In Moritz Hauptmanns Theoriesystem wird die reine Stimmung impliziert, wenn er »drei direct verständliche Intervalle« zum Ausgangspunkt erklärt; weiterentwickelt wird seine Notation in Groß- und Kleinbuchstaben im folgenden Diskurs durch Hermann von Helmholtz und Arthur von Oettingen zur »Buchstabentonschrift«, die das syntonische Komma auch mehrfach berücksichtigt. Sowohl Oettingen als auch Hugo Riemann knüpfen an Leonhard Eulers Tonnetz an; bei letzterem mündet der Diskurs in Schreibweisen zu Unterklängen als »Klangschlüssel« und einer noch dualistisch geprägten Funktionstheorie.

Beginnend mit Helmholtz, der im Rahmen seiner akustischen Experimente auch ein rein gestimmtes Harmonium beschreibt, folgen sein Schüler Shōhei Tanaka, der über die reine Stimmung promovierte, Oettingen und Riemann mit jeweils direktem Bezug zu Helmholtz und eigenen Versuchen. Bei Tanaka und Oettingen entstanden in Zusammenarbeit mit Instrumentenbauern Harmonien in reiner Stimmung.

Für den Harmonischen Dualismus ist die reine Stimmung insofern grundlegend, als dass hier Dur- und Molldreiklänge als naturgegeben konsonante Klänge mit reinen Intervallen der Obertonreihe und deren Spiegelung hergeleitet und theoretische Systeme auf dieser Basis konstruiert werden.

Implikationen bei Hauptmann, dessen System alle weiteren am Dualismus-Diskurs im 19. Jahrhundert Beteiligten elementar beeinflusste, lassen die reine Stimmung an Bedeutung gewinnen. Die sich zeitgleich in der Praxis durchsetzende gleichschwebende Temperierung war in diesem Diskurs allerdings nie Option. Ein physikalischer Ursprung als naturgegebene Legitimation insbesondere des Molldreiklangs einerseits und die ästhetische Perspektive im Sinne mikrointervallischer Konsonanz ganzer Theoriesysteme andererseits hatten mittels praktischer Experimente Einfluss auf den Instrumentenbau; Riemanns in diesem Kontext konstruierten Untertöne blieben als spekulative Theorie physikalisch unbelegt. Eine Vision, die reine Stimmung im bürgerlichen Wohnzimmer zu etablieren, und den Dualismus in der kompositorischen Praxis, bestimmt das Denken am Diskurs beteiligter Autoren.

The epistemological rift between Schenkerian and neo-Riemannian theory runs deep. Particularly in relation to questions of musical time, this rift has profound hermeneutic implications, as can be glimpsed, for example, through a comparison of David Beach’s and Suzannah Clark’s interpretations of the opening exposition of Schubert’s G major String Quartet D. 887. Whereas Beach’s Schenkerian reading highlights with reference to the tonic-dominant axis a teleological — ‘end-accented’ — orientation of the musical discourse, effectively attributing to it a sense of ‘narrative’ time as habitually associated with Beethoven’s heroic style, Clark’s neo-Riemannian perspective discerns in the hexatonic cycling woven into the tonal geometry a fingerprint of Schubert’s ‘lyrical’ imagination, a mode of suspended temporality that she considers decisively ‘non-Beethovenian’ (or, indeed, uniquely ‘Schubertian’). Owing to the specific epistemological calibrations built into each respective theoretical lens, these two interpretations reveal a basic hermeneutic-logical contradiction: (how) is it possible that the same music is teleological and non-teleological at once?

The aim of this paper is to critically reappraise this contradiction. While carrying no real weight in the arena of music analytical plausibility, this contradiction drills down to the bedrock of all modern (post-Gadamerian) hermeneutic philosophy: the cardinal problem that the ‘truth’ produced by a certain ‘method’ is critically shaped by it. Drawing upon Nelson Goodman’s concept of ‘world versions’ — a solipsistic-constructivist theory of conceptualising truth claims — this paper explores to what extent opposing interpretations of musical time can be understood as representing different ‘versions’ arising from the multivalent symbol system which makes up the individual work, the ‘world’. Once cast in this light, the epistemological inconsistencies underpinning the hermeneutics of musical time can be reframed as heuristic opportunities, rather than impasses, in the way that they engage us to rethink the normative grounds for claims about musical time without all too conveniently essentialising it.

Some of Hugo Riemann’s harmonic theories have experienced a revival in the US-music theory since the late 20^th century. Indeed, Richard Cohn’s work has been an evident milestone for the development of Neo-Riemmanian theories within the field of transformational analysis for tonal repertoires. For instance, focusing on parsimony, instead of privileging functionality, has proven extremely useful for the analysis of many passages of 19^th-century chromatic music.

The Neo-Riemmanian approach also provides opportunities for creative thinking and the generation of new scientific knowledge beyond the strict limits of musical analysis. On the one hand, the basic aspects of parsimonious transformations of chords can be mathematically formalized; such a formalism can be exploited to conceive compositional rules by means of particular restrictions in the voice leading and distribution of a pooled reservoir of chords. On the other hand, the use of Neo-Riemmanian visual representations like the Tonnetz may help to explore multimodal aspects of the way we conceptualize music by means of visual patterned structures.

Our lecture-recital is aimed at providing elements of both perspectives mentioned above. We will firstly summarize the key features of the Neo-Riemannian theories for those who are unfamiliar with this approach by using an interactive web application developed within the SMIR (Structural Music Information Research) Project. This introduction will be followed by an explanation of mathematical models of voice-leading strategies for composition, based on graph-theoretical concepts, such as Hamiltonian cycles within the Tonnetz. These ideas will be illustrated through some poetry-based pop songs. For a more meaningful explanation, some of these musical examples will be also accompanied by visual animations of the underlying Neo-Riemannian representations. This audiovisual interaction will prepare the audience for an overall presentation of our current empirical research on multimodal insights of the Tonnetz. We will devote the second part of the lecture-recital to the discussion of the outcomes of an experiment with musicians and non-musicians interacting with computer-based representations within the Tonnetz, and some additional aspects we are exploring in a second ongoing experiment. We will summarize the main results obtained so far and their implications in the context of music theory education.