom within, the latter, of emphasisimposed from without.
Despite his declared intentions to render Hauptmann'sabstractionsmore concrete, Riemann does not actuallydiscussin
this articleany practicalapplications-either for the composer,
the performer, or the analyst-that this relationshipbetween
tonal function and metrical accent might yield. But in his first
major treatise on harmony, Musikalische Syntaxis, Riemann
presentsthis same correlationof harmonyand meter in a somewhat more definite compositional and analytical context.28
Withinthe course of developing a system of harmonicdualism,
inspiredby the theories of Arthurvon Oettingen, RiemannenAccent der Erstzeitigkeit den thetischenAccent nennen, der besonders im
strengen kirchlichenStil der verbreitetste ist, eine gewisse Monotonie abcr
nichtlos werden kann" (ibid., pp. 13-14).
27See,for example, Riemann'sdiscussion(p. 18) of the rhythmthat opens
the last movement of Beethoven's Piano Sonata, op. 14, no. 2, where his reference to harmonyand meter is simply metaphoricaland not based at all on the
actualharmoniccontent of the passage.
28HugoRiemann, MusikalischeSyntaxis(Leipzig, 1877).
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TonalFunctionand MetricalAccent
counters a problem confronted by Rameau at the very beginningof harmonictheory: how can the tonal center of a progression of harmonies be determined? And like his French
predecessor, Riemann appeals to the force of meter for defining tonic function in cases of ambiguous harmonic progressions: "We must therefore come to the conclusion that in the
case of all two-chord progressions, the metrical accentuation
decides which chord is to be consideredthe actualtonic."29As
an example, he compares two differentmetricalsettings of the
same chord progression(Example 9) and notes that in the first
case, the F-majortriad is accented and thus becomes the tonic
in relationto the other chords;whereas in the second case, the
unaccented F triad is merely a "chord of mediation" and the
entire progressionshould be understoodin C major.
Example9. After Riemann,MusikalischeSyntaxis,p. 82
(a)
_
-v
. 9, ___1X
O-)
9
P*
q-6 _6
-
(b)-
-
J
I
J-
1-4
J
J
'AA
.
I'oq
I
J
r r
1,
In attemptingto account for this effect of meter, Riemann
offers an explanation that goes beyond Rameau's rather meager commentson the "greaterperceptibility"that an accentcan
impartto a chord:
29"Wirmiissen daher zu dem Schlusse kommen, dass bei alien zweiklangigen Thesen die metrische Akcentuation entscheidet, welcher Klang als der
eigentlichthetische, . . ist" (ibid., p. 79). In Syntaxis,Riemann uses the term
These to mean the establishment of a tonic through a progressionof chords.
The thetischerKlangor thetischerAkkord is the actualtonic harmony(ibid., p.
15).
11
The accented beat . . . always has precedence over the unaccented
one;. . . thatis, theunaccentedbeatappearsto followorprecedethe
accentedone andthusto be relatedto it;the accentedbeathasa similarmeaningto the tonicchordin a harmonicprogression.It is thereforeconceivablethata progressionappearsmoreeasilyunderstandableif thetonicchordoccurson an accentedbeat.30
It is interestingto observe that Riemannno longerspeaksof any
specialemphasisassociatedwith an accentedbeat andtonic harmony, but instead now refers to the common meaning shared
by these phenomena. He thus continues strongly in the tradition of Hauptmannby appealingto categories of musicalcomprehension,but even more than his predecessor,Riemannsuggests that this relationshipof tonic harmonyand metricalaccent
is an aestheticnorm, one that has at least a minimalapplication
in compositionand analysis.
Unfortunately, Riemann develops his idea no further and
does not really clarifyhow this principleof harmonyand meter
is to function within a more comprehensiveanalyticalsystem.
Indeed, in some of his later writings,he seems to reversehis positionentirelyon the relationshipof harmonyand accentuation.
In his majorstudy on principlesof musicalphrasing,Musikalische Dynamik und Agogik, Riemann proposes that the fundamental dynamic of the "metrical motive" consists first of a
steady growth, a becoming, a "positive development." This is
then followed by a passingaway, a dyingoff, a "negativedevelopment."31In more concrete musical terms, the metrical motive contains a fluctuationin tonal intensity characterizedby a
crescendo to a "dynamic climax" and a subsequent decre30"Dergute Takttheil ... hat immer den Vorzug vor den schlechten ...
d.h. die schlechtenerscheinenihm folgend oder vorausgehend,also auf ihn bezogen, er ist von ahnlicherBedeutung wie der thetische Klang in der harmonnischen These. Es ist daher begreiflich, dass eine These desto leichter verstandlicherscheint, wenn sie die Tonika auf dem guten Takttheilbringt; ..."
