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Harmony and Meter in the Theories of Simon SechterAuthor(s): William Earl CaplinSource: Music Theory Spectrum, Vol. 2 (Spring, 1980), pp. 74-89Published by: University of California Press on behalf of the Society for Music Theory

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Harmonya n d M e t e r in t h e Theories o f

S i m o n Sechter

by WilliamEarlCaplin

A recent exchange of views in Die Musikforschung has

brought into focus a major, unresolved question in the history of

music theory: is the interrelation of pitch and rhythm treated

more consciously and thoroughly by eighteenth-centurytheorists or by nineteenth-century theorists? Gudrun Henneberg

argues that an integration of all musical parameters, including

rhythm, underlies the theories of Sulzer, Kimberger, and Koch

and that their conception opposes the tendency of nineteenth-century theorists to construct absolutist systems of the kind

developed by Moritz Hauptmann and Hugo Riemann.' Wilhelm

Seidel, on the contrary, claims that eighteenth-century theorists

generally hold an aesthetic of "pure" rhythm, whereby the

actual pitches do not participate in creating the rhythmicaleffect. And he credits the major nineteenth-century figures,

again Hauptmann and Riemann, with having incorporated more

' Die Auffassung,dereinzelneFormungsfaktorei inderMusikderKlassik

dem Sinnganzen integriert, widersprichtder Tendenz zu verabsolutierender

Systembildungin der Theorie des 19. Jahrhunderts" GudrunHenneberg,"Was ist der musikalische Rhythmus?-Eine Entgegnung," Die Musik-

forschung, 29 [1976]:466); see also, idem,Theorien urRhythmikund Metrik:

Moglichkeitenund GrenzenrhythmischerundmetrischerAnalyse, dargestelltamBeispielder WienerKlassik, MainzerStudienzurMusikwissenschaft,vol. 6

(Tutzing, 1974).

fully the dynamics of melody and harmony into their systems of

rhythm and meter.2

Independent of this discussion in Germany, the American

theorist Maury Yeston has also contributed to one side of the

argument. Like Henneberg, Yeston finds in eighteenth-century

theory an incipient mediation between pitch and rhythm that

subsequent theorists fail to develop:

The major treatises of the nineteenth century did not continue to

investigaterhythm n the contextof pitchfunction,butrather eparatedissues of the theoryof rhythm romtheconsiderable ontroversies hatarose over the natureof tonal pitch systems. [These controversies]would have becloudedany attempt o base a theoryof rhythmon a

rigorous heoretical ystemof pitchrelations. Thusnineteenth-centurytheoristswere concernedwith rhythmas a self-enclosed system of

organizing time. . ..3

2WilhelmSeidel, review of TheorienzurRhythmik ndMetrik, by Gudrun

Henneberg, in Die Musikforschung,29 (1976): 226-27; idem, "Zum Ver-

standnisder Akzenttheorie:Eine Antwort auf die Entgegnungvon Gudrun

Henneberg," ibid., pp. 468-69; see also, idem, UberRhythmustheorien er

Neuzeit, Neue HeidelbergerStudien zur Musikwissenschaft, vol. 7 (Bern,1975).

3MauryYeston,TheStratification fMusicalRhythm New Haven, 1976), p.19.

This content downloaded from 157.92.4.12 on Sun, 24 Mar 2013 03:30:15 AMAll use subject to JSTOR Terms and Conditions






Theories of Simon Sechter 75

Now it is not my intention in the present study either to evaluate

thepreceding

claims or topropose

an ultimate solution to this

important historical issue; rather, I want simply to introduce into

the debate new evidence from an overlooked and, indeed, unex-

pected source-the Kompositionslehre of Simon Sechter

(1788-1867), the leading Austrian theorist of the nineteenth-

century.A discussion of pitch-rhythm relationships in Sechter's the-

ory may at first seem surprising, because Sechter's ideas of

rhythm, almost entirely derivative of eighteenth-century

models,have been

virtually ignored byhistorians of

rhythmictheory.4 Instead, Sechter has gained renown for being the fore-

most pedagogue of harmony and counterpoint in Vienna (at-

tracting as students both the dying Schubert and the youthful

Bruckner) and for originating the famous Stufentheorie of har-

monic organization.5 Yet, in Volume 2 of his major treatise, Die

Grundsatze der musikalischen Komposition, lie importantstatements on the relation of pitch and rhythm.6 In a chapterentitled "Von den Gesetzen des Taktes in der Musik" ("On the

Laws of Meter in Music") Sechter directly confronts a centralissue of musical composition: how should harmonies be dis-

4Seideldevotes little morethanapageto Sechterandbelittleshis treatment f

harmony and meter as "purely mechanical" (Uber Rhythmustheorien,pp.

107-08).

5Importanttudiesof Sechter'sStufentheorie nclude:ErnstKurth,Die Vor-

aussetzungender theoretischenHarmonikundder tonalenDarstellungssysteme

(Bern, 1913);Ulf Thomson, "Voraussetzungenund Artender6sterreichischen

Generalbasslehre wischen Albrechtsberger nd Sechter," (Ph.D. diss., Uni-versity of Vienna, 1960); Erst Tittel, "Wiener Musiktheorievon Fux bis

Sch6nberg," in Beitrage zur Musiktheoriedes 19. Jahrhunderts,ed. Martin

Vogel, StudienzurMusikgeschichtedes 19. Jahrhunderts,ol. 4 (Regensburg,1966), pp. 163-201; CarlDahlhaus,Untersuchungen ber die Entstehungder

harmonischenTonalitat,Saarbriickner tudienzur Musikwissenschaft,vol. 2

(Kassel, 1968).6Simon Sechter, Die Grundsdtzeder musikalischenKomposition, 3 vols.

(Leipzig, 1853-54) (hereaftercited as Die Grundsitze).

tributedwithin the measures of a work?Sechter's attempttoanswer his

questionyieldswhat

maybe the first detailed nves-

tigation in the historyof music theoryinto the metricalplace-ment of harmonic structures.

