The Influence of Riemann (and Richter) on Music Theory in Scandinavia

Thomas Jul Kirkegaard-Larsen

Even though it is well known that Hugo Riemann’s function theory traveled far and wide beyond the boundaries of German-speaking Musikwissenschaft, the exact impact it has had in other linguistic and national communities—the ways in which it has been adapted, transformed, and combined with local idiosyncrasies—has been subject to limited scholarly scrutiny. Lately, however, the surge of interest in global histories of music theory (see Raz et al. 2019) has given the international music theoretical community new insights into function theory’s many different national adaptations. Recent examples include Gesine Schröder’s entry on this blog and the research project on Chinese reception of European theory to which it refers (see Cheong and Hong 2017; 2018; Ying and Komatović 2017), as well as the 2018 special issue of Zeitschrift der Gesellschaft für Musiktheorie devoted to research in the global reception of European music theories, in which one article focuses on Riemann’s (as well as Schenker’s and Schoenberg’s) dissemination in Brazil (Almada et al. 2018).

It may come as no surprise, then, that Riemann’s function theory also found its way up north, to Scandinavia. More surprising, perhaps, is the fact that even in Scandinavia, in which German was considered the musicological lingua franca for much of the 20th century before it gradually turned towards English, the direct influence of German sources is very limited. Moreover, even though the Swedish, Danish, and Norwegian languages are similar enough to enable cross-national communication—and even though Scandinavian theorists demonstrably have influenced each other across national borders—the function theories of the three countries are remarkably different from each other. This blog entry gives a brief introduction to some of the ways that function theory was received and transformed in Sweden, Denmark, and Norway, and makes reference to some of my own research published in forthcoming articles.



Apart from an article in the Swedish Journal of Music Research from 1931 which primarily discusses Hugo Riemann’s idea of Scheinkonsonanz (Svensson 1931), the first Swedish text on function theory was Sven E. Svensson and Carl-Allan Moberg’s Harmonilära from 1933. Here, Riemann’s direct influence is palpable: the authors adhere to his much criticized theory of harmonic dualism and structure the textbook in the style of Riemann’s Handbuch der Harmonielehre, which—from the third edition and onward—presents the theory of functions in tandem with his earlier theory of Harmonieschritte (Riemann 1898). But though the textbook of Svensson and Moberg has certainly been influential insofar as it introduced function theory to Sweden, until then dominated largely by Aron Bergenson’s Harmonilära (1899) (which was itself modelled on Ernst Richter’s Lehrbuch der Harmonie [1853]), none of Svensson and Moberg’s dualistic aspects are to be found in later publications. Instead, a monistic theory evolved in publications by Ingemar Liljefors (1937; 1951), Harald Göransson (1947; 1950), Valdemar Söderholm (1959), and Henry Lindroth (1960) to mention but a few of the most formative theorists. Unlike the case in Denmark and Norway, there are several Swedish publications clearly inspired by Austro-German function theories, especially those of Hermann Grabner (a main inspiration in Göransson 1947; 1950) and Wilhelm Maler (influential in Tegen 1974 and Smedeby 1978). Thus, present-day Swedish function theory is quite similar to what one finds in German publications, but with many unique characteristics nonetheless. For instance, several Swedish publications group chromatic mediants into a matrix of categorizations along three axes: a particular mediant is either upper or lower; primary or secondary; and even has a subdominant or dominant function—a peculiar addition to David Kopp’s 2002 book on historic mediant theories worthy a study of its own.


Function theory enters Denmark the same year as it enters Sweden: in 1933 with Finn Høffding’s Harmonilære. Høffding’s account of function theory could not have been more different from that of its contemporaneous Swedish counterpart: there are no traces of harmonic dualism, or any reference to Harmonieschritte. In fact, Høffding altogether avoids the term “function,” replacing it with the idea of “affinity” between chords. This term, Høffding explains, is “borrowed from chemistry, in which it designates a substance’s tendency to connect with a certain other” (Høffding 1933, 4; my translation). In effect, there is a change of focus from function residing in the chords to affinity between chords—though in practice, Høffding’s analyses apply function letters in a conventional way, albeit with some terminological innovations. For instance, Høffding presents a new function symbol for the chord on the sixth scale degree as it appears in deceptive cadences: A tilted T symbolizing that it functions as a tonic substitution, conceptually different from Riemann’s Tp, tonic Parallel (later Danish theories write Ts or Tst as shorthands for the tonic substitution). Høffding thus makes way for a new breed of function theory—only fully realized in Svend Westergaard (1961)—in which chords in paradigmatic progressions receive distinct functional suffixes; third related chords are not always a Parallel, a Leittonwechsel, or a Gegenklang (Grabner 1944), but may be analyzed as a substitution of a main function, a derivation, a prolongation, and more. With Teresa Waskowska Larsen and Jan Maegaard’s Indføring i romantisk harmonik (1981), this system evolved into an analytical approach that to a certain extent anticipates later Anglo-American transformational and neo-Riemannain approaches, a point that I discuss furtherly in my article “Transformational Attitudes in Scandinavian Function Theories,” forthcoming in Theory and Practice.


Function theory gets a late start in Norway compared to its neighboring Scandinavian countries. The first publication with traces of function theory is Thorleif Eken’s Harmonilære from 1948. Eken refers to the Danish Harmonilære of Povl Hamburger and Hakob Godske-Nielsen (1939) as his main inspiration; though adding a few function theoretical aspects, Hamburger and Godske-Nielsen’s textbook is closely modelled on that of the Danish J. D. Bondesen (1897), which is in turn strongly influenced by Richter’s Lehrbuch (1853), a book that Bondesen had previously translated to Danish (Richter 1883). In other words, Richter-inspired textbooks such as these, as well as the Norwegian Praktisk harmonilære by Gustav Fredrik Lange (1897), continued to exert influence in much of 20th century Scandinavian theory, especially in Norway. In Eken’s function theory, this influence is still noticeable. Eken uses Roman numerals rather than function letters, but he refers to his numerals as “function numbers.” It was only with Anfinn Øien’s publications (1971; 1975) that function theory seriously entered Norway. Like Eken, Øien looks to the writings of the Danish Povl Hamburger and presents a function theory with the same unique terminology that Hamburger presents in his Harmonisk analyse (1951). In effect, Norwegian theory largely emanates from Hamburger and his analytical practice where the Parallel-term is reserved for instances where there is an actual tonal indication of the Parallel key; for third-related chords that do not imply a change of key, one uses the functional suffixes submediant and mediant instead. This practice continues in Norwegian theory to this day—though the usefulness of function theory has been questioned in the Robert Gauldin-inspired publication by Petter Stigar (Gauldin 1997; Stigar 2004).

Ramifications of Riemann and Richter

The influence of Riemann and Richter in Scandinavia is in itself not the interesting point here. Rather, it is the fascinating and unpredictable ways that the theories have been received, remodelled, and ramified in directions more or less segregated from their origins. There are many reception histories to be written here.

Thomas Jul Kirkegaard-LarsenThomas Jul Kirkegaard-Larsen is a PhD student in Musicology at Aarhus University, Denmark. He holds MA and BA degrees from Aarhus University in Musicology and Scandinavian Languages and Literature. His dissertation focuses on the traditions of Anglo-American Schenkerian theory and Continental-European Funktionstheorie for the purpose of reassessing and bridging the perceived gap between these traditions. Thomas is the winner of the Patricia Carpenter Emerging Scholar Award 2018 as well as a Fulbright Scholarship 2017–18 which supported his stay as a Visiting Research Scholar at the CUNY Graduate Center.


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