Boopadoop

A music theory library for just intonation and other mathematically pure ideas.

Documentation

data CompactWavetable

A data structure for storing the results of a Wavetable on some subset of its domain. Used internally.

Constructors

CompactWavetable

Fields

• getWavetable :: Vector Int32

type Wavetable = Waveform Tick Discrete

A domain- and codomain-discretized Waveform suitable for writing to a WAVE file. See waveformToWAVE.

type DWave = Waveform Double Double

A Double valued wave with time also in terms of Double. This models a real-valued waveform which typically has values in [-1,1] and is typically supported on either the entire real line (sinWave) or on a compact subset (compactWave)

newtype Waveform t a

A Waveform is a function (of time) that we can later sample.

Constructors

Waveform

Fields

• sample :: t -> a

  sample the Waveform at a specified time

Instances

Functor (Waveform t)

Defined in Boopadoop

Methods

fmap :: (a -> b) -> Waveform t a -> Waveform t b

(<$) :: a -> Waveform t b -> Waveform t a

Show (Waveform Double Double)

Show a waveform by pretty printing some of the actual waveform in dot matrix form.

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Double Double -> ShowS

show :: Waveform Double Double -> String

showList :: [Waveform Double Double] -> ShowS

Show (Waveform Double Discrete)

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Double Discrete -> ShowS

show :: Waveform Double Discrete -> String

showList :: [Waveform Double Discrete] -> ShowS

Show (Waveform Tick Discrete)

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Tick Discrete -> ShowS

show :: Waveform Tick Discrete -> String

showList :: [Waveform Tick Discrete] -> ShowS

quotRoundUp :: Int -> Int -> Int

A version of quot that rounds away from zero instead of towards it.

sampleFrom :: (t -> a) -> Waveform t a

Build a Waveform by sampling the given function.

sampleAt :: t -> Waveform t a -> a

Sample a Waveform at specified time. sampleAt = flip sample

sinWave :: Floating a => a -> Waveform a a

Pure sine wave of the given frequency

fastSin :: Double -> Double -> Wavetable

Sine wave that is optimized to store only a small CompactWavetable. Frequency given in

compactWave :: (Ord t, Num t) => (t, t) -> Waveform t Bool

compactWave (l,h) is a wave which is True on [l,h) and False elsewhere

muting :: Num a => Bool -> a -> a

muting True is id while muting False is const 0.

modulate :: (a -> b -> c) -> Waveform t a -> Waveform t b -> Waveform t c

Modulate one wave with another according to the given function pointwise. This means you can't implement phaseModulate using only this combinator because phase modulation requires information about the target wave at times other than the current time.

amplitudeModulate :: Num a => Waveform t a -> Waveform t a -> Waveform t a

Modulate the amplitude of one wave with another. This is simply pointwise multiplication: amplitudeModulate = modulate (*)

phaseModulate

Arguments

:: Num t

=> t

Tuning parameter. Modulation signal is amplitudeModulated by (const beta)

-> Waveform t t

Modulation signal. Outputs the phase shift to apply

-> Waveform t a

Target wave to be modulated

-> Waveform t a

Modulate the phase of one wave with another. Used in synthesis. phaseModulate beta (setVolume 0.2 $ sinWave concertA) (setVolume 0.38 $ triWave concertA) (try beta=0.0005)

changeSpeed :: (Ord a, Fractional a) => a -> a -> a -> Waveform a a -> Waveform a a

Smoothly transition to playing a wave back at a different speed after some time

balanceChord :: Fractional a => [Waveform t a] -> Waveform t a

Play several waves on top of each other, normalizing so that e.g. playing three notes together doesn't triple the volume.

mergeWaves :: Num a => [Waveform t a] -> Waveform t a

Play several waves on top of each other, without worrying about the volume. See balanceChord for a normalized version.

waveformToWAVE :: Tick -> Int -> Wavetable -> WAVE

waveformToWAVE outputLength gives a WAVE file object by sampling the given DWave at 44100Hz. May disbehave or clip based on behavior of doubleToSample if the DWave takes values outside of [-1,1].

triWave :: (Ord a, RealFrac a) => a -> Waveform a a

Triangle wave of the given frequency

stdtr :: Num a => a

Arbitrarily chosen standard tick rate, used in testWave

testWave :: String -> Wavetable -> IO ()

