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international Journal o f Musicolony 2 1993
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Carol K. Baron (New York)
At The Cutting Edge: Three American Theorists
at The End of The Nineteenth Century'
Summary. Three music-theoretical documents produced in the United States
during the last two decades of the nineteenth century by Bernhard Ziehn, Julius Klauser, and George Ives predated European theorists in accounting for
progressive trends in musical composition. They recognized anomalies in
theory, questioned conventional assumptions, and introduced new categories
for analysis - symptoms of a period of crisis and transition in intellectual history.
From roughly the time of Wagner's death in 1883 through the second decade
of the twentieth century, innovative theoretical works that evolved in both the
United States and Europe questioned the then current grammatical and syntactical assumptions in music. Three musicians in the United States, George
Ives (1 845- 1894). Bemhard Ziehn (1845- 1912), and Julius Klauser (18541907) - born within nine years of each other - were among the earliest theorists to respond to compositional practice in the second half of the nineteenth
century. The phenomenon of three Americans at the end of the nineteenth
century at the cutting edge of this field, while separated from the leading European practitioners of music theory, requires a logical explanation. I found
that Thomas Kuhn's theory for the history of science in The Structure of Scient@c Revolutions1 provided a basis for such understanding. His interpretation
of how categories and paradigms change, albeit in another field, was too compelling to leave untried in regard to the theoretical crisis in music that lasted
well into the twentieth century.
*
I am grateful to Severine Neff for introducing me to Ziehn's work; later, learning of
my interest in late nineteenth-century American theory, she generously made available her copy of Kiauser's book. I want to thank Milton Babbitt and Robert Wason for
reading an earlier version of this paper and making helpful suggestions.
The initial version of this paper was read at the 1990 meeting of the Society for Music
Theory in Oakland, California.
1 Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: University of
Chicago Press, 1962; 2nd ed., 1970).
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The backgrounds of the three American theorists were decidedly different.
Ziehn was born in Germany and came to the United States in 1868 at the age
of twenty-three. He settled in Chicago nineteen years before the German publication in 1887 of his textbook, Harnwnie- und Modulationslehre.2 Ziehn's
most advanced formal education is reported to have been gained in Erfurt,
Germany at a teachers' seminary. According to his biographer, he was selftaught in music - there is no evidence of his having been formally educated.3
When he first came to the United States, Ziehn taught German and mathematics, as well as music theory and history, before being able to devote himself
only to teaching piano and music theory.4 Klauser was an American, born in
New York City and raised in Farmington, Connecticut. His father was Karl
Klauser, a Swiss emigre who had an impressive reputation as a music editor
and arranger. Julius was sent abroad for music studies with Salomon Jadassohn at the Leipzig Conservatory from 1871 to 1874.5 After returning to the
United States, he settled in Milwaukee and became a music teacher. He wrote
two full length studies. The earlier one, The Septonate and The Centralization
of The Tonal System: A New View of The Fundamental Relations of Tones,
published in Milwaukee in 1890, will be discussed in this paper.6 George Ives
lived in Danbury, Connecticut - the state his ancestors settled in two centuries
earlier. His formal theoretical studies with Charles A. Foeppl, a German immigrant who lived in the Bronx, lasted from 1860 to 1862, when they were
interrupted by Ives's engagement as a Union Army bandmaster, and resumed
from 1866 to 1868.7 George Ives wrote an essay that was left unfinished by his
untimely death in 1894. Extant portions of two different copies - one a manuscript, the other a typescript - have been preserved. The sources for many
2 Bernhard Ziehn, Harmonie- und Modulationslehre (Berlin: Verlag Chrs. Friedrich,
1887, 1888, 1910); revised, incomplete English trans., Manual of Harmony, Vol. I
(Milwaukee: Wm. A. Kaun, 1907).
3 H.J. Moser, Bemhard Ziehn, der deutsch-mrikanische Musiktheoretiker (Bayreuth:
Verlag Julius Steeger, 1950), 9-1 1.
4 Ibid., p. 171.
5 A letter from Jadassohn to Karl Klauser, dated Leipzig March 9, 1873, regarding Julius's progress as his student, was advertised in a catalogue of J.J. Lubrano (Great
Barrington, MA, 1990).
6 Julius Klauser, The Septonate and The Centralization of The Tonal System: A New
View of The Fundamental Relations of Tones and A Simplificationof The Theory and
Practice of Music (Milwaukee: William Rohlfing and Sons, 1890). The final chapter,
on chromaticism and modulation, of Klauser's second work, The Nature of Music:
Original Harmony in One Voice (Cambridge, MA: The Riverside Press, 1909) was
incomplete at his death; the remainder of this study was published posthumously.
7 John Kirkpatrick, ed., in Charles Ives, Memos (New York: W.W. Norton, 1972), Appendix 13, "George Edward Ives (1845-1894) and his family," pp. 246-247.
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of Ives's ideas, as well as the objects of his criticism, can be traced through
this work.*
George Ives is the only musician under consideration who did not study in
Germany and whose family's native language was English. However he, like
the other two, had access to contemporary European music through performances andlor scores. Also, most of the leading works in European theory
were published in the United States soon after their European pub1ications;g
since the most important German theoretical studies were available in English
in the United States, the language factor is relatively unimportant. Ives used
Jadassohn's textbook for his son Charles' studies.10 Furthermore, Ives studied
German, and among his extant translations are passages from the first nine
pages of the first chapter of Helmholtz's Lehre von den Tonempfindungen
from an edition that predated the first English edition in 1875.11 Thus, al8 George Ives's essay is discussed in David Eiseman, "George Ives As Theorist: Some
Unpublished Documents," Perspectives of New Music 14, (1972): 139-147; Laurence
Wallach, The New England Education of Charles Ives, Ph.D. diss., Columbia University, 1973; and Carol K. Baron, "George Ives's Essay in Music Theory: An Introduction and Annotated Edition," American Music, Vol. 10, No. 3 (Fall 1992): 239288, which contains the first published edition of his essay and an account of George
Ives's relationships to his theoretical amd pedagogical predecessors. The extant
portions of the original document are housed in the Charles Ives Collection, John
Hemck Jackson Music Library, New Haven (negative photostat nos. 7398-7419).
9 These include works by the following theorists, with the earliest dates of their American publications: Gottfried Weber (1846), A.B. Marx (1851), Ernst Friedrich Richter
(1867), Simon Sechter (1871), Salomon Jadassohn (1885), and Hugo Riemann
(1887), among others. Karl Friedrich Weitzmann's studies were made available in
textbook form, with his approval and participation, by his American student E.M.
Bowman as Bowman's-Weitvnan's [sic] Manual of Musical Theory (New York:
Pond, 1877). (This work was later translated into German as Handbuch der Theorie
der Musik [Berlin: F. Schmidt, 18881.) The American Homer Noms published a twovolume textbook based on the theoretical approach of his teachers at the Paris
Consewatoire (1895). Furthermore, German periodicals were available in the United
States. The Neue Zeitschrift fur Musik, a Leipzig publication, lists distributors in
Boston, New York, and Philadelphia as well as in Berlin, Prague, Zurich, Vienna, and
Warsaw. Other important works published elsewhere in English were available in the
United States, such as those by Herman Helmholtz (1875) and Moritz Hauptmann
(1888); the earlier published original German texts were also available here. (Full citations are given in due course for works referred to in the text.)
10 Salomon Jadassohn, Lehrbuch der Harmonie (Leipzig: Breitkopf u. Hartel, 1883). An
English edition appeared almost immediately as A Manual of Harmony, trs. Paul Torek and H.B. Pasmore (Leipzig: Breitkopf & Hartel, 1884); also with the same title,
tr. T. Baker (New York: G. Schirmer, 1893).
11 Hermann Helmholtz, Lehre von den Tonernpfindungen als physiologische Grundlage
fir die Theorie der Musik (Brunswick, 1963); Eng. tr. by Alexander Ellis, On the
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though George Ives was educated in the United States, his music education
was as essentially German as those of Klauser and Ziehn.
Kuhn's revolutionary interpretation of historical change portrays scientific
development as a succession of tradition-bound periods punctuated by noncumulative breaks. Among the underlying assumptions of Kuhn's theory are
that knowledge is limited by the paradigm supporting the "facts"; that a paradigm must be shared by a group of specialists (208); that paradigm change is
rare; and that "normal science," which is cumulative, is concerned with puzzle-solving and the application and testing of established theoretical paradigms. Paradigms provide the concepts, procedures and, of no less importance, the language and tools through which ideas and new findings can be
articulated. Kuhn's concepts can be transferred to the history of music theory
in which "normal theory" consists of the analytical, critical, and speculative
activities that apply, test, and develop operative paradigms.
The process Kuhn postulates for paradigm change involves (1) the awareness of an anomaly in theory developed under the original, operative paradigm, (2) the transition to crisis, (3) the ability to recognize the anomaly empirically and theoretically in a tentative theory that can achieve a "match" with the
empirically-recorded analysis or discovery, and (4) the introduction of different categories and procedures (61-65). The last two steps involve "extraordinary" work leading to paradigm change which, in contrast to "normal" work,
is rare - in small or large matters - in science (or music theory). In the final
step (3,a potential paradigm must overcome the resistance of the professional
community which seeks to protect and remain loyal to the existent practice; it
must gain the acceptance of a community of scholars to achieve paradigmatic
status (176).12 This paper is concerned with crisis: with stages (3) and (4), as it
Sensations of Tone As A Physiological Basis for the Theory of Music (1875) based on
the 3rd German edition (1877). reprinted (New York: Dover Publications, 1954);
henceforth, Sensations. Evidence for dating George Ives's translation is found in Carol
K. Baron, "George Ives's Essay," op. cit., p. 243.
12 The professional isolation that spared the Americans from peer pressure precluded the
possibility of even a potential candidate for paradigmatic status from attaining that
status, since there was no professional community to accept, defend, refine, or help
develop the new theories. Under these circumstances, the stage during which a professional group is "converted (Kuhn 144) could never be achieved.
This circumstance differs fromthat of an active professional community that ignores a
theory, no matter how brilliant it is, because a) it "[canlnot be used to articulate the
paradigm from which it derived," i.e., function in "normal" theory (Kuhn 35), or b) it
is "not sufficiently fundamental to evoke the malaise that goes with crisis" (Kuhn 82).
The radical work of H.J. Vincent (1819-1901), described by Robert Wason in
"Progressive Harmonic Theory in the Mid-Nineteenth Century," Journal of Musicological Research 8 (1988:55-90) provides an exemplary instance of work likely
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was articulated in the American works considered here; tangentially, it is concerned with the relationship of these works to theory practiced at that time in
Europe.
~ e s ~ itheir
t e disparate backgrounds and geographical separation, the three
Americans were able to produce work, at a considerably earlier date than most
of their European counterparts, that was salient in its response to progressive
trends in composition. The documents discussed here were published or put
into written form between 1887 and 1894.13 They shared incisively critical
attitudes towards the German theoretical tradition from which they emerged,
and they are aggressively forward-looking, albeit in different ways.~Incontrast
to most of their European contemporaries, the three Americans were emphatically pragmatic in their orientation, empirically deriving conclusions andlor
systems from musical practice and directly applying them to logically-derived
pedagogical constructs. Here again they responded, as a group, well in advance of European theorists to the prevailing situation.14
ignored for these reasons. Vincent's tonal system, based on symmetrical major- and
minor-third divisions of the octave, and his description of symmetrical inversion,
using nine as the sum of inversion, were too idiosyncratic and abstractly logical to be
used by the theoretical establishment at that time. Therefore, as interesting and proleptic as Vincent's theory of tonality is to late-twentiethtentury readers, it was irrelevant to the professional community in his own time. Furthermore, note that thwretical topics f b m different periods may appear to be the same when, in fact, they address different issues and are relevant for different reasons. For example, recent
theories about cyclic structures were acquired in and applied to a different musical
universe.
13 According to Robert W. Wason, Viennese Harmonic Theoryfrom Albrechtsberger to
Schenker and Schoenberg (Ann Arbor: UMI Research Press, 1985), "with most works
of the period [Riemann's work is the given exception] the gulf which separated
'speculation' and the outmoded 'practical' textbooks was simply unbridgeable. Neither
'$-actical' harmony nor 'speculative1theory - regardless of method - had much to do
with musical practice," a situation Wason dates as late as the middle of the first
decade of the twentieth century when the early works of Schenker (1906) and Louis
and Thuile (1907) were published (p. 117).
14 The contemporary Austrian theorist Josef Schalk (1857-1900) (and undoubtedly
others not yet documented in research) shared some concerns with the theorists
discussed in this paper, raising novel and sometimes similar ideas, and will be referred to again. I have based my position on evidence from several late nineteenth-century German theory textbooks and articles (among them those works listed in footnote
9) and from the following studies, to which I am much indebted for a panoramic view
of the field of nineteenth-century theory, its antecedents, and early twentieth-century
developments: Martin Vogel, ed., Beitriige zur Musiktheorie des 19. Jahrhunderts
(Regensburg: Gustav Bosse Verlag, 1966); Peter Rummenholler, Musiktheoretisches
Denken im 19. Jahrhundiert (Regensburg: Gustav Bosse Verlag, 1967); Carl
Dahlhaus, Untersuchung iiber die Entstehung der harmonischen Tonalitat (Basel: Ba-
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The chronological priority of a discovery or a theory in the historical
process of paradigm change is inherently interesting in itself (even if it is less
significant than the articulation of the crisis or the ultimate paradigm change).
I want to suggest several reasons that may facilitate our understanding the
synchronic emergence, at the end of the nineteenth century, of three such different and innovative music-theoretical personalities in the United States. One,
the remoteness of Ives, Klauser, and Ziehn from the obligations and pressures
imposed by direct association with the established European academies may
have been the decisive factor in their accomplishment. Established professional communities tend to resist change because their status and vested interests
could be threatened by having a new paradigm replace its predecessor (144).
The normal recalcitrance of professionals to change would have been less potent in the United States than in Europe, since there existed no established professional community in music theory.15 Another reason is their relative lack of
commitment to the old paradigms, a trait usually displayed by people "so young or so new to the crisis-ridden field that practice has committed them less
deeply than most of their contemporaries to the world-view and rules determined by the old paradigm" (144). While the Americans were neither particularly young nor new to the field at the time they wrote, they were certainly less
committed to prior paradigms than their European counterparts, just as they
were less loyal to European establishments, discovering personal power and
satisfaction in their independence and in their critical natures - the power and
satisfaction frequently identified with youth. A third reason is that the prominent European theorists, by their devoted and thorough application of outworn
methods, enabled the Americans removed from the professional hub of intellectual activity to articulate the need for change. The anomalies in theory were
clarified by the steadfast application of the old "rules" of classical harmony to
renreiter Kassel, 1968), Eng. tr. Robert 0.Gjerdingen (Princeton: Princeton University Press, 1990); William C. Mickelsen, Hugo Riemann's Theory of Harmony
(Lincoln: University of Nebraska Press, 1977); Robert W. Wason, Viennese H a m nic Theory (op. cit.), "Progressive Harmonic Theory" (op. cit.), and "Schenker's Notion of Scale-step in Historical Perspective," JMT 27.1 (1983): 49-73; and Lee Rothfarb. Ernst Kurth as Theorist Md Analyst (Philadelphia: University of Pennsylvania
Press, 1988).
15 By contrast to the situation in the United States, note Wason's statement in
"Progressive Harmonic Theory" that the publication of H.J. Vincent's progressive
work, Die Einheit in der Tonwelt (Leipzig: Heinrich Matthes, 1862), in Leipzig rather
than in Vienna, where Vincent lived and worked, "may give some idea of the power
which Sechter's ideas exerted in his home city during their heyday" (p. 58 f.). See
footnote 12.
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the new music, preparing the way for the less committed Americans to define
the crisis.16
Works from a period of crisis typically express a widely-felt "need"; they
contribute new ways of focusing on a problem by pointing out the inadequacies of current theories and suggesting alternative solutions. The anomalies
in European music theory, precipitated by chromaticism and tonal ambiguity
in practice, were the motivating issues for these progressive American works.
