8.3 Summary

A fundamental musical and acoustical relationship is the octave. Pitches that are one or more octaves apart are heard musically as different instances of the same sound. A one-octave increase in pitch corresponds to a doubling of frequency.

For musical purposes, a pitch range of one octave is divided into discrete steps, known as scales, the individual pitches of which are given letter names (A, A♭, B, etc.). The pattern of pitches in a scale is repeated in other octave ranges, as can be seen on a piano keyboard, and pitches that are one or more octaves apart share the same musical letter name. Subscripts are sometimes added to the letter name to distinguish different pitches that share the same name, for instance A₁, A₂, A₃, etc.

Equal separation of pitch does not correspond to equal separation of frequency. For instance, the pitch step from A₄ to B₄ is the same as the pitch step from A₅ to B₅, but the frequency step is different. However, the ratio of the frequencies in each step is the same.