Music.Theory.Tiling.Canon

Contents

Synopsis

# Documentation

type S = [Int] Source #

Sequence.

type R = (Int, S, [Int], [Int]) Source #

Canon of (period,sequence,multipliers,displacements).

type V = [Int] Source #

Voice.

type T = [[Int]] Source #

Tiling (sequence)

p_cycle :: Int -> [Int] -> [Int] Source #

Cycle at period.

take 9 (p_cycle 18 [0,2,5]) == [0,2,5,18,20,23,36,38,41]

type E = (S, Int, Int) Source #

Element of (sequence,multiplier,displacement).

e_to_seq :: E -> [Int] Source #

Resolve sequence from E.

e_to_seq ([0,2,5],2,1) == [1,5,11]
e_to_seq ([0,1],3,4) == [4,7]
e_to_seq ([0],1,2) == [2]

e_from_seq :: [Int] -> E Source #

Infer E from sequence.

e_from_seq [1,5,11] == ([0,2,5],2,1)
e_from_seq [4,7] == ([0,1],3,4)
e_from_seq [2] == ([0],1,2)

r_voices :: R -> [V] Source #

Set of V from R.

rr_voices :: [R] -> [V] Source #

concatMap of r_voices.

Retrograde of T, the result T is sorted.

let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]
in t_retrograde [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r

The normal form of T is the min of t and it's t_retrograde.

let r = [[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]
in t_normal [[0,7,14],[1,6,11],[2,3,4],[5,9,13],[8,10,12]] == r

r_from_t :: T -> [R] Source #

Derive set of R from T.

let {r = [(21,[0,1,2],[10,8,2,4,7,5,1],[0,1,2,3,5,8,14])]
;t = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]}
in r_from_t t == r

# Construction

fromList :: MonadPlus m => [a] -> m a Source #

msum . map return.

observeAll (fromList [1..7]) == [1..7]

perfect_tilings_m :: MonadPlus m => [S] -> [Int] -> Int -> Int -> m T Source #

Search for perfect tilings of the sequence S using multipliers from m to degree n with k parts.

perfect_tilings :: [S] -> [Int] -> Int -> Int -> [T] Source #

t_normal of observeAll of perfect_tilings_m.

perfect_tilings [[0,1]] [1..3] 6 3 == []
let r = [[[0,7,14],[1,5,9],[2,4,6],[3,8,13],[10,11,12]]]
in perfect_tilings [[0,1,2]] [1,2,4,5,7] 15 5 == r
length (perfect_tilings [[0,1,2]] [1..12] 15 5) == 1
let r = [[[0,1],[2,5],[3,7],[4,6]]
,[[0,1],[2,6],[3,5],[4,7]]
,[[0,2],[1,4],[3,7],[5,6]]]
in perfect_tilings [[0,1]] [1..4] 8 4 == r
let r = [[[0,1],[2,5],[3,7],[4,9],[6,8]]
,[[0,1],[2,7],[3,5],[4,8],[6,9]]
,[[0,2],[1,4],[3,8],[5,9],[6,7]]
,[[0,2],[1,5],[3,6],[4,9],[7,8]]
,[[0,3],[1,6],[2,4],[5,9],[7,8]]]
in perfect_tilings [[0,1]] [1..5] 10 5 == r

Johnson 2004, p.2

let r = [[0,6,12],[1,8,15],[2,11,20],[3,5,7],[4,9,14],[10,13,16],[17,18,19]]
in perfect_tilings [[0,1,2]] [1,2,3,5,6,7,9] 21 7 == [r]
let r = [[0,10,20],[1,9,17],[2,4,6],[3,7,11],[5,12,19],[8,13,18],[14,15,16]]
in perfect_tilings [[0,1,2]] [1,2,4,5,7,8,10] 21 7 == [t_retrograde r]

# Display

elemOrd :: Ord a => a -> [a] -> Bool Source #

Variant of elem for ordered sequences, which can therefore return False when searching infinite sequences.

5 elemOrd [0,2..] == False && 10 elemOrd [0,2..] == True

A .* diagram of n places of V.

v_dot_star 18 [0,2..] == "*.*.*.*.*.*.*.*.*."

A white space and index diagram of n places of V.

>>> mapM_ (putStrLn . v_space_ix 9) [[0,2..],[1,3..]]
>
>  0   2   4   6   8
>    1   3   5   7


Insert | every n places.

with_bars 6 (v_dot_star 18 [0,2..]) == "*.*.*.|*.*.*.|*.*.*."

v_dot_star_m :: Int -> Int -> V -> String Source #

Variant with measure length m and number of measures n.

v_dot_star_m 6 3 [0,2..] == "*.*.*.|*.*.*.|*.*.*."

v_print :: Int -> [V] -> IO () Source #

Print .* diagram.

v_print_m :: Int -> Int -> [V] -> IO () Source #

Variant to print | at measures.

v_print_m_from :: Int -> Int -> Int -> [V] -> IO () Source #

Variant that discards first k measures.