Their authors observed and experienced music differently from their predecessors. No longer concerned with arguments about the relative merits of German
harmonic theory and Viennese step theory.17 the documents of Ziehn, Klauser,
and Ives, jointly, open the following topics to criticism: staff notation, pitch
and interval nomenclature, the analytical practice of plurisignificance, altered
tones, majorlminor dualism, acoustical explanations for harmony or tonal relations, figured bass, four-part harmony, and fundamental bass theories,
among others. They needed to restructure past theoretical knowledge to make
it correspond to their own experiences.18
While the three theorists had responded to the same crisis, they identified
the "novelties" in composition in different ways. Their differences can be attributed, at least in part, to their having emerged from somewhat different
traditions and influences: theoretical works that each of them knew formed the
basis of their criticism and new theories. Each of the works considered in this
paper is unique and idiosyncratic - characteristics of works produced during
periods of crisis.19 Since the style and thrust of the arguments are so different,
16 Kuhn explained the function of resistance to change in the scientific community: "By
ensuring that the paradigm will not be too easily surrendered, resistance guarantees
that scientists will not be lightly distracted and that the anomalies that lead to paradigm change will penetrate existing knowledge to the core. The very fact that a significant scientific novelty so often emerges simultaneously from several laboratories is
an index both to the strongly traditional nature of normal science and to the wmpleteness with which that traditional pursuit prepares the way for its own change" (Kuhn
64).
17 Introducing Ernest Kurth's historical position, Lee Rothfarb (in Ernst Kurth, op. cit.,
p. 108) summarized the traditional European concerns as "the reality of 'dualism,' the
relevance of psycho-acoustics, and the relative merits of 'step' theory and 'function'
theory."'
18 "A new theory, however special its range of application, is seldom or never just an
increment to what is already known. Its assimilation requires the reconstruction of
prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process
that is seldom completed by a single man and never overnight" (Kuhn 7).
19 Kuhn's characterization of work done during periods of crisis is apposite to the works
discussed in this paper: "The proliferation of competing articulations, the willingness
to try anything, the expression of explicit discontent, the recourse to philosophy and
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I will discuss the works separately, in the order that they were either published
or put into written form. Some questions about tuning in theory and practice at
the end of the nineteenth-century remain controversial to the present day; therefore, I will conclude with a discussion of tuning and notation - the latter, an
issue associated with tuning at that time.
Bernhard Ziehn's contribution to this period of crisis is epitomized by his aggressive denial that modem music could be explained by any theoretical system. His position is made clear in his highly polemical articles and in the
format of Hannonie- und Modulationslehre.20 His position was a familiar response in a period of crisis or transition, as described for the sciences by
Kuhn, who writes that "scientists may conclude [at such times] that no solution will be forthcoming in the present state of their field. The problem is
labelled and set aside for a future generation with more developed tools"
(Kuhn 84).
Ziehn ridiculed musical systems and, implicitly, all system-building. He
focused his criticisms on logical arguments based on speculation, brutally attacking theory's most prestigious practitioners. He characterized the theories
of Riemann and Hauptmann as "illusions" (Scheingebilde).21 In his own theoretical works, Ziehn eschewed even fully-formulated explanations, let alone
system-building. In Hannonie- und Modulationslehre, he adopted the role of
the ultimate empiricist, using charts, lists, and numerous examples from literature; he classified types of chordal configurations with only the sparsest annotations. This format avoided the pitfalls (and the seeming futility) of inferential constructs. Through it, Ziehn avoided the need to seek solutions to the
to debate over fundamentals, all are symptoms of a transition from normal to extraordinary research" (Kuhn 91).
20 Harmonie- und Modulationslehre, op. cit. Most of his articles were collected posthumously in ed. Julius Goebel, Jahrbuch der Deutsch-Amerikanische Historischen Gesellschaft von Illinois, Bd. 26-27 (1927).
21 In Bernhard Ziehn, "Julius Klausers Septonat," in ed. Julius Goebel, Jahrbuch, op.
cit.: 75-76. He called Riemann an "iirgsten und geschwiitzigsten Musikmeister dieses
Jahrhunderts" (the worst and most garrulous music manager of this century) and
Hauptmann an "odenFinsterling" (a tedious ignoramus or obscurantist, i.e., a creature
of the dark) (p. 75). See footnote 60 for Ziehn's criticism of Klauser's work, which
particularly irritated him because of its expressions of "such undoubting certainty" (so
unverzagter Sicherheit).
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difficult questions about tonality, modulation, and long-range pitch structures
that were raised by the music of Liszt, Bruckner, and Wagner.
Ziehn's work has never been placed in a credible cultural or historical perspective. Like the composer Charles Ives, he has been cast as a genius-innovator, self-taught, who evolved out of the cultural nothingness that characterized the United States but who, in Ziehn's case, benefitted from his German
birth. Fermccio Busoni praised him as "a theoretician who points to the possibilities of undiscovered lands - a prophet through logic. As a master of harmony he stands alone."22 An article written about him in 1933 is entitled
"Bernhard Ziehn Precursor"; it touts his accomplishments as a "true prophet,"
anticipating and formulating in theoretical terms the compositional methods of
forward-looking composers.23 Without doubt, he exerted a formidable cultural
influence on the German emigres in Chicago who gathered and published his
articles fourteen years after his death.% In fact, Ziehn was a highly respected
and accomplished teacher whose students included some fine musicians and
composers. Yet the extravagant nature of the claims made about him and his
ensuing reputation were as symptomatic of crisis and transition as his work aspects of the search for new, satisfactory explanations.
Almost nothing factual is known about Ziehn's musical education. His biographer Hans Joachim Moser raises the possibility that Ziehn, prior to leaving
Germany, was influenced by the work of Johann Christian Lobe (1791-1881),
a respected theorist considered to be in the vanguard during the period before
Ziehn's departure. However, it is more likely that Ziehn either studied with
Carl Weitzmann (1808-1880) or, at least, was influenced by his publications.
Evidence for this assertion lies in Ziehn's respect for Weitzmann, as demonstrated in an article that harshly criticizes many major theorists other than
Weitzmann,z and in the many examples in Hannonie und Modulationslehre
22 Fermccio Busoni, "Die Gotiker von Chicago, Signale (1910), 163; repr. in Wesen und
Einheit der Musik (Berlin, 1956).
23 Winthrop Sargeant, Musical Quarterly, xix (1933), pp. 170-171, is otherwise a fine
introduction to Ziehn's ideas.
24 Goebels, op. cit.
25 Ziehn never subjected Weitzmann to the tongue-lashings he bestowed on all of the
most eminent nineteenth-century theorists in the article, "Ueber neuere und neueste
Harmonielehre" (in Goebel. Jahrbuch, op. cit., [1905]: 306-335). He even gave
Weitzmann a back-handed compliment when he wrote that since Mozart and Beethoven permitted a certain progression, "then even Weitzmann, who is truly more important than Hauptmann despite this, had no right to say: of such kind there is no such
thing and it's not valid" ("so hat auch Weitzmann, der doch wahrlich mehr bedeutet
als Hauptmann kein Recht zu sagen: dergleichen gibt's nicht und geht nicht" (p. 312).
In general, Klauser accepted the validity of Weitzmann's work.
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credited to the Weitzmann publication, Contrapunkt-Studien.26 Certainly,
Ziehn could also have known the American or German editions of the textbook based on Weitzmann's work, but that was hardly necessary." Weitzmann
was awarded an important prize in a competition for an original work in theory, which was then published in nine installments of the 1860 issues of Neue
Zeitschrifrfitr Musik, the journal that sponsored the competition.28 From what
is known of his precocity, Ziehn would likely have read this work before emigrating in 1867.
Weitzmann and Ziehn shared a vital interest in canons. Weitzmann wrote
two books of puzzle canons entitled Musikalische Ratsel;29 Ziehn published
the Canonical Studies.30 Ziehn's reputation has been largely associated with
his article, "Uber die symmetrische Umkehrung,"31 probably because of the
compositionally provocative nature of symmetrical inversion - a term he coined - which eclipsed in prominence the comprehensive Harmonie- und Modulationslehre. Tracing the technique of symmetrical inversion back to the
Renaissance use of contrary motion, Ziehn then developed inversion (as well
as canonic imitation) with the chromatic license that allowed for precise
imitati0n.3~
26 Karl F. Weitzmann, Contrapunkt-Studien (Leipzig: J. Schuberth, c. 1874).
27 See footnote 9.
28 Karl F. Weitzmann, "Harmoniesystem," Neue Zeitschriji fir Musik, Nos. 1-9, Jan.Feb. (Leipzig, 1860). See footnote 9; also Wason, "Progressive harmonic theory," p.
56, for interesting details about the competition.
29 Karl F. Weitzmann, Musikalische Ratsel (Leipzig: J . Schuberth, 1870).
30 Canonical Studies: a New Technic in Composition.Canonische Studien: ein neue
Compositions Technik, a bilingual edition (Milwaukee and Berlin, 1912); abridged in
English, Canonical Studies (London, 1976).
3 1 In Goebel, Jahrbuch (op. cit.), pp. 186-217.
32 See David W. Bemstein, "Symmetry and Symmetrical Inversion in Turn-of-the Century Theory and Practice," Music Theory and the Exploration of the Past, David
Bemstein and Christopher Hatch, eds. (Chicago: University of Chicago Press, forthcoming).
Harmonie- und Modulationslehre, pages 158-9, contains a short section called
"Symmetrische Umkehrung," which Ziehn defines as an extension of contrary motion
("Der Verfaser d.B. das durch ihn enveiterte Contrarium reversurn, welches er in
dem vorliegenden Buch bisweilen enwendet die 'symmetrische Umkehrung"').Ziehn
first applied symmetrical inversion to iibungenfiir Klavierspieler (1881), in which he
took advantage of the symmetrical potential for piano exercises beginning on D or Ab.
Ziehn's interest in imitative techniques was reflected particularly in the monumental
study of Bach's Art of Fugue by his student Mittelschulte.
Ziehn seems not to have known Vincent's 1st unsre Harmonielehre wirklich eine
Theorie? (Vienna: Rorich, n.d., 1894 in Baker's Biographical Dictionary of Mu-
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More to the point, the origin of most of Ziehn's ideas can be found in
Weitzmann's; they addressed many of the same issues. Therefore, in describing the following highlights of Ziehn's work, I will compare some of them to
earlier statements by Weitzmann. Ziehn's goal was to identify all conceivable
types of "chords" and progressions, particularly those representative of modem music. His methodology consisted of identifying different types of simultaneities in music, categorizing them, and placing them in short progressions
(along with showing them in their original musical contexts) - an extension of
Weitzmann's method.33 Ziehn applied his method to hundreds of examples
from a broad spectrum of musical literature - from the Renaissance through
Bruckner, ~ i s z and
c Wagner.
Weitzmann had extended the notion of the independent chord to include
augmented and diminished triads, diminished seventh triads, and sevenths
built on every diatonic step. He also recommended the recognition of other
frequently encountered combinations, particularly the augmented-sixths, as
independent chromatic chords. In Ziehn's 1887 publication, the independent
chord included any triad, seventh, or ninth built on combinations of major,
minor, diminished, and augmented thirds. He emended this formulation for the
1907 edition, in which chords were built only on combinations of major, minor, and diminished thirds. Weitzmann had built all chords from combinations
of major and minor thirds.34 Ziehn's section on suspensions as alternative readings for dissonant and chromatic chords was also prefigured by Weitzmann.35
sicians), which provides a systematic basis for symmetrical inversion in mod 12 (see
footnote 12), no where suggested in Ziehn's article.
33 In Harmoniesystem (op. cit.) and in his three early works: Der iibermiissige Dreiklang (Berlin: Guttentag, 1853), Der verminderte Septimenukkord (Berlin: Guttentag,
1854), and Geschichte des Septimen-Akkordes (Berlin: Guttentag, 1854). Wason, in
"Progressive Harmonic Theory," calls the short progressions "voice-leading minutiae"
... "traceable ultimately to Vogler," which "would remain the usual pedagogical approach to 'chromatic' harmony for many years" (79).
34 In "Progressive Harmonic Theory," Wason describes Weitzmann's idea of what constitutes "natural" chords and intervals, as well as certain inconsistencies therein. For
example, Weitzmann treated the augmented triads and diminished-seventh chords as
natural only after explaining the derivation of their chromatic elements in the flat
sixth of the minor subdominant transferred to major and the sharp seventh of the major dominant transferred to minor. Ziehn no longer needed this rationalized nicety.
Weitzmann did not accept the independence of ninth chords, associating them with
organ tones and suspensions.
35 Weitzmann identified as independent chords all forms of dissonant and chromatic
chords whose simultaneities had previously been identified in suspension formations,
and in delayed or contracted resolutions, thus finding their justification (Rechtfertigung) in melodic origins (Harmoniesystem, p. 45). In summary, Weitzmann concluded that any consonant chord can follow any other consonant chord and, with few
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In both Ziehn and Weitzmann, applying theoretical concepts from a later period to works from an earlier one has strange analytical consequences, as when
Weitzmann locates independent augmented and diminished chords in music
by Caldara, Monteverdi, and Schutz but disregards their voice-leading origins.36
Focusing on chromatic or "altered chords" in the context of possible progressions or resolutions, Ziehn began with the assumption that "any chord can
proceed to any chord." He included Weitzmann's exceptions.37 His system of
chord classifications was devoid of diatonic references - to either keys or
scale steps. Although Ziehn began his study with chords built on the diatonic
scales, he almost immediately stripped away references to tonal relationships
except in the one section on modulation, a topic which also is treated only
with short progressions. The classifications are abstract, with chord types
identified by their configurations and spelling. Weitzmann's influence is seen
here, also, through his idea that there is no practical advantage to naming the
various combinations known as altered chords, since they are derived from
diatonic chords and move in the same directions as the original chords with,
however, directions clarified and intensified.38 Either to establish historical
precedence or corroboration for his claims, Ziehn identified these "chord types" in older music, especially that of Beethoven and Bach.39 Ziehn's classifi-
36
37
38
39
exceptions, all dominant-seventh chords can resolve to any triad when chromatic and
enharmonic passing notes are permitted (Ibid, p. 18). He labels dissonant chords
moving to other dissonant chords "deceptive progressions" ("Trugfortschreitung");
they are permissible as long as they follow normal voice-leading rules for resolution
(Ibid., p. 46). Ziehn developed the radical aspects of Weitzmann's work, which gained
neither the attention nor the disciples for Weitzmann that they later gained for Ziehn,
demonstrating Kuhn's point that works not fundamental in either normal theory or
paradigm building "could be recognized as counterinstances and still be set aside for
later work" (Kuhn 82).
Der iibermiissige Dreiklang (Berlin: Guttentag, 1853), p. 36.
Footnote 25 cites the reference in which Ziehn disagreed with Weitzmann's claim that
the seventh of a seventh chord could not be tied to a tone (i.e., have a tone in common) in the chord of resolution.
Weitzmann stated that the application of a chromatic sign to the tones of the original
or fundamental harmonies created altered chords and that the original chord is regained (and identified) by cancelling the accidentals (Bowmen-Weitzmann, pp. 233-235
passim). Weitzmann rejected the German chord identification and labelling system,
first developed by Gottfried Weber, avoiding, like Ziehn, the need to deal with the
complexities and ambiguities of tonal priority and modulation.
Not distinguishing between styles sometimes led to peculiar interpretations of older
music, and even of nineteenth-century chromatic music. In this matter, Ziehn's
doctrinaire approach lead to absurdities similar to those of Weitzmann, who located
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cation system reflected his perception of the grammar of contemporary
practice and its syntax; it was persuasive to many professionals in his time.
