phy1020.DVI

Chapter 14

Music

Musicis a sequence of sounds created for enjoyment or artistic expression. The sounds may be produced by
the human voice (singing), or by any number of musical instruments. Music is a vast field, and we can only
hope to touch on some of the most basic ideas of music theory here; the interested reader is referred to the
references in Appendix A for more information.

14.1 Pitch

To begin, music consists of a sequence of sounds of short duration (callednotes); each of these notes is at a
specific frequency (calledpitch). Not just any frequencies are used, though; musical notes are selected from
a set of discrete frequencies.
We find that if we hear a sound at frequencyf, then to our ears a sound at twice that frequency (2f)
sounds “similar”, but higher. To get musical notes, the interval between frequencyfand2f, known as an
octave, is divided into twelve equal parts (in a logarithmic sense) so that each note is higher in frequency than
the next lower note by a factor of^12

p

2 1:059463. Each factor of^12

p
2 change in frequency is called ahalf
step, and two half steps make awhole step. The complete set of 12 notes in an octave (each separated in pitch
by a half step) is called thechromatic scale.
Early musicians discovered that musical compositions sounded better when they used only certain subsets
of these 12 notes, rather than all 12. One of the best-known of these subsets (orscales) consists of 7 of the
12 notes in an octave; these notes were named (in order of increasing pitch) C, D, E, F, G, A, and B. In this
scale, called theC major scale, notes B and C (of the next octave) are one half step apart in frequency, as are
notes E and F; the others are a whole step apart.
Each octave contains the 12 notes in the chromatic scale, which are given the following names, in order
of increasing pitch:

Table 11-1. The musical notes.

CF]/G[

C]/D[ G

DG]/A[

D]/E[ A

EA]/B[

FB