Revisiting Helmholtz and related theories on consonance and dissonance : software, sound examples, and citations

Abstract

The 200th birthday of H. von Helmholtz motivated to revisit his theory on consonance and dissonance. Other related theories are, for example: 1890, C. Stumpf, "Verschmelzung" (tone fusion), listening experiments with organs 1965, R. Plomp and W. Levelt, model based on the critical bandwidth or the ear 1969, A. Kameoka and M. Kuriyagawa, model based on psycho-physical measurement 2008, M. Ebeling, modeling the ear as an auto-correlator

This supplementary material relates to a publication, which compares these models. The publication will be referenced to by an alternative identifier.

MATLAB code to re-evaluate the models.

Part A: MATLAB code to generate the figure 3 in Ebeling's 2008 publication. Ebeling.m

Part B: MATLAB code to compare the model of Kameoka with Ebeling's model. Ebeling_2_Kameoka.m and Kameoka_Fig7.mat

Part C: MATLAB code to compare the model of Plomp with Ebeling's model. Ebeling_2_Plomp.m and Plomp_Fig11.mat

Part D: MATLAB code to run Ebeling's model across 2 octaves compared with Helmholtz Helmholtz_Ebeling_2.m and Helmholtz.mat

Sound examples

Part E: These are examples of sixth intervals as suggested for Gregorian chanting (Archemandrit, 2012). The underlying natural inonation implies, that respective partials of a sound are just intonated. The sounds are generated by a platform provided by the orthodox monastery in Buchhagen, Germany, Orthodoxes Dreifaltigkeitskloster Buchhagen - Heiliger Gesang

In ascending order: eight_2_five.wav thirteen_2_eight.wav five_2_three.wav twentyseven_2_sixteen.wav twelfe_2_seven.wav

Part F: These are sound examples of Lithuanian Sutartines found under 1 (lmta.lt) .

Skud_sutart.wav Skudučių sutartinė „Šieno du kupečiu” Ragu_sutart.wav Ragų sutartinė „Skudutis“ Kankliu_sutart.wav Kanklių sutartinė „Aš sodely stovėjau“ Lumzd_sutart.wav Lumzdelių sutartinė

In particular, the analysis of the 30 second long duet with Lumzdeliai flutes contains almost only dissonant intervals, namely just intonated intervals of 7/6 (9 times), 9/8 (3 times), 10/9 (11 times), and 11/10 (7 times).

References of the mentioned publication which should be digitally archieved beyond the capability of private repositories:

Blench, R. (2021). Eurasian folk vocal polyphony traditions. Electronically published at http://www.rogerblench.info/Ethnomusicology/Papers/General -> Eurasian folk traditions

Erlich, Paul (2001). The forms of tonality. Electronically published at lumma.org/tuning/erlich/erlich-tFoT.pdf

Rastoropov, D. (2012). A Brief Comparison of Albanian Iso-Polyphony and Lithuanian Sutartines. Electronically published, to be found under in the Scholar profile of Dimitri Rastoropov

Sabat, M. (2009). An Informal Introduction to the Helmholtz–Ellis Accidentals. Electronically published at marsbat.space/pdfs/legend.pdf

References related to this publication

Archimandrit, J. (2012). Der Weg zum naturtönigen Kultgesang (engl.: The path to natural tone worship). Verlag des Heiligen Dreifaltigkeitsklosters Buchhagen. ISBN 978-3-926236-09-8 [Titel anhand dieser ISBN in Citavi-Projekt übernehmen] .

Ebeling, M. (2008). Neuronal periodicity detection as a basis for the perception of consonance: A mathematical model of tonal fusion. The Journal of the Acoustical Society of America, 124(4), 2320-2329.

Kameoka, A., and Kuriyagawa, M. (1969). Consonance theory part I: Consonance of dyads. The Journal of the Acoustical Society of America, 45(6), 1451-1459.

Kameoka, A., and Kuriyagawa, M. (1969). Consonance theory part II: Consonance of complex tones and its calculation method. The Journal of the Acoustical Society of America, 45(6), 1460-1469.

Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. The Journal of the Acoustical Society of America, 38(4), 548-560.

Stumpf, C. (1883). Tonpsychologie, Vol. I. Leipzig: S. Hirzel.

Stumpf, C. (1890). Tonpsychologie, Vol. II. Leipzig: S. Hirzel.

Stumpf, C. (1897). Neueres über Tonverschmelzung. Zeitschrift für Psychologie, 15, 280–303.

Stumpf, C. (1898). Konsonanz und Dissonanz. Leipzig: J.A. Barth. (Beiträge zur Akustik und Musikwissenschaft, Heft 1)

von Helmholtz, H. L. F. (1863). Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik: Mit in den Text eingedruckten Holzschnitten. J. Vieweg.

von Helmholtz, H. L. F. von. On the Sensations of Tone as a Psychological basis for the Theory of Music. 2nd English edition translated by Alexander John Ellis, based on the 4th German edition of 1877 with extensive notes, foreword and afterword: 1885. Reprint by Dover Publications, 1954.

von Helmholtz, H. L. F. (1896). Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik. F. Vieweg und Sohn.