Output the first ten seconds of the given DWave to the file test.wav for testing. The volume is also attenuated by 50% to not blow out your eardrums. Also pretty prints the wave.

testDiagram :: PitchFactorDiagram -> IO ()

Outputs a sound test of the given PitchFactorDiagram as an interval above concertA as a sinWave to the file diag.wav for testing.

sequenceToBeat :: Double -> Double -> Beat DWave -> DWave

Converts a rhythm of DWave notes to a combined DWave according to the timing rules of Beat.

sequenceNotes :: (Ord t, Fractional t, Fractional a) => [((t, t), Waveform t a)] -> Waveform t a

Sequences some waves to play on the given time intervals.

buildChord :: (Num a, RealFrac a) => [a] -> a -> Waveform a a

Builds a chord out of the given ratios relative to the root pitch buildChord ratios root

buildChordNoBalance :: [Double] -> Double -> DWave

Builds a chord out of the given ratios relative to the root pitch, without normalizing the volume. (Warning: may be loud)

majorChordOver :: Double -> DWave

Builds a just-intonated major chord over the given root pitch

minorChordOver :: Double -> DWave

Builds an equal temperament minor chord over the given root pitch

concertA :: Num a => a

Concert A4 frequency is 440Hz

envelope :: Double -> Double -> Double -> Double -> Double -> Double -> DWave

Build an envelope waveform with the given parameters: Predelay Time, Attack Time, Hold Time, Decay Time, Sustain Level, Release Time

timeShift :: Num t => t -> Waveform t a -> Waveform t a

Shift a wave in time to start at the specified time after its old start time

seekTo :: Num t => t -> Waveform t a -> Waveform t a

Shift a wave in time such that the new zero is at the specified position

equalTime :: Double -> [DWave] -> DWave

Play several waves in a row with eqqual time each, using sequenceNotes.

setVolume :: Num a => a -> Waveform t a -> Waveform t a

Modify the amplitude of a wave by a constant multiple

emptyWave :: Num a => Waveform t a

The empty wave that is always zero when sampled

discreteConvolve :: (Num a, Num t) => Waveform t [(t, a)] -> Waveform t a -> Waveform t a

Convolve with explicit discrete filter kernel weights.

wackyNotConvolution :: (a -> b -> c) -> Waveform t (Waveform t a) -> Waveform t b -> Waveform t c

This operation is not convolution, but something kind of like it. Use for creative purposes? Should be fast! wackyNotConvolution modf profile w = sampleFrom $ t -> sample (modulate modf (sample profile t) w) t

tickConvolution

Arguments

:: Fractional a

=> Tick

tickRadius

-> Tick

skipRate

-> Waveform Tick (Waveform Tick a)

The kernel of the convolution at each Tick

-> Waveform Tick a

w(t)

-> Waveform Tick a

Perform a discrete convolution. The output waveform is f(t) = int_{t-tickRadius}^{t+tickRadius} (kernel(t))(x) * w(t+x) dx but is discretized such that x is always a multiple of skipRate.

sampledConvolution

Arguments

:: (RealFrac t, Fractional a)

=> t

convolutionSampleRate, controls sampling for x

-> t

convolutionRadius, continuous analogue of tickRadius

-> Waveform t (Waveform t a)

Kernel of convolution for each time

-> Waveform t a

-> Waveform t a

Same as tickConvolution but for arbitarily valued waveforms. Works on DWave for example.

bandpassFilter

Arguments

:: Fractional a

=> Double

bandCenter

-> Double

bandSize

-> Waveform Double a

Makes a filter which selects frequencies near bandCenter with tuning parameter bandSize. Try: optimizeFilter 200 . tickTable stdtr $ bandpassFilter concertA 100

discretize :: Waveform t Double -> Waveform t Discrete

Discretize the output of a Double producing waveform

tickTable

Arguments

:: Double

Sample rate. Each tick is 1/sampleRate seconds

-> Waveform Double a

-> Waveform Tick a

Discretize the input to a Double consuming waveform

tickTableMemo :: Double -> Waveform Double a -> Waveform Tick a

Tries and fails to optimize a Waveform through memoization but actually hangs and eats all your memory.

