Let ε < 0.


Contemporary music and wave functions

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The analysis of contemporary music using harmonious oscillator wave functions

H. J. Lipkin
Department of Musical Physics
Weizmann Institute of Science

The importance of Harmonious Oscillation in music was well known [1] even before the discovery of the Harmonious Oscillator by Stalminsky [2]. Evidence for shell structure was first pointed out by Haydn [3], who discovered the magic number four and proved that systems containing four musicleons possessed unsual stability [4]. The concept of the magic number was expressed by Mozart, who introduced the ‘Magic Flute’ [5], and a Magic Mountain was later introduced by Thomas mann [6]. A system of four magic flutes playing upon a magic mountain would be triply magic. Such a system is probably so stable that it does not interact with anything at all, and is therefore unobservable. This explains the fact that doubly and triply magic systems have never been observed.

A fundamental advance in the application of spectroscopic techniques to music is due to Rachmaninoff [7], who showed that all musical works can be expressed in terms of a small number of parameters, A, B, C, D, E, F, and G, along with the introduction of Sharps [8]. Work along lines similar to that of Rachmaninoff has been done by Wigner, Wagner, and Wigner [9] using the Niebelgruppentheorie. Relativistic effects have been calculated by Bach, Feshbach, and Offenbach, using the method of Einstein, Infeld, and Hoffman [10].

There has been no successful attempt thus far to apply the Harmonious Oscillator to modern music. The reason for this failure, namely that most modern music is not harmonious, was noted by Wigner, Wagner, and Wigner [11].

A more unharmonious approach is that of Brueckner [12], who uses plane waves instead of harmonious oscillator functions. Although this method shows great promise, it is applicable strictly speaking only to infinite systems. The works of the Brueckner School are thus suitable only for very large ensembles.

A few very recent works should also be mentioned. There is the Nobel-Prize-winning work of Bloch [13] and Purcell [14] on unclear resonance and conduction. The work of Primakofiev should be noted [15], and of course the very fine waltzes presented by Strauss [16] at the ‘Music for Peace’ Conference in Geneva.


[1] G. F. Handel, The Harmonious Blacksmith (london, 1757)

[2] Igar Stalminsky, Musical Spectroscopy with Harmonious Oscillator Wave Functions, Helv. Mus. Acta. 1 (1801) 1

[3] J. Haydn, The alpha-Particle of Music; the String Quartet Op 20 (1801) No 5

[4] A. B. Budapest, C. D. Paganini, and E. F. Hungarian, Magic Systems in Music

[5] W. A. Mozart, A Musical Joke, K234567767 (1799)

[6] T. Mann, Joseph Haydn and His Brothers (Interscience, 1944)

[7] G. Rachmaninoff, Sonority and Seniority in Music (Invited Lecture, International Congress on Musical Structure, rehovoth, 1957)

[8] W. T. Sharp, Tables of Coefficients (Chalk River, 1955)

[9] E. Wigner, R. Wagner, and E. P. Wigner, Der Ring Die Niebelgruppen. I Siegbahn Idyll (Bayrut, 1900)

[10] J. S. Bach, H. Feshbach, and J. Offenbach, Tales of Einstein, Infeld and Hoffman (Princeton, 1944)

[11] E. P. Wigner, R. Wagner, and E. Wigner, Gotterdammerung!! and other unpublished remarks made after hearing ‘Pierrot Lunaire’

[12] A. Brueckner, W. Walton, and Ludwig von Beethe, Effective Mass in C Major

[13] E. Bloch, Schelomo, an Unclear Rhapsody

[14] H. Purcell, Variations on a Theme of Britten (A Young Person’s Guide to the Nucleus)

[15] S. Primakofiev, Peter and the Wolfram-189

[16] J. Strauss, The Beautiful Blue Cerenkov Radiation; Scient’s Life; Wine, Women and Heavy Water; Tales from the Oak Ridge Woods

From the Proceedings of the Rehovoth Conference on Nuclear Structure, held at the Weizmann Institute of Science, Rehovoth, September 8-14, 1957.

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