Last Updated：2025/12/29
Sentence
The
eighty
six-note
segments
were
originally
tabulated
by
Hauer
and
are
the
basis
of
his
twelve-tone
system.
Each
of
[Josef
Matthias]
Hauer's
tropes
consists
of
two
hexachords
of
mutually
exclusive
content,
so
that
each
pair
of
hexachords
includes
all
twelve
tones
of
the
semitonal
scale.
Only
eight
hexachords
may
be
associated
in
this
way
with
their
own
transpositions.
These
generate
the
eight
tropes
illustrated
in
examples
141
and
128.
Each
of
the
remaining
seventy-two
hexachords
must
be
paired
with
a
dissimilar
hexachord
in
order
to
form
a
trope.
Quizzes for review
The eighty six-note segments were originally tabulated by Hauer and are the basis of his twelve-tone system. Each of [Josef Matthias] Hauer's tropes consists of two hexachords of mutually exclusive content, so that each pair of hexachords includes all twelve tones of the semitonal scale. Only eight hexachords may be associated in this way with their own transpositions. These generate the eight tropes illustrated in examples 141 and 128. Each of the remaining seventy-two hexachords must be paired with a dissimilar hexachord in order to form a trope.
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