solidSlice :: Tick -> Tick -> Wavetable -> Wavetable

Optimize a Wavetable by storing its values in a particular range. Uses (tickEnd - tickStart + 1) * sizeOf (_ :: Discrete) bytes of memory to do this.

optimizeFilter :: Tick -> Wavetable -> Wavetable

Optimize a filter by doing solidSlice around t=0 since those values are sampled repeatedly in a filter

fourierTransform :: Tick -> Double -> Waveform Tick (Complex Double) -> Waveform Double (Complex Double)

Take the Fourier Transform of a complex valued Tick sampled waveform

realDFT

Arguments

:: Tick

Radius of Fourier Transform window in Ticks. Try 200

-> Double

Sampling rate to use for the Fourier transform. Try the sample sample rate as the Wavetable

-> Wavetable

-> Wavetable

Take the Fourier Transform of a Wavetable

skipTicks

Arguments

:: Tick

n

-> Waveform Tick a

-> Waveform Tick a

Skip every n ticks in the in the given Waveform. sample (skipTicks n w) k = sample w (n*k)

exploitPeriodicity

Arguments

:: Tick

Period in Ticks of the Wavetable.

-> Wavetable

-> Wavetable

Optimize a Wavetable that we know to be periodic by storing it's values on one period. Takes period * sizeOf (_ :: Discrete) bytes of memory to do this.

usingFFT :: Tick -> Wavetable -> Wavetable

Attempts to do a fast fourier transform, but the units of the domain of the output are highly suspect. May be unreliable, use with caution.

fft :: [Complex Double] -> [Complex Double]

Cooley-Tukey fft

semi :: Floating a => a

12 tone equal temperament semitone ratio. Equal to 2 ** (1/12).

allSemis :: Floating a => [a]

12 tone equal temperament ratios for all semitones in an octave.

takeFinAlignments :: Floating a => Int -> [[a]]

List multiples of the single octave semitone ratios upto a certain amount.

newtype PitchFactorDiagram

A pitch factor diagram is a list of prime exponents that represents a rational number via diagramToRatio. These are useful because pitches with few prime factors, that is, small PitchFactorDiagrams with small factors in them, are generally consonant, and many interesting just intonation intervals can be written this way (see perfectFifth and majorThird).

Constructors

Factors

Fields

• getFactors :: [Integer]

Instances

Show PitchFactorDiagram

Defined in Boopadoop.Diagram

Methods

showsPrec :: Int -> PitchFactorDiagram -> ShowS

show :: PitchFactorDiagram -> String

showList :: [PitchFactorDiagram] -> ShowS

Semigroup PitchFactorDiagram

PitchFactorDiagrams are combined by multiplying their underlying ratios (adding factors).

Defined in Boopadoop.Diagram

Methods

(<>) :: PitchFactorDiagram -> PitchFactorDiagram -> PitchFactorDiagram

sconcat :: NonEmpty PitchFactorDiagram -> PitchFactorDiagram

stimes :: Integral b => b -> PitchFactorDiagram -> PitchFactorDiagram

Monoid PitchFactorDiagram

mempty is the unison PFD, with ratio 1.

Defined in Boopadoop.Diagram

Methods

mempty :: PitchFactorDiagram

mappend :: PitchFactorDiagram -> PitchFactorDiagram -> PitchFactorDiagram

mconcat :: [PitchFactorDiagram] -> PitchFactorDiagram

diagramToRatio :: Fractional a => PitchFactorDiagram -> a

Convert a factor diagram to the underlying ratio by raising each prime (starting from two) to the power in the factor list. For instance, going up two perfect fifths and down three major thirds yields: diagramToRatio (Factors [4,2,-3]) = (2 ^^ 4) * (3 ^^ 2) * (5 ^^ (-3)) = 144/125

diagramToFloatyRatio :: PitchFactorDiagram -> Rational

Similar to diagramToRatio, but simplifies the resulting ratio to the simplest ratio within 0.05.

diagramToSemi :: Floating a => PitchFactorDiagram -> a

Convert a PFD to its decimal number of semitones. Useful for approximating weird ratios in a twelvetone scale: diagramToSemi (normalizePFD $ Factors [0,0,0,1]) = diagramToSemi (countPFD (7/4)) = 9.688259064691248

normalizePFD :: PitchFactorDiagram -> PitchFactorDiagram

Normalize a PFD by raising or lowering it by octaves until its ratio lies between 1 (unison) and 2 (one octave up). This operation is idempotent.

