Documentation

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

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

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)

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

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

Build a Waveform by sampling the given function.

Sample a Waveform at specified time. sampleAt = flip sample

Pure sine wave of the given frequency

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

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

muting True is id while muting False is const 0.

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.

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

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)

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

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

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

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].

Triangle wave of the given frequency

Arbitrarily chosen standard tick rate, used in testWave

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.

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

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

Sequences some waves to play on the given time intervals.

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

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

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

Builds an equal temperament minor chord over the given root pitch

Concert A4 frequency is 440Hz

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

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

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

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

Modify the amplitude of a wave by a constant multiple

The empty wave that is always zero when sampled

Convolve with explicit discrete filter kernel weights.

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

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.

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

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

Discretize the output of a Double producing waveform

Discretize the input to a Double consuming waveform

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

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

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

Take the Fourier Transform of a complex valued Tick sampled waveform

Take the Fourier Transform of a Wavetable

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

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.

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.

Cooley-Tukey fft

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

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

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

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).

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

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

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

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.

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

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

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

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

Inverts a PFD. invertPFD = scalePFD (-1)

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

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.

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).

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

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

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

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.

Interval of one octave, ratio is 2.

Interval of a perfect fifth 3:2

Interval of a major third 5:4

Interval 7:4

Interval of a major second 9:8

Interval 25:16

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]

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

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

Convert Discrete to the Double it represents.

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

Round toward zero

Perform fast Discrete multiplication.

Make a function of doubles a function of discretes

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