Complement (music)

Note that musical set theory broadens the definition of both senses somewhat.

[1] Taking the names of the intervals as cardinal numbers (fourth etc.

Where we are using more generic names (such as semitone and tritone) this rule cannot be applied.

However, octave and unison are not generic but specifically refer to notes with the same name, hence 8 + 1 = 9.

[citation needed] In twelve-tone music and serialism complementation (in full, literal pitch class complementation) is the separation of pitch-class collections into complementary sets, each containing pitch classes absent from the other[2] or rather, "the relation by which the union of one set with another exhausts the aggregate".

In contrast, "where transpositionally related sets show the same difference for every pair of corresponding pitch classes, inversionally related sets show the same sum.

[clarification needed]In set theory the traditional concept of complementation may be distinguished as literal pitch class complement, "where the relation obtains between specific pitch-class sets",[3] while, due to the definition of equivalent sets, the concept may be broadened to include "not only the literal pc complement of that set but also any transposed or inverted-and-transposed form of the literal complement,"[8] which may be described as abstract complement,[9] "where the relation obtains between set classes".

Traditional interval complementation: P4 + P5 = P8
Integer interval complementation: 5 + 7 = 0 mod 12
Literal pc complementation: the pitch or pitches not in the set on the left are contained in the set on the right and vice versa
Side-slipping complementation : C 7 chord / Lydian dominant scale ( chord-scale system ) and complement Play ⓘ .
Combinatorial tone rows from Moses und Aron by Arnold Schoenberg pairing complementary hexachords from P-0/I-3 [ 6 ]
Example of abstract complementation drawn from Arnold Schoenberg 's Fünf Klavierstücke . [ 12 ]