Ziehn's identification of nine types of altered seventh chords by their arrangements of major, minor, and diminished thirds is probably his best-known set
of classifications. The tertian configurations of these chords are facilitated by
enharmonic spellings.40 They are labeled with arbitrarily assigned Roman numerals, bearing no relationship to scale steps. In Example 1, three of Ziehn's
nine seventh-chord types are shown; they contain two major thirds and one
diminished third.
Example I (Ziehn, Modulationslehre, 13)
Example 2 presents the remainder, types IV through IX.
Example 2 (Ziehn, Ibid., 14)
Types IV through IX all contain one major, one minor, and one diminished
third. Since all nine types contain a diminished third, each of them is transformed into an augmented sixth chord in one of its inversions. Ziehn also
shows all nine types using the same diminished third and then shows each of
them transformed to augmented sixth chords through inversion. The resolution
of these altered seventh chords involves the contraction of the diminished
third.41
Using the same principles, Ziehn also constructed different types of altered
triads with permutations using two kinds of thirds. Types I and 11 contain one
independent augmented and diminished chords in music by Caldara, Monteverdi, and
Schiitz, in Der iibenniissige Dreiklang, op. cit., p. 36.
40 Ziehn, Harmonie- und Modulationslehre (1887), pp. 13-17. The dependence of these
chords on enharmonic spellings for their tertian configurations - the only form used may be thought of as anachronistic, since these configurations cannot be identified
aurally as triads: the identification is visual only.
41 "...bei alterirten Septimenaccorden [ist] die verminderte Ten. [aufzulosen]"
(Harmonie- und Modulationslehre, p. 14).
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major and one diminished third; Types 111 and IV contain one minor and one
diminished third; Type V consists of a minor third under an augmented third,
and VI consists of an augmented third under a minor third, both embraced by
an augmented fifth; Type VII consists of a major third over an augmented
third, and VIII consists of an augmented third over a major third, both embraced by a doubly-augmented fifth; Types IX and X, respectively, contain an
augmented third under a diminished third, and a diminished third under an
augmented third.42
Ziehn's classifications are problematic because they are based on chords in
root positions in which even the roots can be altered.43 He developed what he
entitled "Das enharmonische Gesetz" (the enharmonic law), which states that
every tone, in every verticality built on thirds, is a potential root through inversion and enharmonic spellings.44 Although Ziehn seems to be suggesting
different syntactical relationships, his dependence on chord formations based
on root position configurations is inconsistent with their remoteness from root
42 Ziehn gives reasons for not including the following two combinations:
1. Triads with two augmented or two diminished thirds: "One can properly disregard
the construction of two diminished or two augmented thirds; when in these harmonies
the quality of thirdness, thus the quality of a chord, which also presents itself to the
eye, remains to the ear still more incomprehensible than the triads numbered V to X."
("Von Verbildungen zweier verminderten oder zweier iibermassigen Terzen kann man
fiiglich absehen; dehn wenn in diesen Harmonie'n das Terzenhafte, also Accordische,
sich auch dem Auge darstellt, so bleibt es dem Gehor doch noch unfassbarer als in
den Dreiklangen Nr. V bis X".) (Ziehn 1887,20).
2. Major seventh chords: "The enharmonic transformations of the three major seventh
chords are useless constructions because they all have in them the unresolvable interval of the double-diminished third [BCDb or D#-F'J]." ("Die enharmonischen Verwechselungen der drei grossen Septimenaccorde sind "nbrauchbare Gestaltungen, da
ihnen sammtlich ein nicht aufliisungsfahiges Interval1 eigen ist: die doppeltverminderte Ten. (his des od. dis fes.") (Harmonie- und Modulationslehre, p. 56).
43 Altered mots are used in seventh-chord Types 111, IV, V, and VIII of Examples 1I
and 12, and the triad Types 111, VI, VII, IX, and X.
44 "Das enharmonische Gesetz: In jedem Dreiklange oder Septimenaccorde irgend einer
Art, sowie im grossen Nonenaccorde, kann jede Umkehrung die Grundform eines anderen, aus denselben Tonen bestehenden Accordes sein; also jeder accordische Tone
kan Grundton werden" (Ziehn, Harmonie- und Modulationslehre, p. 56). (The enharmonic law: In every triad or seventh chord of any kind, as well as in major ninth
chords, every inversion of the original form can become another configuration of the
same notes; therefore every chord tone can become a root tone.)
This concept, not mentioned in the 1907 English revision, was probably intended
for inclusion in the second volume of the English edition, which was destroyed in a
fire (see Severine Neff, "An American Precursor of Non-tonal Theory: Ernst Bacon
[1898-19901, Current Musicology 45 [I9871 p. 25, note 8).
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functions. Schoenberg rejected this concept of altered roots in his later, more
authoritatively realized work: "The assumption of a raised root" is "incorrect
in a system that considers roots (that can only be unraised ones) its unit of
measure."4s While basing his chord types on root positions, Ziehn seems to
have been suggesting, through the format of his presentation, that symmetrically-inverted pairs are inversionally equivalent, as in the following paired triadic configurations and their associated progressions in Example 3: Types I
and 11, and Types I11 and IV.
Example 3. Altered triads with types I and 111 and types I11 and IV symmetrically paired
(Ziehn, Ibid., pp. 17 and I9)46
Ultimately, such structures as Ziehn devised are arbitrary when no system
supports them; yet they are a significant reflection of the late-nineteenth-century theoretical enterprise."
45 Arnold Schoenberg, Theory of Harmony, Roy E. Carter, trans. (3rd ed. Harmonielehre, 1922) (Berkeley: University of California Press, 1978), p. 246; Harmonielehre,
1st ed. (Vienna: Universal Edition, 1911). After relating chord roots and altered
chords directly to the diatonic system, Schoenberg discussed the danger of vagrant
chords to that system. In correspondence, Robert Wason offered that Schoenberg
followed "Sechter, and the Viennese party line, on this matter." However, Schoenberg
then pursued the "dangerous" direction to its, for him, logical conclusion and suggested "the establishment of a new conceptual unit (auffassungseinheit): the chromatic scale" (Schoenberg 1978, 247). At the interim stage in the development of the
atonal paradigm in which Ziehn worked, Schoenberg's conclusion - part of his
compositional development - was probably not possible.
46 Using numerous examples, Ziehn showed each triad in three positions, in closed and
open voicing. The paired triads, in all of these progressions, moved in inversionalsymmetry.
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Ziehn reinterpreted the meaning of several terms, shifting them from their
original diatonic context to a more neutral or ambiguous tonal realm. For example, while Ziehn is credited with having translated the term "mehrdeutigkeit" into the English term "plurisignificance," he gave it a new, non-traditional meaning. Instead of just signifying different interpretations of the same
chords in multiple keys, Ziehn extended its meaning to signify different
interpretations of intervals created by multiple spellings48 and by their appearance in multiple chord types.49 He also categorized individual tones in
multiple chord positions.50
Another example of Ziehn's radically expanding traditional definitions is
available in his definitions of "wesentlicheund ziiLfallige Dissonancen":
Essential dissonances are those non-consonant harmonies which can be resolved into a
consonant triad. Essential dissonances are or can be: the diminished and the augmented
triad, the chromatic triads, the diatonic and the chromatic Seventh- and Ninth chords, and
the dissonant intervals of these chords.
Accidental dissonances are harmonies which do not occupy a place by themselves, but
depend evidently upon the following or preceding harmony. The separate tones which make
the harmony an accidental dissonance also receive that name. To the accidental
dissonances belong: suspension, after-beats, anticipations, passing tones and chords, and
organ-points. Another kind of accidental dissonances are those dissonant chords which can
not be resolved into a consonant triad; such as the doubly diminished Seventh-chords, the
pseudo triads, Seventh- and Ninth chords, and chords containing an augmented third [i.e.
other than the augmented triadl.51
Ziehn discusses the chromatic and whole-tone scales in regard to their appearances in literature, prior to presenting his abstract examples. In the section
on the whole-tone scale, he calls attention to relationships between the chromatic scale, the augmented triad, the diminished seventh chord, and the
47 Another peculiar paradox exists in Ziehn's method, as problematic as the one in his
theory of altered roots. Since altered, or chromatic, triads are all those that are not
major or minor, what are the chromatic triads in Ziehn's system which are major or
minor but not diatonic? In light of this impasse, note Klauser's rejection of the concept of alteration as ephemera, in the next section of this paper.
48 Ziehn, Harmonie- und Modulationslehre (1887), p. 13.
49 Ziehn, Manual of Harmony, p. 56.
50 Ibid., p. 6. See Severine Neff, "An American Precursor," pp. 7-8 for a discussion of
statistical operations applicable to Ziehn's broad interpretations of plurisignificance.
51 Manual of Harmony, p. 5. In the 1887 edition, in which augmented thirds were accepted, Ziehn said the following in regard to constructions from "a diatonic and an augmented third" ("Bildungenaus einen Leitereigenen und einer iibenniissigen Terz"):
"These, like the other altered triads, are accidental dissonances" ("Dieserwie auch die
noch iibrigens alterirten Dreikliinge, sind zufallige Dissomnzen [p. 201). The augmented triads were eliminated in the revised edition.
209
whole-tone scale (mod-12 symmetrical cycles). He harmonizes the chromatic
scale with parallel chords and sequences. His treatment of the whole-tone
scale, harmonized with various sequences, such as dominant sevenths in the
cycle of fifths,= is similar to harmonizations found in Weit2mann.a
Ziehn never expressed the need for nomenclature and notation based on the
chromatic scale (forcefully presented by Ives and Klauser, as we shall see).
Instead he treated enharmonicism as a phenomenon that needed, itself, to be
categorically recognized and formalized in theory. I believe his treatment of
enharmonicism is the underlying meaning of his "Enharmonic Law." In effect,
he addressed the problem of tuning and notating twelve equally tempered tones in his own way - within a complex "nonsystem." His response to enharmonicism is very different from that of Klauser and Ives, as will be seen.
The substitutions for V-I progressions by other "leading-tone" chords in nineteenth-century music diminished the significance of the dominant-tonic relationship. In his disregard of fifth relationships and in his treatment of cadences, Ziehn recognizes the dissipated power of the dominant-tonic relationship
in contemporary music. His ideas become clarified in the chapter on cadence
in the 1907 revised edition: "These cadences ... are not confined to the narrow
limit of dominant and tonic." Indeed, all cadences ending on the tonic are called perfect and, referring to traditional theory, Ziehn says the authentic cadence and the plagal cadence are simply two among many which have "special
names."% This idea, not yet developed in the earlier 1887 edition, appears in
Ziehn's 1905 article, "Ueber neure und neueste Harmonielehren": "To still
speak of dominants and 'dominants' today is an anachronism. We may use the
word because it is traditional; however, its original meaning has long been
lost. The dominant domineers no longer ...".55
Probably because he denied underlying systematic bases for nineteenthcentury music, and because he introduced totally objective categories for all
progressions (particularly those of altered chords) in order to displace their
syntactically diatonic interpretations, Ziehn's perceptions have been associated
with atonal music.56 Whether or not that particular association is valid, Ziehn's
52
53
54
55
Ziehn. Harmonie- und Modulationslehre,pp. 150-154.
Weitzmann, Harmoniesystem, p. 53, examples 3 and 4.
Ziehn, Manual of Harmony. p. 28.
"Heute noch von Dominanten also 'Dominanten' zu sprechen, ist ein Anachronismus.
Wir diirfen zwar das Wort gebrauchen, weil es althergebracht ist; doch seine urspriingliche Bedeutung hat es langst verloren. Die Dominanten dominieren nicht
mehr ... " (Goebel, Jahrbuch, p. 331).
56 Even in his treatment of inversional symmetry in his early work, particularly the
Harmonie- und Modulationslehre, Ziehn used limited progressions of abstractly configured simultaneities. In his later writings and in his compositions, however, he see-
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approach certainly called attention to the unsatisfactory theoretical explanations that prevailed.
Ill
Julius Klauser's novel theory of tonality exemplifies a revolutionary, pre-paradigmatic work in numerous ways. It examines the most fundamental issues
concerning theorists at the end of the nineteenth century: the acoustical basis
of music; the structure of tonal relationships; notation; and tuning. The primary features of his theory, the septonate and centralization, cited in the title
of his 1890 publication, The Septonate and The Centralization of The Tonal
System: A New View of The Fundamental Relations of Tones and A Simpl@cation of The Theory and Practice of Music, are idiosyncratic and find no
precise corroboration in the work of any other theorist, to my knowledge.57
There are some strong similarities between Klauser's ideas and those which
emanated from the Austrian tradition promulgated by Simon Sechter's students. They are particularly noteworthy because they call to mind Heinrich
Schenker's work.58 In brief, the ideas Klauser shared with this tradition include
a contrapuntal orientation, ascribing melodic origins to dissonance, the
possibility of interpreting chord inversion contrapuntally, the interpretation of
dissonant chords contextually, concern with the idea of an underlying
"tonality," and distinguishing between modulation and transitory shifts in tonic
orientation. There are also important differences between his work and the
Austrians, particularly in regard to the significance of acoustics to music, of
med to understand symmetrical inversion as an organizational principle. (See Severine Neff, "An American Precursor" for a photostat and analysis of Bernhard Ziehn's
Albumblatt.)
57 Wason characterizes Vincent's interval categories as "an early attempt (perhaps the
earliest) to relate all twelve tones to a tonal center" (in Progressive Harmonic Theory,
p. 71; from Die Einheit in der Tonwelt, p. 13). Klauser might have encountered Vincent's Die Einheit in Leipzig, where the work was published several years before
Klauser studied there; but Vincent does not appear among the theorists mentioned in
Klauser's work, and their music-structural ideas are not comparable. As will become
clear, Klauser was highly dissatisfied with his studies with Jadassohn, although they
lasted for three years. It seems that he would have been susceptible to suggestions
from other theorists, though these have not been determined.
58 Robert Wason identified this Viennese school in the second half of the nineteenthcentury as the immediate historical predecessor for many of Heinrich Schenker's
ideas, in Viennese Harmonic Theory and in "Schenker's Notion of Scale-Step in Historical Perspective: Non-Essential Harmonies in Viennese Fundamental Bass Theory," Journal of Music Theory Vol. 27, No. 1 (1983): 49-73.
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21 1
figured bass, of fundamental bass theory, and of the fifth relationship - all of
which Klauser either rejected or eschewed.
The Septonate was Klauser's response to his Leipzig studies with Jadassohn,
a conservative representative of the German tradition whom Klauser judged
full of irreconcilable contradictions and arbitrary rules. If the breadth of his
theoretical background is limited to just those theorists he mentioned, Klauser
appears to have been a well-informed scholar of the German school, not the
Austrian school.59 The Septonate presented theories that were basic to the
pedagogical methods he developed as a music teacher in Milwaukee - in
contradistinction to what he had been taught.60 Klauser's autonomous development of a radical theory from conservative European theory bears out
Thomas Kuhn's hypothesis that resistant theoretical paradigms point the way
to their own replacement and facilitate independent breaks with traditional
knowledge by perpetuating anomalies that are persistent imtants to normal
theoretical activity. Given our present knowledge, The Septonate and the
Centralization of the Tonal System seems to have emerged in isolation and had
little impact - the latter, an aspect of its American destiny.
Julius Klauser's work aspired to being a "science" of music, i.e., a study based on scientific principles. Klauser believed the traditionally-accepted genesis
for music in acoustics and physiology was misleading, deeming these fields
irrelevant for music (99; 270).61 He turned, instead, to the newly-developing
science of "Tonpsychologie,"the title of Carl Stumpfs 1883 publication, to
59 Klauser mentions the following theorists: G. Weber, Man. Hauptmann, Richter,
Weitzmann, Dehn, Jadassohn, and Riemann, all Germans having an harmonic orientation (passim). Since no ties have been found between Klauser and the Viennese
theorists, possible precedents for many aspects of his theory still need to be investigated.
60 Although Klauser seems to have been quite isolated from the professional field of
music, his work caught the attention of Bernhard Ziehn, who gave it a devastating
review in a local German newspaper in Chicago on November 11, 1890. The review is
reprinted in Bernhard Ziehn. "Julius Klausers Septonat," Jahrbuch, op. cit.: 75-76.
