Renaissance Music and Experimental Science

Drake, Stillman

doi:10.2307/2708256

Cited by 31 publications

(11 citation statements)

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“…Apart from Pythagoras [3,5,6] and Helmholtz [8], we will, in closing, also briefly explain how our theory mathematically bridges other subsidiary psychophysical theories such as Stumpf [30], Euler [11], Galilei [33,34,61], and Zhu [12].…”

Section: Scopementioning

confidence: 98%

The Science of Harmony: A Psychophysical Basis for Perceptual Tensions and Resolutions in Music

Chan

Dong

2019

Research

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This paper attempts to establish a psychophysical basis for both stationary (tension in chord sonorities) and transitional (resolution in chord progressions) harmony. Harmony studies the phenomenon of combining notes in music to produce a pleasing effect greater than the sum of its parts. Being both aesthetic and mathematical in nature, it has baffled some of the brightest minds in physics and mathematics for centuries. With stationary harmony acoustics, traditional theories explaining consonances and dissonances that have been widely accepted are centred around two schools: rational relationships (commonly credited to Pythagoras) and Helmholtz’s beating frequencies. The first is more of an attribution than a psychoacoustic explanation while electrophysiological (amongst other) discrepancies with the second still remain disputed. Transitional harmony, on the other hand, is a more complex problem that has remained largely elusive to acoustic science even today. In order to address both stationary and transitional harmony, we first propose the notion of interharmonic and subharmonic modulations to address the summation of adjacent and distant sinusoids in a chord. Based on this, earlier parts of this paper then bridges the two schools and shows how they stem from a single equation. Later parts of the paper focuses on subharmonic modulations to explain aspects of harmony that interharmonic modulations cannot. Introducing the concept of stationary and transitional subharmonic tensions, we show how it can explain perceptual concepts such as tension in stationary harmony and resolution in transitional harmony, by which we also address the five fundamental questions of psychoacoustic harmony such as why the pleasing effect of harmony is greater than that of the sum of its parts. Finally, strong correlations with traditional music theory and perception statistics affirm our theory with stationary and transitional harmony.

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Section: Scopementioning

confidence: 98%

The Science of Harmony: A Psychophysical Basis for Perceptual Tensions and Resolutions in Music

Chan

Dong

2019

Research

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“…Vincenzo's experiments went beyond tinkering with instruments into a full-scale test of a physical law. Here the scientific innovation was profound enough (it made Vincenzo perhaps the first experimentalist in the history of European science [2]) that people have wanted to see Galileo involved in the process. One must keep in mind that Vincenzo and Galileo never mentioned each other in their published writings and that in Viviani's and Niccolò Gherardini's biographies [7,Vol.…”

Section: Music: Tension On Stringsmentioning

confidence: 99%

“…The third gives the energy required to achieve the range 10000, assuming that initial angle 45 • will require the kinetic energy of a fall from 5000 of the same units. Although the entries in the table are whole numbers, their large size guarantees several significant digits most of 2 The page is reproduced in [3] [7]. Let's call the two weights w 1 (in air) and w 2 (in water); the weights are recorded in grani (1 grano = 0.049g [1]) as integers plus a fraction, with denominators mostly low powers of 2.…”

Section: The Legacy Of Antiquitymentioning

confidence: 99%