The Theories of Helmholtz in the Work of Varèse

Abstract

In 1905 Varèse discovered the French edition of Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik [On the Sensations of Tone as a Physiological Basis for the Theory of Music] of Hermann von Helmholtz (1863), the explicit intention of which was to bring together the common frontiers of science and music. This discovery was a revelation for the 22-year-old composer that went on to condition his whole philosophy of sound. The experiences of the German scientist, achieved with the aid of sirens, resonators or tuning forks, caught the imagination of the young composer. This article investigates the importance of the theories of Helmholtz for the Varèsian aesthetic and tries to put into context the methods of composition inspired by these experiments concerning the spectral constitution of timbres, resultant sounds and beating. We also examine the ways in which a change in the understanding of consonance, initiated by Helmholtz, drove Varèse towards an original conception of atonality.

Keywords:

• Atonality
• Beating
• Helmholtz
• Consonance
• Resultant Sounds
• Varèse

Notes

[1] The French translation of the title is misleading since it was not Helmholtz's intention to propose a theory of music, but rather a theory of the auditory sensations as applied to music. A better translation would be: La théorie des sensations auditives comme fondement physiologique de la théorie de la musique (A Theory of the Auditory Sensations as a Physiological Foundation for a Theory of Music). We will use the abbreviation TPM to refer to Helmholtz's treatise, since it is this edition that was read by Varèse. The citations from the TPM are from the English edition, published by Dover (1954).

[2] In 1927, with this in mind, Varèse made contact with Harvey Fletcher, director of acoustic research at the Bell Telephone Laboratories.

[3] The work of Poincaré had an immense impact on the collective imagination. Apollinaire, Delaunay, Gleizes, Matisse, Metzinger, Tablada and Valéry were fascinated by the fourth dimension. On this subject, cf. Lalitte (2009).

[4] The sound obtained was continuous, since it persisted for as long as the experimenter left the electro-magnet active, but less intense. It was necessary to place next to the tuning fork a resonator, which had the same frequency.

[5] The double siren consists of two Dove sirens having several series of holes on each disc. Both of them turn with the same speed, but it is possible to turn by hand one of the two air nozzles, injecting air across one of them in a way that marginally varies the frequency.

[6] Two tones of frequency f ₁ and f ₂ sound simultaneously, producing a difference tone corresponding to f ₂−f ₁ and summation tone corresponding to f ₁+f ₂ (Rossing, Moore & Wheeler, 2002, 157–159).

[7] Chou (2006, p. 356) claims to have seen another version of the diagram reduced to two levels.