It would be a mistaketojudge Sechter's formulationson theextent to which they fulfill his main intention, namely, to

providepractical nstructionor the studentof composition,forit will become apparent oon enough thathis rathersimplisticrules and primitiveexamples only begin to treatthe wealthof

possibilitiesopen to the nineteenth-century omposer. Rather,the value of Sechter's

prescriptslies in their

expressionof

fundamentalprinciplesrelating harmonyandmeter,principlesthat can function as normsof analysis, not inviolable laws of

composition.To begin my discussion, I will sketchindividuallySechter's

theory of harmony, developed in the first volume of Die

Grundsatze,andhistheoryof meter,whichopensthechapteronlaws of meter nVolume2;Iwill thenexamine nmoredetailthe

way Sechterrelatesthese two domainsandevaluate thehistori-

cal and theoreticalsignificanceof his ideas.Sechter'sStufentheoriebrings the fundamental-bassheoryof Rameau,as transmitted ndmodifiedby KirnbergerandhisassociatesJ.G. Sulzer andJ.A.P. Schulz), to its fullestexpres-sion. Followingthelead of theseearlier heorists,Sechterholdsthatevery harmony s defined by afundamental bass, a pitchthatlies below the actuallysoundingmusicaltexture.7Further-

more, he determines he syntacticalsuitabilityandtonalmean-

ing of a harmonic progressionby two related, yet distinct,

factors:1) the intervalof fundamental-bassmotion, and2) thescale degrees(Stufen)uponwhichthe fundamentalbassesrest,as indicatedbytheRomannumeralsntroducedbyAbbeVoglerandpopularizedby GottfriedWeber.

7"Also brauchtman ausser dem Bass, welchen man horen lassen will, zur

richtigenVorstellungnoch einen tieferen, welcher die Fundamentaltone derdieGrundtone erStammaccorde nthalt,welchenmandaherFundamentalbassnennt" (Die Grundsdtze, 1:14).







76 Music Theory Spectrum

As a rule, Sechter prefers that the fundamental bass descend

by the interval of a fifth or third.8 Sechter admits that some

progressions by ascending fifths and thirds are acceptable, for

instance, the progressions from I to V or from IV to I, but warns

that others are to be avoided.9 If the fundamental bass appears to

ascend stepwise, Sechter adopts Kimberger's procedure (itselftaken from Rameau's "double-employment") of placing a

"concealed" (verschweigener) bass between the two regularfundamental tones of the progression in order to create the

"more natural" motion of a descending third and descendingfifth (see Example 1).10 Going further than his predecessors,

Sechter also inserts a concealed bass between the fundamental

tones of an apparent descending-second progression, such that

two descending fifths result (see Example 2).11

Example 1. Die Grundsatze,1:18

In Noteii in C dur so :

---

oder mil Versclhweigung deszweiten Fun(lamentes so :

C A D

8The fundamentalbass can also be said to ascendby the inversion of these

intervals,the fourthor sixth;for convenience, though,referencewill be made

throughout he rest of this studyto motionby fifths and thirdsrather han their

inversions.

9DieGrundsitze, 1:22-24. Sechter'sgeneralcriterion or theacceptability f

chord progressionsis curious, for it arises from an apparent echnicalityof

counterpoint.He holds thata chordprogresses properlywhen its fifth chord-

factor is1) preparedby

thepreceding

chord and2)

resolvedstepwise

in the

following chord. These conditions are satisfied by all descending-fifthand

descending-third rogressions.He then addsthat f thefifthcannotbe prepared,then theroot, which is the note thatcreatesthe intervalof a fifth with thefifth

chord-factor,mustbe preparednstead. This condition s fulfilledbyall ascend-

ing fifths and thirds. But Sechteralso stipulates hat f the intervalof the fifth is

diminished,then the fifthchord-factor,andnotthe root, must be prepared nd

properlyresolved. Since Sechter develops his theorywithin a system of justintonation,he regards he intervalbetween the second and sixth scale degreesto

be "diminished" along with the interval between the fourth and seventh de-

grees. Consequently, heonly ascending ifthand thirdprogressions hatsatisfy

his requirements re:I-V, IV-I, VI-III, IV-VI, I-III, and III-V. "Bei derQuintmuss entweder sie selbst oder der Ton, wogegen sie eine Quintmacht,vorbereitetsein und eines davon stufenweise weiter gehen. ... Ist aber die

Quint alsch, so muss sie selbst vorbereitet ein und dannentvwederogleich um

eine Stufe herabgehen oder zuvor noch Sept werden" (ibid., 1:14).10"Um zum Beispiel den Schrittvom Dreiklangder lten zu jenem der 2ten

Stufenaturgemisszu machen,mussdazwischenderSeptaccordder 6ten Stufe

entweder wirklich gemacht oder hinein gedacht werden" (ibid., 1:18); cf.

JohannPhilippKirberger, Die wahrenGrundsdtze umGebrauch der Har-

Example 2. 1:33

Vollstindig: L'nvollstundiig:

I

monie (Berlin, 1773), pp. 51-53 (This work was actually written byKirnberger'sstudent, Johann Abraham Peter Schulz); also, Jean-PhilippeRameau,Generationharmonique Paris, 1737), p. 129.

1Die Grundsatze,1:32-33. Theorists oday mightbe skepticalof Sechter's

procedure,but ArnoldSchoenberg,for one, was sufficientlyconvinced of themusical ogic of thisexplanation hathe incorporated echter's dea nto his ownHarmonielehre ArnoldSchoenberg,TheoryofHarmony,trans.Roy E. Carter

[Berkeley, 1978], pp. 137-39); see Tittel, "Wiener Musiktheorie,"p. 197.








As regards he interrelationshipf the scale degrees, Sechter

is well known forarranginghe sevendiatonicstepsintoacircle

of descending fifths, the so-called sechtersche Kette

("Sechter-chain"). This model of harmonicorganizationoc-

cupies a leading position in his theory, manifestedby its fre-

quentuse in exemplifyingmodulation,chromaticism,andeven

enharmonictransformations.Most historians,however, have

overlookedthe presence of a second model within Sechter's

system, a model based on the priorityof the first, fifth, and

fourth degrees of the scale. At the very beginning of Die

Grundsiitze,Sechterranks themajor

triads on these three de-

grees as the most importantharmonies n the majormode.12 n

so doing, he reaffirmsHeinrichChristophKoch's originaldis-

tinctionbetween "essential" and "non-essential"chordsand,as will become more apparentbelow, anticipates he theoryof

functionalharmonydevelopedby HugoRiemann.13As groundsfor assigningspecial significance to the I, V, and IV chords,which he later calls the primary chords, Sechter cites two

characteristics.14 irst, only the dominant and subdominant

harmoniescandirectly

alternatewith the tonic,creating

what

Sechtertermsa "mutual effect" or Wechselwirkungsee Ex-

ample 3).15Second, the perceptionof a tonalityrequiresthe

presenceof all threeprimarychords:"In orderfor a triad o be

recognizedas a tonic, at least the triador seventhchord of the

dominant and the triad of the subdominant must be heard

12DieGrundsdtze, 1:12.

