Owner`s manual
12
Some pitch terminology
The pitch of a periodic waveform is defined as the number of times the
periodic element repeats in one second. This is measured in Hertz (abbrevi-
ated Hz.). For example, the pitch of A4 (the A above middle C on a piano) is
traditionally 440Hz (although that standard varies by a few Hz. in various
parts of the world).
Pitches are often described relative to one another as intervals, or ratios
of frequency. For example, two pitches are said to be one octave apart if
their frequencies dier by a factor of two. Pitch ratios are measured in units
called cents. There are 1200 cents per octave. For example, two tones that
are 2400 cents apart are two octaves apart. The traditional twelve-tone
Equal Tempered Scale that is used (or rather approximated) in 99.9% of
all Western tonal music consists of tones that are, by definition, 100 cents
apart. This interval of 100 cents is called a semitone.
The twelve equally-spaced tones of the Equal Tempered Scale happen to
contain a number of intervals that approximate integer ratios in pitch. The
following table shows these approximations:
INTERVAL CENTS NEARBY RATIO IN
RATIO CENTS
minor second 100 16/15 111.75
major second 200 9/8 203.91
minor third 300 6/5 315.64
major third 400 5/3 86.31
perfect fourth 500 4/3 498.04
tritone 600
perfect fifth 700 3/2 701.65
minor sixth 800 8/ 813.69
major sixth 900 5/3 884.36
minor seventh 1000 16/9 996.09
major seventh 1100 15/8 1088.27
octave 1200 2 1200.00
As you can see, the intervals in the Equal Tempered Scale are NOT equal
to the harmonious integer ratios. Rather, the Equal Tempered Scale is a
compromise. It became widely used because once a harpsichord or piano is
tuned to that scale, any composition in any key could be played and no one
chord would sound better or worse than that same chord in another key.