Documentation

The pattern datatype, a function from a time Arc to Event values. For discrete patterns, this returns the events which are active during that time. For continuous patterns, events with values for the midpoint of the given Arc is returned.

converts a ratio into human readable string, e.g. 1/3

converts a time arc into human readable string, e.g. 13 34

converts an event into human readable string, e.g. ("bd" 14 23)

atom is a synonym for pure.

silence returns a pattern with no events.

withQueryArc f p returns a new Pattern with function f applied to the Arc values passed to the original Pattern p.

withQueryTime f p returns a new Pattern with function f applied to the both the start and end Time of the Arc passed to Pattern p.

withResultArc f p returns a new Pattern with function f applied to the Arc values in the events returned from the original Pattern p.

withResultTime f p returns a new Pattern with function f applied to the both the start and end Time of the Arc values in the events returned from the original Pattern p.

withEvent f p returns a new Pattern with events mapped over function f.

timedValues p returns a new Pattern where values are turned into tuples of Arc and value.

overlay combines two Patterns into a new pattern, so that their events are combined over time. This is the same as the infix operator <>.

stack combines a list of Patterns into a new pattern, so that their events are combined over time.

append combines two patterns Patterns into a new pattern, so that the events of the second pattern are appended to those of the first pattern, within a single cycle

append' does the same as append, but over two cycles, so that the cycles alternate between the two patterns.

fastcat returns a new pattern which interlaces the cycles of the given patterns, within a single cycle. It's the equivalent of append, but with a list of patterns.

slowcat does the same as fastcat, but maintaining the duration of the original patterns. It is the equivalent of append', but with a list of patterns.

cat is an alias of slowcat

listToPat turns the given list of values to a Pattern, which cycles through the list.

maybeListToPat is similar to listToPat, but allows values to be optional using the Maybe type, so that Nothing results in gaps in the pattern.

run n returns a pattern representing a cycle of numbers from 0 to n-1.

fast (also known as density) returns the given pattern with speed (or density) increased by the given Time factor. Therefore fast 2 p will return a pattern that is twice as fast, and fast (1/3) p will return one three times as slow.

density is an alias of fast. fast is quicker to type, but density is its old name so is used in a lot of examples.

fastGap (also known as densityGap is similar to fast but maintains its cyclic alignment. For example, fastGap 2 p would squash the events in pattern p into the first half of each cycle (and the second halves would be empty).

slow does the opposite of fast, i.e. slow 2 p will return a pattern that is half the speed.

The <~ operator shifts (or rotates) a pattern to the left (or counter-clockwise) by the given Time value. For example (1%16) <~ p will return a pattern with all the events moved one 16th of a cycle to the left.

The ~> operator does the same as <~ but shifts events to the right (or clockwise) rather than to the left.

(The above means that brak is a function from patterns of any type, to a pattern of the same type.)

Make a pattern sound a bit like a breakbeat

Example:

d1 $ sound (brak "bd sn kurt")

Divides a pattern into a given number of subdivisions, plays the subdivisions in order, but increments the starting subdivision each cycle. The pattern wraps to the first subdivision after the last subdivision is played.

Example:

d1 $ iter 4 $ sound "bd hh sn cp"

This will produce the following over four cycles:

bd hh sn cp
hh sn cp bd
sn cp bd hh
cp bd hh sn

There is also iter', which shifts the pattern in the opposite direction.

iter' is the same as iter, but decrements the starting subdivision instead of incrementing it.

rev p returns p with the event positions in each cycle reversed (or mirrored).

palindrome p applies rev to p every other cycle, so that the pattern alternates between forwards and backwards.

Only when the given test function returns True the given pattern transformation is applied. The test function will be called with the current cycle as a number.

d1 $ when ((elem '4').show)
  (striate 4)
  $ sound "hh hc"

The above will only apply `striate 4` to the pattern if the current cycle number contains the number 4. So the fourth cycle will be striated and the fourteenth and so on. Expect lots of striates after cycle number 399.