13HeinrichChristophKoch, Versuch einer Anleitung zur Composition, 3vols. (Leipzig, 1782-93), 1:53;Riemann'stheorycanbe foundin anynumber

of his matureworks, e.g., GrundrissderKompositionslehre,2 vols. (Leipzig,

1889) and Vereinfachte Harmonielehre oder die Lehre von den tonalen

Funktionender Akkorde(London, 1893).14In he chapter"Vom einstimmigenSatze" in Volume 2, Sechterspecifi-

cally distinguishesthe primary riads(Hauptdreiklange) rom the remaining

secondarytriads(Nebendreiklinge) (Die Grundsdtze,2:151).

15Ibid.,1:13.

Example 3. Wechselwirkung,1:13

.....; -.......- -....

before."16 Thus, the primary chords acquire structural impor-tance within a key by virtue of their special syntactical relation-

ship as well as their capability of expressing tonality.As Sechter proceeds to consider the use of chords on the other

scale degrees, the secondary chords, two general schemes

emerge: 1) the minor triads on the sixth, second, and third

degrees can be arranged to follow by a descending third the

primary chords on the first, fourth, and fifth degrees respec-

tively (see Example 4a); 2) the minor triads can be so ordered

that they "imitate" the descending-fifth V-I cadence (see

Example 4b). The diminished triad on the seventh degree fits

into both schemes either by being placed a third below the II

Example4. 1:13

llierzu ein Schluss:a. -

__..

~ b ' -_. _' I--- __

, Damitmaneinen Dreiklangalsjenen derTonica wirklicherkennenkann,missen wenigstens auch Dreiklangoder Septaccordder Dominant und Drei-

klang der Unterdominant orhergehortwerden" (ibid., 1:101).







78 MusicTheorySpectrum

chord or byjoiningwiththe IV chordto completethe circle of

descendingfifths (see Example 5).17This second scheme, of

course, yields Sechter's famous Kette; but it is important oappreciatea change in emphasis in this model of harmonic

organizationfrom Sechter's originaldistinctionbetween pri-maryandsecondarychords. In the circle of descendingfifths,thedominantandtonicharmoniesretain heir structuralmpor-tance at the close of the progression, but the subdominant

harmony,residingfarthest from the concludingtonic, is con-

signedthe most subordinatepositionof all. In the first scheme

(Example 4a), on the contrary,the integrityof the primary-chord model, as I will call it, is more completely preservedinsofaras eachof the minorsecondary riads s linkeddirectly oone of the primary riadslying a thirdabove. As will be seen

shortly, both models of harmonicorganization-the circle offifths model and the primary-chordmodel-find further ex-

pressionin Sechter'sprinciples relatingharmonyand meter.

Example . 1:13

i oelcr ? .....-.

Butbefore tuingirectly- to that issue, I want to consider

But before turningdirectly to that issue, I want to considerbriefly some aspectsof metricaltheorythat will pertain o thediscussion below. Although specific definitionsvary widely,

'7Ibid., 1:13.

theoristsgenerallyagreethatmeterconcerns heorganization fmusicaltime into specially differentiated vents thatalternate

with each othermore or less regularly.This differentiationofevents is conventionallydesignatedbya varietyof metaphoricalpairsof terms, such as accent-unaccent, trong-weak,upbeat-downbeat,andarsis-thesis.Furthermore,metricalorganizationis conceived to be hierarchical, n that the alternationof ac-cented andunaccented vents canoccursimultaneouslyat vari-ous levels of structure.Finally, an individualmeter is labeled

"duple," "triple," "quadruple,"and so forthaccording o thenumberof unaccentedevents thatregularlyalternatewith ac-centedones.

In evaluating any theoryof meter, it is useful to distinguishbetween two points of view underwhich the theory can beformulatedandappliedanalytically.Inthefirst, musicaleventsbecome accented or unaccentedaccording to their locationwithin a preexistentmetricalframework,a framework hat isdefinedby suchnotationaldevicesas timesignatures,bar ines,andbeamings.Thisnotated-meterpoint of view, as it can be

called, has beenadoptedby

most theorists,indeed, to such anextent thatthis viewpointhas come to dominateour everydaynotions of meter. Nevertheless, there are some seriousobjec-tions to this conception, of which the most significantis the

simple observation that the notationoften fails to correspondwith the metricalinterpretationhat the unprejudicedistener

actually hears. Hence, theorists have become increasinglyawareof the factthatnotationmayverywell representmeterbutnot necessarilydetermine t. And thus a second pointof viewassumes thatthe musical events themselvescanexpress, so to

speak,ametricalnterpretationndependently f thenotation.A

theoryformulated rom thisexpressed-meterpointof view, as Iwill call it, seeks to discover the specific musical forces-be

they dynamic, durational,or tonal-that are responsiblefor

creatingmetricallyaccentedandunaccentedevents.To be sure, almost all theories of metercontain in varying

degreeselementsof boththenotated-meter ndexpressed-meter







Theories of SimonSechter 79

positions, and, as I hope to makeclear, Sechter'stheoryis no

exception. Fortunately, t will notbenecessaryhereto enter nto

a detailedstudyof his approachbecause n most essentialpointsit conforms to thegeneralconceptionof meterdiscussedabove.Like most late eighteenth-century ndearlynineteenth-centurytheorists,Sechterdescribesmetricalorganizationas ahierarchyof accents and unaccents: he first beat of every measurebringsthe primaryaccent, while the following beatscontain different

grades of secondaryaccentuationor else remain completelyunaccented.18Example 6 presentsSechter's representation faccents ntwo differentmetersatuptofive levelsof structure. n

applyinghis theoryto the analysisof realmusic, Sechteroper-ates for the most partwithin a notated-meter ointof view: themusical events acquiretheir metricalinterpretationwhen they

Example . 2:15

fr v > _"- --- I--: -

:-_

^^W L F-_U. S. W.

