Many pitch sets can be represented as a set of registrally
represented pitches. A registrally represented pitch is an
ordered pair (c,r) where r (the register) is an integer and
all pitches with the same c (class) are considered equivalent
in some sense. For example, in this work, diatonic pitches are
represented by strings such as ``C
4,'' indicating a class of
C and a register of four. Most pitch sets that can be represented
registrally are tuned such that an increment of register by one
corresponds to a doubling of frequency. This type of tuning is called
a register-doubling tuning. Western music and many other musics
of the world use register-doubling tunings.
Since all such tunings deal with register in the same way, it is
useful to think of them as being built from a tuning of all pitches in
register zero (all pitches of the form (c,0)). To form a tuning of
all registers, all that is necessary is to add some simple, generic
``machinery'' around the register-zero tuning. The register-zero
tuning takes only class information as input since the input's
register is known to be zero by definition. Figure
3.4 is a block diagram of a register-doubling tuning built
from a register-zero tuning, 
, surrounded by appropriate
machinery. The block labeled ``2x'' exponentiates its input.
