The Logic of Six-Based Minor for Harmonic Analyses of Popular Music

Harmonic analyses of popular music typically take the minor tonic to be Roman numeral “one.” By nature, this “one-based” approach requires a new numbering scheme when songs shift between relative key centers. Recent scholarship has argued, however, that popular music often involves ambiguity between relative tonalities, as exemplified in the “Axis” progression, if not sometimes a tonal fusion of two relative keys. I thus argue for the utility of a “six-based” approach to the minor tonic, where the minor tonic is taken to be scale-degree 6. This six-based approach, common among practitioners of popular music as seen in the Nashville number system, avoids the forced choice of a single tonic, and it thus offers a consistent way to track chord function and behavior across shifts between relative key centers. After considering these shifts in a diatonic context on the levels of both phrase and song form, I posit that popular music involves three possible tonalities, together which form a “triple-tonic complex” akin to Stephenson’s three harmonic palettes: a major system, a parallel-minor system, and a relative-minor system. I conclude by considering how chromatic chords common in a major key, such as II and ".fn_flat('')."VII, correspond to their counterparts in the relative minor, IV and ".fn_flat('')."II, thereby collapsing the landscape of diatonic modes into three modal complexes. Overall, the paper serves to reveal the logic of six-based minor—why it is useful, what issues it resolves, and what insights it can afford us about harmonic syntax in popular music.

What Are the Truly Aural Skills?

I argue that current models of aural skills instruction are too strongly linked to music theory curricula. I examine harmonic dictation as a case study, demonstrating that the system of roman-numeral/inversion-symbol labels can interfere with our ability to determine what exactly students are hearing and can distract students from more directly perceptual goals. A pilot study suggests that focusing on bass lines and schemata may make our harmonic dictation training more relevant to perception. I propose that a skill is “truly aural” to the extent that it engages working memory with minimal knowledge-based mediation. Finally, I consider the current state of aural skills instruction and suggest a number of curricular revisions. The more radical proposals call for redesigning aural skills classes to focus on perceptual skills and relocating knowledge-mediated listening to the music theory classroom. Other proposals take a more measured approach to integrating perceptual skills with otherwise traditional curricula.

Sal-Frankish NUM-NUM Compounding in the Lex Salica

This article presents evidence that Sal-Frankish had a word for ‘500’, sunde, which corresponds to the Roman numeral D, being half of M ‘1000’. With this analysis, the Sal-Frankish numbers become transparent, even the two higher values of the so-called chunnas. The neologism sunde was a back formation from tusunde ‘thousand’, which was analysed as tu ‘two’ + sunde ‘500’. This back formation was possible in the contact language Sal-Frankish for both segmental reasons (ongoing occlusion of [θ] to [t]) and stress, but not in Old Low Franconian, Old Middle Franconian, Old Saxon or OHG.

Digitale Edition und Harmonische Analyse mit MEI von Anton Bruckners Studienbuch

The poster shows the results obtained in the project “Digital Music Analysis with the Techniques of the Music Encoding Initiative (MEI) using Anton Bruckner’s compositional studies as an example” (2017 to 2019). On the one hand, the project had the goal of presenting a digital edition of Anton Bruckner’s study book, which he produced during his lessons with Otto Kitzler from 1861 to 1863. An edition of the music in the textbook encoded with MEI and displayed using Verovio and the facsimile can be displayed simultaneously. On the other hand, an automated harmonic analysis of this music was to be designed. For this purpose, keys are recognized using the Krumhansl-Schmuckler algorithm that is based on a resource of pitch classes which are compared with reference values and thus their similarity is calculated. Based on this, chord recognitions are carried out, which are then linked to the keys in the last step and converted to a roman numeral analysis.

Fluctuating Tonality and Monotonality in Schoenberg’s Op. 6, No. 8 “Der Wanderer”

Briefly yet tantalizingly outlined in his Theory of Harmony, interpretation of Schoenberg’s concept of fluctuating tonality has proved fruitful in the discussion of his late tonal repertoire, leading to scholarship such as Christopher Lewis’s 1987 article “Mirrors and Metaphors: Reflections on Schoenberg and Nineteenth-Century Tonality.” In this paper, I review Schoenberg’s descriptions of fluctuating tonality and of monotonality, and examine the interaction between these concepts through a close reading of Schoenberg’s “Der Wanderer” (Op. 6, no. 8). The analysis features adapted Schenkerian methods used in conjunction with traditional Roman numeral and root/quality analysis. Rather than suggesting a background principle of paired tonics as argued by Lewis in his analysis of “Traumleben” and “Lockung” (Op. 6, no.1 and no. 7), I interpret fluctuating tonality as a surface- to middleground-level phenomenon that can obscure the tonality of a composition that ultimately remains monotonal.