--- ~ --_ -D~ ? ? ---- ---

areplacedinto the a prioriframeworkof accents. At the same

time, however, Sechter s consciousof the limitations nherent

to the notated-meterapproach.He notes, for example, thatcomposersoften fail to indicatetrue changes of meter in thecourse of their compositions; thus they frequentlynotate a

passage such as that in Example7a entirely in one meter, asshown inExample7b.19As I nowproceed othecentral opicof

my investigation-the interrelationship of harmony andmeter-it will be important o consider the extent to whichSechter'sdissatisfactionwithnotatedmeter,evident nExample7, becomes translated into the definite awareness of an

expressed-meterpointof view.

Example . 2:90

T 7__' 7r Mt il' S

, -- r? r.:

f- + L--l-- - --__- ?aEZj7 ----

a)~~ ~~.. 1 ~I _ _ _ _ _~.~ .

F~1Fi ti _ __

8' ?C t Ct 517 7

~~71

--- I-F77:bzzjiz

51$-_ - __ _.____ _ _L"i*- TiZ U~i______________-__

With the unpretentious tatement, "Now we come to theapplicationof harmony o meter," Sechterbeginshis importantdiscussion of how the composer should arrangespecific har-monies withina metricalscheme.20Sechterfirst observesthat

19Ibid.,2:86-90.

20'"Nun kommen wir zurAnwendungder Harmonie auf den Takt" (ibid.,2:15).8Ibid.,2:12.








the "simplest way" to distribute chords in a piece of music is to

introduce one new fundamental bass at the beginning of each

measure (see Example 8).21He then puts forth a corollary rule: a

change of harmony must coincide with the onset of every

measure, no matter how many chords the measure contains.

"All the remaining ways [of distributing chords] share with the

simplest way the fact that with each new measure, a new

fundamental bass must either actually enter, or at least appearto

enter; the latter, however, should seldom happen."22

Example 8. 2:91

I_ _?Ai0

Thus, Sechter introduces a principle that, when stated con-

versely, continues to be taught to all beginning students of

theory: do not repeat a harmony across the bar line. To be sure,

Sechter is not the first theorist to raise this injunction. Already in

the mid-eighteenth century, Rameau cautions against syncopat-

ing the fundamental bass, and subsequently both Kirberger and

Vogler discuss the poor effect of continuing the same harmony

21"Die einfachste Art bleibt immerhindiejenige, wo nur mit jedem neuenTakteein neuer Fundamentalbassintritt. . ." (ibid.).

22 'Alle iibrigenArtenhabenmitder einfachstendasgemein, dassmit edemneuen Takte auch ein neuer Fundamentalbass ntweder wirklich eintrittoder

wenigstens einzutreten scheint, welches Letztere indess selten geschehenmuss" (ibid.). It is not clear what Sechter means by a fundamentalbass that

"seems to enter" since he offers no further xplanationand cites no examples.

from a weak beat to a strong one.23 But this idea has a more

significant function in Sechter's system than is the case with

these earlier theorists, for as he proceeds to consider more

complicated harmonic-metric combinations, one fundamental

principle emerges that unifies all of his observations: the com-

poser must clearly indicate the primary metrical accents by

creating a decisive change of harmony at the beginning of everymeasure.

Sechter's main task, then, is to develop criteria for determin-

ing the metrical decisiveness of harmonic progressions. And not

surprisingly, he formulates his rules in terms of fundamental-

bass motion. Thus, as regards the arrangementof two harmonies

in a measure, Sechter states:

The least conspicuousway for the fundamentalbass to containtwotones in a duplemeter s if thefundamental assleapsby adescendingthird from the firstbeat to the second beatandthenagainleaps by an

ascendingfourth or fifth in orderto make the entrance of the nextmeasuremore perceptible.24 See Example 9)

Example9. 2:16

q_ - - -- ~--- --r - l

23Rameau,Generationharmonique,p. 175;JohannPhilippKirberger, Die

Kunst des reinen Satzes in der Musik, 2 vols. (Leipzig, 1771-9), 2:32-4;Georg Joseph Vogler, Tonwissenschaftund Tonsezkunst Mannheim, 1776),

pp. 36-7.

24"Die am wenigstenauffallendeArt, dem Fundamentalbasse wei Tone ineinemzweizeitigenTaktezu geben, istdie, wenn man hn vondemTone,denerbeim ersten Takttheilehat, beim zweiten Takttheile um eine Terz abwarts

springen,undsodann,umden Eintrittdes nachstenTaktes uhlbarer umachen,ihnwiederumeine QuartoderQuintaufwarts pringen asst" (DieGrundsitze,2:16).







Theoriesof SimonSechter 81

Sechteradds that the ascending-thirdprogressioncan also be

used withinthe measure,in which case the descendingfifth is

thepreferredmotioninto thefollowingdownbeat see Example10).25

The distribution f harmonies s poorwhen thetwo chordsof

the measure ormafifth-relationship,while thebeginningof the

next measure s approachedby the leapof a third see Example11). Sechter explains the inadequacyof this arrangementby

noting, "In thatway, the new measurewould be weaklyarticu-

lated because thereis less differencebetween the chords than

therepreviouslywas."26In other words, the second and third

chordsin Example 11 are less differentiatedhan the first andsecondchords.Presumably, he source of the differentiation s

the numberof common-tonesbetween the chords. Since pro-

Example 0. 2:17

X I 1 I9 ,_

Example 1. 2:16

nmtt: b. 1 1

25Ibid.26 'Dadurchwiirdeder neueTaktmattangedeutet,weil die Accordezu wenig

Unterschiedhaben, und doch zuvor mehr Unterschiedhatten" (ibid.).

gressions by a thirdresult ntwocommon-tones, he chords acksufficient differentiationorarticulatingheprimaryaccentof a

measure. The chords of a fifth progression,on the contrary,have only one common-tone;hence, the greaterdifference be-

tween these chordsrenders heprimaryaccent "morepercepti-ble." Sechter does not explain any further why third-

progressionsareincapableof indicating heprimaryaccent,yetthe statementsand examples that he does offer promptaddi-tional speculation.