countPFDFuzzy :: Double -> PitchFactorDiagram

Same as countPFD but makes an effort to simplify the ratio from a Double slightly to the simplest rational number within 0.0001.

countPFD :: Rational -> PitchFactorDiagram

Calculates the PitchFactorDiagram corresponding to a given frequency ratio by finding prime factors of the numerator and denominator.

intervalOf :: PitchFactorDiagram -> Double -> Double

Converts a PFD into an operation on frequencies. intervalOf perfectFifth concertA is the just intonation E5.

scalePFD :: Integer -> PitchFactorDiagram -> PitchFactorDiagram

Scale a PFD by raising the underlying ratio to the given power. scalePFD 2 perfectFifth = addPFD octave majorSecond

invertPFD :: PitchFactorDiagram -> PitchFactorDiagram

Inverts a PFD. invertPFD = scalePFD (-1)

addPFD :: PitchFactorDiagram -> PitchFactorDiagram -> PitchFactorDiagram

Adds two PFDs together by multiplying their ratios. addPFD minorThird majorThird = perfectFifth

printTheSequence :: Int -> IO ()

Prints the natural numbers from the given value up to 128, highlighting primes and powers of two. Interesting musical intervals are build out of the relative distance of a prime between the two nearest powers of two.

data Beat a

A rhythm is represented as a rose tree where each subtree is given equal amounts of time. Leaves are either a Beat of type a or empty (a rest).

Constructors

RoseBeat [Beat a]

Beat a

Rest

Instances

SummaryChar a => Show (Beat a)

Show the rhythm by printing the summary characters, or . for rests.

Defined in Boopadoop.Rhythm

Methods

showsPrec :: Int -> Beat a -> ShowS

show :: Beat a -> String

showList :: [Beat a] -> ShowS

class SummaryChar a where

Class for things that can be summarized in a single character, for use in printing out rhythms.

Methods

sumUp :: a -> Char

Instances

SummaryChar DrumRack

Defined in Boopadoop.Rhythm

Methods

sumUp :: DrumRack -> Char

data DrumRack

A rack of drums. Simple enumeration of the different possible drum types.

Constructors

Kick

Snare

Instances

SummaryChar DrumRack

Defined in Boopadoop.Rhythm

Methods

sumUp :: DrumRack -> Char

rockBeat :: Beat DrumRack

The standard rock beat (or half of it) played on the DrumRack

primeBeat :: Beat a -> Beat a

Force there to be only prime divisions of time in the rhythm. This is done without affecting the actual rhythm. This operation is not uniquely valued in any way, and this algorithm prefers small primes first.

octave :: PitchFactorDiagram

Interval of one octave, ratio is 2.

perfectFifth :: PitchFactorDiagram

Interval of a perfect fifth 3:2

majorThird :: PitchFactorDiagram

Interval of a major third 5:4

mysterySeven :: PitchFactorDiagram

Interval 7:4

majorSecond :: PitchFactorDiagram

Interval of a major second 9:8

mystery25 :: PitchFactorDiagram

Interval 25:16

counterExample :: PitchFactorDiagram

Interval 199:200. Should be mostly consonant to your ear but has non-small PFD: [-3,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]

newtype Discrete

Discrete x represents x/discFactor as a floating point number in [-1,1].

