Generalized Interval System Explorer

Lewin's GIS: spaces, intervals, and group structure — Tsao, Ch. 1

Musical Space (S)

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SOURCE s ∈ S

TARGET t ∈ S

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Interval-Class Equivalences (ic)

In , interval i and interval n−i are inversionally equivalent. Interval classes pair:

▶ Group structure of IVLS ()

The Cayley table below shows the group operation (addition mod ) on IVLS. Highlighted cells show all ways to reach the currently computed interval.

Based on Ming Tsao, Abstract Musical Intervals (2007), Ch. 1.  |  Intervals displayed in hexadecimal (A=10, B=11).