The Uncertainty Principle

Abstract

Musical notes have something to do with the simultaneous presentation of the time and frequency domains as they are to be found in the three-dimensional Illustration 28 ff (Chapter 2) of periodic signals. The height of the notes on the lines of the score gives the pitch of the tones; that is in the final analysis the frequency. The form of the notes gives their duration in time. Notes are written by composers as if the pitch and length could be determined quite independently of each other. Experienced composers have, however, long been aware of the fact that, for example, the low notes of an organ or a tuba must last a certain time in order to be felt to be sonorous. Sequences of such low notes can therefore only be played at reduced speed.