The function seqP allows you to define when a sound within a list starts and ends. The code below contains three separate patterns in a stack, but each has different start times (zero cycles, eight cycles, and sixteen cycles, respectively). All patterns stop after 128 cycles:

d1 $ seqP [
  (0, 128, sound "bd bd*2"),
  (8, 128, sound "hh*2 [sn cp] cp future*4"),
  (16, 128, sound (samples "arpy*8" (run 16)))
]

every n f p applies the function f to p, but only affects every n cycles.

every n o f' is like every n f with an offset of o cycles

foldEvery ns f p applies the function f to p, and is applied for each cycle in ns.

sig f takes a function from time to values, and turns it into a Pattern.

sinewave returns a Pattern of continuous Double values following a sinewave with frequency of one cycle, and amplitude from 0 to 1.

sine is a synonym for sinewave.

sinerat is equivalent to sinewave for Rational values, suitable for use as Time offsets.

ratsine is a synonym for sinerat.

sineAmp d returns sinewave with its amplitude offset by d. Deprecated, as these days you can simply do e.g. (sine + 0.5)

sawwave is the equivalent of sinewave for (ascending) sawtooth waves.

saw is a synonym for sawwave.

sawrat is the same as sawwave but returns Rational values suitable for use as Time offsets.

triwave is the equivalent of sinewave for triangular waves.

tri is a synonym for triwave.

trirat is the same as triwave but returns Rational values suitable for use as Time offsets.

squarewave1 is the equivalent of sinewave for square waves.

square is a synonym for squarewave.

envL is a Pattern of continuous Double values, representing a linear interpolation between 0 and 1 during the first cycle, then staying constant at 1 for all following cycles. Possibly only useful if you're using something like the retrig function defined in tidal.el.

(The above is difficult to describe, if you don't understand Haskell, just ignore it and read the below..)

The spread function allows you to take a pattern transformation which takes a parameter, such as slow, and provide several parameters which are switched between. In other words it spreads a function across several values.

Taking a simple high hat loop as an example:

d1 $ sound "ho ho:2 ho:3 hc"

We can slow it down by different amounts, such as by a half:

d1 $ slow 2 $ sound "ho ho:2 ho:3 hc"

Or by four thirds (i.e. speeding it up by a third; `4%3` means four over three):

d1 $ slow (4%3) $ sound "ho ho:2 ho:3 hc"

But if we use spread, we can make a pattern which alternates between the two speeds:

d1 $ spread slow [2,4%3] $ sound "ho ho:2 ho:3 hc"

Note that if you pass ($) as the function to spread values over, you can put functions as the list of values. For example:

d1 $ spread ($) [density 2, rev, slow 2, striate 3, (# speed "0.8")]
    $ sound "[bd*2 [~ bd]] [sn future]*2 cp jvbass*4"

Above, the pattern will have these transforms applied to it, one at a time, per cycle:

• cycle 1: `density 2` - pattern will increase in speed
• cycle 2: rev - pattern will be reversed
• cycle 3: `slow 2` - pattern will decrease in speed
• cycle 4: `striate 3` - pattern will be granualized
• cycle 5: `(# speed "0.8")` - pattern samples will be played back more slowly

After `(# speed "0.8")`, the transforms will repeat and start at `density 2` again.

fastspread works the same as spread, but the result is squashed into a single cycle. If you gave four values to spread, then the result would seem to speed up by a factor of four. Compare these two:

d1 $ spread chop [4,64,32,16] $ sound "ho ho:2 ho:3 hc"

d1 $ fastspread chop [4,64,32,16] $ sound "ho ho:2 ho:3 hc"

There is also slowspread, which is an alias of spread.

There's a version of this function, spread' (pronounced "spread prime"), which takes a *pattern* of parameters, instead of a list:

d1 $ spread' slow "2 4%3" $ sound "ho ho:2 ho:3 hc"

This is quite a messy area of Tidal - due to a slight difference of implementation this sounds completely different! One advantage of using spread' though is that you can provide polyphonic parameters, e.g.:

d1 $ spread' slow "[2 4%3, 3]" $ sound "ho ho:2 ho:3 hc"

`spreadChoose f xs p` is similar to slowspread but picks values from xs at random, rather than cycling through them in order. It has a shorter alias spreadr.

Decide whether to apply one or another function depending on the result of a test function that is passed the current cycle as a number.

d1 $ ifp ((== 0).(flip mod 2))
  (striate 4)
  (# coarse "24 48") $
  sound "hh hc"

This will apply `striate 4` for every _even_ cycle and aply `# coarse "24 48"` for every _odd_.

Detail: As you can see the test function is arbitrary and does not rely on anything tidal specific. In fact it uses only plain haskell functionality, that is: it calculates the modulo of 2 of the current cycle which is either 0 (for even cycles) or 1. It then compares this value against 0 and returns the result, which is either True or False. This is what the ifp signature's first part signifies `(Int -> Bool)`, a function that takes a whole number and returns either True or False.

rand generates a continuous pattern of (pseudo-)random, floating point numbers between `0` and `1`.

d1 $ sound "bd*8" # pan rand

pans bass drums randomly

d1 $ sound "sn sn ~ sn" # gain rand

makes the snares' randomly loud and quiet.