(ibid., p. 76).
31HugoRiemann, MusikalischeDynamikundAgogik (Hamburg, 1884), p.
11.
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12
MusicTheorySpectrum
scendo. When Riemannturnsto the issue of how harmonicprogressionsare to be expresseddynamically,we learnthat the motion from a tonic to a dominantrepresentsa harmonicbecoming, a positive development, and that the return back to the
tonic is a passing away, a negative development. Thus, "the
simpleconnectionof both factorsmust be the crescendofor the
harmonic positive and diminuendo for the harmonic negative."32As illustratedin Example 10, the dominantharmonyis
thereforedirectlyassociatedwith the dynamicclimaxof a metrical motive.
Example 10
dynamicshading:
negative
positive
T-D
-
D-T
greatestintensification
There is much evidence throughoutRiemann'streatise that
the dynamicclimax, the moment of greatest intensity, correspondsto the primarymetricalaccentof a measureas definedby
the traditionaltheory of meter. For example, Riemann notes
early in his treatise that "the bar line indicates the position of
the dynamicclimaxof the motive. The note that follows the bar
line always forms the strong point of the motive."33But if the
32". . . die schlichte Verbindungbeider Faktoren muss das crescendo fur
das harmonisch-positiveund das diminuendo fur das harmonisch-negative
sein;..." (ibid., p. 186).
33". . der Taktstrich[anzeigt]die Stelle des dynamischenHohepunktsdes
Motivs. ... Die dem Taktstrichfolgende Note bildet stets den Schwerpunkt
des Motivs" (ibid., pp. 12-13).
dynamicclimaxis meantto representa metricalaccent, then the
relationbetween harmonyand meter presented here is exactly
the opposite of that proposed in his earlier works, where the
tonicharmony,not the dominant,is linked to the accentedbeat
of a metricalunit. Has Riemann now completely changed his
view? Or can some way be found to reconcile these apparently
opposingpositions? I believe that furtherexaminationreveals
an answerto these questions.
Despite the strongevidence suggestingthat the "dynamicclimax" is Riemann's reformulationof the traditional"metrical
accent," he discusses a number of anomalous situations that
point to a fundamentalincongruityof these two concepts. For
example, in his treatmentof syncopation, Riemann firstraises
the possibilityof "displacing"the dynamic climax away from
the event following the bar line (p. 52), and he returnsto this
idea of dynamicdisplacementwhen consideringthe effects of
harmony.Thus, in some of his examples (Example 11), the dynamicclimax, which is associatedwith the dominantharmony,
is moved back from the metricalaccent, and Riemanndoes not
suggestat all that this displacementin any way upsets the basic
metricalorganization,as indicatedby the barlines.34
Thus we could perhaps conclude that, despite a number of
statementsto the contrary,Riemann'stheory of dynamicshading is not a theory of meter at all, in that it is not a theory of
metricalaccent, but ratherthat it is exclusivelya theory of performance. Therefore, the relationshipthat he draws between
harmony and dynamics must not be compared in the same
terms with his earlier speculationson the connection between
tonal functionand metricalaccent. In fact, the two apparently
conflictingpositions actually complement each other: if tonic
harmonynaturallyexpresses itself as metricallyaccented, or at
least possesses some intrinsicaccentuation,then it is unnecessary, and perhaps even undesirable, for the performerto add
34Riemannhas added the crescendo-decrescendosigns to these examples in
orderto indicatehis understandingof their dynamicshading.
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TonalFunctionand MetricalAccent
Example 11. Riemann, Musikalische Dynamik und Agogik, p. 188
(a)
Il:R
f
i i
mji.
i Ii
I
.
I I t
1f 1 II
- LT P
rrrr r U Beethoven, Sonata, op. 31, no. 1
(b)
f[
.I .'=
0=J=
V
"7
^ 4
=J
J
6^ 1-.9
Jfz
Beethoven, Sonata, op. 57
anyspecialintensificationto the tonic chord. Indeed, a more interestingand expressiveaestheticeffect would be createdby impartingdynamicstressto the dominantharmonyin orderto offset the accentscreated by the tonic harmony.
