Roland VK-8 Owner's Manual page 26

Playing the Organ
What Are "Feet?"
Historically, the "feet" (" ' " symbol) indications of the harmonic bars originate in
the length of the pipes of a pipe organ. The length of pipe used to produce the
reference pitch (the fundamental) for the keyboard is eight feet. Reducing the pipe
to half its length produces a pitch one octave higher; conversely, doubling the pipe
length creates a pitch one octave lower. Therefore, a pipe producing a pitch one
octave below that of the reference of 8' (eight feet) would be 16'; for one octave
above the reference, the pipe would be 4', and to take the pitch up yet another
octave it would be shortened to 2'.
On tone wheel organs, the pitch relationship shown in the diagram does not hold
true in a certain region of the keyboard (p. 25). In the high range of the keyboard,
high-pitched feet are "wrapped around" one octave down. High footages will be
"folded back" for high notes, while low footages will be folded back for low notes.
Folding back the high-frequency portion prevents the high-frequency sounds
from being unpleasantly shrill, and folding back the low-frequency portion
prevents the sound from becoming "muddy." On the VK-8 faithfully simulates
this characteristic.
As you can see from the relation of the pitches, the 5-1/3' pitch is unique in that it
is not arranged in order of pitch. The reason is that the 5-1/3' sound blends not
with the 8' (fundamental), but with the 16' pitch. Acoustic instruments produce
sound consisting of frequencies at integer multiples of the fundamental frequency;
double, triple, and so on. These are called "integer harmonics." Relative to the 8'
pitch that is the basic pitch of an organ, the 5-1/3' pitch is not an integer multiple,
and does not blend.
However, relative to the 16' pitch (which is one octave lower), 5-1/3' is an integer
multiple and therefore does blend. (Starting at 16', the 5-1/3' pitch is three times
higher.) Because 5-1/3' blends with 16', these two harmonic bars are colored
differently than the other harmonic bars, and are placed together.
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