Riemann Ideen Zu Einer

8/13/2019 Riemann Ideen Zu Einer

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Yale University Department of Music

Riemann's "Ideen zu Einer 'Lehre von den Tonvorstellungen' ": An Annotated TranslationAuthor(s): Robert W. Wason, Elizabeth West Marvin and Hugo RiemannSource: Journal of Music Theory, Vol. 36, No. 1 (Spring, 1992), pp. 69-79Published by: Duke University Presson behalf of the Yale University Department of MusicStable URL: http://www.jstor.org/stable/843910.

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Riemann's most severelycriticalcontemporarieshadto admirehisvir-tuoso handlingof the earlier sources(even thoughhe was occasionallyself-servingthere as well), but it was clear to at least one of them thathis historyof harmonictheory was essentially the historyof Rie-mann's harmonictheory. 4Riemann's firstperiod 5 is known to most American theoristslargely through secondary sources. While translations of these earlyworks would be useful, the secondary sources are fortunately quitecomplete, at least with regardto his ideas on harmony.6The crowningachievementof Riemann's second period in the realm of practicalharmonyis his theoryof tonal functions --the work for which mostAmericans probably know him best. Yet like most of Riemann'sideas, this theory too has continued to generate controversy.' Thedocuments that survive from Riemann's thirdperiod are fragmen-tary, but they are not without interest.8Here, one sees the maturetheorist trying to reconcile music-theoreticalviews he has held formost of his life withrecent researches in empiricalscience, and, in thesecond essay, with research n earlymusicand the newly-foundeddis-ciplineof ethnomusicology. Presumably,the crowningachievement ofthat period, had Riemann lived long enough to complete it, wouldhave been a comprehensive Lehre von den Tonvorstellungen(thephrase remains untranslated at present for reasons that will becomeclear later). The firstof the two essays, presented in complete trans-lation here, deals exclusively with matters related directly to Rie-mann's harmonic theories; thus, sufficient secondary literaturealreadyexists to provide a context for its criticalreading. It is hopedthat the present translationwill contribute to a resurgenceof interestin Riemann'swork, one result of whichmaybe to providethe contextfor a criticalreadingof the second essay in the near future.Already in Section I, but especially in sections III and IV of thisfirst essay, Riemann deals with familiaraspects of his theory of har-mony. Despite its quaint and occasionally awkward character( under-thirds, over-thirds, and the like), most of the terminologyin this translation corresponds with that used by one of his morewidely-knownEnglishtranslators,Henry Bewerung (1862-1923). Animportantexception is the term Klangvertretung,which has been sub-jected to a bewildering array of translations that are not only awk-ward, but inaccurate. One of the keystones of Riemann's notion oftonal imagination, Klangvertretung,denotes a psychologicalprocess-ing of each soundingnote into a mental representationthat considerseach of its six harmonicmeanings(as root, third or fifthof a majororminor chord). Thus, for example, John Fillmore's translation of Ri-emann's Die Natur der Harmonik, which rendersthe term chord

