Documentation

Ratios for lmy_wtp. lmy = La Monte Young. wtp = Well-Tuned Piano.

let c = [0,177,204,240,471,444,675,702,738,969,942,1173]
in map (round . T.ratio_to_cents) lmy_wtp_r == c

The pitch-class of the key associated with each ratio of the tuning.

mapMaybe lmy_wtp_ratio_to_pc [1,1323/1024,7/4] == [3,8,0]

The list of all non-unison ascending intervals possible in lmy_wtp_r.

length lmy_wtp_univ == 66

Collated and sorted lmy_wtp_univ.

let r_cents_pp = show . round . T.ratio_to_cents

import qualified Music.Theory.Math as T 

let f (r,i) = concat [T.ratio_pp r," = "
                     ,r_cents_pp r," = #"
                     ,show (length i)," = "
                     ,unwords (map show i)]

putStrLn $ unlines $ map f lmy_wtp_uniq

3:2 = 702 = #9 = (3,10) (4,9) (5,10) (6,11) (6,1) (7,0) (7,2) (8,1) (9,2) 7:4 = 969 = #7 = (3,0) (5,2) (6,7) (7,10) (8,9) (11,0) (1,2) 7:6 = 267 = #6 = (4,8) (5,7) (6,2) (7,11) (9,1) (10,0) 9:7 = 435 = #4 = (4,1) (5,0) (6,9) (11,2) 9:8 = 204 = #6 = (3,5) (4,2) (6,8) (7,9) (11,1) (0,2) 21:16 = 471 = #6 = (3,7) (5,9) (6,0) (7,1) (8,2) (10,2) 27:14 = 1137 = #2 = (4,6) (9,11) 27:16 = 906 = #3 = (4,7) (8,11) (9,0) 49:32 = 738 = #3 = (3,11) (5,1) (6,10) 49:36 = 534 = #1 = (5,11) 63:32 = 1173 = #5 = (3,2) (4,5) (8,7) (9,10) (1,0) 49:48 = 36 = #2 = (5,6) (10,11) 81:56 = 639 = #1 = (4,11) 81:64 = 408 = #1 = (4,0) 147:128 = 240 = #3 = (3,6) (5,8) (10,1) 189:128 = 675 = #3 = (3,9) (4,10) (8,0) 441:256 = 942 = #2 = (3,1) (8,10) 567:512 = 177 = #1 = (3,4) 1323:1024 = 444 = #1 = (3,8)

Gann, 1993, p.137.

cents_i lmy_wtp == [0,177,204,240,471,444,675,702,738,969,942,1173]

import Data.List 
import Music.Theory.Tuning.Scala 
scl <- scl_load "young-lm_piano"
cents_i (scale_to_tuning 0.01 scl) == cents_i lmy_wtp

let f = d12_midi_tuning_f (lmy_wtp,-74.7,-3)
import qualified Music.Theory.Pitch as T
T.octpc_to_midi (-1,11) == 11
map (round . T.midi_detune_to_cps . f) [62,63,69] == [293,298,440]
map (fmap round . T.midi_detune_normalise . f) [0 .. 127]

Ratios for 'lmy_wtp_1964.

La Monte Young's initial 1964 tuning for "The Well-Tuned Piano" (Gann, 1993, p.141).

cents_i lmy_wtp_1964 == [0,149,204,240,471,647,675,702,738,969,1145,1173]

import Music.Theory.Tuning.Scala
let nm = ("young-lm_piano_1964","LaMonte Young's Well-Tuned Piano (1964)")
let scl = tuning_to_scale nm lmy_wtp_1964
putStr $ unlines $ scale_pp scl

Euler diagram for lmy_wtp.

let dir = "homerohanswhmtdatadot/" let f = unlines . T.euler_plane_to_dot_rat (3,True) writeFile (dir ++ "euler-wtp.dot") (f lmy_wtp_euler)