Physics Behind Music An Introduction

Combinations of tones that are consonant (“nice”) are those that exhibit no slower beats. Beats occur when two periodic signals are close to the same frequency. For sinusoidal signals, the beat frequency is simply the difference between the two signals. For complex signals, one must also consider differences between multiples of the signal frequency. Thus, consonant combinations are those where the ratio of the frequencies is equal to a rational number. Of particular importance are rational numbers involving the ratio of small integers. The musical fifth corresponds to a frequency ratio of 3 to 2 and is an important part of music. A set of note frequencies used for a musical scale can be justified based on consonant combinations, and variations of the details of those choices, known as temperaments, are useful in music for practical reasons. In particular, the equal-tempered scale used for keyboards, based on multiples of the 12th root of 2, is very common.