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substitution, is certainly misleading (Riemann/Fillmore,28). Mick-elsen, on the other hand, chooses to render the term as chord-representation (Mickelsen, 85); this, althoughan improvementoverFillmore,still does not captureRiemann'smeaning.Elsewhere, Mick-elsen offers Klang-representation Mickelsen, 216), following Be-werung, who prefers to transliterate Klang as clang (Riemann/Bewerung, passim). Of crucial importancehere is the translationofthe term Klang, which has a more specific meaning to Riemann thansimply chord, as Fillmore and Mickelson would translateit. Klangencompassesboth an over-chord and an under-chord to use Fill-more's terminology) and therefore connotes a tonal complex aboveand below the pitch in question; hence, the translationof Klangver-tretunghere is representationof a tonal complex.The notion of Klangvertretung, ogether with the more familiarmusical ogic and the less familiarTonvorstellung, orm the basis ofthe psychological sphere of musicalactivitythat Riemann postulates,as Rummenh6llerhas remarked.9While Riemann's earlier workshaddealt with the first two ideas, the present work attemptsthe first in-vestigationof Tonvorstellung.Yet, Riemann admits that this notion isnot really a new one; indeed, the very opening of the present articlestresses the continuityand evolution of ideas fromhis dissertationon,and examplesof Riemann'semphasisupon the logical understandingof music may be found in any number of his works. Even Riemann'sfamous theoryof tonal functionsabstractshis earlier harmonictheoryfrom its material source in a move toward the psychologicaldomainthat becomes much more pronouncedin the presentwork (Rummen-haller, 104). It seems certainthatRiemann saw this theoryas a furtherstep towards an understandingof the mental processingof music, aswell as a means of expressingin notation the musical-logicalactivitiesthat occur in the musical imagination.In the present essay, Riemann sets forth these prioritiesfrom theoutset: the ultimatework to which he hopes his ideas will contributeis an obvious revision of Helmholtz's Lehre von den Tonempfindungen(our emphasis). In Riemann'sestimation, Helmholtz'sprimaryerrorwas to place too much stock in physical and physiological investiga-tions. CarlStumpf (1848-1936), the pioneering empiricalpsychologistand ethnomusicologist, fares little better in Riemann's essay.1' Ac-cording to Riemann, instead of producing a true Tonpsychologie,Stumpf becamebogged down in the detail-work of the preliminary

tone-psychologicalinvestigationof intervals (p. 82).11 In directcon-trast to these empirical, inductive approaches,Riemann places thefocus of his deductive nvestigationsquarelyon the mind, declaringultimatelythat

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the 'Alphaand Omega'of musicalartistrys notfound in the actual,sounding music, but ratherexists in the mental image of musicalrelationshipshatoccursin the creativeartist's magination-a mentalimagethat ivesbefore t is transformedntonotationandre-emergesnthe magination f thehearer.Theprocessof notating n artistic reationas well as thesoundingperformance f theworkaremerelyexpedientsto transplantmusicalexperiencesrom thecomposer's maginationntothe imaginationof the musicallistener.(p. 82, Riemann'semphasis)Thus, in the face of the empirical,materialist nvestigations by Helm-holtz and Stumpf,Riemannclingsresolutelyto an independentexist-ence of mind, maintainingthat his method is deductive. 12What,one mightask, is the relationshipof this mentalmusic to the sound-ing music of the externalworld?Though it would be unfair to accuseRiemannof ignoringthis question--and, indeed, we shall returnto itlaterin this Introduction--his fuzziness on thispoint was the source ofsubsequentcriticism;moreover, it is at the heart of one of the majordifficultiesin translatingthe work.With a clearer idea of Riemann'sagenda, we are now in a positionto consider the most important problems of translation. They beginrightat the outset, with the title itself. We have chosen to render Rie-mann'sproposed study as On the Imaginationof Tone, primarilybecause it underscores the work's relationshipto Helmholtz by par-alleling Ellis's translation. At the same time, it seems clear that Ellismade a wise choice, since this form of the title begs an unresolvablequestionof translation(whichEllis presumablychose to beg as well):whetherLehre can be taken to mean theory. Given that Riemann'sLehreremainedincomplete, diviningthe true nature of the theoryto which these ideas were to be a contribution is difficultindeed.The translationof Tonvorstellungen resentsan even more difficultproblem.The dictionarydefinitionof Vorstellungs alreadyconfusing:a common, concretemeaningof the verb vorstellen s tointroduce,toplace before, though in certaincontexts it may take on the more ab-stractmeaning, to represent. On the other hand, the reflexiveverbsich vorstellenhas an abstractmeaning,retainingthe placingbeforeas a metaphor-- to place before the mind, to imagine. Thus themeaning of the noun Vorstellung n common speech may vary fromintroduction o idea. Beyond these commonmeanings, however,the word has a long historyas a philosophicalterm, and indeed, a his-tory of controversyamong translatorsof Kant and Schopenhauer.While most translatorsof Kant'sworksrender Vorstellungas rep-resentation, '3 Wolfgang Schwarz argues strongly and persuasivelyfor presentation n a recent revised translation, because it avoids

