Music.Theory.Tuning.Graph.Euler

Euler plane diagrams as dot language graphs.

http://rohandrape.net/?t=hmt-texts&e=md/euler.md

Documentation

rat_mul :: Rational -> Rational -> Rational

fold_ratio_to_octave_err of *.

rat_div :: Rational -> Rational -> Rational

fold_ratio_to_octave_err of /.

tun_seq :: Int -> Rational -> Rational -> [Rational]

n = length, m = multiplier, r = initial ratio.

tun_seq 5 (3/2) 1 == [1/1,3/2,9/8,27/16,81/64]

all_pairs :: [t] -> [u] -> [(t, u)]

All possible pairs of elements (x,y) where x is from p and y from q.

all_pairs "ab" "cde" == [('a','c'),('a','d'),('a','e'),('b','c'),('b','d'),('b','e')]

euler_align_rat :: T2 Rational -> T3 [Rational] -> T2 [T2 Rational]

Give all pairs from (l2,l1) and (l3,l2) that are at interval ratios r1 and r2 respectively.

pc_pp :: (Integral i, Show i) => i -> String

Pretty printer for pitch class (UNICODE).

unwords (map pc_pp [0..11]) == "C♮ C♯ D♮ E♭ E♮ F♮ F♯ G♮ A♭ A♮ B♭ B♮"

cents_pp :: Rational -> String

Show ratio as intergral (round) cents value.

type RAT_LABEL_OPT = (Int, Bool)

(unit-pitch-class,print-cents)

rat_label :: RAT_LABEL_OPT -> Rational -> String

Dot label for ratio, k is the pitch-class of the unit ratio.

rat_label (0,False) 1 == "C♮\\n1:1"
rat_label (3,True) (7/4) == "C♯=969\\n7:4"

rat_id :: Rational -> String

Generate value dot node identifier for ratio.

rat_id (5/4) == "R_5_4"

rat_edge_label :: (Rational, Rational) -> String

Printer for edge label between given ratio nodes.

zip_sme :: (t, t, t) -> [u] -> [(t, u)]

Zip start-middle-end.

zip_sme (0,1,2) "abcd" == [(0,'a'),(1,'b'),(1,'c'),(2,'d')]

type Euler_Plane t = ([[t]], [(t, t)])

Euler diagram given as (h,v) duple, where h are the horizontal sequences and v are the vertical edges.

euler_plane_r :: Ord t => Euler_Plane t -> [t]

Ratios at plane, sorted.

euler_plane_map :: (t -> u) -> Euler_Plane t -> Euler_Plane u

Apply f at all nodes of the plane.

euler_plane_to_dot :: (t -> String, t -> String, (t, t) -> String) -> Euler_Plane t -> [String]

Generate dot graph given printer functions and an Euler_Plane.

euler_plane_to_dot_rat :: RAT_LABEL_OPT -> Euler_Plane Rational -> [String]

Variant with default printers and fixed node type.