Numbers coming from this pattern are random, but dependent on time. So if you reset time via `cps (-1)` the random pattern will emit the exact same _random_ numbers again.

In cases where you need two different random patterns, you can shift one of them around to change the time from which the _random_ pattern is read, note the difference:

d1 $ jux (|+| gain rand) $ sound "sn sn ~ sn" # gain rand

and with the juxed version shifted backwards for 1024 cycles:

d1 $ jux (|+| ((1024 <~) $ gain rand)) $ sound "sn sn ~ sn" # gain rand

Just like rand but for whole numbers, `irand n` generates a pattern of (pseudo-) random whole numbers between `0` to `n-1` inclusive. Notably used to pick a random samples from a folder:

d1 $ n (irand 5) # sound "drum"

Randomly picks an element from the given list

d1 $ sound (samples "xx(3,8)" (tom $ choose ["a", "e", "g", "c"]))

plays a melody randomly choosing one of the four notes "a", "e", "g", "c".

Similar to degrade degradeBy allows you to control the percentage of events that are removed. For example, to remove events 90% of the time:

d1 $ slow 2 $ degradeBy 0.9 $ sound "[[[feel:5*8,feel*3] feel:3*8], feel*4]"
   # accelerate "-6"
   # speed "2"

Use sometimesBy to apply a given function "sometimes". For example, the following code results in `density 2` being applied about 25% of the time:

d1 $ sometimesBy 0.25 (density 2) $ sound "bd*8"

There are some aliases as well:

sometimes = sometimesBy 0.5
often = sometimesBy 0.75
rarely = sometimesBy 0.25
almostNever = sometimesBy 0.1
almostAlways = sometimesBy 0.9

sometimes is an alias for sometimesBy 0.5.

often is an alias for sometimesBy 0.75.

rarely is an alias for sometimesBy 0.25.

almostNever is an alias for sometimesBy 0.1

almostAlways is an alias for sometimesBy 0.9

someCyclesBy is a cycle-by-cycle version of sometimesBy. It has a `someCycles = someCyclesBy 0.5` alias

degrade randomly removes events from a pattern 50% of the time:

d1 $ slow 2 $ degrade $ sound "[[[feel:5*8,feel*3] feel:3*8], feel*4]"
   # accelerate "-6"
   # speed "2"

The shorthand syntax for degrade is a question mark: ?. Using ? will allow you to randomly remove events from a portion of a pattern:

d1 $ slow 2 $ sound "bd ~ sn bd ~ bd? [sn bd?] ~"

You can also use ? to randomly remove events from entire sub-patterns:

d1 $ slow 2 $ sound "[[[feel:5*8,feel*3] feel:3*8]?, feel*4]"

wedge t p p' combines patterns p and p' by squashing the p into the portion of each cycle given by t, and p' into the remainer of each cycle.

whenmod has a similar form and behavior to every, but requires an additional number. Applies the function to the pattern, when the remainder of the current loop number divided by the first parameter, is greater or equal than the second parameter.

For example the following makes every other block of four loops twice as dense:

d1 $ whenmod 8 4 (density 2) (sound "bd sn kurt")

superimpose f p = stack [p, f p]

superimpose plays a modified version of a pattern at the same time as the original pattern, resulting in two patterns being played at the same time.

d1 $ superimpose (density 2) $ sound "bd sn [cp ht] hh"
d1 $ superimpose ((# speed "2") . (0.125 <~)) $ sound "bd sn cp hh"

splitQueries p wraps p to ensure that it does not get queries that span arcs. For example `arc p (0.5, 1.5)` would be turned into two queries, `(0.5,1)` and `(1,1.5)`, and the results combined. Being able to assume queries don't span cycles often makes transformations easier to specify.