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any association of duplicatingor copying thingswhich themselves aregiven nowhere but in the presentationswe have of them. '14 o Kant,a presentationsignifiesanymodificationof the mind, as suchbelong-ing to the inner sense (Schwarz, 269). Terminological correctnessandconsistencyareespecially importantfor Kant, because, in describ-ing the genesis of ideas, he employs a clear hierarchyof terms be-ginning with Vorstellung-the first stirringof the mind. A consciousVorstellungmarksPerzeption,progressingeither to Empfindung sen-sation) or Erkenntnis(whichSchwarzrenders as cognition ),the lat-ter consisting inthe determinate reference of given presentationstoan object (Schwarz, 263). The next step from cognition s either toAnschauung (whichSchwarzrenders intuition )-- thatpresentationwhich can precede any act of thinkingsomething (Schwarz,266)--orto Begriff (concept), which refers mediatelyto the object throughacommon characteristic Schwarz, 115). From concept one movesto empiricalconcept or pure concept, and from the latter ulti-mately to the idea (Idee), which is formed from conceptsbut whichtranscendsexperience.Thus, thougha Vorstellungmightappearto bewhat one thinks of as an idea in common parlance, the two termsarewidelyseparated n Kant'susage. Schwarzbemoansthe inflation-aryuse of Ideefor all kinds of presentations, citingKanthimself,whoremarksthat anyoneused to these distinctionsmust find it abhorrentto hear the presentationof red color called an idea (Schwarz, 115).Though the terms Anschauung and Vorstellung are used bySchopenhauer,theirmeaningsdifferconsiderablyfrom Kant'susage.Accordingto Schopenhauer, Vorstellung s the exceedinglycompli-cated physiological process in the brain of an animal, the result ofwhich is the consciousness of apicturethere. '5WhileSchopenhauer'sexplanation retains the metaphor of setting something before themind, this exceedingly complex physiological process has movedmuch closer to a Kantian idea. Consequently, it is perhapsunder-standablethat an earlier, less criticaltranslationrenderedDie WeltalsWille und Vorstellungas The Worldas Will and Idea.16 Schopenhau-er's use of Vorstellungis also considerably closer to Riemann's-despite Handschin's claim that Riemann's Lehre von denTonvorstellungens echterKantianismus. 17Now, if one is willing to sacrificethe settingbefore metaphor,other translationsbecome available. CarlJ. Friedrich,the translatorof a popularized ersion of Kant, addresses the problemas follows:

Even more perplexing s the term Vorstellung.Another substantivewith a distinct verbal connotation,the term is often translatedasrepresentation r presentation. ut thisusageis oftenmisleading

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as the verb vorstellen means primarily to imagine, and ... the de-rivativenounmaymean:(a) the act of imagining, b) the thing imag-ined, and (c) the imagein the mind.'8isFriedrich'sapproachto the problem proves to be the most practicalwith respect to Riemann's work. In fact, the act of imagining andthe image in the mind are precisely the two most prevalentmean-ingsof the term, as Riemannunderstands t. The thing magined, onthe other hand, is indistinguishable rom the imagein the mind. Forwhile musicmay exist in the outer world, such music s only a trans-mitting agent from an inventingmind to a receivingmind. When wethink of music, we are not imaginingthingsin the outer world;on thecontrary,our mental musicalimagesare the music. Indeed, in an ear-lier essay that Riemann himself cites in the presentwork, he goes sofar as to say:

The mechanical,materialallure of the real tone is so strongthat to acertainextent it even actsobstructively n the consciouspursuitof themoreintricate onalmanuveringshat one finds n the highestartisticachievements.Thus I question. . whetherhearingas an act of re-ceptioncaneverachievethe highdegreeof perfection hatis availableto the tonal imagination.19Friedrich'sapproachto Vorstellungalso works because the hierar-chy of terms and the terminologicalexactitude found in Kant is no-tably absent, and thus one need not-and cannot--distinguishbetween the firststirringsof the mindand the final idea :Vorstellungis a nearly ubiquitous, all-purpose term for Riemann. (And thus itmust be admittedfrom the outset that the exactepistemologicalstatusof Tonvorstellungs difficult to pin down. Riemann's essay is barelysaved from this dilemma by the structurethat his familiarbrand oftechnical music theory imposes on it, despite the essay's apparently

philosophicaltheme.)20 In order to capturethe breadthof the term,this translation generally favors imagination over conception,since the latter is more at home in restrictive, technical contexts. Itmust be rememberedthatwhile the term Tonvorstellungens renderedas the imaginationof tone in the title, partiallyin an attemptto re-tain the parallelism with Helmholtz's title, Riemann uses the termmuchmore broadlythan this English equivalent. Thus, in the bodyof the essay, Tonvorstellung,or its plural, is rendered variously astonal imagination, tonal understanding, tonal images, and oc-casionally tonalconception (to differentiatemore finely from per-ception or sensation ),as context demands. The verbalderivativeistreated in like fashion.Earlier we posed the question about the relationshipof these in-ward tonal images to outer, sounding music. It was Handschin's74



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opinion that with the notion of Tonvorstellung,Riemann had entirelyignoredthis problem, fallinginto a subjective dealism (Handschin,124-126). Seidel comes to Riemann's defense on this, pointing outthat Riemann inquires into the recognizablecharacteristics hat animaginedtone has in common with an actuallysounding tone, whenthe latter is correctly imagined (Seidel, 85). By inquiringinto therelationshipbetween purely mental musical activityand music in theouter world, Riemannmoves from a theory of musicalcognition toat least the beginningsof a theory of musicalperception. In fact, ifthere is a central theme to this wide-ranging, five-partessay, it is pre-ciselythe relationshipbetween musicof the mind and that of the outerworld;true, Riemannhardlyresolves thatdichotomy,but in each sec-tion, he treats some aspectof the musical magination and then goeson to attemptan investigationof the relationbetween the object of hisinquiryand soundingmusic.The music of the mind- Tonvorstellung-rests upon two interre-lated notions, which Rummenh6llerregardsas basic axioms of Rie-mann'sepistemology (Rummenhiller, 107): representationof tonalcomplexes (described above), and the principle of the greatesteconomy of the musical imagination. Already in Section I of theessay (which deals with the single tone) Riemann defines represen-tation of tonal complexes and then proceeds to the second notion,according o which the mind movesdirectlytowardrejectionof morecomplicatedstructures,where other possible meanings suggest them-selves thatweigh less heavilyon the powersof interpretation . . (p.88). Still speaking of the single tone, Riemann introducesexamplesfrom the real world of music: simple tunes that undergo peculiar al-terationsby whole and half step. The examples are not mere curios-ities, however; their point is that no power on earth can force thehealthymusician to hear somethingother than . .. bothersome into-nationalerrors (p. 90, below), rather than true modulations -thelatterwould become understandable nly throughthe representa-tion of tonal complexes and the arrangementof key relationshipsthat Riemann will develop as a consequence of this theory in SectionIV. Riemann ends Section I with more questionsaboutwhat the mindactuallyimagines;though he had earliermaintained that inthe caseof intensive musical temperaments, all the attributes of actuallysoundingmusicobtain (p. 83), his remarkson the aestheticvalue ofstring quartet music (p. 91) make it clear that processes involvingpitch and rhythmare central to the musicalimagination.In Section II, Riemann turns to the phenomenon of tonal mo-tion. That such motion may be located in tonal space withexactitudethroughthe phenomenonof absolutepitch leads to an investigationof that as well. Just intonation represents a cognitive law for

