Similarity relation (music)

Similarity relation <phonos file="Similarity relation.mid">Play</phonos>. 047 followed by 047t and 0478, respectively. 047t and 0478 are in the relation R_p, as they are with ten other sets.

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:

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

See also

• Equivalence class (music)

Further reading

• Isaacson, Eric (1990). "Similarity of Interval-class Content Between Pitch-class Sets: The IcVSIM Relation". Journal of Music Theory. 34: 1–28. doi:10.2307/843860.