hmt-0.15: Haskell Music Theory

Safe Haskell | None
Language | Haskell98

Music.Theory.Z12.Lewin_1980

Description

David Lewin. "A Response to a Response: On PC Set Relatedness". Perspectives of New Music, 18(1-2):498-502, 1980.

Synopsis

- rel :: Floating n => (Int -> [a] -> [n]) -> [a] -> [a] -> n
- t_rel :: Floating n => [Z12] -> [Z12] -> n
- ti_rel :: Floating n => [Z12] -> [Z12] -> n

# Documentation

rel :: Floating n => (Int -> [a] -> [n]) -> [a] -> [a] -> n Source #

REL function with given ncv function (see `t_rel` and `ti_rel`).

t_rel :: Floating n => [Z12] -> [Z12] -> n Source #

T-equivalence REL function.

Kuusi 2001, 7.5.2

    let (~=) p q = abs (p - q) < 1e-2
    t_rel [0,1,2,3,4] [0,2,3,6,7] ~= 0.44
    t_rel [0,1,2,3,4] [0,2,4,6,8] ~= 0.28
    t_rel [0,2,3,6,7] [0,2,4,6,8] ~= 0.31

ti_rel :: Floating n => [Z12] -> [Z12] -> n Source #

T/I-equivalence REL function.

Buchler 1998, Fig. 3.38

    let (~=) p q = abs (p - q) < 1e-3
    let a = [0,2,3,5,7]::[Z12]
    let b = [0,2,3,4,5,8]::[Z12]
    let g = [0,1,2,3,5,6,8,10]::[Z12]
    let j = [0,2,3,4,5,6,8]::[Z12]
    ti_rel a b ~= 0.593
    ti_rel a g ~= 0.648
    ti_rel a j ~= 0.509
    ti_rel b g ~= 0.712
    ti_rel b j ~= 0.892
    ti_rel g j ~= 0.707