Constructors

Discrete

Fields

• unDiscrete :: Int32

Instances

Bounded Discrete

Defined in Boopadoop.Discrete

Methods

minBound :: Discrete

maxBound :: Discrete

Eq Discrete

Defined in Boopadoop.Discrete

Methods

(==) :: Discrete -> Discrete -> Bool

(/=) :: Discrete -> Discrete -> Bool

Fractional Discrete

Defined in Boopadoop.Discrete

Methods

(/) :: Discrete -> Discrete -> Discrete

recip :: Discrete -> Discrete

fromRational :: Rational -> Discrete

Num Discrete

Defined in Boopadoop.Discrete

Methods

(+) :: Discrete -> Discrete -> Discrete

(-) :: Discrete -> Discrete -> Discrete

(*) :: Discrete -> Discrete -> Discrete

negate :: Discrete -> Discrete

abs :: Discrete -> Discrete

signum :: Discrete -> Discrete

fromInteger :: Integer -> Discrete

Ord Discrete

Defined in Boopadoop.Discrete

Methods

compare :: Discrete -> Discrete -> Ordering

(<) :: Discrete -> Discrete -> Bool

(<=) :: Discrete -> Discrete -> Bool

(>) :: Discrete -> Discrete -> Bool

(>=) :: Discrete -> Discrete -> Bool

max :: Discrete -> Discrete -> Discrete

min :: Discrete -> Discrete -> Discrete

Show Discrete

Defined in Boopadoop.Discrete

Methods

showsPrec :: Int -> Discrete -> ShowS

show :: Discrete -> String

showList :: [Discrete] -> ShowS

Show (Waveform Double Discrete)

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Double Discrete -> ShowS

show :: Waveform Double Discrete -> String

showList :: [Waveform Double Discrete] -> ShowS

Show (Waveform Tick Discrete)

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Tick Discrete -> ShowS

show :: Waveform Tick Discrete -> String

showList :: [Waveform Tick Discrete] -> ShowS

doubleToDiscrete :: Double -> Discrete

Breaks when the double is not in [-1,1]

discreteToDouble :: Discrete -> Double

Convert Discrete to the Double it represents.

discFactor :: Num a => a

This is the conversion factor between the internal value of a Discrete and the value it represents.

properFloor :: RealFrac a => a -> Int32

Round toward zero

multiplyDiscrete :: Discrete -> Discrete -> Discrete

Perform fast Discrete multiplication.

disguise :: (Double -> Double) -> Discrete -> Discrete

Make a function of doubles a function of discretes

newtype Tick

A discrete representation of time. See tickTable for the sampling rate.

Constructors

Tick

Fields

• unTick :: Int32

Instances

Enum Tick

Defined in Boopadoop.Discrete

Methods

succ :: Tick -> Tick

pred :: Tick -> Tick

toEnum :: Int -> Tick

fromEnum :: Tick -> Int

enumFrom :: Tick -> [Tick]

enumFromThen :: Tick -> Tick -> [Tick]

enumFromTo :: Tick -> Tick -> [Tick]

enumFromThenTo :: Tick -> Tick -> Tick -> [Tick]

Eq Tick

Defined in Boopadoop.Discrete

Methods

(==) :: Tick -> Tick -> Bool

(/=) :: Tick -> Tick -> Bool

Integral Tick

Defined in Boopadoop.Discrete

Methods

quot :: Tick -> Tick -> Tick

rem :: Tick -> Tick -> Tick

div :: Tick -> Tick -> Tick

mod :: Tick -> Tick -> Tick

quotRem :: Tick -> Tick -> (Tick, Tick)

divMod :: Tick -> Tick -> (Tick, Tick)

toInteger :: Tick -> Integer

Num Tick

Defined in Boopadoop.Discrete

Methods

(+) :: Tick -> Tick -> Tick

(-) :: Tick -> Tick -> Tick

(*) :: Tick -> Tick -> Tick

negate :: Tick -> Tick

abs :: Tick -> Tick

signum :: Tick -> Tick

fromInteger :: Integer -> Tick

Ord Tick

Defined in Boopadoop.Discrete

Methods

compare :: Tick -> Tick -> Ordering

(<) :: Tick -> Tick -> Bool

(<=) :: Tick -> Tick -> Bool

(>) :: Tick -> Tick -> Bool

(>=) :: Tick -> Tick -> Bool

max :: Tick -> Tick -> Tick

min :: Tick -> Tick -> Tick

Real Tick

Defined in Boopadoop.Discrete

Methods

toRational :: Tick -> Rational

Show Tick

Defined in Boopadoop.Discrete

Methods

showsPrec :: Int -> Tick -> ShowS

show :: Tick -> String

showList :: [Tick] -> ShowS

Show (Waveform Tick Discrete)

Defined in Boopadoop

Methods

showsPrec :: Int -> Waveform Tick Discrete -> ShowS

show :: Waveform Tick Discrete -> String

showList :: [Waveform Tick Discrete] -> ShowS