Similarity relation
Encyclopedia
In music
, a similarity relation or pitch-class similarity is a comparison between sets
of the same cardinality (two sets containing the same number of pitch classes), based upon shared pitch class
and/or interval class
content.
Allen Forte
originally designated four types: Rp (maximal similarity with respect to pitch class), R0 (minimal similarity), R1 (first order maximal similarity), and R2 (second order maximal similarity). In Rp one pitch class is different, in R0 all are different, and in R1 and R2 four interval classes are the same.
Rp is defined for sets S1 and S2 of cardinal number n and S3 of cardinal number n-1 as:
Meaning that S1 and S2 each have all the pitch-classes of S3 (transposed or inverted), plus one.
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, a similarity relation or pitch-class similarity is a comparison between sets
Set (music)
A set in music theory, as in mathematics and general parlance, is a collection of objects...
of the same cardinality (two sets containing the same number of pitch classes), based upon shared pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
and/or interval class
Interval class
In musical set theory, an interval class , also known as unordered pitch-class interval, interval distance, undirected interval, or interval mod...
content.
Allen Forte
Allen Forte
Allen Forte is a music theorist and musicologist. He was born in Portland, Oregon and fought in the Navy at the close of World War II before moving to the East Coast. He is now Battell Professor of Music, Emeritus at Yale University...
originally designated four types: Rp (maximal similarity with respect to pitch class), R0 (minimal similarity), R1 (first order maximal similarity), and R2 (second order maximal similarity). In Rp one pitch class is different, in R0 all are different, and in R1 and R2 four interval classes are the same.
Rp is defined for sets S1 and S2 of cardinal number n and S3 of cardinal number n-1 as:
- Rp(S1,S2) iffIf and only ifIn logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....
(S3 ⊂SubsetIn mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
S1, S3 ⊂ S2)
Meaning that S1 and S2 each have all the pitch-classes of S3 (transposed or inverted), plus one.
Further reading
- Isaacson, Eric. (1990). "Similarity of Interval-class Content Between Pitch-class Sets: The IcVSIM Relation", Journal of Music Theory 34: 1-28.
External links
- "Similarity relation", SolomonsMusic.net.