Both’ mathematics and music are international languages. Notes of music are signs which reach the ear through sound-waves in the atmosphere. They are produced by vibrating a vocal chord or a string of metal or sheep gut, by blowing through a wooden tube, and by other mechanisms for producing vibrations. The vibrations are arranged in two ways: (1) by varying relations of pitch or frequency of waves, either in sequence,’ called “melodic structure,” or simultaneously, as in a chord, called “harmonic structure”; (2) by varying the time of the release of sound-waves, including the rate of
melodic sequence, and so imposing repeated orderly divisions.
These factors can be analyzed as mathematical relations, though it does not follow that music is a branch of mathematics. Nowhere are its structure and order more dramatically shown than when a great symphony orchestra finishes tuning its instruments, and at the tap of the conductor’s baton begins, for instance, the opening bars of Beethoven’s Seventh Symphony. What a change from chaos to order, to the pleasure of perceiving structure in sound!
When a group of people play or listen to the same composition, they are perceiving as a rule meanings similar to those of the composer. Minds meet. The variety of interpretation can change the meaning within narrow limits. The meanings are indescribable in words, but are readily perceived as order and relation. In addition, they seem to have a definite effect connected with the rhythm of pulse, breathing, and other human processes. Emotional effects are tied to the physiological. Perhaps musical structure comes close to the structure of the human nervous system.
Modern composers are probably on a surer track when they invent new mathematical relations of harmony and rhythm than when they are concerned with bombarding all music prior to 1900. If they are trying to reflect human society in 1938, no discords could be strident enough. The task is obviously beyond them. Disorderly music is a contradiction in terms and in physical fact.