Ziehn, known for his biting, sarcastic reviews of studies by leading European theorists, called the book an example of "solche Spielerei" (such games) as he had addressed many times in the past (p. 75; see footnote 21).
61 "I regard the introduction of acoustics into music as one of the most, if not the most,
effectual hindrance to the development of a true science of music. In music we deal
with relations of full, not simple, musical tones, with the analysis of key-relations, key
harmony; and just as soon as we thus relation tones. all elementarv tones vanish from
consciousness and are positively not heard, except on a terminal Tonic-harmony"
(Klauser 270).
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find music's natural, scientific basis.62 Stumpf s work nurtured Klauser's vision
of music rooted in innate human perception; it provided Klauser with the
criteria that elevated perception to scientific status, capable of providing
empirical evidence through statistical, experimental methodologies. Klauser
used his students in experiments that presumably revealed what tone-related
phenomena they recognized simply and directly, how the gifted heard, and
what the potential is for training average and ungifted students. He concluded
that strict voice-leading (31), consonance and dissonance, harmonics (or
chord-tones) and by-tones (or non-essential dissonances), "tone-progression
and tone-repose" (55) were intuited through an innate, commonly-held
harmonic sense unique to human beings.63
Klauser committed himself to no less than a total overhaul of Western music theory, to replacing "despotic" pedagogical methods (he cited examples
from Jadassohn's classes) with a "logical" method "that combined theory with
practice by teaching the language of music itself' (24). Attributing the "faulty
methods" to weaknesses inherent in the prevailing conceptions of the tonal
system, he drew attention to "what is generally considered a necessary divorce
of theory from practice" (13).64 The highlights of his work that follow are
62 "Musicpsychology is distinctively a music science and lies outside of the province of
the usual psychologist, who is no musician, and who, because there is no exact
science of music, depends on physicists and physiologists for music science. But a
Helmholtz and Tyndall, a Ribot and Weismann, are not musicians, nor do they claim
to be" (Klauser 270). Klauser justified his experimental direction by citing other music theorists who had made reference to psychology in their own works, stating: "That
we must look to psychology tor efficient solutions of musical problems is either directly stated or it is suggested in a thousand ways in all important theoretical works
on Music" (Klauser 269). Although Stumpf s name is never mentioned, "music psychology," "tone psychology," and "psychical" appear throughout.
63 Anticipating the response that Klauser's ideas may call to mind the theorist of the next
generation, Ernst Kurth, I would say that such a comparison is valid only in so far as
the "latent energy" in Kurth's musical psychodynamics is tied to Klauser's "bytones"
(non-essential dissonances), and melody is the point of departure for both of them (see
Lee Rothfarb, E m t Kurth, p. 114-115. Klauser does not go beyond the analysis of the
simplest up and down horizontal directions determined by leading tones.
In addition to psychology, Klauser turned to other informed directions of his time,
particularly from the field of evolution, referring to the theories of Herbert Spencer
(1820-1903), Charles Darwin (1809-1882), and August Weismann (1834-1914) - all
involved in speculation about the origins of music. He, himself, gathered data from
"Nature" in the wild - animals, birds, water, wind, etc. -to identify tonality as a natural phenomenon and its origins in nature (Klauser 272-3).
64 This paper is not the appropriate vehicle to compare Klauser's rhetoric, in regard to
the teaching of theory, to Schenker's; therefore, I want only to point out that they are
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213
intended to give the reader some sense of Klauser's innovative, idiosyncratic,
and largely intuitive accomplishment.
Klauser's underlying premise is that music study should begin with counterpoint ("from which [the student] should derive his earliest intelligence of
harmony" [117]).65 Klauser took issue with the harmonic orientation of existing tonal systems as scientifically unsubstantiated (167). He judged thorough
bass and four-part harmony dogmatic, illogical, and overly complex (187188), and given bass practice no more than a necessary pedagogical crutch,
developed to compensate for confused ideas and a lack of musical sensitivity
(187).66 He shrewdly expressed his contempt for current theory pedagogy
when he wrote: "Where our masters violate the rules, the refined musical
sense had to decide whether the violations were actual or only appeared as
violations in the light of the rules" (270).67 His contrapuntal orientation
provided the single essential premise for his theory. He interpreted contrapuntally dissonant and chromatic relationships, primarily in the music of Beethoven, Wagner, and Brahms.
sometimes disturbingly similar, the explanation for which seems to lie in their having
confronted the same crisis.
65 Klauser stated this conclusion at approximately the same time that the Viennese theorist Josef Schalk (1857-1900) raised questions about the limits of harmonic analysis
and the potential value of a contrapuntal orientation in "Aufsatz uber die Chromatik,"
Austrian National Library, F 18 Schalk 410, p. 16 (see Wason, Viennese Harmonic
Theory, p. 111). Although Schalk opened what would seem to have been a fruitful line of inquiry, he did not pursue it any further. Unlike Klauser, Schalk remained essentially "a chord-to-chord analyst," as Lee Rothfarb describes him in E m t Kurth as
Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988) p. 185.
The contrapuntal corrective to the excesses of the hannonic orientation in theory (and
in some music) was previously suggested by Heinrich Bellermann in Der Contrapunctus (Berlin: Springer, 1862), who saw "the style of many compositions of his day
... as nothing more than a 'setting of ready-made chords one after the other,' a method
'recommended even in instruction manuals"' (ix; from Lee Rothfarb, "Emst Kurth's
Die Voraussetzungender theoretischen Harmonik and the Beginnings of Music Psychology," Theoria 4 119891, p. 19, footnote 24). Although Schenker said Bellermann
"hardly digresses from the great model of Fux" (in Counterpoint, ed. William Rothgeb and Jurgen Thym, Eng. tr. [New York: Schirmer Books, 19891, p. 18; orig. Kontrapunkt [Vienna: Universal-Edition, 1910), he discussed Bellermann's work at length
and credited him with new insights.
66 "The student is at present struggling with and is overwhelmed by multifarious rules
and exceptions to rules: these rules are the immediate outgrowths of the given bass
fallacy and the otherwise insurmountable difficulties that attend the handling of four
voices at the outset" (Klauser 191).
67 His indignation can be compared to Ziehn's criticism of Weitzmann, in footnote 25.
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Klauser theorized that the genesis of a musical composition is found in its
melody or, what Klauser called, its "prominent voice." This notion, taken from
A.B. Marx,68 seems to have been derived from the melodic primacy of contemporary works, in which melody was the principle determinant of form. The
"prominent voice" is described as the "governing idea" or "central thought."
He cites the sketch books of Beethoven and other composers for evidence that
melody is the point of departure in the compositional process and that "the
development and elaboration of thought into harmony and form is [sic] a later
process" (188).69 Elaboration also includes a composition's stylistic character.
such as its being vocal or instrumental (165). As a teacher, Klauser believed
the prominent voice should be the starting point even in student exercises.70
Klauser's specific formulation of the prominent voice marks a fundamental
change in the history of music-theoretical ideas preceding the Schenkerian
"revolution," because it identified a series of single tones that inherently contains suggestions for its harmonic elaborations as a new analytical category
which, in its refined Schenkerian form, later became paradigmatic. The melody "governs" harmonic tones (consonances) and bytones (non-essential dissonances)," determining those "concomitant" vertical harmonies, not only the
formal design of a composition (165) (as in Marx's analyses): "The harmony
that is inherent in every such series [of tones] determines in what relation one
tone stands to the other tones ... Every one-voiced series of tones, and therefore every series of tones, is a coalition of melody, harmony, and rhythm"
68 Of the treatises of A.B. Marx (1795-1866), Klauser wrote: "[they] are still among the
best in use" (Klauser 190). In the concluding section of The Septonate, he said: "I
have no doubt that, had he lived to fulfill his purpose. Marx would have placed music
on its actual scientific basis, and it is almost certain that his analyses would have been
distinctively musico-psychological" (Klauser 271). Marx's Die Lehre von musikalischen Komposition (4 vols. [Leipzig, 1837-471)was his most influential work.
69 Charles Rosen, tracing musical developments leading to the atonality of the Second
Viennese School, submits that "melody was the principal basis of form in all nineteenth-century music after Beethoven ... because harmonic relationships no longer
possessed the force and influence they had throughout the eighteenth century" (Arnold
Schoenberg [New York: The Viking Press, 19751, p. 34).
70 Klauser states that the given bass, although also a single line, is never by its nature a
principal voice; a cantusfirmus, however, could be: "To study harmony apart from a
central thought, or governing voice, is to venture upon the impossible and absurd.
This is exactly what is required by current systems of Harmony and Thorough Bass.
In all of these systems the student harmonizes fundamental or given basses, not one of
which basses, could ever be mistaken for a central thought ... . Although the central
thought may be in the bass, it never appears in the given basses alluded to above"
(Klauser 166).
71 In regard to the term "bytone" Klauser wrote: "I use the word bytone in preference to
the terms 'accessory tone' or 'neighbor tone,' on account of brevity and fitness."
-
International Journal of Musicology 2 1993
215
(72).72 These statements (and others below) bring to mind Schenker's idea of
"harmonic unfolding" (Auskomponierung) in the melodic, temporal sequence.73 Harmonic motion - "harmonic governance" in Klauser's terms - is dependent on the "Principle of Progression" (his replacement for conventional
voice-leading rules), which he defined as the natural attraction and direction in
horizontal relationships centered around the tonic.74
The Septonate represents the simplest level of diatonic relationships centered around the tonic; it was invented to replace the scale as the fundamental
diatonic unit. (It is shown in Example 4.)
-
Example 4. The Septonate (Klauser 44, from Exs. 8 and 9)
Attempting to develop a system which was consistently expressive on all
levels, Klauser rejected the scale as the fundamental unit in music because it
misrepresents psychological musical tendencies, i.e., (1) its eight tones include
two tonics; and (2) its motion towards the fourth step in the ascending scale
and towards the fifth step in the descending scale imply other tonics. On a
more complex level, the septonate itself functions as the basis of its chromatic
72 "All elaborations of the central thought, both harmonic and rhythmic, entirely depend
on the nature of the central thought itself: the direction of progression, the diatonic,
chromatic, and harmonic steps, the pitch, klang-color, dynamics, and rhythm of the
central thought place the entire character and treatment of the accompanying voices in
a subservient relation (165).
73 Compare the Klauser quotation to this statement from Heinrich Schenker's early work,
"The Realization of the Triad' in Harmony (English tr. and annotations by Oswald
Jonas [Chicago: University of Chicago Press, 19541, p. 133; original, Harmonielehre
([Vienna; Universal, 19061): "But in all cases we do not need three voices to produce
these consonant intervals; i.e., the concept of the triad is not tied, as one might think,
to the concept of real three-phony. Rather it may be fulfilled by two voices, even by a
single one. In the latter alternative, Nature as well as art is satisfied if the course of a
melody offers to our ear the possibility of connecting with a certain tone its fifth and
third"; also "The Motif as Interpreter of the Harmonic Contents," p. 21 1. Schenker
speaks of "horizontal harmonies" on p. 206 of Harmony.
74 "This principle ... is implicated in both harmony and rhythm. To progress in the direction toward which a tone is attracted is to follow on rhe line of least resistance ....
which for brevity's sake I call the key-track ... . Progression on the key-track is wmmonly known as pure and strict voice leading" (Klauser 41). All notes are either harmonics or bytones, and motion is created by their interaction.
216
International Journal o f Musicology 2 1993
extensions around the centralized tonic - more about this shortly. The
septonate consists of two conjunct scale-halves surrounding the tonic note. It
incorporates the natural voice-leading tendencies surrounding the tonic into a
fundamental, abstract pitch collection. Directionally oriented - one ascending,
one descending - these scale-halves converge on the tonic, represented literally as the central tone (in C major, G A B ascend, F E D descend), as drawn
in Example 4, above.75
Klauser demonstrates the harmonic implications in a diatonic series of tones
with the half-scales of the septonate. He analyzes the four tones of the rising
scale-half as follows:
under 4: Dominant
under 3: Passing by-tone
under 2: Leading-tone (dominant)
(center) 1: Tonic
In Example 5, using the rising scale-half, the consonant harmonic tones in
the horizontal ascending series of tones, G-B in C, are connected by a passing
note, or bytone, which by definition is a dissonance. The dominant (called
"under-dominant') to tonic bass progression demonstrates the "natural concomitant harmony" for the rising scale-half in the horizontal series of tones,
with the "harmonics" separated by passing tones (Klauser 77-78).
.
International Journal of Musicology 2 1993
217
in Example 6, from the initial over-dominant tone, F, to the terminal tonic tone, C (78).
Example 6 (Klauser 81,from Exs. 54 and 55)
The same harmonies - under-dominant and tonic - are associated with both
the ascending and descending scale-halves. The functions of the four tones in
the under scale-half in Example 5 are mirrored in those of the over scale-half
In this example, Klauser interprets the underlying harmony for the first three
tones as an under-dominant going to the tonic, and treats the 614-chord as a
passing chord. In the single voice in C major, F-D in the descending scale-half
are connected by the passing tone E;76 then, the same interpretation is
maintained even when other voices are added, forming a ninth chord and then
an eleventh chord: "The harmony of the under-Dominant klang prevails in the
mind even when other voices are added" (81). In this instance, Klauser treats
the ninth and eleventh as extensions of the under-dominant seventh - the only
"typical dissonant harmony" or essential dissonance - and therefore as, themselves, essential dissonances, although he generally treats them as bytones.
(Klauser's distinction between the two classes of dissonance, and his alternative interpretations for ninths and elevenths are discussed below.)
Directional tendencies in the scale-halves are located in the septonate's
"four half-steps" - two upleaders and two downleaders. The upleaders precede
the tonic in the rising scale halves; the downleaders begin the series in falling
scale halves (198): In the C septonate (see Example 4), C and F can function
as downleaders; E and B as upleaders. When C functions as a downleader and
E functions as an upleader, they are potentially instruments of directional
changes to other tonics, i.e., to G and to F, respectively. Since Klauser interpreted every half-scale as functioning according to "two distinct and positive
characters," up and down (80), and assigned the same directional tendencies to
75 Analytical notation uses "u."and "0."to indicate the "under- and overtones in relation
to the centralized tone, the tonic; tones are numbered according to their distance from
the center as follows: u[nder] 4, u.3, u.2, 1 , o[ver] 2,0.3,0.4.
This terminology has nothing to do with either acoustical partials or Riemann's undertone and overtone classifications; Klauser, moreover, claimed to have introduced
his system "of over and under intervals, scales, and chords in [his] Harmony classes
several years before the Riemann system was known to [him]" (Klauser 110).
76 There is a similar example in Harmony, where Schenker also speaks of "horizontal
harmonies" (p. 206). In Free Composition, Section 169 (p. 61), Schenker states that
the dissonant passing tone is "a means of composing-out"(tr. Emst Oster [New York:
Longman, 19791: orig. Der Freie Satz, Vol. I11 of Neue Musikalische Theorien and
Phantasien [Vienna: Universal Edition, 19351). Oswald Jonas recommends the section
of the Jahrbuch, 11, 24ff., entitled "The Dissonance Always Consists of Passing Notes; It Never Constitutes Harmonies."
V
I V
I
Example 5 (Klauser 78.Ex. 46)
-
218
-
.
fnrernational Journal of Musicolony 2 . 1993
International Journal of Musicology 2 1993
the half-steps created by chromatic and enharmonic tones, chromatic motion
(including that leading to other tonics) is also linearly determined.
Klauser's depiction of the literally centralized tonic seems to have been a
totally original idea. He cited the septonate's pedagogical advantage over the
scale as clarifying the directional tendencies of the diatonic tones - what
Klauser called the "keytrack." Therefore deviation from the natural direction
of a specific half-scale, i.e. to its tonic, can "[change] the concomitant harmony, [destroy] our sense of the Tonic ..., and in some instances [arrest] motion" (76) - Klauser's reduction of syntax to psychological affects.
