Yale University Department of Music !"#$%&'()*+%,)--')-.'%/0'1/0"#2'"3'4*5+0-5$"-5 6*%/"#7589':$;;$),'<)+;$- 4"*#=09'>"*#-);'"3'!*5$='1/0"#2?'@";A'BC?'D"A'B'76*%*,-?'EFCG8?'++A'BHEIBJF K*L;$5/0.'L29'Duke University Press'"-'L0/);3'"3'%/0'Yale University Department of Music 4%)L;0'MNO9'http://www.jstor.org/stable/843534 . 6==0550.9'BPQPRQBPEE'EH9PF Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=duke. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Duke University Press and Yale University Department of Music are collaborating with JSTOR to digitize, preserve and extend access to Journal of Music Theory. http://www.jstor.org MORITZ HAUPTMANN AND THE THEORY OF SUSPENSIONS WilliamCaplin Perhaps no other major theorist of the eighteenth and nineteenth centuries presents such difficulties of comprehensionand interpreta- tion as Moritz Hauptmann(1792-1868). On glancingthrough his main treatise, Die Natur der Harmonik und der Metrik,1 the casual reader finds none of the usual features of a Kompositionslehreby Weberor Marx-no tables of intervals or chords, few rules of voice leading, no examples of actual works-nor does he find the extensivelists of inter- vallic proportions and detailed descriptions of acoustical experiments that typify the mathematical-physicalorientation of the harmonicsys- tems of Rameau, Tartini, and Vogler. The readerrather is confronted with over 350 pages of dense prose that aboundsin metaphysicaljargon and that is accompanied by illustrations using note names, Roman numerals,lines, and curvesin ways that resembleno previoustheoretical work. Indeed, Hauptmann'streatise is unique both in its mode of presenta- tion and in its conception of music theory. Hauptmannis the first, and indeed the only, theorist of the modern era who has attempted to ex- plain all harmonicand metric phenomenaon the basis of a sole universal principle: "in all aspects of its [music's] harmonic-melodic,as well as its metric-rhythmicexistence, there will always be only one law to be 251 referred to for its correct and intelligible organization."2To say that Hauptmann is unique, however, does not mean that he stands fully outside the theoretical traditions of his age. In his belief that music theory should be founded upon immutable laws, he clearlyfollows the path initiated by Rameau, and his attempt to embraceall musicalrela- tionships reflects the "encyclopedic tendencies" characteristicof other majortheorists in the first half of the nineteenth century.3 Accordingto Hauptmann,"Music is universallyintelligible in its ex- pression. It is not for the musician alone, but for the common under- standingof mankind."4Hauptmann thus searchesfor principlesof music theory that actually transcendthe purely musical: "That which is mu- sically inadmissibleis not so becauseit is contraryto a rule determined by musicians,but because it is contrary to a naturallaw given to musi- cians from mankind, because it is logically untrue and internally con- tradictory. A musical fault is a logical fault, a fault for the general understandingof mankind,and not for a specificallymusical understand- ing."5 For a Germanthinker of the mid-nineteenthcentury, the "logic" referredto in this statement is the dialecticsof metaphysicalidealism. 6 Throughouthis theory, Hauptmannemploys the three dialecticalcom- ponents of identity (unity, equalitywith self), duality (inneropposition, something divided within itself), and unity of duality, in order to demonstrate that all musical phenomena come into being and have an intelligible relationshipwith each other throughtheir expressionof this universallogic. Thus he declares, for example, that there are only three directly intelligible musical intervals-the octave, which representsa state of unity; the fifth, which produces an opposition to this unity; and the major third, which unifies this opposition and creates at the same time a new entity, the major triad.7 Hauptmannapplies this dia- lectical approachto the theory of meter as well. He claimsthat metrical unity finds its expression in the duple meter; an opposition is created by the triple meter; and a reconciliationof this opposition comes about through the quadruplemeter." As he proceeds to elaborate both his harmonic and metrical systems, Hauptmann appeals continually to these three dialectical components in order to distinguishbetween mu- sical phenomena that are logical and comprehensibleand those that violate the universallaws of nature and should thus be banned from compositionalpractice. As a consequence of Hauptmann'semphasis throughout his writings on "system," "logical meanings,""universal laws," and the like, most historianshave focused their critical attention on Hauptmann'sgeneral concept of theory construction and the specific role that dialectics plays within this theory. To be sure, had Hauptmanndone nothing more than reformulate traditional ideas into a systematic whole, his 252 importancefor the history of music theory would have been substantial nonetheless: for by basing a theory of both harmony and meter on a limited set of fundamentalprinciples, Hauptmannestablished a new standard of theoretical investigation in music, one that enormously influenced the majorGerman theorists who succeededhim in the course of the nineteenth century.9 But Hauptmann'ssignificance transcends the mere influence of his methodology on later thinkers. An examina- tion of the actual content of his theories revealsthat he advocatesnew and importantconceptions of harmonyand meter. Hauptmann'streatment of a single theoretical issue-the suspension dissonance-will highlight some of these innovations. The practicalad- vantage of choosing this specific issue over the myriadother topics that constitute a complete theory of music is the fact that the suspension dissonancenot only addressesquestions of harmony, but also those of meter, for an essential attribute of this dissonancetype is its required placement on a metrically accented portion of a measure.1 Since Hauptmannis the first figure in the history of music theory to treat both harmony and meter on an equal footing, an examinationof how he defines and explains the suspensiondissonance allows us to explore his contributionsto both of these majorareas of theoreticalthought. In order to clarify Hauptmann'sspecial approachto the suspension, it will be useful to consider briefly its treatment by previoustheorists. Throughoutthe baroque theory of counterpointand thoroughbass,the suspension was frequently designated the "syncope" and was distin- guished from the ornamentalor "passing"dissonance by its voice lead- ing and metrical placement.11 Beginning with Rameau's theory of harmony, the single category of the syncope evolved into two distinct dissonance forms-the seventh chord and the suspensionchord. Both of these chordaltypes were consideredto be harmonicstructures and were analyzed in terms of their fundamentalbass. Chordscomposed of orna- mental, passing dissonances were also incorporatedinto the new har- monic theory, but these chords were understood to be nonharmonic structuresthat lacked a true fundamentalbass. 12 The complete separation of the syncope dissonanceinto two cate- gories, seventh chords and suspensionchords, was not achievedimmedi- ately. Early in the eighteenth century, Rameau still believed that all harmonic dissonances have their origin in a single dissonant form, namely, the chord of the seventh.And in orderto explain the behavior of dissonant chords that have intervallicstructures different from that of the seventh chord, he introduced one of his most controversial notions-the chord of supposition. In the case, then, of what we today term the 4-3 suspension,shown in the second measureof Example 1, Rameau considersthe dissonantnote, F, to be the seventh of a chord whose root is G (as analyzed in line a); and he regardsthe C in the bass 253 I . F.a Romeo 7 7 F.B. Kim erger 7 Example 1 tifth root Example2 Sfifth roo0 Example 3 tnirdI Example4 254 voice as a "supernumarary"sound, one that does not belong to the actual harmony. This extra note below the seventh chord "supposes" the true fundamental bass, G, which lies directly above the actual bass, hence the term "chord of supposition."13The theoretical advan- tage that Rameau achieves from this ratherbizzare account is a unified conception of dissonanceas a harmonicseventh. But his view has some serious drawbacks.In the first place, the seventh harmony is missing both its third and fifth. These notes, B and D, have been replacedby doubling the note of supposition,C.