User`s manual

8
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 (abbre-
viated Hz.). For example, the pitch of A3 (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 differ 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 5/4 386.31
perfect fourth 500 4/3 498.04
tritone 600
perfect fifth 700 3/2 701.65
minor sixth 800 8/5 813.69
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
01-39 AT3 man layout RGB 03/05/2001, 1:30 pm8