Truncates a pattern so that only a fraction of the pattern is played. The following example plays only the first three quarters of the pattern:

d1 $ trunc 0.75 $ sound "bd sn*2 cp hh*4 arpy bd*2 cp bd*2"

Plays a portion of a pattern, specified by a beginning and end arc of time. The new resulting pattern is played over the time period of the original pattern:

d1 $ zoom (0.25, 0.75) $ sound "bd*2 hh*3 [sn bd]*2 drum"

In the pattern above, zoom is used with an arc from 25% to 75%. It is equivalent to this pattern:

d1 $ sound "hh*3 [sn bd]*2"

Use within to apply a function to only a part of a pattern. For example, to apply `density 2` to only the first half of a pattern:

d1 $ within (0, 0.5) (density 2) $ sound "bd*2 sn lt mt hh hh hh hh"

Or, to apply `(# speed "0.5") to only the last quarter of a pattern:

d1 $ within (0.75, 1) (# speed "0.5") $ sound "bd*2 sn lt mt hh hh hh hh"

You can use the e function to apply a Euclidean algorithm over a complex pattern, although the structure of that pattern will be lost:

d1 $ e 3 8 $ sound "bd*2 [sn cp]"

In the above, three sounds are picked from the pattern on the right according to the structure given by the `e 3 8`. It ends up picking two bd sounds, a cp and missing the sn entirely.

These types of sequences use "Bjorklund's algorithm", which wasn't made for music but for an application in nuclear physics, which is exciting. More exciting still is that it is very similar in structure to the one of the first known algorithms written in Euclid's book of elements in 300 BC. You can read more about this in the paper [The Euclidean Algorithm Generates Traditional Musical Rhythms](http:/cgm.cs.mcgill.ca~godfriedpublicationsbanff.pdf) by Toussaint. Some examples from this paper are included below, including rotation in some cases.

- (2,5) : A thirteenth century Persian rhythm called Khafif-e-ramal.
- (3,4) : The archetypal pattern of the Cumbia from Colombia, as well as a Calypso rhythm from Trinidad.
- (3,5,2) : Another thirteenth century Persian rhythm by the name of Khafif-e-ramal, as well as a Rumanian folk-dance rhythm.
- (3,7) : A Ruchenitza rhythm used in a Bulgarian folk-dance.
- (3,8) : The Cuban tresillo pattern.
- (4,7) : Another Ruchenitza Bulgarian folk-dance rhythm.
- (4,9) : The Aksak rhythm of Turkey.
- (4,11) : The metric pattern used by Frank Zappa in his piece titled Outside Now.
- (5,6) : Yields the York-Samai pattern, a popular Arab rhythm.
- (5,7) : The Nawakhat pattern, another popular Arab rhythm.
- (5,8) : The Cuban cinquillo pattern.
- (5,9) : A popular Arab rhythm called Agsag-Samai.
- (5,11) : The metric pattern used by Moussorgsky in Pictures at an Exhibition.
- (5,12) : The Venda clapping pattern of a South African children’s song.
- (5,16) : The Bossa-Nova rhythm necklace of Brazil.
- (7,8) : A typical rhythm played on the Bendir (frame drum).
- (7,12) : A common West African bell pattern.
- (7,16,14) : A Samba rhythm necklace from Brazil.
- (9,16) : A rhythm necklace used in the Central African Republic.
- (11,24,14) : A rhythm necklace of the Aka Pygmies of Central Africa.
- (13,24,5) : Another rhythm necklace of the Aka Pygmies of the upper Sangha.

prrw f rot (blen, vlen) beatPattern valuePattern: pattern rotate/replace.

prr rot (blen, vlen) beatPattern valuePattern: pattern rotate/replace.

preplace (blen, plen) beats values combines the timing of beats with the values of values. Other ways of saying this are: * sequential convolution * values quantized to beats.

Examples:

d1 $ sound $ preplace (1,1) "x [~ x] x x" "bd sn"
d1 $ sound $ preplace (1,1) "x(3,8)" "bd sn"
d1 $ sound $ "x(3,8)" ~ "bd sn"
d1 $ sound "[jvbass jvbass:5]*3" |+| (shape $ "1 1 1 1 1" ~ "0.2 0.9")

It is assumed the pattern fits into a single cycle. This works well with pattern literals, but not always with patterns defined elsewhere. In those cases use preplace and provide desired pattern lengths: @ let p = slow 2 $ "x x x"

d1 $ sound $ preplace (2,1) p "bd sn" @

prep is an alias for preplace.

protate len rot p rotates pattern p by rot beats to the left. len: length of the pattern, in cycles. Example: d1 $ every 4 (protate 2 (-1)) $ slow 2 $ sound "bd hh hh hh"

The <<~ operator rotates a unit pattern to the left, similar to <~, but by events rather than linear time. The timing of the pattern remains constant:

d1 $ (1 <<~) $ sound "bd ~ sn hh"
-- will become
d1 $ sound "sn ~ hh bd"

~>> is like <<~ but for shifting to the right.

pequal cycles p1 p2: quickly test if p1 and p2 are the same.

discretise n p: samples the pattern p at a rate of n events per cycle. Useful for turning a continuous pattern into a discrete one.

randcat ps: does a slowcat on the list of patterns ps but randomises the order in which they are played.

