Documentation

Normal form, value with occurences count (ie. exponent in notation above).

Degree of Efg, ie. sum of exponents.

efg_degree [(3,3),(7,2)] == 3 + 2

Number of tones of Efg, ie. product of increment of exponents.

efg_tones [(3,3),(7,2)] == (3 + 1) * (2 + 1)

Collate a genus given as a multiset into standard form, ie. histogram.

efg_collate [3,3,3,7,7] == [(3,3),(7,2)]

Factors of Efg given with co-ordinate of grid location.

efg_factors [(3,3)]

let r = [([0,0],[]),([0,1],[7]),([0,2],[7,7])
        ,([1,0],[3]),([1,1],[3,7]),([1,2],[3,7,7])
        ,([2,0],[3,3]),([2,1],[3,3,7]),([2,2],[3,3,7,7])
        ,([3,0],[3,3,3]),([3,1],[3,3,3,7]),([3,2],[3,3,3,7,7])]

efg_factors [(3,3),(7,2)] == r

Ratios of Efg, taking n as the 1:1 ratio, with indices, folded into one octave.

import Data.List
let r = sort $ map snd $ efg_ratios 7 [(3,3),(7,2)]
r == [1/1,9/8,8/7,9/7,21/16,189/128,3/2,27/16,12/7,7/4,27/14,63/32]
map (round . ratio_to_cents) r == [0,204,231,435,471,675,702,906,933,969,1137,1173]

0: 1/1 C 0.000 cents 1: 9/8 D 203.910 cents 2: 8/7 D+ 231.174 cents 3: 9/7 E+ 435.084 cents 4: 21/16 F- 470.781 cents 5: 189/128 G- 674.691 cents 6: 3/2 G 701.955 cents 7: 27/16 A 905.865 cents 8: 12/7 A+ 933.129 cents 9: 7/4 Bb- 968.826 cents 10: 27/14 B+ 1137.039 cents 11: 63/32 C- 1172.736 cents 12: 2/1 C 1200.000 cents

let r' = sort $ map snd $ efg_ratios 5 [(5,2),(7,3)]
r' == [1/1,343/320,35/32,49/40,5/4,343/256,7/5,49/32,8/5,1715/1024,7/4,245/128]
map (round . ratio_to_cents) r' == [0,120,155,351,386,506,583,738,814,893,969,1124]

let r'' = sort $ map snd $ efg_ratios 3 [(3,1),(5,1),(7,1)]
r'' == [1/1,35/32,7/6,5/4,4/3,35/24,5/3,7/4]
map (round . ratio_to_cents) r'' == [0,155,267,386,498,653,884,969]

let c0 = [0,204,231,435,471,675,702,906,933,969,1137,1173,1200]
let c1 = [0,120,155,351,386,506,583,738,814,893,969,1124,1200]
let c2 = [0,155,267,386,498,653,884,969,1200]
let f (c',y) = map (\x -> (x,y,x,y + 10)) c'
map f (zip [c0,c1,c2] [0,20,40])

Generate a line drawing, as a set of (x0,y0,x1,y1) 4-tuples. h=row height, m=distance of vertical mark from row edge, k=distance between rows

let e = [[3,3,3],[3,3,5],[3,5,5],[3,5,7],[3,7,7],[5,5,5],[5,5,7],[3,3,7],[5,7,7],[7,7,7]]
let e = [[3,3,3],[5,5,5],[7,7,7],[3,3,5],[3,5,5],[5,5,7],[5,7,7],[3,7,7],[3,3,7],[3,5,7]]
let e' = map efg_collate e
efg_diagram_set (round,25,4,75) e'