User Manual

10
column, etc.). The sound that is thus generated
can be graphically represented as a waveform
(a graph of the sound’s pressure over time)
that is periodic. This means that each cycle
of waveform repeats itself fairly exactly, as in
the periodic waveform shown in the diagram
below:
Because of its periodic nature, this sound’s
pitch can be easily identified and processed by
Auto-Tune Evo.
Other sounds are more complex. This
waveform:
is of a violin section playing a single note in
unison. Our ears still sense a specific pitch,
but the waveform does not repeat itself. This
waveform is a summation of a number of
individually periodic violins. The summation is
non-periodic because the individual violins are
slightly out of tune with respect to one another.
Because of this lack of periodicity, Auto-Tune
Evo would not be able to process this sound.
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 (abbreviated 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
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.