List the set classes of a given modulus

Enter mod (max 28)

Show only card

Show Info:
decimal numbers
interval-class vectors
TICS vectors
z-related sets
M5-related sets
fourier partitions
show only z-related sets

The decimal number is an identification number. It is the sum of 2x for all pitch classes x in the set. For example, the set {0, 1, 4, 6} is represented by the number: 20 + 21 + 24 + 26 = 83.

The interval-class vector shows how many of each interval class is contained in the set (1 through mod/2). It also shows the number of common tones under transposition.

The TICS vector is John Rahn's term for the vector that shows the number of common tones at the various TnI inversion indexes (0 through mod-1).

The z-related sets are the set classes that share the same interval-class vector.

The Fourier partition is my term for the partition of the set that includes the most cyclic collections possible (in mod12 the cyclic collections are [06], [048], [0369] and [02468t]).

An asterisk '*' next to the set indicates that the set class is inversionally symmetrical.

Adjust font size