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Language	Haskell2010

Music.Theory.Interval.Barlow_1987

Description

Clarence Barlow. "Two Essays on Theory". Computer Music Journal, 11(1):44-60, 1987. Translated by Henning Lohner.

Synopsis

barlow :: (Integral a, Fractional b) => a -> b
disharmonicity :: (Integral a, Num b) => (a -> b) -> (a, a) -> b
harmonicity :: (Integral a, Fractional b) => (a -> b) -> (a, a) -> b
harmonicity_m :: (Eq b, Integral a, Fractional b) => (a -> b) -> (a, a) -> Maybe b
harmonicity_r :: (Integral a, Fractional b) => (a -> b) -> Ratio a -> b
harmonicity_r_100 :: (RealFrac b, Integral a) => (a -> b) -> Ratio a -> Int
type Table_2_Row = (Double, [Int], Rational, Double)
mk_table_2_row :: Rational -> Table_2_Row
table_2 :: Double -> [Table_2_Row]
table_2_pp :: Table_2_Row -> String

Documentation

barlow :: (Integral a, Fractional b) => a -> b Source #

Barlow's indigestibility function for prime numbers.

map barlow [1,2,3,5,7,11,13] == [0,1,8/3,32/5,72/7,200/11,288/13]

disharmonicity :: (Integral a, Num b) => (a -> b) -> (a, a) -> b Source #

Compute the disharmonicity of the interval (p,q) using the prime valuation function pv.

map (disharmonicity barlow) [(9,10),(8,9)] == ([12 + 11/15,8 + 1/3] :: [Rational])

harmonicity :: (Integral a, Fractional b) => (a -> b) -> (a, a) -> b Source #

The reciprocal of disharmonicity.

map (harmonicity barlow) [(9,10),(8,9),(2,1)] == ([15/191,3/25,1] :: [Rational])

harmonicity_m :: (Eq b, Integral a, Fractional b) => (a -> b) -> (a, a) -> Maybe b Source #

harmonicity_r :: (Integral a, Fractional b) => (a -> b) -> Ratio a -> b Source #

Variant of harmonicity with Ratio input.

harmonicity_r barlow 1 == 1/0

harmonicity_r_100 :: (RealFrac b, Integral a) => (a -> b) -> Ratio a -> Int Source #

Variant of harmonicity_r with output in (0,100), infinity maps to 100.

type Table_2_Row = (Double, [Int], Rational, Double) Source #

Set of 1. interval size (cents), 2. intervals as product of powers of primes, 3. frequency ratio and 4. harmonicity value.

mk_table_2_row :: Rational -> Table_2_Row Source #

Given ratio r generate Table_2_Row

table_2 :: Double -> [Table_2_Row] Source #

Table 2 (p.45)

length (table_2 0.06) == 24
length (table_2 0.04) == 66

table_2_pp :: Table_2_Row -> String Source #

Pretty printer for Table_2_Row values.

mapM_ (putStrLn . table_2_pp) (table_2 0.06)

>    0.000 |  0  0  0  0  0  0 |  1:1  | Infinity
>  111.731 |  4 -1 -1  0  0  0 | 15:16 | 0.076531
>  182.404 |  1 -2  1  0  0  0 |  9:10 | 0.078534
>  203.910 | -3  2  0  0  0  0 |  8:9  | 0.120000
>  231.174 |  3  0  0 -1  0  0 |  7:8  | 0.075269
>  266.871 | -1 -1  0  1  0  0 |  6:7  | 0.071672
>  294.135 |  5 -3  0  0  0  0 | 27:32 | 0.076923
>  315.641 |  1  1 -1  0  0  0 |  5:6  | 0.099338
>  386.314 | -2  0  1  0  0  0 |  4:5  | 0.119048
>  407.820 | -6  4  0  0  0  0 | 64:81 | 0.060000
>  435.084 |  0  2  0 -1  0  0 |  7:9  | 0.064024
>  498.045 |  2 -1  0  0  0  0 |  3:4  | 0.214286
>  519.551 | -2  3 -1  0  0  0 | 20:27 | 0.060976
>  701.955 | -1  1  0  0  0  0 |  2:3  | 0.272727
>  764.916 |  1 -2  0  1  0  0 |  9:14 | 0.060172
>  813.686 |  3  0 -1  0  0  0 |  5:8  | 0.106383
>  884.359 |  0 -1  1  0  0  0 |  3:5  | 0.110294
>  905.865 | -4  3  0  0  0  0 | 16:27 | 0.083333
>  933.129 |  2  1  0 -1  0  0 |  7:12 | 0.066879
>  968.826 | -2  0  0  1  0  0 |  4:7  | 0.081395
>  996.090 |  4 -2  0  0  0  0 |  9:16 | 0.107143
> 1017.596 |  0  2 -1  0  0  0 |  5:9  | 0.085227
> 1088.269 | -3  1  1  0  0  0 |  8:15 | 0.082873
> 1200.000 |  1  0  0  0  0  0 |  1:2  | 1.000000