Set Class Reference Table

How to read this table

• Forte — catalog number (cardinality–index, e.g. 3–11).
• Prime form — canonical label in parentheses; T = 10, E = 11.
• ICV — interval-class vector (ic1 through ic6).
• Sym — transpositional symmetry, inversional symmetry as two integers. Transpositional symmetry = number of T_n operations that map the set onto itself (always ≥ 1; T₀ is always counted). Inversional symmetry = number of T_nI operations that map the set onto itself (0 means none).
• Complementary set classes are shown side by side; each row on the left pairs with the same-numbered row on the right.

Elevated symmetry (T-sym > 1 or I-sym > 0)

High symmetry (T-sym ≥ 3 or I-sym ≥ 3)

Z Z-related pair (same ICV, not T/I-equivalent)

Monads & Undecachords cardinality 1 ↔ 11 · 1 set class each

Monads (1 note)

Forte	Prime Form	ICV	Sym
1–1	(0)	000000	12, 12

Undecachords (11 notes)

Forte	Prime Form	ICV	Sym
11–1	(0123456789T)	ttttt5	12, 12

Dyads & Decachords cardinality 2 ↔ 10 · 6 set classes each

Trichords & Nonachords cardinality 3 ↔ 9 · 12 set classes each

Tetrachords & Octachords cardinality 4 ↔ 8 · 29 set classes each (+ 6 Z-pairs)

Pentachords & Septachords cardinality 5 ↔ 7 · 38 set classes each (+ 2 Z-pairs)

Hexachords cardinality 6 · 50 set classes · 20 self-complementary · 15 Z-pairs