To establish a scientific basis for his horizontal interpretation of harmony,
Klauser reinterpreted the conventionally vertical ramifications of the harmony-generating tonic. Borrowing the German word "klang" from acoustical
and harmonic theories where it described the relationship of a tone to its resonating overtones or partials, he applied it to the horizontal series - to the septonal abstraction in Example 4 and, by extension, to any diatonic melody. The
seven tones become a "whole or unit" (41) with innately understood (or felt)
relationships. In the horizontal context, the term "klang" - or "keyklang," as
he sometimes called it - signifies the "definite character" individual tones gain
through their relationship to a central tonic (Klauser 41).77 This "character" is
directional, controlling every aspect of voice-leading and modulation. These
relationships are exemplified in the structure of the septonate.
Klauser's tonic is the sole "harmonic generator" within a key, producing a
"pure physical harmony" or "perfect harmony" (161), and is the "point of absolute repose" (167) of conventional theory.78 Yet in the natural form of the
tonic triad, Klauser claims that the tonic tone is centralized, with the major
third above and the perfect fourth below the central tone or root (as shown in
Example 7) - completely unconventional.
77 Having given the word new meaning, he noted that his use of the term was unique and
unrelated to its conventional use in acoustics (Klauser 270).
Concern with this "definite character" of tones in relation to the tonic was
particularly intense at the end of the nineteenth century among musicians and
pedagogues. See Ellis in Helmholtz, Sensations: p. 279, describing the affects
ascribed to the intervals of the scale by the Tonic Sol-Faists, discussed in the
following section on George Ives.
78 Every isolated or detached tone is an "harmonic generator" and produces its natural
physical harmony (Klauser 161): "The Tonic-harmony is identical with the perfect
physical harmony of a detached, or an isolated tone. Thus any tone that we conceive
as a Tonic generates the only perfect harmony that exists in music" (Klauser 167).
219
3
*
=-
etc.
4
4
etc.
Example 7 (Klauser 162, Ex. 142)
Klauser framed the issue of the literal centralization of the tonic, which underlies his entire system, as a challenge to the theoretical community: "The
question of first importance is whether a Tonic is a central tone or not. If a
Tonic is a central tone, a revolution in the treatment of all theoretical and
practical problems in music cannot be averted. If every musician hears that a
Tonic is a central tone, then I say it is" (73). He claimed that this arrangement,
which replaces the tonic root as generator of the overtone series, was derived
from experiments in music psychology. Moreover, since the centralized tonic
of the central tone stratum (defined by the central septonate, i.e. surrounding
middle C) is replicated by non-equivalent octave strata in all registers, the
stacking of two thirds, which had been amved at through the contraction of
the tones of the overtone series to make the tonic triad, would have been further illogical in this system.79
The centralized tonic created some problems for Klauser. The most serious
one was how to explain the significance of the motion of the bass. Through
what seems to have been a misunderstanding of Sechter's fundamental bass
concept, Klauser added a "ground voice or bass" (consisting of the octaves ofchord-centers) to pure voice-leading progressions derived from within the
limits of the septonate (Example 8).
79 "Manifold experiments on average musical children and adults of all ages, trained or
untrained in music, have without exception proved that such a detached tone generates the same harmony in all minds": "Our first selection in rising is the harmonic 3d;
in failing the harmonic 4th ... In other words, the selection of any other save the
tones indicated above would cost an effort and would seem most unnatural" (Klauser
161). (It must be mentioned that Klauser's experiments seem never to have been either
authenticated or disproved.) Tonic centrality is one of the issues which Klauser used
in discrediting the validity of acoustics for music and music theory. (See footnote 61
for his opinion of the relationship of acoustics to music.)
.
220
International Journal o f Musicolo~y2 1993
O . I V u . 1 ~O.IV
O.IV
U.TV
O.IV
Example 8 (Klauser pp. 195-6, Ex. 173j80
Such a misunderstanding is suggested by Klauser's use of the term
"fundamental bass": to contrast the Roman numerals in traditional systems of
harmony, which indicate what he calls the "fundamental bass," with the Roman numerals in his system, which indicate "chord-centers" (171). In addition,
he makes a totally idiosyncratic distinction between "the fundamental tone" or
"groundtone," and the root of a chord or chord-center.
The centrality of the root in this system obliterates the significance of the
fifth; in the septonate, the under- and over-dominant refer to tones that are a
fourth away from the tonic. Indeed, Klauser calls the rising fourth - not the
rising or falling fifth - "the closest harmonic relation that exists in music"
(103). Since the septonate defines primary relationships surrounding a tonic,
"to trespass outside of this circle in either direction is to cross over from one
80 The full range of pitches - the "extended range" - is achieved by adding septonates
above and below the central septonate of any key. Each septonate maintains its own
voice-leading integrity according to the "Principle of Progession."
The Roman numerals in Example 8, used for chord designations, correspond to the
Arabic numerals in Example 4 that designate the steps of the septonate. The letters
above the chords mark its form: centered (c.), over (o.), or under (u.) in relation to the
root.
.
International Journal of Musicology 2 1993
22 1
Septonate to another." Tonal relationships, as will be seen even more clearly
and indeed dramatically in the subsequent description of his system of relationships, are directly to the tonic within each septonate. (This is the vision of a
musician immersed in nineteenth-century chromaticism, certainly not one
emerging from a Baroque or classical orientation.)
Klauser's rejection of the validity of inversion is consistent with his definition of chords as confluences of horizontal voices in counterpoint. He classified "positions of chords" as "three forms" of a triad - under, over, or above having the same root or center. However, they are treated as three individual,
independent entities (169): Identifying positions in relation to the chord-center
"by no means impl[ies] three positions of one and the same chord" (178). "The
essence of harmony lies in Progression, that is, I say, in the co-progression of
two or more voices," in contrast to "strings of chords" (164) that are not necessarily valid as independent simultaneous entities.
Klauser understood the notion of extending the tonic harmony in time by
associating it with non-harmonic tones, as Schenker did. He expressed it as
follows: "The full Tonic-harmony [i.e., the tonic chord operating in all strata
or registers (Klauser 168)] [is a] ... reliable means of enabling the student to
command the full scope of the System by associating bytones with [their] harmonics" (Klauser 181).8' To demonstrate the extension of the tonic harmony
with "bytones" - passing notes, neighbor notes, accented neighbor notes, and
suspensions - Klauser uses: 1.) examples of simple elaborations of one voice the prominent voice or central thought (181-182);82 and 2.) examples of elaborations of all voices of the tonic triad, showing "keyklangs" related in the
context of "co-progressions" through the interplay between the notes of the
tonic chord and the bytones (216).
Klauser distinguished two classes of dissonances, "dissonant harmonics"
(what Kirnberger called "wesentliche"- essential) and bytones (what Kirnberger called zufallige - variously translated as non-essential or accidental) by
how they resolve and by the "rhythmo-harmonic" implications of the Prominent Voice.83 Klauser's definition of bytones and dissonant harmonics, which
81 Comparison to Schenker's ideas must, of necessity, be tightly condensed. In Free
Composition (Der freie Satz), op. cit., Schenker states that "the dissonant passing tones, including the passing seventh, is itself a means of composing-out"
(auscomponierung) (Section 169, p. 61).
82 "The reader may object that suspensions require at least two voices for treatment. This
is, however, not the case" (Klauser, 184). Compare to Schenker's statement in footnote
73.
83 Johann Philipp Kirnberger's definitions of essential and non-essential dissonances can
be found in his "The True Principles for the Practice of Harmony," trans. David W.
Beach and Jurgen Thym, Journal of Music Theory 23 (1979), p. 17I.
222
-
International Journal of Musicology 2 1993
follows, differs from Kirnberger's definition of non-essential and essential
chords mainly in its use of the chord-center in lieu of the fundamental bass.
Herein lies a shift from the significance of the bass line to that of the top line:
Bytones antagonize a chord-center and its harmony; they lie a step and half-step over
and under the harmonics of a chord-center; they are resolved into these harmonics of a
chord-center; they do not change the character of this harmony; when they are resolved, no
change of harmony is anticipated.
The dissonant harmonic, on the other hand, is not resolved into the harmony of the
chord-center which it antagonizes; it completely changes the character of the harmony of
a chord-center; it at once transforms a consonant harmony into a dissonant harmony, and
at once excites a progression to the harmony of another chord-center (2 15; italicized by
Klauser).*4
Klauser provided many original examples (as well as some cited from literature) of both diatonic and chromatic bytones in one voice (147-148; 181182). Furthermore, several examples show diatonic and chromatic diminutions, which he called "interpolated tones," elaborating chromatic bytones.
These examples were designed to demonstrate delayed resolutions: "The resolution of an intermediate [chromatic tone] may be delayed indefinitely without
dissipating the anticipation of progression" (148).
Dissonant harmonics are chords configured like the dominant seventh
(Klauser's "under-dominant" seventh), which he calls the "typical" dissonant
harmonic. It is the model for all chords having the same configuration (218).
The under-dominant keyklang has a natural basis, since it is the only one that
"generates a dissonant harmonic in the mind" (217).85
84 Klauser's new definitions of essential and non-essential dissonances and for the concept of "klang," like Ziehn's reinterpretation of mehrdeutigkeit and essential and
"accidental" (or non-essential) dissonances, are comparable to those aspects of, what
Kuhn would have called, "extraordinary research," in science, which leads to paradigm change.
85 In his 1909 posthumously published second work - a conservative and derivative
work - Klauser essentially abandoned the septonate (although he referred to it in passing) and divided the notes of the scale into two harmonic genres: do, mi, sol represent the consonant genre or tonic; ti, re, fa, la represent the dissonant genre (62-63) or
cadence tones, an idea traceable to Bernhard Klein (via Siegfried Dehn) and C.F.
Weitzrnann (see Wason "Progressive Harmonic Theory, 73f.). Klauser formulated the
idea as follows: In C major, the tonic chord C, E, G constitutes the consonant genre;
B, D, F, A constitute the dissonant genre or cadence tones. The dominant chord is
formed by adding G below, called the first nexus tone which links both genres. The
subdominant is formed by adding C above, the second nexus tone.
Klauser never discussed cadences in The Septomte, using the term only in relation
to Example 6. Consider the following statement by Charles Rosen as a possible explanation: "The power of the simple dominant as the basic polar force against the to-
International Journal of Musicology 2 . 1993
223
His interpretations of other chords containing dissonant tones are subject to
qualifications determined by their resolutions and the harmonic implications
of the prominent voice, as expressed in the above definitions. For example,
Klauser treated the ninths and elevenths in Example 6, above, as essential dissonant harmonies, although he defined ninths and elevenths as bytones (nonessential dissonances), because they can resolve into one of the components of
the under-dominant chord (219-220). He explains this exception as follows:
The fact that these dissonant keyklangs are resolvable into the fourklang [seventh chord]
does not mean that they must be so resolved. The fact that there is a typical dissonant harmony does not mean that there are no chords of the Ninth and Eleventh, or fiveklangs and
sixklangs. Melorhythmo-harmonic inter-relations determine how these combinations are to
be treated (220).
In regard to analyzing secondary Seventh chords (I,, o.IV7, u.iii7, o.iii,, u.ii7,
o.ii7), Klauser said the interpretation "depends on the Prominent Voice, or
central thought" (Klauser 219). Although he provided no examples, his meaning is clear.
In his treatment of suspensions, Klauser criticized the notion of the threestaged process (preparation, suspension, resolution), because it implies that a
note of the first chord is prolonged in order to sound with the second chord;
Klauser stated that the relationship of the suspended tone to the first chord
ceases to exist once the second chord sounds. In keeping with his contrapuntal
orientation, Klauser focused on the changing quality of the suspended voice:
from a consonance, to a dissonance, to a consonance.
Klauser's criteria for suspensions are demonstrated in numerous examples
that broaden the possibilities for interpreting contrapuntal phenomena as suspensions. His material can be reduced to the following statements that have
been culled from his text:
1. A suspension is intimately concerned with rhythmical accents and therefore with the Principle of rhythmo-harmonic Progression.
2. Any delay in the resolution of a tone results in a Suspension.
3. The term resolution in itself implies ... a dissonant tone.
4. A tone held over beyond the point where the harmony changes is always
a bytone (225).
5. The tone held over may be a harmonic or a bytone (227).
6. This delay in a resolution may be extended indefinitely through a number
of measures [Example 91 (225).
nic gradually weakened during the early nineteenth century, and much more remote
triads were used instead" (Arnold Schoenberg, p. 30). A similar observation was made
when discussing Ziehn's work, for which see footnote 55.
International Journal of Musicology 2 1993
Especially in this section on suspensions, Klauser revealed an awareness of the
concept Schenker called "prolongation," a concept he intuited but could not
define. A major paradigm revision, involving the hierarchical levels Schenker
Example 10 (Klauser 229. Ex. 225)
Klauser's analysis of this example, unfortunately, goes no further than the notion of the extended suspension, making no distinction in the text between a)
and b). In a), an unstable 614 chord is treated as a double suspension that is
extended through a neighbor note in the bass and chromatic passing notes in
the alto and bass. In b), a stable 614 chord is prolonged for the first three
measures by the two inner voices through neighbor notes and accented passing
tones. Klauser's superficial analysis of his own example is actually characteristic of the level on which he verbally developed many of his ideas.
7. A Suspension [does not] necessarily involve a series of two harmonies,
or chords ... [It may] occur in relation to but one harmony, or chord.
8. The tone in Suspension, instead of being resolved into the anticipated
tone, ... [may be] resolved into another component of the antagonized
chord.
9. Resolution into the antagonized harmony [can be] entirely omitted
(Klauser 228).
Klauser also includes an example of the technique now referred to as
"rhythmic contraction," which he explains as follows:
10. Constant Suspension ... is due to the fact that at the exact point where
one ~ u s ~ e n s i bshould
n
be resolved a new Suspension is initiated by a
change of harmony [Example 101 (229).
Example 9 (Klauser 226. Ex. 2 16)
224
86 The level of insight Klauser
of anomalies that violate the
ce": "Produced inadvertently
tion requires the elaboration
87 The under-Dominant, like th
the fact that the most domina
have called the under-Domi
Seventh chord, which is a c
the under-Dominant while
monics" (Klauser 81). by wh
borated through passing ton
on p. 217.)
88 Klauser's system implies mo
as such, it underlies his sys
discussion of monotonality i
in 1882. The following trans
bert P. Morgan, "Schenker a
18 (Spring, 1978). p. 94:
'This modem concept of k
key, of tonality, is not, h
foreign to the scale can al
acquire their own particula
later introduced, was needed
actually be understood.86
Before describing his syst
to the fact that Klauser never
"chord" - the resulting confl
his system. Klauser applied
"physical harmony") only to
minant tones (I, V, IV - and
minant).87 As for the other k
do not generate their respect
monics of the primary tones,
phenomenon, although this
amples of simple harmoniza
over-dominant chords provid
Klauser's notion of centra
lationships. His model of the
a "tone-stratum." There is a
presents the tonic centers of
centralized tonic and tonic tri
groups of tones and three l
around the tonic:Ss
International
International Journal of Musicology 2 1993
Septonnte.
b)
Primary
Intermediates.
c)
Secondary
Intermetlintes.
The relationship of tone connections even allows for a further extension, namely
that of the relationship of keys to one another. Just as the principal tone of a chord
is related to its secondary tones (the fifth and third and more distantly related
tones), so is the principal chord related to the secondary chords (the fifth-related
chords, third-related chords, etc.), and the principal key to the secondary keys (the
fifth-related keys, third-related keys, etc.).
Klauser acknowledged Riemann's contribution as follows: "Although the Riemann
system is very skillfully executed, and although through its medium some of the phenomena of modem harmony and modulation may be explained with some plausibility,
the Septonal System with the Principle of Progression, on which it is based, will place
both the Riemann system and the referred to phenomena in a new light" (Klauser 97).
