Gustav Andreas Lautier (1797-unknown), a German lawyer, philosopher, and musician, appears to be the first thinker to apply a comprehensive philosophical framework systematically to musical theory. Drawing on Georg Wilhelm Friedrich Hegel’s discussion of the basic thought-determinations that attempt to grasp what is absolute: Being, Essence, the Concept, and the Idea in Phänomenologie des Geistes (1807) and Enzyklopädie der philosophischen Wissenschaften (1827, 2nd edition), Lautier reformulates dialectical logic into a doctrine of “infinite dualism.” He interprets musical intervals—particularly the second, third, and fourth—through a threefold conceptual structure, further extending this to sixfold intervallic relations and the principle of the “infinitely divided” fourth as the highest harmonic law. His entire interpretation of musical phenomena is grounded in this threefold conceptual model. From this foundation, he reinterprets scales, fundamental bass, and harmonic progression within a unified philosophical system.

This paper investigates Lautier’s philosophical framework and its systematic application to music intervals in his book System des Grundbasses der Musik und Philosophie (1827). He stands in a view of the combination of Schelling’s philosophy of absolute identity and Hegel’s philosophy of dialectical reasoning as the foundation of his interval theory. A close examination of his interval theory will reveal how music theory in early nineteenth century Germany was shaped by contemporary philosophical thought.

Although Lautier is typically mentioned only marginally in scholarship, evidence from a February 1828 letter from Hauptmann to Franz Hauser indicates a significant engagement with Lautier’s System des Grundbasses der Musik und Philosophie. Moritz Hauptmann described the work as intellectually demanding yet compelling, referring to it as a “new system” grounded in the concept of “infinite dualism.” This characterization is striking given that Hauptmann’s own theory has likewise been described as a “new system” influenced by Hegelian philosophy.

However, there is never strong evidence either from Hauptmann's own theory or the external evidence to prove that he directly inherits some related ideas from Hegel. By comparing Lautier and Hauptmann's interval theory, it shows that Hauptmann ultimately fails to demonstrate convincingly how the notion of the Absolute can be meaningfully grounded in music from either a practical or a theoretical standpoint.

In his famous satirical pamphlet Il teatro alla moda (1720), Benedetto Marcello charges contemporary opera composers with ignorance of the modes: "He will not know which or how many are the modes or tones … Rather, concerning this, he will say that there are only two modes, major and minor." What then was the relevance of modal theory for Settecento compositional practice? In answering this question, I turn to Marcello’s little-studied Lettera famigliare—a polemical critique of Antonio Lotti’s Op. 1 Duetti—in which he upholds the twelve modes “using geometric demonstrations” (i.e., harmonic/arithmetic octave divisions), while dismissing major-minor keys as “unreasonable.” This paper argues that Marcello’s motivation for preserving modal theory was twofold: first, it was a consequence of the theory’s mathematical underpinnings; and second, the theory afforded practical nuances that Marcello perceived to be missing in contemporary major-minor key theory.

In discussing Lotti’s duets, Marcello invokes modal theory alongside major-minor key terminology. His notions of “key” and “mode”—both designated by the term “tuono”—pertain to distinct stylistic phenomena: the former describes general tonal coherence, the latter fugal imitation. While major-minor keys could account for general issues of tonal focus, only modal theory, for Marcello, could supply the divided octaves and proper interval species necessary for fugue.

Marcello’s application of modal theory to stile concertato duets was atypical. I suggest that this view of contemporary practice reflects Marcello’s Pythagorean rationalism. Moreover, the mutability of Marcello’s term “tuono” indicates a more flexible tonal perspective than our modern compartmentalization of keys and modes. Marcello’s “keys” and “modes” are not so much distinct categories as practical and theoretical sides of the same coin.

Finally, Marcello’s application of modal theory to “common-practice” tonal style suggests that historical theories of mode and key do not align with “modal” or “tonal” styles in contemporaneous music. Marcello provides no historical justification for using modal theory to explain tonally-irregular scale degree inflections, nor does he restrict modal theory to stile antico polyphony or use as a stylistic topos. On this basis, I argue that modal theory’s a priori basis in rational speculation preceded and justified its subsequent applications in practice.

Mode in late Beethoven has been understood as occurring primarily through mode-signifying scale degrees coloring the major or minor keys (Biamonte, 2001; Tuttle, 2016; Grajter, 2020). But this may overlook older forms of modal behavior predicated on mode-signifying half steps in relation to a final, rather than as inflections of an a priori diatonic scale. Some of Op. 131’s more enigmatic harmonic features—the ambiguous closes of the tonic-key bookend movements, wherein tonic major emerges as V/iv, and the fugue’s subdominant rather than dominant answers—cannot neatly be summarized as modally inflected scale degrees. Instead, this paper argues that, in the above, Beethoven employs two Phrygian conventions, which historically emblematize the mode’s signal half steps, as they had absorbed into Baroque tonal practice.

First, Phrygian Points of Imitation: through an examination of J.C.F. Fischer’s mi fugue in his Ariadne Musica, whose subject is the Phrygian hymn Aus tiefer Noth, I show that explicitly Phrygian fugues could feature subdominant answers in which the tonic subject’s 5–!6 is transposed to 1–!2. Second, Phrygian Tonal Closes: through exploring historical surveys of the change from modes to keys by Harold Powers and Joel Lester, I highlight the emblematic Phrygian half steps in the Phrygian Tonal Closes !vii–I and iv–I. I explore these closes in Bach’s chorale setting of Aus tiefer Noth, and suggest, again, their origins in mode-signifying half steps.

Having surveyed the above historical antecedents, I return to Op. 131 to demonstrate how these Baroque Phrygian strategies parallel key moments in the Quartet. While this interpretation supports the accepted notion that Beethoven’s late style, beyond being forward-looking and experimental, also engages with historical practices, further, it suggests an expanded view of his modal thinking, beyond harmonic and melodic inflections or major or minor keys, to include modally-idiomatic Points of Imitation and Cadences.