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Riemann;possessorsof absolute pitch who claim to hear enharmonicdistinctions in soundingmusic are to be regardedwith skepticism,hewarns,for such distinctionsoccuronly in the tonal imagination.21Rie-mann ends the section with one of his more thought-provokingspec-ulations: the realization of ascents and descents in concrete casesleads, for every melodicformation,to the recognitionof a middlelev-el, which forms the point of indifference or ascents and descents(p. 96). Accordingto Riemann, this middlelevel, whichmay be atthe beginningof a piece, formsthe absolute basis for relative ascentsand descents within the piece.In Section III, Riemanntreats the familiar representationof tonalcomplexes in such detail that it can only be considered digressive.Yet the end of the section is once againoccupiedwithproblemsof realmusic. Riemannbringsup the perennialproblemof the dissonant Ichord (as discussed by Hauptmann-and Sechter, for that matter).While the Law of the Greatest Possible Economy of the MusicalImagination seems to necessitate such an interpretation n the mu-sical imagination, ourmusicalpracticeknowsnothingof [thisprob-lem], and our tonal consciousness is even less aware that d:f:awouldnot be a pureminorchord,but rather a type of diminishedtriad. .. .Indeed, in this late essay Riemann maintainsthat we even imaginea117chord with two purefifths,andnot as a compositeof dominantandsubdominant,for otherwisewe would not be able to imaginethe dom-inant of 11.22 Thisenharmonic dentificationof acousticalvalues thatdiffer by a syntonic comma is simply indispensable to our musicalhearing (p. 100).In SectionIV, in whichthe Lawof the GreatestPossibleEconomyof the Musical Imagination yields the boundaries of an otherwiseendless key-relation scheme, Riemann seems less able to relate thisnotion to real music, endingmerelywith the feeble assertionthat tra-ditional theories of rhythm, motive, and phraseology can form thebasis of a theory of tonalimagination n these areas. But in SectionV, Riemannturnsto the imaginationof what he calls complexvoicemotions. Here, he attemptsto take melodic and harmonicintervalsof real musicwhose interpretationsare not immediatelyapparentandconsider them the composite of simpler, understandable motionsthroughwhat he calls auxiliarymental images (Hilfsvorstellungen).Though Riemann never says so explicitly, one presumes that suchcomplex motions are difficultor impossible to account for directlyby the stringsof thirds and fifths developed in Sections III and IV.Thus, for example, Riemann chooses to imagine the dominant andsubdominant in succession when negotiating the melodic tritone.23After attempting to extend this technique briefly to more complexchromaticprogressions, Riemann concludes:76



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That we imaginetonal relationshipshoroughly n the sense of puretuning s beyond question .. howit is possible n spiteof this thattheimperfectcompensatoryntonationof our commonlyused temperedmusicsatisfiesus andprovesto be a usablemeansof allowing he tonalimaginingsof the composerto ariseonce againin the imaginationofthe listener must be reserved for discussion in a later, new study(p. 109).

Thus, the climax of the essay placesthe dichotomyof the mind andthereal world once more in center stage, the last lines reiteratingRie-mann's belief that the future of music theory depends on developinghis theory of enharmonic identification. 24Significantly,this is theone law Riemannproposes that reachesbeyond the mind to the outerworld;that he places its development at the top of the agendafor thenextgeneration f theorists mphasizesheimportancef developingmechanisms to explain the relationshipbetween his cognitivelawsandsoundingmusic. Had thisbeen the startingpointof his new, laterstudy, Riemann's Lehre von den Tonvorstellungenmight well havebeen the first step towards a Theoryof MusicalPerception.

NOTES TO THE INTRODUCTION1. One who has shownconsiderablenterest s DavidLewin,whosevariouscom-ments on andinterpretations f Riemann'swork will be cited as appropriatebelow.2. See, for example,Counterpoint; Translationf Kontrapunkt y HeinrichSchenker, rans. John Rothgeband JiirgenThym (New York and London,1987),1:xxv, xxx, 7-9, 135-39, amonga numberof possiblepagereferences.3. ElmarSeidelprovidesa tabular ist of Riemann'spublications n harmonyonpp. 41-42 of DieHarmonielehreHugoRiemanns, n Beitrage urMusikthe-

