The present study offers an extended neo-Riemannian examination of chromatic-third relations in selected Bruckner compositions of the 1880s, and it constitutes the first such examination of the composer's music. Owing to its inherent indifference towards the notions of tonal centre and conventional harmonic syntax, a neo-Riemannian transformational model seems particularly apt for the analysis of the music selected – music in which non-functional chord progressions, symmetrical divisions of the octave and the temporary suspension of tonic centricity are featured. The characteristics of the works analysed here suggest an evolution in Bruckner's handling of chromaticism, from the seemingly sui generis mixture of plagal and chromatic-third relations in the coda of the opening movement of the Sixth Symphony, to a more methodical use of hexatonic-polar transformations in the motet Ecce sacerdos magnus, to the exhaustive, almost systematic exploration of hexatonic cycles in the finale of the Eighth Symphony.
Insertions between the structural dominant and tonic of underlying perfect cadences delay and intensify progressions of harmony, voice leading and hypermetre. More disruptive than other evaded cadences, these cadential interventions ultimately still serve to unify the music through motivic development. Brief analysis of excerpts from the works of J.S. Bach and Haydn demonstrates the traditional use of cadential intervention and prepares for the analysis of an idiomatic approach by Shostakovich. His Prelude in C♯ minor, Op. 34 No. 10, and Second Piano Trio, Op. 67, contain extraordinary cadential interventions that seem to break continuity, on the one hand, yet serve vital unifying roles in the larger context of each piece, on the other. Since both structural and hermeneutical meaning in the Trio hinges on interpretation of its tonal closure, the cadential intervention at its conclusion receives special attention. Modified Schenkerian analysis invites an alternative approach, showing how an underlying complete tonal structure may substantiate a complete narrative.
Although the second theme (ST) group is a crucial landmark in Classical sonata form, where it is usually articulated with great clarity, in many instances its beginning cannot be so easily discerned, especially in Beethoven. The problem is that no matter how powerful a single rule may be, none by itself can identify all those locations which may be considered an ST beginning. This article therefore proposes that an ST beginning depends on the presence of several musical signals, each of which contributes to its expression. These include: (1) tonic harmony of the new key, (2) beginning and end functions in the manner of one of Caplin's theme types, (3) preparation by a phrase-ending chord, (4) the textural gap of Hepokoski and Darcy's medial caesura (MC) and, at the ST beginning itself, (5) a change in texture, (6) a change in dynamic and (7) characteristic melodic material. A sonata deformation in any of the first three signals sets off a teleological ST process, which attempts to compensate for the deficiencies of the signal. By contrast, the deformation of an absent MC gap can produce an integrated ST or, if combined with an absent preparatory chord, a spontaneous ST.
In this essay I analyse the form of Wagner's overture to Der fliegende Holländer (1841) as part of a constellation that also includes the composer's published programme for the overture as well as the stage action and a few key musical events in the opera. To that end, I use analytical tools inspired by the ‘new Formenlehre’ (William Caplin's theory of formal functions and James Hepokoski and Warren Darcy's theory of sonata form) in conjunction with aspects of narrative and intertextuality. I argue that Wagner's innovative use of musical form in the overture functions as a background against which events in the opera are thrown into relief, so that both can be understood as two essentially different versions of the same narrative. In the overture, sophisticated manipulation of the conventions of musical form generates a symphonic narrative, while changes to the narrative in the opera are articulated by the reworking of aspects of that same musical form at crucial moments in the drama. Both the overture's form and the opera's dramaturgical design gain in significance through an intertextual dialogue that Wagner sets up between his opera and the model of Weber's Der Freischütz (1821).
The notion that pitch-class sets might occupy some form of multi-dimensional space has engaged a number of theorists over the years. The ‘space odyssey’ in this article delves into several new issues, such as a methodology for the creation of a comprehensive array of bonded inclusional growth chains, the formation of a diatonic-to-chromatic, M5-induced spectrum of symmetrically arranged set classes and a simple method for establishing levels of affinity between set classes. These investigations lead to the advancement of a sixfold system of genera and to hierarchical distributions of all set classes, furnishing a distinct shape or profile to the whole set-class universe and to each of the genera. A productive way of producing a three-dimensional model incorporating all set classes presents itself if four foci, the ‘bichromatic’ 6–7 (0,1,2,6,7,8), hexatonic 6–20 (0,1,4,5,8,9), octatonic 6–30 (0,1,3,6,7,9) and whole-tone 6–35 (0,2,4,6,8,10), are granted their own spatial ‘homes’ at distant points on an M-invariant axis placed perpendicular to a diatonic 6–32 (0,2,4,5,7,9) to chromatic 6–1 (0,1,2,3,4,5) axis. A transparent globe would seem to be the most suitable vehicle for the representation of this arrangement, where the chromatic and diatonic foci take the ‘north’ and ‘south’ poles and the other four take their positions around the ‘equator’.