11-8
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Intonation
Most modern western music uses what is known as equal temperament. This means that the
interval between each semitone of the 12-tone octave is precisely the same as every other
semitone. However, many different intonation intervals have evolved over the centuries and
across cultures and instruments, so equal temperament will not sound appropriate for certain
styles of music. The PC3A supplies you with 17 different factory intonation maps which are
useful for a range of different styles. By changing the value for this parameter, you select from
among the intonation maps stored in the PC3A’s memory. You can further customize each map
or create your own by editing a map (see
Editing Intonation Maps
below.) Each of these maps
defines different intervals between each of the semitones in a single octave (used for all octaves)
by setting pitch offsets for each note in cents.
Scroll through the list of Intonation maps, and listen for the differences between semitones. Some
of the intervals between semitones may be quite different from equal temperament, but you’ll
notice that all notes are precisely tuned with notes that are an octave apart. This is because the
intonation maps set the intervals within a single octave, and apply those intervals to each octave.
Like many instruments before the adaptation of equal temperament, most of these intonation
maps were designed to sound best in one specific key. Though some may have historically been
in a different key, all of the PC3As factory intonation maps are set to root note C by default. You
can change the root key of the current intonation map by using the Int.Key parameter (see the
Intonation Key (Int.Key)
section below.)
List and Description of Intonation Maps
0 None
No intonation map is used, intonation is equal but cannot be edited.
1 Equal
No detuning of any intervals. The standard for modern western music.
2 Classic Just
Tunings are defined based on the ratios of the frequencies between intervals.
The original tuning of Classical European music.
3 Just Flat 7th
Similar to classic Just, but with the Dominant 7th flatted an additional 15 cents.
4 Harmonic
The perfect 4th, Tritone, and Dominant 7th are heavily flatted.
5 Just Harmonic
Approximation of a historical intonation.
6 Werkmeister
Named for its inventor, Andreas Werkmeister. It’s fairly close to equal
temperament, and was developed to enable transposition with less dissonance.
7 1/5th Comma
Approximation of a historical intonation based on the comma system.
8 1/4th Comma
Approximation of a historical intonation based on the comma system.
9 Indian Raga
Based on the tunings for traditional Indian music.
10 Arabic
Oriented toward the tunings of Mid-Eastern music.
11 BaliJava1
Based on the pentatonic scale of Balinese and Javanese music.
12 BaliJava2
A variation on 1Bali/Java, slightly more subtle overall.
13 BaliJava3
A more extreme variation.
14 Tibetan
Based on the Chinese pentatonic scale.
15 CarlosAlpha
Developed by Wendy Carlos, an innovator in microtonal tunings, this intonation
map flats each interval increasingly, resulting in an octave with quarter-tone
intervals.
16 Pyth/aug4
This is a Pythagorean tuning, based on the Greek pentatonic scale. The tritone is
12 cents sharp.
17 Pyth/dim5
This is a Pythagorean tuning, based on the Greek pentatonic scale. The tritone is
12 cents flat.