As hasalreadybeennoted,Sechterstipulates hat n all cases,thebeginningof every measuremust be accompaniedby a new

fundamentalbass, or in otherwords, by a changeof harmony.But by discouragingthe use of third-progressionsnto thedownbeatof a measureandby appealing o the relativelack ofdifferentiation reatedby such progressions,Sechtersuggeststhat motion of the fundamentalbass by a thirddoes not fullyachievegenuineharmonicchange. Or, put differently,he inti-mates that despite the literal differenceof fundamentalbass,third-related hords represent,to some extent, the same har-

mony, and thus this "single harmony" should not be used

acrossthebar ine. Ofcourse,suchaninterpretationf Sechter'views cannot be reconciled within a strict Stufentheorie,whereineachof theseven fundamental assesof a keydefinesadistinctharmony.His ideasbring o mind, rather,analternative

approach,namely, a theoryof functionalharmonysuch as thatof HugoRiemann's,in whichthreeharmonic unctions-tonic,dominant,andsubdominant-can be expressednotonly by the

originalI, V, andIV harmoniesbut also by "substitute" chordson VI, III, and II

respectively,chords that form a third-

relationshipwith the originalharmonies.It can be recalled hatananticipation f Riemann's unctional

theory is alreadyfound in Sechter's primary-chordmodel ofharmonicorganization(see again Example 4a). To be sure,whenSechter irst ntroduces hismodel, he does not implythatthe subordinate hordsexpress the same harmonic unction astheprimary hords ying a thirdabove. Butwhen he laterstates








that progressions by thirds cannot be used to articulatethedownbeatof a measurebecausetheyareinsufficientlydifferen-

tiated,he raises the possibilityof reducing hird-relatedhordsto one harmonic unction. In this way, he bringshis primary-chord model a step closer to Riemann'stheory.

One additionalmusicalexamplereinforcesperhaps he fore-

going interpretation.Sechter notes thatExample 12 is "moretolerable"(ertrdglicher) hanExample11 becauseatleast"the

beginningof the new measureis not articulatedmore weaklythan the second beat in the preceding measure."27 n other

words,thesecondbeat in the first measureof Example12is not

madestronger han the downbeatof measure wo becausethirdprogressionsare used throughoutboth measures. Of course,Sechterstillrefershereexclusivelyto fundamental-bassmotionwhen he regards achof thedescending-third rogressions o be

metricallyweak. Nevertheless, it is temptingto speculatethatSechterunconsciouslyperceivesthedecisivechange nfunctionfrom tonic to subdominant t thebeginningof the second meas-ure to be sufficient meansfor articulatinghe primaryaccent,thus makingthe example "more tolerable."

Example 2. 2:16

crtratlichcr: I

? '- ~e,~.. ,. - -- ,~- - ~-

Before moving on to examine Sechter'sprinciplesfor threeandmorechordspermeasure, etuspausebrieflyto consider he

27,, So wirddoch derEintritt es neuenTaktesnicht matterbezeichnet,als derEintritt des zweiten Takttheils im vorigen Takte" (ibid.).

generalposition underwhich he relates harmonyand meter.

Strictlyspeaking, all of his statementsare formulated rom a

notated-meter point of view: the composer sets thefundamental-bassprogressions into a preexistent metricalframework.Nonetheless,byusingsuchphrasesas "to make heentranceof the next measuremoreperceptible"and "the newmeasurewouldbe weaklyarticulated,"Sechterspeaks ntermsthatstronglyconnotean expressed-meterpointof view, one inwhich the harmonicprogressionsthemselves are directly re-

sponsible orrenderinghe metercomprehensibleothelistener.To be sure, Sechter never specifically claims that harmony

createsmeter,yet his concern that a primaryaccent be clearly"pointed out" (angedeutet)by a decisive change of harmonyreveals anawarenessof expressedmeter hat farsurpassesmost

previoustheory.In the course of discussinghow three chords shouldbe dis-

tributed n a measure,Sechterintroducesanotherprincipleof

harmonyandmeter.First,he restates he basicrequirementhatthe downbeatof every measuremustbe articulatedmore deci-

sively than heprecedingupbeat.Hethen summarizes hemetri-

cal qualitiesof harmonicprogressions."Leaps of a thirdareweak, butleapsof a fourthor fiftharedecisive;however, leapsof an ascendingfourthanddescendingfifth are the most deci-sive."28 Withthe generaldistinctionbetweenthirdsandfifths,Sechtermerely repeatshis earlierposition.Buthe thenraises anew issue by accordingdescending-fifthprogressionsgreatermetricalstrength hanascendingfifths. Unfortunately,he doesnot try to justify this refinement,and an appeal to his formercriterion of harmonicdifferentiationobviously fails, because

both the ascendingand descendingvarieties of the fifth pro-gressioncreatejust one common-tonebetweenthe chords.

28"Matt sind Terzensprunge,entscheidend aber die Quarten-und Quin-tenspriinge; erQuartsprungufwartsundderQuintsprung bwarts ind aberamentscheidendsten" ibid., 2:19).







Theories of SimonSechter 83

Nevertheless, Sechter does provide the basis for a likely

explanation when he states early in his treatise that all descend-

ing fifths are "imitations" of the V-I cadential progressionand, in a later passage, specifically shows that a dominant-tonic

relationship is expressed at each step in the circle of descendingfifths (see Example 13).29 Sechter stops short, though, of relat-

ing such dominant-to-tonic expression directly to meter. Other

theorists, however, have moved in this direction: both Abbe

Vogler and, later, Moritz Hauptmann hint at a connection be-

tween tonic harmony and metrical accent,30and Hugo Riemann

formulates this relationship even more explicitly.31 Indeed, a

number of prominent theorists today recognize that the motion

Example 13. 2:26

Tonia Dominant, Ton., Do Ton.,Do, Ton, Do., Ton, Do.,Tonica.Dominanl, Ton., Domn.,Ton.,Dom., Ton, Dom., Ton., Dom.,

F'_

F_ __

Ton., Dom., Ton., Dom., Tonica, u. s. w.

29Ibid.,1:17. "Da ubrigens ederSchritt inthe circle of fifths]einen Tonfall

bezeichnet, wenn auch nur der von der 5ten zur Iten Stufe den eigentlichenSchlussfall bildet: so kann jeder Accord gewissermassen einen Abschnitt

machenund zugleich Veranlassungeines folgenden Abschnitteswerden, d.h.

jeder Fundamentalton anngewissermassenerst als Tonica, dann als Oberdo-

minantgelten. . ." (ibid., 2:25).