This attemptto reconcileRiemann'scomplexviews bringsto
a close my surveyof how earliertheoriststreat the relationship
of tonal function and metrical accent. The results can now be
summarizedby delineatingthe spectrumof possiblestancesthat
a theoristcan take when confrontingthis problematicissue. At
one extreme, a theorist can simply deny that any kind of relationshipexists;this would appearto be WallaceBerry'sposition
when he states that tonal function is metricallyneutral. But of
the major eighteenth- and nineteenth-centurytheorists, I have
not yet discoveredany who explicitlyreject the notion that harmonicprogressionshave metricalconsequences. This is not entirely surprising, however, because questions of harmonic-
13
metric interactionwere not sufficientlydeveloped during this
periodso that a theoristfelt himselfcompelledto treatthe topic.
It appears, then, that we have heard only from those theorists
who believed in some genuine correlationbetween these harmonic and metricphenomena.
At the other extreme of the spectrum,a theoristcan be convinced that metrical accent and tonic harmony are so powerfully interrelated that they must always be coupled in actual
musicalpractice. Such a theorist would arguethat just as a suspension dissonancemust alwaysbe placed on the downbeatof a
measure, so too must a tonic fall at all times upon a metrical
accent. This, of course, is the view advocated by Vogler
throughouthis writings, a view whose inadequaciesare so apparentas to requirelittle refutation.
Between these two extremes lies a variety of possible positions on the extent to which harmonyand meter relate and the
actualconsequencesto be drawnfrom this relationship.For example, a theorist may recognize a conceptual or metaphorical
connectionbetween the phenomena without exactly specifying
what musical results thereby arise. Thus Hauptmann relates
tonic harmonyto metricalaccent as a mutualmanifestationof a
logicalcategoryof perceptionbut specificallystates that any actual combinationof harmonicprogressionsand accentualpatternshas equal syntacticalvalidityin a musicalwork. And even
when he claimsthat varyingarrangementsof harmonieswithin
a metricalscheme yield different "innermeanings,"it remains
unclearwhetherhe is referringto a specific,musicalmeaningor
rathera general, metaphysicalone.
Less abstractare the views of Rameau and Sechter; both of
these theorists propose a relationshipbetween tonic harmony
and metrical accent that has distinctly musical consequences.
For Rameau, this correlationof harmonyand meter manifests
itself in the ability of an accent to determine tonal function in
cases of ambiguousprogressionsof consonanttriads.For Sechter, this same harmonic-metricrelationshipproducesquite the
opposite results, whereby it is the motion from dominant to
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14
MusicTheorySpectrum
tonic that is used by the composer to determine, or at least to
articulatedecisively, the intended metricalaccent.
The views of Hugo Riemann, which represent the most
complex attitudetowardthis issue, also lie between the two extreme positions mentioned before. Starting his career with
rather abstract Hauptmannian principles of musical logic,
Riemann develops an incipient notion of tonal function as an
expression of metrical accent, one that recalls Sechter's concern with the metrical articulationof harmonic progressions.
Riemannthen appliesthis idea more concretelyalong lines suggested by Rameau, wherebymetricalplacementis seen as decisive for clarifyingan ambiguoustonal function. Finally, in his
theory of musical phrasing, Riemann seems to contradictthis
relationshipbetween harmony and meter by associating the
dominantharmony,not the tonic, with the dynamicclimaxof a
metricalmotive. I suggested, however, that insofaras dynamic
climaxis not a determinantof metricalaccent, then Riemann's
apparentlyconflictingviews can actually be regardedas compatible, wherebythe inherentaccentuationof tonic harmonyis
balancedby a performedaccentuationof dominantharmony.
To conclude, the historicalevidence clearlyindicatesthat althoughsome of the most importanttheorists of the eighteenth
and nineteenth centuries recognized a significantrelationship
between tonic harmonic function and metrical accentuation,
they achievedlittle consensuson the natureof this relationship
andthe musicalconsequences-be they compositional,analytical, or generallyaesthetical-that follow from it. And as noted
at the very beginning of this study, this lack of general agreement continues to haunt present-dayinquiriesas well. I would
hope, then, that this examinationof the historicalrecordmight
help to throw into relief some of the many problems that remain to be solved and to stimulate further investigation into
this controversialissue of music theory.
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