Magical sound square
The phenomenon of magic squares can also be found in music . Anton Webern referred to the Sator Square in order to explain the construction of his twelve-tone rows, which - as in the case of his String Quartet Op. 28 - already have cancer, reversal and reversal of cancer inscribed in them in addition to the basic figure.
The composer Michael Denhoff first published a magical sound square in 1993 in the “Neue Zeitschrift für Musik”. There he explained in an essay "From image-sound to sound-image" the relationship between his music and the works of various painters.
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The middle movement of his orchestral work "MELANCOLIA - Approaches to a copper engraving by Albrecht Dürer " (1980) is based on a magical sound square, in which, analogous to the number square in Dürer's copper engraving " Melencolia I ", a three-tone chord stands for each of the 16 numbers , there are “four three-tone chords - horizontal, vertical, diagonal, etc. s. w. read - always the total of all twelve notes. In addition, each chord is mirrored into another in its interval constellation via the center of the square. ”(Denhoff). In Denhoff's sound square, which consists only of major seventh sounds (with two exceptions) with different “fillings”, the reflections of the center correspond to the sum 17 when added accordingly in Dürer's number square. In addition to horizontal, vertical and diagonal addition to the sum 34 (with Dürer) and the chromatic total (with Denhoff), with this number and sound square there are further addition possibilities always the value 34 and the chromatic total of all twelve tones (e.g. B. the four outer corner numbers and lengths, the four inner and other mirror-inverted groups of four). In his 1981 work "MAGIC SQUARE for 6 players and amplified metronome", Denhoff refers to all these possibilities and uses them as a "rule of the game" for music that allows each musician to decide on the duration of the sounds when designing his part Numbers links.
literature
- Michael Denhoff: From image-sound to sound-image - the relationship between image and music in my pieces to Dürer, Goya and others. In: New magazine for music . Volume 154, 1993, No. 6, pp. 14-19
- Walter Gieseler: Harmonics in the music of the 20th century. Moeck-Verlag, Celle 1996, ISBN 3-87549-058-4 , Volume 1, p. 32; Volume 2, p. 48