30Vogler,Tonwissenschaft,pp. 36-37; MoritzHauptmann,The Nature of

Harmonyand Metre, trans. W. E. Heathcote(London, 1888), p. 326.31"The accented beathas a similarmeaningto the tonic chord n a harmonic

progression.It is thereforeconceivablethat a progressionappearsmoreeasilyunderstandablef the tonic chordis broughton an accentedbeat. . ." ("er [theaccented beat] ist von ahnlicherBedeutung wie der thetische Klang in der

harmonischenThese. Es ist daher begreiflich, dass eine These desto leichter

verstandlich erscheint, wenn sie die Tonika auf dem guten Takttheil

bringt. . .") (Hugo Riemann,MusikalischeSyntaxis [Leipzig, 1877], p. 76).

from dominant to tonic, as an expression of tonal stability,

directly relates to the succession upbeat-to-downbeat, and this

harmonic-metric phenomenon surely lies at the heart ofSechter's observations.32

The use of four or more chords in a measure gives Sechter the

opportunity to discuss how harmony can articulate multi-level

metrical organization. He recommends that in a quadruple me-

ter, for example, the composer should consider ways to make

the secondary accent on the third beat more decisive than the

unaccented second beat, at the same time reserving the greatest

strength for the primary accent at the beginning of the following

measure. To accomplish this, he calls upon his favorite model ofharmonic organization -the circle of fifths - and claims that the

closer a progression lies to the concluding tonic, the stronger is

its metrical articulation. In other words, the most decisive pro-

gression is V to I, less decisive is II to V, even less so VI to II,

and so forth.33Example 14 presents a small sample drawn from

Sechter' s many illustrations of how the circle of fifths can be set

in a variety of meters and rhythms. In each case, the secondaryaccent is articulated by a more decisive harmonic progression

than the preceding beat, while the approach to the downbeat ofthe following measure contains the strongest motion, V-I.

32See GrosvenorCooperandLeonardB. Meyer, TheRhythmicStructureofMusic (Chicago, 1960), p. 118; Carl Dahlhaus, "Uber Symmetrie und

Asymmetrie n MozartsInstrumentalwerken," eue Zeitschriftur Musik, 124

(1963): 209. Not all theoristsagreeon this point;WallaceBerry, forexample,holds that tonal function is metricallyneutral StructuralFunctions in Music

[EnglewoodCliffs, N.J., 1976], p. 330).33"Wennman, wie billig, dafir sorgen will, dass der Eintrittdes dritten

Takttheilsentscheidendersei als jener des zweiten, entscheidenderaber derEintrittdes erstenTakttheils m neuenTakte als jener des zweiten, drittenundviertenTakttheils,undderFundamentalbass ochTonfalle,d.h. Schritte n die

Unterquintoder Oberquart,machensoll: so ist nothig zu bemerken,dass derSchrittvon derSten zur lten Stufe am entscheidendsten,minderentscheidendder Schrittvon der2ten zurStenStufe, nochminder enervonder 6ten zur2ten,wieder minder ener von der3ten zur6ten, noch minder ener von der7ten zur3ten, nochminderjener onder4ten zur7tenStufeist" (DieGrundsatze,2:22).








Example 4. 2:23-24

9-,,v----: : :

oder: oder:' ". ~?~~ORia-'IT-- --- , . ----

Thus these examples appear o satisfy fully his conditionsfor

achievingmetricaldifferentiationwithin the measure.

At firstthought, Sechter'srankingof the seven descending-fifthprogressions eems plausibleenough: hegreater heprox-

imity to the tonal center, the greaterthe tonal stability, and

hence, thegreater hemetrical xpression.But further eflection

casts serious doubt on such a direct harmonic-metric orre-

spondence. The problemconcerns the very natureof accent

itself, for anindividualevent canbe perceivedas accentedonlyin relationto surrounding vents that are clearly unaccented.

Hence, in orderto create a secondaryaccent in a quadruplemeter, the third beat must not only be precededby a weak

secondbeat,as Sechterrequires,but also be followedbya weak

fourthbeat, a fact thathe simplyoverlooks.In everyone of his

examples, however, the fourthbeat of the measurecontainsa

moredecisive harmonicprogression hanthe precedingbeat, a

conditionthattheoreticallyconflicts with the perceptionof the

thirdbeatas accented.Thebasic causeof thisdiscrepancys that

Sechter'smodelof ever-increasingharmonic-metricxpression(whichI have illustratednExample15)failstocorrespondwith

the model of alternatingaccentsand unaccents hathe himself

offers in his theoryof meterearlier n the treatise Example6).

Consequently,Sechter's rankingof the descending-fifthpro-

gressionsfalls shortof realizinghis goal of hierarchical,metric

articulation.

Since Sechterdevotesseveralpagesof his treatise o discuss-

ing the metricalsignificanceof the circle of fifths, it is possiblethat some other motives-both musical and strictly

theoretical-may have inducedhim to proposethis harmonic-

metricrelationship.Forexample, in perceivingthe undeniable"drive to the cadence" associated with the circle of fifths,Sechtermay verywell have attributedhisrhythmicalqualityto

meter. Or, to take anotherexample, Carl Dahlhaus has sug-

gested thatSechtermay have triedto use meter as additional

justificationfor establishinghis Kette as a paradigmof har-monic tonality.34Of course, both of these possibilities suffer

fromthe same defect discussed before:the scales of measuring

ever-increasingharmonicstrength,on the one hand, and alter-

natingmetricaccentuation,on theother,aresimply incompati-ble.

This concludesan examinationof Sechter'sprinciplesrelat-

ing specific fundamental-bassprogressionsto meter. As he

considersthearrangementf five to eightchords n a measure,Sechtersimplyappliesthe threebasic rules for the placementof

harmonies hathavealready

been discussed:1)progressions

bya descendingor ascendingthirdshould be usedonly within the

measurebecausetheylack sufficientharmonicdifferentiationo

articulatethe primaryaccent; 2) descending fifths are more

metricallydecisive thanascendingones, duemost likely to the

dominant-tonic xpression nherent n all descending-fifthpro-

gressions;3) secondaryaccentuationwithin themeasurecan be

indicatedby the circle of descendingfifths, since the metrical

34 In der SequenzI-IV-VII-III-VI-II-V-I, dem Anschauungsmodellder TheorieSechters,sindzwarbeideMomente-die vollstandigeSkalaunddie

Progression n Quintschritten-enthalten;doch begrundetdas aussereZusam-

mentreffenkeinen inneren Konnex. Und Sechter scheint den Mangel selbst

empfunden u haben,denn anentlegenerStelle, ineinemKapitel iber Gesetze

des Taktes,' skizziert er einen vermittelden Gedanken. Je naher ein Fun-

damentschritt n der Sequenz der abschliessendenTonika komme, um so

'entscheidender' ei er" (Dahlhaus,Untersuchungen, . 31) (emphasisadded).