89 "During the process of modulation and before a modulation has been consummated,
these secondary intermediates occur in relation with the initial key, and in this relation they appear as and must be classed as Enharmonics" (Klauser 151-152). (More
will be said about Klauser's ideas on modulation.)
Klauser noted that among the secondary intermediates "there are ten such
keys, although only two of them (Cb and Fa) are at all common in musical
Example I 1 (Klauser 104, Ex. 89)
a)
1. the seven principal tones of a major key;
2. the ten primary intermediates, which are the tones nearest to the principal
tones, appearing above and below them, in harmonics (chords) and as
bytones; and
3. the ten secondary intermediates (or enharmonic tones) which always resolve into the primary intermediates.89
Since each of these tones is a potential tonic center or key, each of them
would, through modulation, become the center of its own septonate and tone
stratum: "Thus inside of a single tone-stratum we can modulate from and to
any one of twenty-seven keys" (105). Example 11 shows the full "central" tone stratum, i.e. all the tones related to the "central key" of C (105). The seven
principals and the primary intermediates - seventeen tones - are included in
"key groups"; the secondary intermediates are included in the "full tone-strata."
226
-
90 "The large number of chords t
of consonant and dissonant c
to other keys, but which ... I
although theory has hitherto
In summary, tonal relationsh
following three levels:
1. The first relationship, w
2. The second relationship
and primary intermedia
principal tones and "do
although they may (145)
discussed below."90
Example 12 (Klauser 185. Ex. 166
writings, appearing only as e
ding key in a composition" (1
This centralized system ex
chords. Thus, the first group
one of the seven principals
whose Tonic-center is a prim
group includes every key
(105). The first group of inte
The second group of interva
termediates, from primary in
termediates to primary inter
steps from principals to seco
to secondary intermediates,
intermediates (143). Chords,
types of relationships, and e
consonances and dissonances
tions of tones are interpret
which are in( icated by the nu
International
228
International Journal o f Musicolonv 2 1993
3. The third relationship, which consists of motion between principals and
secondary intermediates, and between primary intermediates and secondary
intermediates.
Klauser provided an analytical reduction for the following example of primary intermediates in a chordal context (i.e., "as harmonics'):
Example 13 (Klauser 149, from Exs. 129 and 131)
The reduction clarifies the upper and lower neighbor notes (or bytones) in the
parallel melodies in the top voices as elaborations of A and C, which consist
of principals and intermediates in G major. Klauser describes F4 in the first
measure and Dmin the third measure91 of the bass line as downmediants and
"harmonics." Although they both function as passing tones and as component
parts of consonant chords, Klauser never uses the term "passing chord." for
the reasons discussed above. The contrapuntal interpretation is clear; and here,
as elsewhere, no chord quality or label is ever assigned or discussed.
In Klauser's system, keys are related directly to the central key of a key
stratum - they are not related by either degrees of pitch invariance among
diatonic collections or by fifths. The tones that create "minor" are treated as
variants of major, consisting of primary intermediates. Major and minor are
modes of one key; there is no such thing as an independent minor key (107) or
introduce "foreign" tones, practical music in the compositions of the masters has
always included them in one key" (Klauser 21 1).
91 Klauser criticizes the d h f measure 3 for being incorrectly notated and changes it to
eb. The example is from Beethoven's Sonata Op. 14, No. 2.
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a "pure minor key" (96).92 The closest key relationships are in the "triunity,"
i.e., between the tonic and the two dominants that frame the septonate. The
tonic is connected to them melodically by the ascending and descending steps
of the scale-halves. With the exception of the triunity, Klauser says "every key
stands in some more or less close or in some more or less removed relation to
the central key" (105), i.e. the principals and intermediates are removed by
literal intervallic distances from the originating tonic. In regard to the ten
primary intermediates, he expresses relatedness as follows: The ten primary
intermediates "are intimately related to the principals nearest over and under
them; ... in practical music they are employed freely both as harmonics and
bytones; [and, most impressively in the theory-historical context] even though
they appear as harmonics they do not necessarily modulate outside of a key ...
these ten klangs are keyklangs and are part and parcel of the key itself'
[underlining by Klauser] (145).
Klauser, in effect, made a statement about monotonality by using the key
stratum to denote a global, all-inclusive sense of key, although he was never
more explicit.93 From his tonal inclusiveness to his concept of transitional
modulation, Klauser's incipient perception of what Schenker called
"tonicalization" is evident.94 Klauser reasoned that "a central thought may shift
through several keys and then return to the initial key without blotting out of
recollection the presidence [sic] of the initial key. Such modulations are
transitory; they often occur in a single phrase; they occur in successive phrases where the same phrase is imitated in other keys; they occur in sequences
and cadenzas" (262). All tones, chords, intervals, and keys from the three
levels of relationships are operative in "transitory" modulations which, "strictly speaking, ... do not shift the key." For analytical purposes, Klauser stated
that "keyklangs and chords should be thought and marked according to the
92 Such variants can be supported within a key as long as the tonic and the two dominants, i.e. the three primary tones, are retained. In the minor mode, the minor third is
included among the fixed tones (109). Minor variations, like other chromatic variations, are dependent on the principal tones, i.e. the major collection. Klauser shows a
variety of mixed scales which he identifies as major, minor, or mixed (109).
93 Footnote 88 dealt with this question.
94 In his contemporary study of 1888, Schalk was more explicit: "Up to now, theory has
been satisfied with demonstrating the transition from one key to another. In so doing,
the dependence of the second key upon the first is then entirely neglected, and [the
second] is viewed and treated just as independently. But [the fact] that this is not so in
a work of art is proved by each return to the main tonality, which, like a faint beacon,
must guide the composer over even the most remote tonalities" ("Das gesetz der Tonalitat," Bayreuther Bliitter 11 (1888), p. 195; from Wason, Viennese Hannonic
Theory, p. 106).
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three Relationships in the initial key."9s Klauser defined "positive" modulations as "directly" shifting the key. The examples he gives are all from Beethoven piano sonatas, where key changes are im-mediate - without any
transition - and maintained over an extended period. For the analysis of "positive" modulation, Klauser states that "the keyklangs and chords should be
thought and marked according to the three Relationships in each succeeding
key" (263).96
The centralized system Klauser proposed to explain the relationship of
diatonicism and chromaticism carried with it new grammatical and syntactical
categorizations. Like Ziehn, Klauser wanted to demonstrate the progressions
his system had newly analyzed and defined. He turned to actually computing
the possibilities, concluding that "there are 18,954 ways in which a Prominent
Voice can modulate", i.e. move "out of and into any one key" (265).
Since Klauser's tonal system is chromatic, rather than diatonic, each tone
was conceived as maintaining its identity and integrity in relation to the tonic;
therefore tones, intervals, and chords are immutable, a concept that he claimed
involves a revolution in the prevailing concept of the Tonal System in two particulars: 1.
a tone cannot be changed by the process commonly known as raising and lowering
tones, and 2. the musical alphabet of seven letters is incomplete. There being more tones
than letters within the limits of one octave, it is only reasonable that there should be as
many letters as there are tones within such limits (Klauser 38-39).
95 In Harmonielehre of 1906, Schenker stated: "Not only at the beginning of a composition but also in the midst of it, each scale-step manifests an irresistable urge to attain
the value of the tonic for itself as that of the strongest scale-step. If the composer
yields to this urge of the scale-step within the diatonic system of which the scale-step
forms part, I call this process tonicalization and the phenomenon itself chromaticism"
(p. 256).
It is necessary to point out one significant difference in the work of Schenker and
Klauser: Schenker focused on the diatonic steps - Klauser's seven principals. Had
Klauser developed Schenkef s analytical sophistication, he probably would have included the ten primary intermediates as steps that could be tonicized.
96 Schalk argued that "the notions of chromatic progression and true chhnge of key
(modulation) have become so confused that they are extremely difficult to disentangle. Most importantly, the domain of a key must be thought of in a broader sense than
it has been. Then it will not be necessary to find continual modulations where merely
chromatically altered chords occur, and actual modulation can be saved for those
places where a second key becomes truly independent for one or more periods or
sections" ("Das Gesetz," op. cit., p. 194f.; quoted from Wason, Viennese Harmonic
Theory, p. 106). As will be seen, George Ives also was critical of chord analysis
showing "continual modulations."
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23 1
His first revolutionary "particular" corresponds to his system of three levels
of relationships: "Altered,or changed, chords do not exist ... Chords are what
they are ... The only change a chord can undergo is the change of its relation"
(185-186).97 The primary intermediate and secondary intermediate tones "are
... as individual and unchangeable as the principals themselves" (145). He
dismissed notions of "foreign tones" and dissonances "implied by 'unmistakeable means of modulation"' (undoubtedly secondary dominants, learned
during his studies with Jadassohn) as "artificial guides" in modulation. He recommended the analysis and guide of the "concomitant harmony of the central
thought" (257). (His use of the terms "augmented" and "diminished" indicate
lengths of steps only, not qualitative modifications of primary, or diatonic,
intervals [l46]).
Klauser's second "particular" involves the need for a new notation and nomenclature for twelve tones that would eliminate sharps, double sharps, flats,
etc. and "the supreme chaos wrought" by them (245). In addition to using a
different name for each tone, he suggested "signs to describe the exact relation
in which an individual tone with an individual name occurs" (252-253).98
Klauser's motivation was two-fold: 1. visual logic and consistency for all keys
- "the sharps and flats work very well in the central key of C, for in this key
there is a logical connection between a sharp and an upmediate, and between a
flat and a downmediate" - and 2. indicating the three relationships, which
would be consistent with his notion "that tones are individual and immutable"
(243).99 Notation was a pertinent issue among theorists at this time. Its criticism accounted for very tangible, albeit limited, ways to express dissatisfaction with the operative theoretical models. In the following section on the
essay by George Ives, for whom notation was a major and complex issue, his
97 Klauser noted that in the prevailing systems "most of the chords of the second Relationship and all the chords of the Third Relationship are commonly classed as altered,
or changed, chords." In the 1884 English translation of the work of his teacher Jadassohn (Manual of Harmony, tr. Paul Torek and H.B. Pasmore, [Leipzig: Breitkopf and
Hlrtel, 18841, the term "derived," used instead of "altered," is defined as follows:
"Derived tones [are] obtained by raising the natural tone or lowering the next upper
tone next to the natural tones" (Jadassohn 4).
98 Klauser described an unwieldy "provisional" notational system that uses keyklang and
chord-center numbers for "principals," slashes for "up- and downmediates." and double slashes for secondary intermediates, added to traditional nomenclature. This system introduced relationships into notation; since these symbols are consistent in all
keys, Klauser proposed these interim measures during a period of acclimation to
change.
99 Klauser gave no hint at how he would eliminate sharps and flats: "What symbols are
to be substituted for them, and what my general scheme for a new notation is, are
matters which I have preferred to reserve for a separate publication" (245).
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and Klauser's responses to notation and those of several European theorists
will be compared.
An issue related to notation, tuning was also a major theoretical concern
during the second half of the nineteenth century, generally expressed as a
conflict between the advocates of pure intonation and the advocates of equal
temperament. Since this issue attracted wide interest among theorists, I will
treat it, including Klauser's position, in the context of my discussion of Ives's
ideas on this matter.
Klauser's isolated revolution in tonal theory locates Schenker's work in a
history determined by necessity, revolution, and paradigm change. While the
suggestive insights and accomplishments of Schenkerian intellectual predecessors have gained significance mainly by their appositeness to the future
paradigm, their work nevertheless shaped the period in which the necessity for
change was clarified. Klauser's vision is tied to his historical position and
nineteenth-century musical models, which go far toward explaining why, on
the one hand, he was able to develop a contrapuntal conception of harmony
and tonality and why, on the other, he could not achieve the unique Schenkerim integration of the vertical and horizontal dimensions in his conception of
tonality. His melodic orientation reflected the extended melodic lines and weakened harmonic influence in the music of his own time. Schenker, by contrast, had the historicist's perspective, motivated by practices of his own time
but returning to common-practice tonality in Beethoven and the eighteenth
century at a time when that language was no longer practiced. To summarize,
treated diachronically, Klauser articulated the period of crisis in music theory
at the end of the nineteenth century, anticipating by about fifteen years many
aspects of the paradigmatic work of Schenker, particularly harmony's horizontal dimension and the temporal extension of the triad through non-harmonic
tones.100 Treated synchronically, Klauser is part of the progressive theoretical
sensibility in the United States that recognized the implications of advanced
chromaticism.
The contrast between Ziehn's and Klauser's analytical procedures and the
theoretical systems they imply is compelling. Working during the same period,
approaching much of the same music with the characteristic empirical rigor I
have suggested, and criticizing the European theoretical establishment from
the perspective of well-versed students of that establishment, they nevertheless
developed theoretical precepts that might even be evaluated as diametrically
opposed. Their differences were derived from their aesthetic judgments, which
determined how they discriminated among individual repertories and how they
100 It is unlikely that Schenker knew Klauser's work. In regard to crisis engendering numerous unrelated responses, see footnote 16.
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233
interpreted the compositional techniques used in nineteenth-century repertory.
Klauser, who held the neo-classicism of Brahms in highest esteem and
compared the underlying contrapuntal core of Wagner's works to Bach's twoand three-part writing, sought out the tonal realities underlying the
chromaticism of contemporary music. His aesthetic values were, later, also
those of Heinrich Schenker.101 Ziehn, the advocate of Liszt and Bruckner, saw
a different reality, in which chromatic verticalities characterized nineteenthcentury music. He was a powerful observer of foreground activity which, in
the repertory he valued, was far more interesting and dynamically urgent than
underlying tonal frameworks, frequently obfuscated by both extended
tonicizations and extended passages of tonal ambiguity. Voice-leading, in so
far as he acknowledged it, was therefore perceived only as a local
phenomenon. Both the works of Ziehn and Klauser reflect a period of
incomplete understanding, marked by inspired insight. They both understood
that traditional theories were inadequate or inapplicable. Klauser was theoretically more original and more profound in penetrating the nature of the relationships between harmony and melody, chromaticism and diatonicism.
Ziehn's work was proleptic, seeing music from the perspective of its newest,
most innovative features, implying the possibility of a new linguistic matrix
without being able to define it. Parachronistically evaluated, his text and the
format of his examples have implied an atonal sensibility to those scholars
drawing a connection to Schoenberg and to other atonal composers of the
101 "For in pure instrumental composition Brahms is at present the exponent of the highest intellectual development in music, one of the incontrovertible proofs of this fact
being this, namely, that the compositions of this profound musical thinker are but
slowly gaining proselytes even among musicians. The strong intellectual fibre of
Brahm's mind and its lofty and noble discourse cannot be generally appreciated until
long after the plane of music education has been elevated from intuition and mere
feeling to intelligence and discrimination, to the feeling of ideas" (Klauser 186). The
kernel of Klauser's aestheticjudgement is contained in the following statement: "From
a purely musical point of view, the differences in the masterworks of successive
epochs are in point of harmonic rhythm, and melodic conception, and all these works
stand simply in the relation of simple to more elaborate ... . Composers like Liszt,
Berlioz, and many others of less prominence, have, in their search for extreme effects
and questionable musical originality, too often strayed from the beaten track: such of
their works as are fullest of these transgressions already show signs of decay and, like
the works of many writers of earlier epochs, they are doomed to oblivion" (Ibid. 153).
(Klauser did not seem to share in the polemics of the Wagner-Brahms controversy perhaps only a European concern.)
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early twentieth century.102 Yet ironically, in notable contrast to Julius Klauser
and George Ives, as will be seen. Ziehn doesn't mention the chromatic scale
until the end of his book, where it is followed by a discussion of the whole- '
tone scale.
