Similarity relation

Similarity relation  Play (help·info). 047 followed by 047t and 0478, respectively. 047t and 0478 are in the relation R_p, as they are with ten other sets^[1].

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: R_p (maximal similarity with respect to pitch class), R₀ (minimal similarity), R₁ (first order maximal similarity), and _R2 (second order maximal similarity). In R_p 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^[1]:

R_p(S₁,S₂) iff (S₃ ⊂ S₁, S₃ ⊂ S₂)

Meaning that S₁ and S₂ each have all the pitch-classes of S₃ (transposed or inverted), plus one.

[T]he pc similarity relation R_p is not especially significant when taken alone, since by that measure a given set may be similar to many others. When R_p is combined with the [interval-class] similarity measures, however, a considerable reduction is effected.

—Allen Forte^[2]

Sources

1. ^ ^{a b} Forte, Allen (1977). The Structure of Atonal Music, p.47. ISBN 0300021208.
2. ^ Forte (1973), p.49. quoted in Schuijer, Michiel (2008). Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, p.148. ISBN 978-1-58046-270-9.

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.