oriedes 19. Jahrhunderts,d. MartinVogel (Regensburg,1966),39-92. A listof publishedEnglish ranslations f these works arrangedhronologically)ol-lows:New Lessons n Harmony.. to which s addedTheNatureof Harmonyby Dr. HugoRiemann, rans.JohnFillmore Philadelphia, 887)(citedbelowas Riemann/Fillmore );armonySimplified, rans.HenryBewerung Lon-don, 1896) (cited below as Riemann/Bewerung); Consonanceand Disso-nance:A Discussionof theProblemof HarmonicDualism translation f DasProblemdes harmonischenDualismus[Leipzig, 1905], trans. S. HarrisonLovewell(Boston, 1925; ypescriptn BostonPublicLibrary ndin New YorkPublicLibrary);Historyof Music Theory BooksI and II), trans.RaymondHaggh (Lincoln, 1962);Hugo Riemann'sTheoryof Harmony:A StudybyWilliamC. Mickelsen nd History f MusicTheory,Book III by HugoRie-mann, trans. and ed. WilliamC. Mickelsen(Lincoln,1977) (cited below asMickelsen );MarkMcCune, HugoRiemann's UeberTonalitAt':A Trans-lation, Theoria1 (1985):132-150.77



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4. Inthe foreword to the Historyof MusicTheory]Herr Riemann aysthathehas strivenat the veryleastnot to leaveout anything ssential o the courseofthe development of theory],and to givea coherentaccountof the genesisofthe various onceptsof the 'present-dayheory Lehre].'To theextentthatthisapplies o thewritings f antiquity,t is moreor lesstrue.However,sincebytheterm 'present-dayLehre' Riemann understands nly his own Harmonieleere(under hepresentcircumstances,his wordcannotbe writtenmorecorrectly),... that claim is made underfalse pretenses. BernhardZiehn, UeberDr.HugoRiemannsGeschichtederMusiktheoriem9.-19. Jahrhundert', n Ge-sammelte Aufsiitze zur Geschichte und Theorie der Musik, ed. J. Goebel (Chi-cago, 1927),292:(Ourtranslation.)*Fora recent(andmorebalanced)view of Riemann'sversionof the historyof harmonic heory, see Scott Burnham, Methodand Motivation n HugoRiemann'sHistory of HarmonicTheory, Music Theory Spectrum 14/1(1992):1-14.5. MickelsendividesRiemann'sife and workinto threeperiods: he firstperiodfrom1872-1890, he secondfrom1890-1909,and the third rom 1909 o 1919.See, for example,his Table of Contents,pp. v-vi.6. A fundamentalarticle is RichardMiinnich, Von Entwicklungder Rie-mannschenHarmonielehre nd ihremVerhiltniszu Oettingenund Stumpf,Riemann-FestschriftLeipzig,1909;rpt. Tutzing,1965):60-76. ElmarSeideloffersthe mostcomprehensive iscussion f Riemann'swritings n harmonynDieHarmonielehreHugoRiemanns, itedabove.(Muchof Mickelsen's extis baseduponMiinnichandSeidel.)An articleby GerhardWuensch urnishesa good introduction o Riemann in English: Riemann'sMusicalTheory,Studies n Music(Ontario)2 (1977):108-24.Riemann's Systemof TonalFunctions ervesas Lewin'spointof depar-ture in a mostimaginative xploration f the formalproperties f thissystem,andothersderived rom t;see DavidLewin, AFormalTheoryof GeneralizedTonalFunctions, ournalof MusicTheory 6/1(1982):23-60. In the midstofan articleon Wagner,Lewin aunches nto an excursus ontainingan extraor-dinarydiscussionof the relationship etweenRiemann'sharmonic ystemandthemuchbetter-known tufentheorie;ee Amfortas's rayeroTiturelandtheRole of D in Parsifal:The Tonal Spacesof the Dramaand the EnharmonicC6/B, Nineteenth-Centuryusic7/3(1984):336-349. In addition,Lewin'sre-cent book Generalized Musical Intervals and Transformations (New Haven,1987)containsa numberof sectionsthat are indebted to Riemann.See, forexample,the harmonicpace hatLewindescribeson pp. 20-22, as well ashisChapter , whichstudiesnetworksnvolvingransformationsf RiemannianKlangs. or thelatter,Lewincites asa precedentRiemann'sGrosseKompo-sitionslehre, vol. 1, Der homophone Satz (Melodielehre und Harmonielehre(BerlinandStuttgart,1902),479-480.7. Seidel(pp. 83-92) recountsmuchof the historyof thiscontroversy.Also seeHellmut Federhofer, Akkord und Stimmfiihrungin den musiktheoretischenSys-temen von Hugo Riemann, Ernst Kurth und Heinrich Schenker (Vienna, 1981),13-31 and Robert W. Wason, Viennese Harmonic Theoryfrom Albrechtsbergerto Schenkerand Schoenberg Ann Arbor, 1985), 126-7. For a moresympa-

