Differential Coherence

Psychomusicology: Music, Mind, and Brain, 2016

Organised Sound, 2012

arXiv: Sound, 2016

Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present in timbre, musical tuning, harmony, and melody, and it is used for conveying sensations, perceptions, and emotions in music. It involves the physical properties of sound waves and is used to study melody and harmony through musical intervals and chords. From the perspective of complexity, the macroscopic properties of a system with many parts frequently rely on the statistical properties of its constituent elements. Here we show how the tonal consonance parameters for complex tones can be used to study complexity in music. We apply this formalism to melody, showing that melodic lines in musical pieces can be described in terms of the physical properties of melodic intervals and the existence of an entropy extremalization principle subject to psych...

2011

The project began when Richard asked me to respond to his scientific approach to consonance and dissonance, which we abbreviate to C/D, from my point of view as a composer, performer and occasional theorist. Scientific approaches to C/D include those of Helmholtz, Stumpf, Cazden, Leonard Meyer, Terhardt and Krumhansl. We compare these with the composer’s viewpoint of James Tenney in his 1988 book “The history of consonance and dissonance”. We will also consider relevant writings of Heinrich Schenker and Arnold Schoenberg, and more recently of Karol Berger, Lawrence Dreyfus, and Pieter van der Merwe.

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.

The concept of consonance has proven to be a malleable one, whose multiple understandings have gone through many expansions and evolutions. In the 6th century BC, Pythagoras judged consonance, or symphonos, in terms of mathematical ratios. He recognized that the pitch of a string is related to its length and that the degree to which two simultaneous tones sound consonant is determined by the simplicity of their length ratios [1]. For example, a ratio of 2/1 is considered simpler, and therefore more consonant, than one of 4/3, because the integers involved are smaller. Two centuries later, another prominent Greek theorist, Aristoxenus, presented a radically different viewpoint: that the musician's ear should be the ultimate arbiter of consonance . Such a subjective approach challenged the entire mystical relationship of music and numbers that formed the basis of Pythagoras's interpretation of consonance. In the first part of this paper, we look at how the mathematical and experiential understandings of consonance have manifested in the field of psychoacoustics, from the foundational theories of Helmholtz to the more recent work of Terhardt and Tramo. The second section of the paper presents four measures of consonance: Benedetti's "index of softness," Euler's gradus suavitatis, Tenney's harmonic distance and Sabat's tunability index. After comparing how these four measures of consonance rate both familiar and foreign intervals, I argue for a middle path of judging consonance that draws from both the rationalism of Pythagoras and the subjectivism of Aristoxenus.

The European Physical Journal Plus

At present, there are two approaches that aim at explaining on physical grounds the psychoacoustic perception of consonance and dissonance for dyads, whose pioneers have been, respectively, Galilei and Helmholtz: One is based on the “compactness” of the waveform of the combined signal, while the other on the absence of “roughness” due to possible beats. We perform a detailed study of each approach and find that none of the associated model versions, not even the more refined ones, is fully satisfactory when faced to perceptual data on dyads. We show that combining the two approaches results instead in a surprisingly successful agreement with perceptual data: This demonstrates that compactness and roughness are both necessary ingredients for a phenomenological description of consonance and dissonance. Graphical abstract

2005

Abstract: The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo’s conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners ’ hearing activity.

Attention, Perception, & Psychophysics, 1979