Set Theory Calculator

Normal/prime form, ICV, T/I relatedness, embedding number — Tsao, Ch. 8–9

Input Set A (pitch-class set in Z₁₂)

Clear

Comma-separated (0,1,4,6), space-separated (0 1 4 6), or unseparated (0146 / 014A)

Normal Form

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Prime Form

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Cardinality

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Forte Name

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▶ Show normal form derivation steps

Interval Class Vector

[ — — — — — — ]

▶ T/I Relatedness checker (Algorithms 8.9.0 & 8.9.1)

Enter a second set B to check whether A and B are related by transposition (T-related) or inversion (I-related). All witnessing operations are listed.

SET B

T-related (Alg. 8.9.0)

Enter set B above

I-related (Alg. 8.9.1)

Enter set B above

▶ Embedding number EMB(A, B)

EMB(A, B) counts how many distinct T_n or I^u_v images of A are subsets of B. Enter a superset B below (A is the set above).

SUPERSET B

Enter superset B to compute EMB

Based on Ming Tsao, Abstract Musical Intervals (2007), Ch. 8–9.  |  Normal/prime form: Straus algorithm.  |  Hex: A=10, B=11.