Ives's essay is not a systematically-conceived study or textbook, although it
contains instructional "lessons" in rudimentary topics.103 The rudimentary topics are barely covered, and Ives even expressed disinterest in teaching them,
recommending the use of available published textbooks several times in the
course of the essay. This document was meant to communicate ideas which
Ives thought unique: to supplement, rather than to replicate, information
available elsewhere, for example, in published textbooks. Conventional instructional lessons are hardly begun, only to be interrupted by interpolations
containing Ives's sharply critical music-theoretical ideas. These ideas were
developed essentially in solitude, with the important exception of his son
Charles. His need to convey them, even to the next-to-musically illiterate
audiences to whom they were generally directed, implicitly conveys the
earnestness behind his pursuits in music.
George Ives's views are particularly interesting because of the authorities he
turned to, the physiologist Hermann Helmholtz and the English pedagogue
John Curwen and, by implication, because of the theorists he rejected. Ives's
synthesis is practical, reflecting his roles as bandmaster and choir director; it is
also critical and complex, reflecting the music-cultural resources that had been
available to and valued by this New Englander, while also reflecting the
quality of his analytical and theoretical acumen in light of the challenges confronting musicians in his day.
Helmholtz's Lehre von den Tonempflndungen seems to have been the main
source of Ives's musical growth subsequent to completing his studies with
Charles Foeppl. In the essay, Ives included a lesson on harmony as acoustically-derived, which he derived from Helmholtz, a topic not even alluded to in
102 Sigmund Levarie, "Ziehn" entry in The New Grove Dictionary of American Music,
Vol. 4 (1986) describes his work as "pointing to the later language of Scriabin and
Schoenberg."
103 The provenance of the essay is fully described in Baron. "George Ives's Essay," op.
cit. Portions of the material on George Ives's work appeared in that article in another
form.
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235
Foeppl's lessons.104 Ives also turned to the Tonic Sol-faists, a group of music
educators who followed John Curwen (18 16-1880). Curwen, an English
Congregationalist minister, had applied just intonation to the solfege syllables
and developed a pedagogical method which became the basis of music
education in Great Britain from around the middle of the century. His work
was much favored by Helmholtz, a strong proponent of just intonation.los Ives
recommended that the "Tonic sol-fa syllables" be learned thoroughly, and that
the student use John Curwen's harmony textbook. Ives used the Tonic Sol-fa
system in training his chorus and was a member of the American branch of the
Tonic Sol-faists.106
George Ives addressed three issues at the basis of the crisis in theory: 1.) the
nature of dissonance; 2.) notation and its nomenclature; and 3.) tuning. He
identified tuning systems as correlates of tonal systems and notational systems
in what may have been a unique effort in Western theory at that time. For Ives,
these issues were not only interrelated, they were combined in ways that
invalidated the authority of the European theorists.
Ives's description of dissonance as a relative characteristic - relative in several dimensions - can be traced directly to Helmholtz.107 Ives demonstrated
that dissonance was qualifiable by register, not an absolute value, whereby
dissonant intervals were rougher-sounding in lower registers. ("Try the exercises an octave or two lower or higher and see how they sound. Or try some
thirds [in lower registers] ... . Notice how rough they sound. When most of
church music was simply [for] men's voices only, fifths and octaves only were
called consonants and thirds were called dissonances as well as sevenths.")l08
104 The six student notebooks George Ives used for in his lessons with Foeppl are housed
in the John Herrick Jackson Music Library, New Haven. At the end of George's final
student notebook, numbered "6," there are the translations from the first nine pages of
Helmholtz, beginning with the heading, "From the Theory of Helmholtz," as previously described ii the introductory section of this article.
105 Helmholtz discussed the Tonic Sol-fa system at length in the appendix entitled "Just
Intonation in Singing" (Sensations, pp. 422-429). Helmholtz's annotator and editor,
Alexander Ellis, was the first President of the Tonic Sol-fa Society in England.
106 Evidence for Ives's association with the Tonic Sol-fa Society is found in Baron,
"George Ives's Essay," pp. 243-244.
107 Henry and Sidney Cowell (in Charles Ives Md His Music [New York: Oxford University Press, 19691, rpt. [New York: Da Capo Press, 19831) claim that "one of Helmholtz's books was in the family library" (p. 19). It cannot be found at the present time.
108 See Baron, George Ives's Essay, p. 270 for the statement in context. Helmholtz's statement on this topic is found in Sensations, p. 190: "For the harmoniousness of either
interval [major or minor] it is necessary that the disturbing beats should be very rapid.
Hence in the upper part of the scale these intervals are pure and good, but in the lower
part they are very rough." Since the medieval perception of thirds was based on the
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This view, traceable to Helmholtz, was not, to my knowledge, found in
nineteenth-century music theory.109 Ives's adoption of it is a measure of his
openness to what were, at that time, unconventional ideas, and his confidence
in making independent analytical and theoretical judgments based on his aural
perceptions.110
The difference between the "aesthetic" and the "natural" bases for dissonance was another issue on which Ives diverged from the mainstays of the
theoretical community. Ives turned to Helmholtz again, to his idea that dissonance was a matter of "taste and habit" and open to changes in perception and
aesthetic expression.111 Discussing the seventh tone of the overtone series - a
minor seventh above the fundamental - the pragmatic Ives wrote: "This 7th
note produces what all musicians call a dissonance but sounds in some cases
to me only like a partial dissonance and is used so much that we get used to it
and treat it as if it were as much of a consonance as our other tones."Il2 For
109
110
111
112
use of only men's voices, "all antiquity, therefore, refused to accept Thirds as consonances."
Helmholtz, Sensations, pp. 184 and 190ff. Helmholtz was first to observe the effect of
register on tone quality. The task of establishing the the scientific basis for this relationship was left to philosopher-scientist Ernst Mach, in "Zur Analyse der Tonemfindungen," Sitzungsbericht der Kaiserlichen Academie der Wissenschaften, Mathematisch-Natunvissenschaftliche Clarse, 92, (Vienna, Kaiserlische Academie, 1885):
1283-1289 (discussed in Robert Cogan, New Images of Musical Sound [Cambridge,
MA: Harvard University Press, 19841, p. 12). Ives's authority was most likely only
Helmholtz (Helmholtz also discussed timbre as a parameter of dissonance.)
Eiseman says, "the article is pragmatic, always concerned with how something
sounds. The student is encouraged every step of the way to play the examples and let
his ear convince him," in "George Ives As Theorist," op. cit., 142.
"We have to furnish a satisfactory foundation for the elementary rules of musical
composition, and here we tread on new ground, which is no longer subject to physical
laws alone ... . We pass on to a problem which by its very nature belongs to the
domain of esthetics. When we spoke previously, in the theory of consonance, of
agreeable and disagreeable, we referred solely to the immediate impression made on
the senses when an isolated combination of sounds strikes the ear, and paid no attention at all to artistic contrasts and means of expression; we thought only of sensuous
pleasure, not of esthetic beauty. The two must be kept strictly apart, although the first
is an important means for attaining the second."
"At every step we encounter historical and national differences of taste. Whether
one combination is rougher or smoother than another, depends solely on the
anatomical structure of the ear, and has nothing to do with psychological motives. But
what degree of roughness a hearer is inclined to endure as a means of musical
expression depends on taste and habit; hence the boundary between consonances and
dissonances has been frequently changed" (Helmholtz, Sensations, p. 234).
Baron, "George Ives's Essay," p. 261. Helmholtz's undoubted dependence on the conservative aesthetic judgements of the contemporary music-theoretical community, de-
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237
George Ives, changing perceptions of dissonance were part of an evolutionary
process in music.113
Ives's sharpest criticism was provoked by the issue of notation. His indictment of theory focused on the staff and nomenclature, in which he found the
basis for prevailing theoretical inadequacies. In one intentionally humorous
example, Ives points to absurdities, from his perspective, in enharmonicchromatic spelling. He accompanies the following example with this comment: "I give the following illustration of what is possible with staff notation.
How does it look? How does it sound?"
Example 14 (from "George Ives's Essay," np # 7407, Charles Ives Collection, courtesy of
Music Library, Yale Universitfi"4
Clearly, what was most important to George Ives about John Curwen's work
was the support it provided for his own disapproval of staff notation, even
though their respective criticisms were prompted by completely different
goals. The Tonic Sol-fa notation that Curwen taught eliminated the staff, using
spite his otherwise pluralistic views, lead him to the following implausible conclusion: "... in modem compositions dissonant chords of the dominant Seventh form the
majority, and consonant chords the minority, ... no one can doubt that this is the reverse of what ought to be the case" (Helmholtz, Sensations, p. 327).
113 See Charles Ives, Memos, p. 48, for George Ives's letter to Orrin Barnum, which contains a powerful discussion of this topic. (The entire letter, as quoted by Charles Ives,
was undoubtedly by Gwrge, contrary to John Kirkpatrick's edition, for which see Baron, "George Ives's Essay," p. 247-248.
European theorists responded selectively to Helmholtz: choosing his support for the
notion of a universal harmonic language derived from nature, while ignoring his conclusions on pluralistic systems and the cultural relativity of dissonance.
114 Ives's cleverness was provoked by an example on page 8 in Jadassohn's 1884 edition
of A Manual of Harmony, demonstrating "the true pitch of the tones in the enharmonic-chromatic scale," in which Gb is lower than F#.
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International Journal of Musicology 2 1993
only solmization syllables.115 However, whereas Curwen was concerned with
the staffs inadequacies in regard to key relationships in just intonation, Ives's
concern was equally related to the staffs inadequacies in expressing chromatic
relationships in temperament.
Ives's goal was a notational system (or several notational systems) that
could logically represent tonal relationships in music, a goal that reflected his
complex understanding of the nature of these relationships - most unusual for
his time. We need to draw inferences from his statements and illustrations to
understand what he meant (as will be shown), because Ives seemed to lack, or
was reluctant to use, the linguistic tools needed to describe some of his conclusions. We sense the writer grappling with the need for theoretical accuracy
and refinement in his essay. He was searching for a sensible way out of the
procrustean bed that the diatonic system and its notation had become, which
was weighted down by the responsibility of explaining chromatic developments.
The need for a notational system that logically represents twelve notes in
equal temperament, which replace the representation and nomenclature of
diatonically-based tones and intervals, emerges from Ives's criticism of the
following characteristics of the staff:
1. The staff misrepresents intervals by its inability to distinguish half steps from whole
steps, falsely labelling all conjunct intervals as seconds.116
2. It bases interval names on the diatonic scale instead of the chromatic scale.
3. Intervals are named by counting notes inclusively instead of representing the spaces
between the notes.
4. It leaves out the chromatic tones, treating them as "accidentals" dependent on the names of the diatonic scales. Ives recommended different names for each of the twelve
notes and suggested integer notation.l17
115 Cunven published many volumes using this format. His notation had the serious drawback that most of its students remained relatively ignorant of conventional notation.
Helmholtz praised it for having "the great advantage in the singer of giving prominence to what is of the greatest importance to him, namely, the relation of each tone to
the tonic .... The ordinary notation gives directly nothing but absolute pitch, and that
too only for tempered intonation" (Helmholtz, Sensations, p. 426).
116 "If they had happened to call each space between two adjacent chromatic steps (or
worse yet what they sometimes call semi- or half tones!) an interval of a First ... or the
space from the first to the third chromatic step as a second ... how much more logical
and true it would have been" (Baron, "George Ives's Essay," pp. 265-266).
117 "After crowding out the poor tones from the staff, they named them without leaving
them any names of their own but made them take the names of the Diatonic Scale tones as their first names even when they were not related to them in the least" (Ibid., p.
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239
Ives also complained about the staffs C-major orientation and inefficiency
in visually describing tonal relationships not in C-major,lla and a concomitant
lack of simple analytical terminology for describing even simple chromatic
elaboration.119 The staff was an anachronism, "pretend[ing] to show to the
eye[,] as the Tones tell the ear[,] the absolute relation of the notes to one
another. It fails even when the notes of the Diatonic scale are used and is very
much worse when it attempts to use what are sometimes called 'accidentals.'
The trouble is that when the 'staff' was first used they didn't use anything but
the Diatonic Scale."l20
Ives shared the conviction that musical notation was antiquated and ineffectual with Julius Klauser and with the Austrian H.J. Vincent121 - all total
strangers, as far as is known - who almost simultaneously produced similar
responses to this aspect of a strong tradition of "normal" theory. As Kuhn
suggests frequently happens, novel and similar theories appear in different
places at the same time because the traditional mode of working "prepares the
way for its own change" (Kuhn 64).122 The recommendations of Ives, Klauser,
and Vincent for a twelve-tone notation do not emerge again until some time
H.J. Vincent handled interval classifications using twelve equal divisions of the
octave and integer notation with far greater sophistication than Ives did in 1st unsere
Harmonielehre wirklich eine Theorie? (see Wason, "Progressive Harmonic Theory",
62 f.). Published in 1894, the same year Ives wrote his essay, Vincent began with
zero, accurately counting the intervallic spaces. Although Ives complained about naming intervals by counting inclusively (in item 3. of the list of criticisms), it seems
not to have occurred to him in begin with zero; he counted to 13 inclusively for the
chromatic scale.
118 "It [the staff ]won't show us a key in the abstract[;] but when we want to talk of notes
in other keys [,I we have to compare [them] with [those in] the key of C" (Baron,
"George Ives's Essay ",p. 267). Klauser made the same observation that the notational
system operates logically only in the key of C major.
119 "If we want to speak of certain steps or intervals (so called) we might have to say,
same as E, D, C in key of C ... and one would have to have the whole system of keys
well in mind to understand what was meant in every other key" (Ibid., p. 267). In this
statement Ives is preparing his criticism of the analytical procedure involving mehrdeutigkeit, subsequently described, as it was used in chromatic music.
120 Ibid., pp. 263-264.
121 Vincent, Ist unsere Harmonielehre, op. cit., p. 3 (from Wason, "Progressive Harmonic Theory," p. 63).
122 The fact that we are still using the same notational system is a measure of several
factors, among them the reluctance of musicians to change and their clever adaptatation of the old system to conceptual discontinuities in composition or theory.
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between 1911, the date of Schoenberg's first edition of Harmonielehre, and
1922, the completion date of the second edition.123
The need for a new notational system drew the attention of several other
European theorists during this period as well, but for two reasons unrelated to
accurately portraying relationships in a twelve-note system:
1. The accurate notation of pure intonation concerned Helmholtz (276f.) and Arthur von
Oettingen (1836-1920), whose system Helmholtz adopted in later editions of Lehre von
den Tonempfindungen.lZ4
2. Alleviating the problem of reading double sharps and flats, a visual problem created
by modulations to keys with high levels of pitch variance, concerned Georg Capellen.125
These concerns with notation were influenced directly by their applications:
accurately notating measurements in pure intonation and the practical concern
of reading accidentals in modem music. They did not, however, address the
relationship of notation to music theory.
George Ives, on the other hand, regarded the analytical system of
plurisignificant chordal relationships (Mehrdeutigkeit) as a negative resultant
123 In a subchapter of the first edition of Harmonielehre, entitled 'The Chromatic Scale
as a Basis for Tonality," Schoenberg suggested "the idea ... to base our thought, not on
the seven tones of the major scale, rather, on the twelve of the chromatic scale" as "a
... more significant way" to deal with secondary dominants and the relationship
between the key and certain minor chords (Theory of Harmony, p. 386-7). Schoenberg
later expanded this chapter, in the process of developing his atonal works, and wrote
in the next edition (unpublished) and in the published third edition (1922): 'That there
are twenty-one note names here, and that their presentation begins with c, is
consistent with and derives from our imperfect notation; a more adequate notation
will recognize only twelve note names and give an independent symbol for e a c h (p.
387). Schoenberg's contemplation of this problem, so many years later, validates, if
that were necessary, the depth of the problem Ives perceived.
124 See Ellis in Helmholtz, Sensations, p. 277f.; Martin Vogel in "Arthur v. Oettingen
und der Harrnonische Dualismus," Beitrage zur Musiktheorie des 19. Jahrhunderts,
op. cit., p. 111; and Peter Rummenholler, "Der logistische Theoriebegriff Arthur v.
Oettingens," Musiktheoretisches Denken im 19. Jahrhundert, op. cit., pp. 83ff. for the
significance of Oettingen's work in notation.
