Fourier Approximations and Music

Part 2: Musical notes

2.1 The essential characteristics of a musical note

Musicians point to three distinguishing characteristics of musical notes: loudness, pitch, and timbre (or "quality"). There are other characteristics, but we will focus on these three in this module.

• The loudness of the note is measured by the magnitude of the changes in air pressure. This is controlled by how hard a piano key is pressed or how hard one blows on the mouthpiece of a saxophone.

• The pitch of the note is the frequency of repetition of the basic pressure pattern. More precisely, the frequency is the number of times the basic pattern is repeated per unit of time. The frequencies of interest to us will be measured in cycles per second -- one cycle per second is called a hertz in honor of Heinrich Hertz. So, for example, a note with pitch 440 hertz has a pressure function that repeats itself 440 times per second, i.e. with period 1/440 seconds. Human hearing is confined to frequencies that range roughly from 20 to 18,000 hertz.

• The timbre of the note includes those characteristics that enable us to tell a piano note from a violin note with the same loudness and pitch.

Of the three characteristics of musical notes, loudness is the most easily understood, and we will not discuss it further at this time. In fact, the major emphasis in this module is to explore just one aspect of timbre. However, we need to say some more about pitch first.

If you want some more practice with the notions of frequency and period (as well as amplitude and phase), you may want to work through the module Sinusoidal Graphs in the Materials for Precalculus section of this library.