Representing Harmony in Computational Music Cognition

Cognitive theories of harmony require unambiguous formal models of how listeners internally represent chords and chord progressions. Previous modeling work often uses representation schemes heavily reliant on Western music theory, such as Roman-numeral and lead-sheet notation; however, we argue that such work should be complemented by models using representations that are closer to psychoacoustics and rely less on Western-specific assumptions. In support of this goal, we compile a network of 13 low-level harmonic representations relevant for cognitive modeling, organised into three symbolic, acoustic, and sensory categories. We implement this collection of representations in an easy-to-use object-oriented framework written for the programming language R and distributed in an open-source package called hrep (http://hrep.pmcharrison.com). We also discuss computational methods for deriving higher-level representations from these low-level representations. This work should ultimately help researchers to construct high-level models of harmony cognition that are nonetheless rooted in low-level auditory principles.

The Language of Music, Music Theory for Non-Majors

The Language of Music, Music Theory for Non-Majors, is a textbook written to share the fundamentals of music notation with students outside of schools of music. Topics covered include rhythmic notation, meter and time signatures, pitch notation, scales, key signatures, intervals, triads and Roman numeral and lead sheet notation.

Plateau Loops and Hybrid Tonics in Recent Pop Music

This paper investigates harmonic progressions built around two major chords and one minor chord, all related by step. In many pop/rock songs, these chords can be analyzed as Aeolian progressions—VI, VII, and i—(Moore 1992; Biamonte 2010; Richards 2017a). Recent songs by Bon Iver, The Chainsmokers, and others, however, use chord loops where the harmonies can be interpreted as IV, V, and vi, which I call the plateau loop for its plateau-like activity: a constant hovering above Roman numeral I or i tonic chords, while retaining an overall consistent pitch-based topography. I interrogate the tonality of these songs, advancing the notion of a hybrid tonic. Hybrid tonics occur when a song or song section lacks a salient Ionian or (less often) Aeolian tonic on which both the harmony and melody concur. Instead, IV or (less often) VI or vi chords can function rhetorically as tonic, especially when the chords sound simultaneously with a melodic ".fn_scaledegree(1)." and occur in a metrically strong position, or initiate a plateau loop. The paper defines plateau loops and hybrid tonics, and explains the theoretical framework that supports them, consulting work by Harrison (1994), Nobile (2016), and Doll (2017) that decouples scale degree from harmonic function. Song examples by The Chainsmokers, Bon Iver, Jónsi, Astrid S., and M83 show how hybrid tonicity operates in varying degrees of prominence in popular music, and can also be contextualized with Spicer’s (2017) theory of fragile, emergent, and absent tonics. By building on prior scholarship, this paper aims to stimulate further inquiry into how tonal structures of recent popular music subtly differentiate themselves from conventions of common-practice tonality.

Stranger Games: The life and times of the spintriae

In 2010 a Roman token was discovered in the mud of the Thames near Putney Bridge in London. When the token was discovered to have an erotic image on one side and a Roman numeral on the other, and was identified in a Museum of London press release as a rare Roman “brothel token”, the press reported on the story in the expected manner, for example: “A Roman coin that was probably used by soldiers to pay for sex in brothels has been discovered on the banks of the River Thames” (Daily Telegraph, 4 Jan 2012) and “Bronze discs depicting sex acts, like the one discovered in London, were used to hire prostitutes-and directly led to the birth of pornography during the Renaissance” (The Guardian, 4 Jan 2012). Even before this particular spate of media interest, these curious tokens have generated confusion, speculation and prurience-often simultaneously. They are of interest to games scholars because the speculation often includes the suggestion these objects may have had a ludic function, and were used as game counters. This paper will look at some of the proposals that have been offered by way of explanation of these peculiar objects.