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theticview, see TomChristensen, TheSchichtenlehref HugoRiemann, nTheoryOnly6/4 (May, 1982):37-44.8. Ideenzu einer 'Lehre von den Tonvorstellungen', ahrbuchderMusikbib-liothekPeters21/22(1914/15; pt.Vaduz,1965):1-26; NeueBeitrigezu einerLehre von den Tonvorstellungen, ahrbuchder Musikbibliothek eters23(1916,rpt. Vaduz,1965):1-21.9. PeterRummenhiller,Musiktheoretischesenken m19. JahrhundertRegens-burg,1967),102.10. SeeElizabethWestMarvin, TonpsychologiendMusikpsychologie: istoricalPerspectives n the Studyof MusicalPerception, Theoria (1987):59-84, fora discussion f the historical ontextof Riemann'snotionof Tonvorstellungen.11. All pageindications n parentheses efer to Riemann's ssay, below.12. But such a deductive method s hardly he deductivemethodof Hauptmann,for example.Rummenhillercharacterizest muchmoreaccurately s induc-tion at a higher evel (Rummenholler, 04).13. ImmanuelKant, Critique f PureReason,trans. NormanKempSmith(NewYork, 1950).14. ImmanuelKant, Critiqueof PureReason,trans. WolfgangSchwarz Darm-stadt,1982),xxii;hereafter ited as Schwarz. chwarz ites the EncyclopediaBritannica ndthe OxfordEnglishDictionaryas corroboration f his choice.Others agree, includingStephanKorner, Kant (New Haven and London,1982).15. ArthurSchopenhauer,TheWorldas Will and Representation,rans. E. F. J.Payne(IndianHills, Colorado,1958),xvii.16. Trans.HaldaneandKemp,5th ed. (London,1906).17. JacquesHandschin,Der ToncharacterZurich,1948),126.18. ThePhilosophyof Kant;ImmanuelKant'sMoral and PoliticalWritings, d.with an introduction y CarlJ. FriedrichNew York, 1949),xxxi.19. Spontane Phantasietditigkeitnd verstandmaiBige rbeit in der tonkiin-stlerischenProduktion, Jahrbuch der MusikbibliothekPeters (1909): 46;quotedby Rummenholler, . 106. (Ourtranslation.)20. ErnstKurth omplainshat Riemann's ssayamounts ssentially o arepetitionof his harmonicheory;see his MusikpsychologieBerlin,1931),47.

21. It mustbe emphasizedhat Riemann'spositionon thisissue s considerably if-ferent from that of Hauptmann,Oettingen,or Helmholtz,all of whomsoughtto introduce ust intonation nto actualmusicalpractice.22. Seidelspeculatesperceptivelyhat Riemannmaywell havegivenup the doc-trine of the apparent onsonance f secondarychordshad he lived longer(Seidel,p. 61).23. CompareLewin'sdiscussionof the harmonicntuition of the tritone(Gen-eralizedMusical ntervals ndTransformations,p. 17-20); Lewin ikewiseap-peals (implicitly)o similarHilfsvorstellungenn pp. 18-19.24. Riemann irstproposed histheory nMusikalischeyntaxisLeipzig,1877); eeespeciallypp. 33-34, 92, and 117through120.

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Riemann Ideen Zu Einer

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