Music.Theory.Tuning.Hs

Harmonic series

Documentation

harmonic_series :: Integer -> Maybe Rational -> Tuning

Harmonic series to nth partial, with indicated octave.

harmonic_series 17 2

harmonic_series_cps :: (Num t, Enum t) => t -> [t]

Harmonic series on n.

harmonic_series_cps_n :: (Num a, Enum a) => Int -> a -> [a]

n elements of harmonic_series_cps.

let r = [55,110,165,220,275,330,385,440,495,550,605,660,715,770,825,880,935]
harmonic_series_cps_n 17 55 == r

subharmonic_series_cps :: (Fractional t, Enum t) => t -> [t]

Sub-harmonic series on n.

subharmonic_series_cps_n :: (Fractional t, Enum t) => Int -> t -> [t]

n elements of harmonic_series_cps.

let r = [1760,880,587,440,352,293,251,220,196,176,160,147,135,126,117,110,104]
map round (subharmonic_series_cps_n 17 1760) == r

partial :: (Num a, Enum a) => a -> Int -> a

nth partial of f1, ie. one indexed.

map (partial 55) [1,5,3] == [55,275,165]

harmonic_series_cps_derived :: (RealFrac a, Floating a, Enum a) => Int -> a -> [a]

Derivative harmonic series, based on kth partial of f1.

import Music.Theory.Pitch

let r = [52,103,155,206,258,309,361,412,464,515,567,618,670,721,773]
let d = harmonic_series_cps_derived 5 (T.octpc_to_cps (1,4))
map round (take 15 d) == r

harmonic_series_folded_r :: Integer -> [Rational]

Harmonic series to nth harmonic (folded, duplicated removed).

harmonic_series_folded_r 17 == [1,17/16,9/8,5/4,11/8,3/2,13/8,7/4,15/8]

let r = [0,105,204,386,551,702,841,969,1088]
map (round . ratio_to_cents) (harmonic_series_folded_r 17) == r

harmonic_series_folded_c :: Integer -> [Cents]

ratio_to_cents variant of harmonic_series_folded.

harmonic_series_folded :: Integer -> Tuning

harmonic_series_folded_21 :: Tuning

12-tone tuning of first 21 elements of the harmonic series.

tn_cents_i harmonic_series_folded_21 == [0,105,204,298,386,471,551,702,841,969,1088]
tn_divisions harmonic_series_folded_21 == 11