Vincent d’Indy, co-founder of the Schola Cantorum and author of the influential Cours de composition musicale (1902–50), was one of the most prominent composers and music-theoretical thinkers in fin-de-siècle France. Studies of d’Indy’s music (Huebner 2004; Deruchie 2013; Saint Arroman 2019; Rovenko 2020) reference his theories but do not engage with his foundational idea of “order relationships.” In this paper, I introduce and extend d’Indy’s theory, developing order-space technologies to analyze non-functional harmonic progressions in “Harmonie” from Poème des montagnes, op. 15 (1881) and “Mirage,” op. 56 (1903). My paper reveals the importance of order-based thinking to both d’Indy’s music-theoretical method and his compositional approach. Beyond connecting d’Indy’s ideas to his music, this research broadens our understanding of interactions between music theory and compositional practice in fin-de-siècle France. It also encourages us to step outside the established paths of twentieth-century French music studies, to look beyond canonic figures, and to embrace new analytical methodologies.

If harmonies are indeed reflexes from the unconscious, as posited by Ernst Kurth, a compelling question emerges: How do music theories, products of our conscious intellect, interact with and interpret the expressive, often subconscious sonic experience of listening to music? While Kurth's theories are frequently discussed, mainly for their contributions to music theory, psychology, and philosophy, their practical use in music analysis remains less explored. Notable scholars like Patrick McCreless, Lee Rothfarb (1988, 1991), and Daphne Tan (2013) have provided pivotal translations and interpretations of Kurth’s seminal works. However, Kurth's writings, while original and perceptive, do not offer a definitive system for practical analysis. Building on these insights, this project articulates a structured analytical framework inspired by Kurth. This framework incorporates his concepts into a practical system balancing musical sensitivity and systematic rigor.

In Kurth’s theories, music is categorized into “inner” and “outer” content. Outer content is defined by tangible, quantifiable elements such as counterpoint, rhythm, and harmonic function. In contrast, inner content delves into musical energetics and subjective experiences, with harmony often portrayed through coloring techniques like shading and brightening. My methodology employs an illustrative system to effectively highlight these aspects in tandem. To demonstrate the practical application of this approach, I conduct a case study of Chopin's Op. 10 No. 6 and Op. 28 No. 9. By employing a Kurthian-inspired analysis and comparing it with Schenkerian interpretations, I aim to deepen our understanding of Chopin's musical landscape and showcase how a Kurthian approach explores emotional and sensory musical dimensions.

Despite their foundational importance, the psychoacoustic underpinnings of Cohn’s neo-Riemannian approaches to hyper-chromatic tonal music—by composers such as Richard Strauss, Alma Mahler-Werfel, and Florence Price—remain underexamined. For instance, Cohn writes: “tonal listeners process intervals…by accommodating their components to a single diatonic collection,” which “dictates that a semitone is heard as a change of degree (minor second), while…nine semitones express a major sixth rather than a diminished seventh” (2004; also Agmon 1986, Temperley 2001). Juxtaposing hexatonic-polar triads C+ and E+ thus creates a psychoacoustic paradox: the vertical ic3 between pc11 and pc8 implores a diatonic interpretation (major sixth, B/G#), while the linear motions C-B/G-Ab invoke a chromatic one (diminished seventh, B/Ab).

Hutchinson (2020/2022) explores functional connotations in similar relationships. Initially perceived as consonant, the ic3 between pc11 and pc8 behaves as a diminished seventh upon resolving to C/G, the intervallic progression retroactively signaling a scale-step context of 7/b6 resolving to 1/5. Perceived consonance becomes reconceived dissonance, an acoustic transfiguration which anchors the progression in tonal-functional linear processes.

Between these perspectives exists a compelling dialogue. Cohn’s approach foregrounds phenomenological experience (Lochhead 1980; Lewin 1986), problematizing diatonicism’s inability to correlate conflicting acoustic signals by preserving diatonic coherence at intra-chordal levels. Hutchinson (2023), conversely, suggests that function in highly chromatic music is perceptible only outside phenomenological time, sacrificing intra-chordal vertical diatonicism for inter-chordal linear coherence. While seemingly incompatible, both perspectives describe different temporal event-points in processes of listening to, and correlating, successions of harmonic relationships: phenomenological and retrospective. In such dialogues, “the ear is constantly constructing new contexts and revising old ones” (Lewin 2015).

Extending this dialogue, I argue that hyper-chromatic tonal syntaxes create situations wherein psychoacoustic signals processed in phenomenological time diverge from perceptions elicited by the same tones in retrospect, thereby creating a plurality of functional potentialities that prompt retrospective re-partitioning. Intra-chordal intervallic relationships initially perceived diatonically are sublimated into chromatic relationships to preserve inter-chordal linear-functional coherence. This hyper-chromatic tonality thus embodies characteristics of “processual” (Schmalfeldt 2011) behavior. Beyond merely exemplifying Weberian Mehrdeutigkeit (Saslaw 1990-1991), complex chromatic relationships invite exploration into re-conceiving perceived pitch relationships within the quintessential tonal vernacular.