Theoriesof Simon Sechter 85

Example 15

II - V V - I

strength of a given progression increases as it nears the conclud-

ing tonic.

Conspicuously missing from these principles, of course, is

any mention of stepwise progressions of the fundamental bass.

But since Sechter explains such apparent motion by a step as

combinations of descending thirds and fifths with a "con-

cealed" bass (see again Examples 1 and 2), the use of these

progressionsis

alreadycovered

bythe

previousrules, and

Sechter obviously feels that additional comment is unneces-

sary.35

Up to this point, I have discussed the metrical placement of

harmonies in terms of their fundamental-bass motion only. But

this does not exhaust Sechter's treatment of the relationship

between harmony and meter, for he is not only concerned with

chords that possess a fundamental bass, but also with those that

function non-harmonically, that is, chords that are reducible to

higher-levelstructures. In a recent

study,Robert P.

Morganhas

shown that Sechter's theory occupies a significant position in

35Ineffect, progressionsby a second could be placedon any beat, since the

motionfromthe concealed bass to the next actuallysoundingbass is always a

descending fifth, a progression hat has no metricalrestrictions.

the history of reduction analysis.36 Morgan cites an examplefrom Volume 1 of Die Grundsitze (see Example 16) in which

Sechter demonstrates how all of the scale degrees in a key (with

the exception of the leading tone) can function as temporary

tonics without losing their identity as individual Stufen. Each

scale degree becomes a local tonic through the presence of

subordinate chords (Nebenharmonien) that do not necessarilyhave a harmonic relation to the broader, controlling tonality.37

Sechter gives an even more detailed account of this reduction

technique in the chapter on laws of meter in Volume 2 of his

treatise, and in so doing he presents some important relation-

ships between meter and the hierarchical analysis of harmony.Sechter first raises the possibility of harmonic reduction in

discussing the use of three chords in a measure of triple meter.

He notes that the simplest arrangement is to place the same

harmony at both the beginning and end of the measure and to let

the chord on the second beat form a Wechselwirkung with the

36RobertP. Morgan,"Schenkerand the TheoreticalTradition:The Conceptof Musical Reduction," College Music Symposium,18 (1978): 72-96.

37Ibid., p. 89-91. "Eine grosse Ausdehnungbekommt das Wesen des

Chromatischen adurch,dassman,ausserder7ten,jede iibrigeStufeals Tonica

ansieht. . ." (Die Grundsdtze, 1:157).

cIC::: C1 < C <

l-IV IV-VII vii-III III I VI --- 11







86 Music Theory Spectrum

Example 16. 1: 158-59

(%--4-nT k--- T--T I-r--= T

?---= -- - -o _lL

''

I I -I

..... o--f -- -....

'--

C G E A F

D G C

____ J j~-=- ____ - -

= .= _= , =;J -j _= _-- -r-- j

--_: -I

-T-7 I

-I -. .., -; -..... -'0-- C_-

1 _9EE _ -J^I __ _ i

C__ E--__-

Ci iG;

surrounding harmony (see Example 17).38 (Wechselwirkung, it

may be remembered, refers to the alternation of tonic and

dominant or tonic and subdominant, as in Example 3, and

recalls Sechter's primary-chord model of harmonic organiza-

tion.) Sechter goes on to point out that the arrangementof chords

in Example 17 actually belongs to the category of just one

harmony per measure "because each second chord [in the

measure] can be considered interpolated, and the fundamental

bass belonging to the beginning and end of the measure is

regarded as the primary harmony."39 Thus, the Wechselwir-

kung converts the initial chord of the measure into a local tonic,which in turn makes it possible to reduce the dominant or

subdominant chord on the second beat. The use of five or more

chords in a measure permits the reduction of more than just the

dominant and subdominant. As Example 18 shows, chords on

other scale degrees can be reduced to a single harmony providedthat a good progression leads back at the end of the measure to

the harmony found at the beginning.40

Example 17. 2:19

_ __2-__ , 1 _ ___ __ _ _C__ Lt_Y--I

-I4T t J' K i+ i---? ..._.-_- --_---_--_I ~ 1 1U S. W.i I/ r 1' " s. w.

38Ibid.,2:19.

39 'Weiljeder zweite Accordals eingeschobenbetrachtetwerdenkann,und

man den Fundamentalton, erzu Anfangund Ende des Taktesgehortwird, als

Hauptsacheansieht" (ibid.).40"Obwohlnun die Selbststandigkeit llersechs Fundamentalnoteniurjeden

Takt[inExample19a]imEinzelnennichtstreitiggemachtwird,so giltdochfur

dasGanze njedemTaktenurderjenigeFundamentalton,erzuAnfangeundzu

Ende desselben geh6rtwird" (ibid., 2:31).








Example 8. 2:31, 34 Example 9. 2:21

-C ^-a-?_9 i

- -- a _

:-;--(--- . a . zzzi

- I -----

_ _....

C | G

~-- .

_"- ----------a---ai --

C G C

03 - $s S4- 7 7 Y S tS S 7

El,..- - %: . .. _.--- 3

E A D1 3- 5 S S 7

X __aT2V

G C

One striking feature in all of Sechter's examples is that

reductionsare confinedto a single measureonly. Althoughhe

does notexplain,nor even show anawareness,of thislimitation

to his reductionanalyses,a probablereasoncan be foundin his

centralprincipleof harmonyand meter: he beginningof every

measuremust be markedby a decisive harmonicchange. Ifreductionswere to span more thanone measure, some of the

primary ccentswould be insufficientlyarticulated.Example19

showshow metricalconsiderationsimitthe extentof reduction.

