Peavey DPM V3 Owner's Manual page 75

The even-tempered scale is particularly useful in harmonically complex music that
modulates a lot. This is because the even-tempered scale breaks an octave down so
that multiplying one frequency by the twelfth root of 2 gives the frequency of the next
higher-pitched semitone. This means that the pitch difference ratio between each
semitone is constant, thus allowing for easy transposition.
However, the twelfth root of 2 is an irrational number. Without going into a lot of con-
voluted math, this means that the even-tempered scale contains small tuning errors
compared to theoretically "perfect" scales, such as just intonation. Just intonation
bases its tunings on ratios of whole numbers, with an implied preference for small
number ratios such as 32, 56, etc.; this ensures that all notes within a given scale are
perfectly in tune with each other. However, again for reasons beyond the scope of this
manual, transposition into keys other than the one for which a just tuning is optimized
can create intervals that are audibly out of tune.
Prior to the days of computers, gaires that used just intonation tended to stay within
a particular key due to the difficulties of modulation. However, considering that it is
possible to shift pitch electronically via transposition, this is no longer as much of an
issue. Example: Suppose you set up a program in just intonation. You can play in the
key of C and have perfect intonation. To modulate, copy the program to another pro-
gram, and transpose it to the key to which you want to modulate. When you want to
modulate, select the copied program, but continue playing as if you were playing in
the key of C. This will allow for alternate tunings and modulation. You could use a se-
quencer to send out program changes that select different programs and accomplish
automatic modulation as you continue to play in the fingerings used in the key of C.
Alternate tuning is considered one of the final frontiers of contemporary music-making.
Some people feel that purer forms of tuning, such as just intonation, are more
beneficial to the mind and body than even-tempered intervals, which are inherently
out-of-tune and therefore grate, albeit subconsciously, on the ear/brain combination. Is
this just hype? Or did we really lose an important element of music by adopting the
even-tempered scale? Experiment and draw your own conclusions.
The DPM V3 includes three "standard" alternate tunings as well as two user-settable
scales. For more information on alternate tunings, check out the following books:
Lou Harrison's Music Primer (Harrison, Lou; C.F. Peters Corp., 1971)
On the Sensations of Tone (Helmholtz, Herman; Dover, 1954)
Genesis of a Music (Partch, Harry; Da Capo Press, 1974)
There is also a newsletter, 1/1, published by the Just Intonation Network. For more in-
formation or a free sample issue, write to JIN, 535 Stevenson St., San Francisco, CA
94103. Finally, the October 1987 issue of Electronic Musician magazine was a special
issue featuring numerous articles on alternate tuning theory and techniques.
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