Aspects of well-formed scales

From the seventeenth century to the present day, tonal harmonic music has had a number of invariant properties such as the use of specific chord progressions (cadences) to induce a sense of closure, the asymmetrical privileging of certain progressions, and the privileging of the major and minor scales. The most widely accepted explanation has been that this is due to a process of enculturation: frequently occurring musical patterns are learned by listeners, some of whom become composers and replicate the same patterns, which go on to influence the next “generation” of composers, and so on. In this paper, however, I present a possible psychoacoustic explanation for some important regularities of tonal-harmonic music. The core of the model is two different measures of pitch-based distance between chords. The first is voice-leading distance; the second is spectral pitch distance—a measure of the distance between the partials in one chord compared to those in another chord. I propose that when a pair of triads has a higher spectral distance than another pair of triads that is voice-leading-close, the former pair is heard as an alteration of the latter pair, and seeks resolution. I explore the extent to which this model can predict the familiar tonal cadences described in music theory (including those containing tritone substitutions), and the asymmetries that are so characteristic of tonal harmony. I also show how it may be able to shed light upon the privileged status of the major and minor scales (over the modes).

ICONEA PUBLICATIONS ISBN 978-1-716-47825-3, 2020

Relative and absolute pitches Dating the texts Systemic duplicity Span and system The nature of intervals Simultaneous intervals and polarity How can dichords fit in with text U.7/80 More philology Allocation of relative pitches Enneatonic pitch-set construction from U.3011 Tridecachord or heptachord The nature of the intervals of the tridecachord Provisional analysis of the intervals terms in CBS 10996 What was the purpose of text CBS 10996 Memory tuning Conclusions Text CBS 1766 First conclusions Heptatonic construction Interlude

Resonance, 2019

Sushan Konar works on stellar compact objects. She also writes popular science articles and maintains a weekly astrophysics-related blog called 'Monday Musings'. Both, human appreciation of music and musical genres, transcend time and space. The universality of musical genres and associated musical scales is intimately linked to the physics of sound and the special characteristics of human acoustic sensitivity. In this series of articles, we examine the science underlying the development of the heptatonic scale, one of the most prevalent scales of the modern musical genres, both western and Indian.

2019

Both, human appreciation of music and musical genres, transcend time and space. The universality of musical genres and associated musical scales is intimately linked to the physics of sound and the special characteristics of human acoustic sensitivity. In this series of articles, we examine the science underlying the development of the heptatonic scale, one of the most prevalent scales of the modern musical genres, both western and Indian.

1983

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Music Theory Online, 2021

In their introduction to The Oxford Handbook of Critical Concepts in Music Theory, editors Alexander Rehding and Steven Rings explain that the word "critical" signals two guiding principles for the collection. First, the selected terms are foundational-"theorists cannot do without them." Second, despite their fundamental nature, the authors approach them "not as se led knowledge but as sites for critical scrutiny" (xv). The authors in the first section, "Starting Points," take up this cause with gusto, invoking historical narratives, mathematical equations, and emergent perceptual phenomena to illustrate the complexities of seemingly simple concepts. In this sense, the essays are delightfully varied, bold, and rich. They are also uniformly well wri en (several authors have an enviable talent for wordplay) and beautifully typeset. (1) Below, I a empt to do some justice to each of the seven essays, although space will only allow a full summary of a few, before concluding with some general thoughts on the section. [1.2] In the opening essay, Bryan Parkhurst and Stephan Hammel demonstrate that the concepts most often taken as starting points in music analysis-"Pitch, Tone, and Note"-are in fact complex cultural formulations, rich with the accumulated residue of economic practices and technological affordances. After their opening gambit (a long list of questions demonstrating the conceptual slipperiness of the three terms), Parkhurst and Hammel divide the potential significations into three rough categories: they will take "Pitch" to designate the material or objective, "Tone" the ideal or perceptual, and "Note" the symbolic or communicative. It is their goal to show how these three categories are "dialectically united" (4), and they call their method a "Marxian Organology"-essentially, an investigation into the history of the technologies and practices of musical production. Three case studies, each focused on one category, demonstrate how economic forces have shaped the conceptual objects of music theory.

It is to the author's credit that while writing this book he composed and recorded a set of twelve pieces in a series of unorthodox scales dividing the octave equally into thirteen, fourteen, fifteen etc. parts (the last piece being in equal temperament with quarter-tones). Yet the book is not presented as an adjunct to his probing compositional experiments. Instead, the publisher says on the dust-jacket that it 'analyzes all the important historical tunings', and Milton Babbitt says: 'In unprecedented detail and with unparalleled rigour, Blackwood determines and examines the various quantizations of the frequency continuum that have been employed and suggested for the "chromatic" systems of Western music'.

Perspectives of New Music, 2015