Sechter remarksthat each measure in this passage actuallycontainsonly two harmonies,becausethe secondchord of the

measure,forminga Wechselwirkungwithits neighbors,canbe

r ^- ;'. -l r--?-- r rr r -I I l I I r

__t^^-!*--1-- - _ - -4 - -iro1- 0-

consideredmerelysubordinate.41 he chordon the fourthbeat,however,mustbe analyzedas agenuineharmony,because"the

weightfrom the fourthbeat to thefirstbeatof the next measures

greater than that from the second beat to the third beat.' 42If, for

example,the dominant hordonthelast beatof thefirstmeasurewere reducedalongwith the secondbeat,then therewouldbeno

truechange of harmonyat the beginningof measuretwo; the

tonic wouldprevail throughout.Thusdespitethe fact that both

of the dominantchordsin measureone are in Wechselwirkung

with thetonic, the seconddominantmustbe consideredgenuinebecause it is the last beat in the measureand must effect the

change of harmony required to articulate the following down-

beat. It is importanto note that harmonicrelationshipsareno

criterionin deciding which of the two dominants s reduced;

rather, the decisive facto thehe metrical placement of the

chords,as Sechterhimselfmakes clear nreferringo the"grea-

ter weight" of the primaryaccent.

41Ibid., 2:21.

42"Hier uss och emerkterden,ass,wenn ier erEintrittesneuenTaktesuchmitdemnamlichenundamentaltoneezeichnetird,der mvorigenakteufdendrittenakttheilam,man deswegenoch enAccord,der ufdenierten akttheilommt,lswirklich,nd lsonicht lseingescho-benbetrachtet;enn asGewichtomvierteniszumrstenakttheile esnachs astenselktesstgrsser,alsjenesom weiteniszum rittenaktheile"(ibid., 2:22).ibid. 2:22).

--I C --ii -- I - II _ -








Two examples of six chords per measure show again how

meter alone determines the harmonic analysis. In Example 20a,

Sechter considers the six chords in each measure of 6/8 meter torepresent just two basic harmonies, because the chords on the

second and fifth eighth-notes are in "intimate Wechselwir-

kung" with their surrounding chords. Each measure in Example20b also has two harmonies only, but here, theNebenharmonien

fall on the second half of beats one and two of the 3/4 meter.43

Sechter then notes, "I have intentionally made the first measure

in these examples similar, in order to meet the objection that

both six-beat meters are the same."44 Sechter's choice of the

word similar to describe the first measures in Example 20 issignificant: the foreground content of each measure may indeed

be identical, but the background harmony is not the same, as the

analyses added under each example reveal. The cause of the

variant interpretations can only be attributed to a sole differen-

tiating factor--meter: setting the same series of chords in differ-

Example20. 2:30

a) tf,= . m rt

C G C A D G

b) IC G C G C A

43Ibid.,2:30.

44"Ichhabe iibrigensabsichtlichden erstenTakt n diesem Beispielejenemim vorigen Beispiele ahnlich gemacht, um dem Einwurfe, es waren beide

sechszeitige Taktarten inandergleich, zu begegnen" (ibid., 2:31).

ent metrical patterns yields different higher-level harmonic

structures.

On the evidence of these, and many other of Sechter's exam-ples, one general principle describes the role of meter in his

reduction analyses: chords located on accented beats and on the

last upbeat of the measure have greater structural importancethan chords residing on the remaining unaccented beats. Such a

principle, of course, generally operates under a notated-meter

point of view; the metrical interpretation of the chords is fixed

prior to their harmonic interpretation. Thus, whereas Sechter

reveals an expressed-meter position when discussing harmonies

that are unequivocally defined by fundamental-bass motion, hereverts to a strict notated-meter viewpoint as soon as he needs an

a priori meter to resolve ambiguities in harmonic reduction. Of

course, Sechter is neither the first theorist, nor the last, to use

notated meter for determining the structural significance of

chords. In the late eighteenth-century, Schulz, writing under the

name of his teacher Kirnberger, observes that non-harmonic

passing chords "can only come on a weak beat because it is

necessary to feel a fundamental harmony on each strong

beat. "45 And our own century has seen an even greater relianceon notated meter for harmonic, as well as melodic, reductions,as the hierarchical analysis of pitch organization in relation to

rhythm has become more widespread. But since the concept of

notated meter is itself theoretically precarious, the validity of its

employment in reduction analyses, be it in Sechter's theory or in

more recent work, is questionable and deserves further investi-

gation.Indeed, I have raised in this study many issues-both histori-

cal and purely theoretical-that require more examination and

45"Sie konnen daherauch nur auf schlechten Taktzeitenvorkommen,weil

bey jedem auf einer guten Taktzeit angegebenen Accord im Gefiihl ein

Grundaccordnothwendig wird" (Kirnberger,Die wahren Grundsitze, pp.34-35).







Theoriesof SimonSechter 89

interpretation.Butas discussedat theoutset, the entirequestionof therelationshipbetweenpitchandrhythm s farfromsettled.

Although I have dealt with the contributionsof one theoristonly, I hopethata stephasbeen takento counter he notion that

nineteenth-century heory ignores significantissues of pitch-rhythm nteraction.To be sure,some shortcomingso Sechter'stheories have been revealed in the precedingdiscussion. Byrequiringa non-reducibleharmonyat theend of everymeasure,he greatly restricts the scope and flexibility of his reduction

analyses. And his rankingof the seven descending-fifth pro-gressionson thebasis of theirproximity o the tonicis irrelevant

to questionsof meterdue to the incompatibilityof measuringtonal andmetrical trength.But Sechter'spositiveachievementsmust be emphasized as well. By holding that third-related

chords shouldnot be used from the end of one measureto the

beginningof the next, because they lack sufficient harmonic

differentiation,Sechter anticipatesfeaturesof functional har-

mony and suggests that his Stufentheorie s a more subtle de-

scriptionof harmonic orces thansome critics, eyeing only the

profusionof Romannumerals,have been willing to acknowl-

edge. In addition, his recognitionthat descending-fifth pro-gressionsaremoredecisivethanascendingones is animportant,earlyreferenceto the metricalexpressionof dominant-to-tonicmotion. Finally, at a time when most theoristsmerelycontinuethe eighteenth-century oncernwith how individual dissonantstructuresare metrically placed, Sechter's interest in the wayprogressionsof consonantharmonies anarticulatemetermarksa significantadvance n thetheoryof harmonic-metric elation-

ships.





caplin, w. e. (1980). harmony and meter in the theories of simon sechter. music theory spectrum, 2,...

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