Music.Theory.Tuning.Et

Equal temperament tuning tables.

Documentation

octpc_to_pitch_cps_k0 :: Floating n => (n, n) -> OctPc -> (Pitch, n)

octpc_to_pitch and octpc_to_cps_k0.

octpc_to_pitch_cps :: Floating n => OctPc -> (Pitch, n)

octpc_to_pitch_cps_k0 of (69,440)

tbl_12et_k0 :: (Double, Double) -> [(Pitch, Double)]

12-tone equal temperament table equating Pitch and frequency over range of human hearing, where A4 has given frequency.

tbl_12et_k0 (69,440)

tbl_12et :: [(Pitch, Double)]

tbl_12et_k0 (69,440).

length tbl_12et == 192
T.minmax (map (round . snd) tbl_12et) == (1,31609)

tbl_24et_k0 :: (Double, Double) -> [(Pitch, Double)]

24-tone equal temperament variant of tbl_12et_k0.

tbl_24et :: [(Pitch, Double)]

tbl_24et_k0 (69,440).

length tbl_24et == 360
T.minmax (map (round . snd) tbl_24et) == (1,32535)

bounds_et_table :: Ord s => [(t, s)] -> s -> Maybe ((t, s), (t, s))

Given an Et table (or like) find bounds of frequency.

import qualified Music.Theory.Tuple as T
let r = Just (T.t2_map octpc_to_pitch_cps ((3,11),(4,0)))
bounds_et_table tbl_12et 256 == r

bounds_12et_tone :: Double -> Maybe ((Pitch, Double), (Pitch, Double))

bounds_et_table of tbl_12et.

import qualified Music.Theory.Tuning.Hs as T
map bounds_12et_tone (T.harmonic_series_cps_n 17 55)

type HS_R p = (Double, p, Double, Double, Cents)

Tuple indicating nearest Pitch to frequency with Et frequency, and deviation in hertz and Cents.

(cps,nearest-pitch,cps-of-nearest-pitch,cps-deviation,cents-deviation)

ndp :: Int -> Double -> String

n-decimal places.

ndp 3 (1/3) == "0.333"

hs_r_pp :: (p -> String) -> Int -> HS_R p -> [String]

Pretty print HS_R. This discards the cps-deviation field, ie. it has only four fields.

hs_r_pitch_pp :: Int -> HS_R Pitch -> [String]

hs_r_pp of pitch_pp

nearest_et_table_tone :: [(p, Double)] -> Double -> HS_R p

Form HS_R for frequency by consulting table.

let f = 256
let f' = octpc_to_cps (4,0)
let r = (f,Pitch C Natural 4,f',f-f',fratio_to_cents (f/f'))
nearest_et_table_tone tbl_12et 256 == r

nearest_12et_tone_k0 :: (Double, Double) -> Double -> HS_R Pitch

nearest_et_table_tone for tbl_12et_k0.

nearest_24et_tone_k0 :: (Double, Double) -> Double -> HS_R Pitch

nearest_et_table_tone for tbl_24et.

let r = "55.0 A1 55.0 0.0"
unwords (hs_r_pitch_pp 1 (nearest_24et_tone_k0 (69,440) 55)) == r

72Et

alteration_72et_monzo :: Integral n => n -> String

Monzo 72-edo HEWM notation. The domain is (-9,9). http://www.tonalsoft.com/enc/number/72edo.aspx

let r = ["+",">","^","#<","#-","#","#+","#>","#^"]
map alteration_72et_monzo [1 .. 9] == r

let r = ["-","<","v","b>","b+","b","b-","b<","bv"]
map alteration_72et_monzo [-1,-2 .. -9] == r

pitch_72et_k0 :: (Double, Double) -> (Midi, Int) -> (Pitch_R, Double)

Given a midi note number and 1/6 deviation determine Pitch' and frequency.

let f = pitch_r_pp . fst . pitch_72et_k0 (69,440)
let r = "C4 C+4 C>4 C^4 C#<4 C#-4 C#4 C#+4 C#>4 C#^4"
unwords (map f (zip (repeat 60) [0..9])) == r

let r = "A4 A+4 A>4 A^4 Bb<4 Bb-4 Bb4 Bb+4 Bb>4 Bv4"
unwords (map f (zip (repeat 69) [0..9])) == r

let r = "Bb4 Bb+4 Bb>4 Bv4 B<4 B-4 B4 B+4 B>4 B^4"
unwords (map f (zip (repeat 70) [0..9])) == r

tbl_72et_k0 :: (Double, Double) -> [(Pitch_R, Double)]

72-tone equal temperament table equating Pitch' and frequency over range of human hearing, where A4 = 440hz.

length (tbl_72et_k0 (69,440)) == 792
T.minmax (map (round . snd) (tbl_72et_k0 (69,440))) == (16,33167)

nearest_72et_tone_k0 :: (Double, Double) -> Double -> HS_R Pitch_R

nearest_et_table_tone for tbl_72et.

let r = "324.0 E<4 323.3 0.7 3.5"
unwords (hs_r_pp pitch_r_pp 1 (nearest_72et_tone_k0 (69,440) 324))

let f = take 2 . hs_r_pp pitch_r_pp 1 . nearest_72et_tone_k0 (69,440) . snd
mapM_ (print . unwords . f) (tbl_72et_k0 (69,440))

Detune

type Pitch_Detune = (Pitch, Cents)

Pitch with 12-Et/24-Et tuning deviation given in Cents.

hsr_to_pitch_detune :: HS_R Pitch -> Pitch_Detune

Extract Pitch_Detune from HS_R.

nearest_pitch_detune_12et_k0 :: (Double, Double) -> Double -> Pitch_Detune

Nearest 12-Et Pitch_Detune to indicated frequency (hz).

nearest_pitch_detune_12et_k0 (69,440) 452.8929841231365

nearest_pitch_detune_24et_k0 :: (Double, Double) -> Double -> Pitch_Detune

Nearest 24-Et Pitch_Detune to indicated frequency (hz).

nearest_pitch_detune_24et_k0 (69,440) 452.8929841231365

ratio_to_pitch_detune :: (Double -> HS_R Pitch) -> OctPc -> Rational -> Pitch_Detune

Given near function, f0 and ratio derive Pitch_Detune.

pitch_detune_to_cps :: Floating n => Pitch_Detune -> n

Frequency (hz) of Pitch_Detune.

pitch_detune_to_cps (octpc_to_pitch pc_spell_ks (4,9),50)

ratio_to_pitch_detune_12et_k0 :: (Double, Double) -> OctPc -> Rational -> Pitch_Detune

ratio_to_pitch_detune of nearest_12et_tone

ratio_to_pitch_detune_24et_k0 :: (Double, Double) -> OctPc -> Rational -> Pitch_Detune

ratio_to_pitch_detune of nearest_24et_tone

pitch_detune_in_octave_nearest :: Pitch -> Pitch_Detune -> Pitch_Detune

pitch_detune_md :: Pitch_Detune -> String

Markdown pretty-printer for Pitch_Detune.

pitch_detune_html :: Pitch_Detune -> String

HTML pretty-printer for Pitch_Detune.

pitch_class_detune_md :: Pitch_Detune -> String

No-octave variant of pitch_detune_md.

pitch_class_detune_html :: Pitch_Detune -> String

No-octave variant of pitch_detune_html.