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Dmitri Tymoczko, Recasting K-nets |
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Figure 4. The chords that are strongly isographic to {C, E, G} and {C, E, A} in 24-tone
equal temperament.
The two equivalence classes are related by quarter-tone transposition or
T_{1/2}. Since each equivalence class is invariant under T_{6},
the two classes are also related by
T_{13/2}. In general, two positively isographic K-nets in 12-tone equal temperament belong to
transpositionally-related equivalence classes in 24-tone equal temperament. In my proposed
notation,
if the K-nets are related by hyper transposition <T_{x}> then the equivalence classes are
related by T_{x}.
Note that only one of the two sets on each horizontal line appears in 12-tone
equal-temperament.