125 Georg Capellen, "Die Einheitlichkeit und Relativitat der Versetzungs-, Oktav- und
Schliissel-Zeichen ohne ~ n d e r u n ~ eam
n Noten- und Liniensystem," Die Musik 3
(1904, erstes Aprilheft): 3-19. In the new notational system he developed, Capellen
used fewer and more neutral marks - small slashes in various positions - to replace
conventional accidental signs. He never suggested an accomodation through twelve
neutral note names. (Capellen's system is very similar to the interim system Klauser
recommended, but he never articulated the need to clarify the relationships of tones to
the tonic - his objectives were much simpler. (I want to thank David Bernstein for
bringing this article to my attention.)
International Journal of Musicology 2 . 1993
24 1
of staff notation; he ridiculed the analyses of chords related to more than one
key in constantly shifting relationships: "In order to try to explain the illogical
products of the staff notation as it is, they have piled names on names and
figures on figures till the poor thing music, either written or sounded, is buried
out of sight and out of hearing."l26 Specific musical ramifications that Ives
foresaw in his attack on this system of analysis can only be hypothesized. He
may have been targeting the anomalousness of possible nontonal (or atonal)
tendencies in then-current theory; or he may have been simply suggesting, as
his Austrlan contemporary Josef Schalk had in a publication just a few years
before, the need to differentiate between chromatic progression and
modulation, a concept predicated on monotonality.127 Although the concepts
of both nondiatonic and monotonal chromatic music were suggested in
Helmholtz's work, particularly in his presentation of F.J. Fktis's culturally
relative definition of tonality, these concepts remained problems at the root of
the theoretical crisis at the end of the nineteenth century.128 By targeting
numerous inadequacies in late nineteenth-century theory, George Ives's
perceptive, independent criticism pointed to a musico-linguistic paradigm
unlimited by diatonicism, a likely model for the imaginative, innovative
directions taken by his son Charles Ives.
We can conclude that the seeming conflict between Ives's advocation of
both Curwen's limited notational system, developed to accommodate relatively
simple diatonic music and, simultaneously, a chromatic notational system, is
illusory. Ives had a complex - a pluralistic - understanding of late-nineteenthcentury "musics," both for the tunings practiced and the types of notations
required for the accurate representation of these tunings. During the crisis
reflecting changing musical systems, tuning was a logical focal point of
theoretical discussion, evoking controversy and some peculiar, seeming contradictions that still call for interpretation. I will, therefore, discuss Ives's vie126 Baron, "George Ives's Essay," p. 266. This system of chordal analysis, introduced by
Gottfried Weber (1779-1839) (Versuch einer geordneten Theorie der Tonsetzkunst [3
vols., 1917-21; 2nd ed., 4 vols., 1830-32; English tr. by J.F. Warner, Theory of Musical Composition [Boston: 0. Ditson 8r Co., 185 11) had been adapted by most of the
theorists Ives would have known.
127 See footnote 96 for Schalk's argument on this matter.
128 Helmholtz wrote: "Modem music effects a purely musical internal connection among
all the tones in a composition, by making their relationship to one tone as perceptible
as possible to the ear. This predominance of the tonic, as the link which connects all
the tones of a piece, we may, with RCtis, term the principle of tonality. This learned
musician has properly drawn attention to the fact that tonality is developed in very
different degrees and manners in the melodies of different nations" (Helmholtz, Sensations, p. 240).
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wpoint on tuning within the framework of contemporary theoretical attitudes
and practices.
George Ives bridged the gap between theory and practice by linking Helmholtz's ideas of cultural differences and evolutionary changes in musical systems to the new developments in modem music - a link that Helmholtz, like
the conservative theoretical community in their analytical treatment of contemporary music, did not make. Ives recognized the chromatic scale and equal
temperament as the basis for contemporary music practice, stating, in effect,
that just intonation and the diatonic scales had become theoretical anachronisms: "Modem music has fitted itself (no one person ever did it) to the
chromatic scale with its thirteen notes in the octave at equal distances
apart."l29 His attitude on this matter was a significant departure from Helmholtz's views.
Helmholtz, to the contrary, interpreted the "new" tuning as "transformations" that alter the pitch of one tone in a chord to facilitate "modulations
which with a single step lead us to comparatively distant keys ... This means
of modulation is often employed by modern composers, (for example, R.
Wagner)." His interpretation of performance practice through tuning by means
of "transformations" recognized characteristics of pure intonation retained in
performances of modem music (339). As for the tuning of keyboard
instruments, Helmholtz referred to the "imperfections of tempered tuning"
(338). "In just intonation these chords are not by any means so unpleasant as
in the tempered intonation of the pianoforte" (339). Helmholtz's English
editor, Alexander J. Ellis, disagreed with him: "From what follows it is
evident that the transformations could only take place in tempered intonation.
The tones confounded ... could not possibly be confounded in just intonation.
Of course Wagner thought only in equal temperament, in which the tones are
absolutely identical" (Helmholtz, p. 339).130
129 Baron, "George Ives's Essay," p. 264.
130 Ellis, the first President of the Tonic Sol-fa Society, also invented the measurement
known as the "cent," which enabled him to analyze equal-temperament for an harmonium by converting the ratios of intervals into cents. He also provided valuable
acoustical tables for the leading piano tuning practices. Yet, the matter of nineteenthcentury (and twentieth-century) tuning may be more complex than thought up to now;
we will soon see that Ellis' assuming to know how Wagner "thought"or tuned his orchestras may have been presumptive.
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The difference in the positions of these two scientists seems to have centered on the issue of enharmonic equivalence, particularly in modulation. Ives's
position seems to have been similar to that of Ellis: On the one hand, he recommended the Tonic Sol-fa system to students and taught just intonation to
his chorus for the relatively simple, diatonic works they undoubtedly sang
because the sound was pleasing, or expressive, or stylistically appropriate. On
the other hand, Ives contended that the chromatic scale and the twelve-tone
equal division of the octave were basic to contemporary music. Ives's approach to the problem may have been pragmatic, rooted in a number of different experiences, for example, in his perception of the tuning differences in
performances he heard of modem music (particularly Wagner's) and earlier
music,l31 and in his work as a practical musician. But Ives, who is known for
his experimental bent - particularly with microtones, which may well have
been stimulated by Helmholtz's discussion of culturally-determined systems may have actually been thinking abstractly about the efficacy of different systems for different musical styles. The distinctions he made between tuning
according to style were at odds with the beliefs of the European community.
The controversy in European theory was more ideological. Robert Wason
has summed up the prevalent view: Helmholtz's work in acoustics "corroborated that age-old belief in the 'naturalness' and superiority of 'simple' tuning
ratios," thus reinforcing "the influence of just intonation in music theory of the
latter half of the nineteenth century and beyond."l32 The notion of a universally-valid tuning system derived from nature had become paradigmatic.
The abstract basis of this epistemological position was, however, matched by
that of "progressives," who speciously argued (as new evidence shows) that
equal temperament was both the practical and the realistic - read that "universal" - basis of Western tonality. Their position was eloquently presented in
this statement attributed to Carl F. Weitzmann: "The strife among the theorists
as to which is best has continued down to the present day, but as nearly all of
the greatest masters, Bach, Haydn, Mozart, Beethoven and others, adopted and
used the Even Temperament, besides the fact that all keyed instruments are
adapted thereto, the strife seems to be one sided ... Gold is of little utility
before being tempered; just so,jifths need tempering, in order to prepare them
13 1 Because George Ives's knowledge of modem music is not supported by references to
musical works in the essay, it is worth noting his reported identification with Wagner's music by Charles Ives in Essays Before A Sonata (New York: W.W. Norton &
Co.. 1961). p. 72.
132 Wason, "Progressive Harmonic Theory," p. 59.
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for practical use."l33 To Ives, operating from pluralistic assumptions, the
arguments from both sides of the controversy would have appeared faulty.
Recent scholarship has not determined precisely what tunings were actually
practiced in the name of either just intonation or equal temperament, the only
certainty being that it was not equal temperament. The significance of how
these issues are finally settled is tied to how we understand this period in the
history of theory. A new perspective on historical tunings has been introduced
that may necessitate the reevaluation of this one-size-fits-all-approach by the
nineteenth-century adherents on both sides of the tuning controversy, which
has been cast as an argument between conservative ideologues fighting a losing battle with the progressive, practical realists. In his historical study of
keyboard tuning systems, Owen H. Jorgensen claims that equal temperament
was not achieved until about 1917; its achievement responded to the needs of
the symmetrical - neutral - divisions of wholetone music.134 Prior to that, different kinds of well-tempered or "irregular" tunings were used.135 "The temperament practice of the late nineteenth century was so different from that of
today that it no longer can be called equal temperament. Nineteenth-century
temperament contained various degrees of 'key coloration' which preserved the
"characters of the keys ...Key-coloration has disappeared in today's tempering
practice, which is reinforced by the philosophy of even-tone-voicing (tone
regulation)."l36 Jorgensen introduces Alexander Ellis's reports of latenineteenth-century tuners who intentionally avoided attempts to recreate even
the quasi-equal tunings that were possible, i.e., making "aesthetic decisions."l37 It is not farfetched to imagine that performing musicians on stringed
and wind instruments also avoided equal temperament, even when performing
Wagner - certainly musicians do that today. As for just intonation, Jorgensen
describes it as "restrictive" and "irregular": "Only half of the harmony in any
variety of just intonation is useful because of the many wolf intervals. The
virtue of just intonation is that the good half of the harmony is the ultimate of
133 Bowman's-Weitmn's Manual, p. 27. Ziehn assumed that equal temperament underlay his enharmonic plurisignificance.
134 Owen H. Jorgensen, Tuning: containing the perfection of eighteenth-century temperament, the lost art of nineteenth-century temperament, and the science of equal temperument (East Lansing: Michigan State University Press, 1991 ), pp. 2-3.
135 "Misleading information has been propagated by many nineteenth- and twentiethcentury writers. They incomtly used the term 'equal temperament' to include all the
systems since the sixteenth century that allowed one to modulate freely through all the
tonalities without encountering wolf intervals" (Ibid., p. 9-10).
136 Ibid., p. 2.
137 Ibid., p. 3.
Intemtional Journal of Musicology 2 1993
245
perfection and harmoniou~ness."~38
For the choral music sung by the Tonic
Sol-faists and George Ives's choir, approximating just intonation would certainly have been a goal.
Although we do not know the specific tunings Ives had in mind when he
referred to equal temperament, what is clear is that he distinguished between
tunings for different musical styles. Klauser was unambiguous in describing
the generic type of tuning needed to accommodate twelve independent tones
and was most accurate in his assessment of tuning practice when he wrote:
"The Tonal System was perfected harmonically when it was developed into a
system of keys. This was accomplished by Temperament ... The degree of the
temperament of a tone must be such as to render each tone in the System
harmonious in all its harmonic relations in one key and in all keys ... Harmony
that arises when we relation keyklangs, furnishes the exact degree of such
temperament" (250). Klauser speaks of "temperament," not "equal" or "even"
temperament, indicating well-temperament or what Jorgensen calls "quasi
equal temperament." Perhaps Klauser's concerns developed along more
conservative lines than those of Ives, since Klauser was concerned with explaining the relationships of all tones to a central tonic while Ives was interested in abstract relationships.
Evaluations of theorists involved in the controversy have been colored by
our assumptions about nineteenth-century tuning practice. For example, conclusions about the statements of Hugo Riemann (1849-1919) on the issue of
tuning - another contemporary of Ziehn, Klauser, and Ives - may need to be
restudied. While unable to relinquish the ideological calling of universal nature in regard to tuning,l39 Riemann seems to have been the only one of the European theorists who tried to define the practical dilemma others never confronted. He framed it as a duality between what is heard and what is perfor138 Ibid., p. 10. Jorgensen's conclusions contradict those of J. Murray Barbour, who argued in "Just Intonation Confuted" (Music and Letters 19 [1938]: 48-60) that nineteenth-century musicians who claimed to have played and sung using just intonation
deceived themselves: "Helmholtz and his followers are wrong, ... singers have no
predilection for so-called natural or just intervals" (p. 53). He later concluded, in Tuning and Temperament (East Lansing, 1951), that both just intonation and meantone
temperament were hypothetical and ultimately invalid;he states that "It is probably
true that all the singers and players are singing and playing false most of the time. But
their errors are errors from equal temperament ... . Equal temperament does remain
the standard, however, imperfect the actual accomplishment may be."
139 Carl Dahlhaus cited the following statement by Riemann, dating from 1912: "Surely
the proper goal of historical research is to reveal the ultimate natural laws, common
all periods, that control all perception and artistic forms" in Untersuchungen iiber die
Entstehung der hannonischen Tonalitat, tr. Robert 0. Gjerdingen, Studies On The
Origin of Hannonic Tonality (Princeton: Princeton University Press, 1990), p. 59.
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med: "What are the recognizable qualities that a mentally conceived tone, if
conceived correctly, has in common with an actually sounding tone?"l40 By
invoking his notion of Tonvorstellung, Riemann distinguished between the
pure intervals that are heard and the tempered intervals that are produced
through practical "artistic deviation" that "blurs the mental concept."l41 Riemann is describing Helmholtz's "transformations." Whatever changes and differences Helmholtz, Riemann, and Ives heard and acknowledged, they had
perceived musicians tuning differently for modem music to accommodate
actual or psychologically interpreted enharmonicism for the new kinds of
modulation.
As isolated observers from the United States, three American theorists at the
end of the nineteenth century were able to contribute up-to-date, novel, and
idiosyncratic theoretical descriptions and definitions of European compositional practices. Synchronically, their orientations developed from their independence, their knowledge of European music and theory, and their critical
capabilities. The dearth of European contemporaries able or willing to meet
the challenge of late nineteenth-century music was symptomatic of the hold on
the European professional community - despite the different traditions that
existed - of the theoretical conventions of the so-called "common practice."
Ziehn, Klauser, and Ives evolved different categories for examination and
new methodological procedures. Their field of study - the observed phenomenological ground - had changed: the same music that had been obseived by
previous theorists and by most of their European contemporaries had, in
effect, become different because it was perceived differently. Former analytical categories and procedures had become ineffectual. The topics that jointly
concerned these theorists included music psychology, particularly perception;
140 Hugo Riemann, "Ideen zu einer 'lehre von den Tonvorstellungen,"' Jahrbuch der
Musikbibliothek Peters 21-22 (1914-15). pp. 4-5; from Mickelsen, Hugo Riemann's
Theory, p.87. For Riemann's peculiar attempts to rationize the conflicts ensuing from
his search for "natural"systems and what he believed were the necessity of enharmonic equivalence, see the entries under "tuning and temperament" in the index to William C. Mickelsen, Hugo Riemann's Theory, particularly p. 87.
141 "Riemann considered this dualism so important that he returned to it at the very end
of his final essay on harmonic theory, claiming that further work on 'enharmonic
identification' would ultimately solve contradictions between tone-psychologal investigations and the experiences of practical musicians" ("Ideen zu einer 'Lehre,'" p. 26;
from Wason, "Progressive Harmonic Theory," p. 84, footnote 23).
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the relationship of counterpoint and voice-leading to harmony; the nature of
progression and cadence; leading tones; definitions of consonance and dissonance; the function of chromaticism in progression and modulation (or smalland large-scale tonal organization); key relationships; analytical categories;
notation and nomenclature; categorizing and computing grammatical and
syntactical possibilities; and tuning.
Diachronically, these three American musicans were among the earliest
contributors to the evolution of twentieth-century theoretical paradigms. Nevertheless, they did not eschew the European traditions. They evaluated innovations, anticipated atonal sensibilities (as Ziehn did), recognized the theoretical anomalies associated with them (as Klauser did), understood their ramifications (as George Ives did), and (directly and indirectly) prepared the way
for new paradigms that explained the musical past as they prepared the way
for new compositional models (like those of the just emerging, gifted youngster Charles Ives) sooner and with greater objectivity than most contemporary
European theorists.