Physics Behind Music An Introduction

Frequency, as events per second measured in hertz (Hz), is introduced as one type of rate that is important for music. Tones associated with music are typically found to correspond to a few hundred events per second. Other rates are considered as examples. Two types of rates are distinguished: additive and multiplicative. For an additive rate, a quantity is added for each interval. A multiplicative rate involves a multiplicative change, such as a percentage change, for each interval. Multiplicative rates lead to exponentially increasing and decreasing behavior. Exponential behavior is often described using logarithms. It is found that the frequency of tones is an additive rate, but the change in the frequency going up and down the keyboard is multiplicative. In particular, octaves are a factor of 2 in frequency.