The fit function takes a pattern of integer numbers, which are used to select values from the given list. What makes this a bit strange is that only a given number of values are selected each cycle. For example:

d1 $ sound (fit 3 ["bd", "sn", "arpy", "arpy:1", "casio"] "0 [~ 1] 2 1")

The above fits three samples into the pattern, i.e. for the first cycle this will be `"bd"`, `"sn"` and `"arpy"`, giving the result `"bd [~ sn] arpy sn"` (note that we start counting at zero, so that `0` picks the first value). The following cycle the *next* three values in the list will be picked, i.e. `"arpy:1"`, `"casio"` and `"bd"`, giving the pattern `"arpy:1 [~ casio] bd casio"` (note that the list wraps round here).

struct a b: structures pattern b in terms of a.

substruct a b: similar to struct, but each event in pattern a gets replaced with pattern b, compressed to fit the timespan of the event.

returns the nth iteration of a Lindenmayer System with given start sequence.

for example:

lindenmayer 1 "a:b,b:ab" "ab" -> "bab"

Removes events from second pattern that don't start during an event from first.

Consider this, kind of messy rhythm without any rests.

d1 $ sound (slowcat ["sn*8", "[cp*4 bd*4, hc*5]"]) # n (run 8)

If we apply a mask to it

d1 $ s (mask ("1 1 1 ~ 1 1 ~ 1" :: Pattern Bool)
  (slowcat ["sn*8", "[cp*4 bd*4, bass*5]"] ))
  # n (run 8) 

Due to the use of slowcat here, the same mask is first applied to `"sn*8"` and in the next cycle to `"[cp*4 bd*4, hc*5]".

You could achieve the same effect by adding rests within the slowcat patterns, but mask allows you to do this more easily. It kind of keeps the rhythmic structure and you can change the used samples independently, e.g.

d1 $ s (mask ("1 ~ 1 ~ 1 1 ~ 1" :: Pattern Bool)
  (slowcat ["can*8", "[cp*4 sn*4, jvbass*16]"] ))
  # n (run 8) 

Detail: It is currently needed to explicitly _tell_ Tidal that the mask itself is a `Pattern Bool` as it cannot infer this by itself, otherwise it will complain as it does not know how to interpret your input.

fit' is a generalization of fit, where the list is instead constructed by using another integer pattern to slice up a given pattern. The first argument is the number of cycles of that latter pattern to use when slicing. It's easier to understand this with a few examples:

d1 $ sound (fit' 1 2 "0 1" "1 0" "bd sn")

So what does this do? The first `1` just tells it to slice up a single cycle of `"bd sn"`. The `2` tells it to select two values each cycle, just like the first argument to fit. The next pattern `"0 1"` is the "from" pattern which tells it how to slice, which in this case means `"0"` maps to `"bd"`, and `"1"` maps to `"sn"`. The next pattern `"1 0"` is the "to" pattern, which tells it how to rearrange those slices. So the final result is the pattern `"sn bd"`.

A more useful example might be something like

d1 $ fit' 1 4 (run 4) "[0 3*2 2 1 0 3*2 2 [1*8 ~]]/2" $ chop 4 $ (sound "breaks152" # unit "c")

which uses chop to break a single sample into individual pieces, which fit' then puts into a list (using the `run 4` pattern) and reassembles according to the complicated integer pattern.

chunk n f p treats the given pattern p as having n chunks, and applies the function f to one of those sections per cycle, running from left to right.

d1 $ chunk 4 (density 4) $ sound "cp sn arpy [mt lt]"

chunk' works much the same as chunk, but runs from right to left.

toScale lets you turn a pattern of notes within a scale (expressed as a list) to note numbers. For example `toScale [0, 4, 7] "0 1 2 3"` will turn into the pattern `"0 4 7 12"`. It assumes your scale fits within an octave, to change this use toScale size`. Example: toscale 24 [0,4,7,10,14,17] (run 8)` turns into `"0 4 7 10 14 17 24 28"`

`swingBy x n` divides a cycle into n slices and delays the notes in the second half of each slice by x fraction of a slice . swing is an alias for `swingBy (1%3)`

cycleChoose is like choose but only picks a new item from the list once each cycle

`shuffle n p` evenly divides one cycle of the pattern p into n parts, and returns a random permutation of the parts each cycle. For example, `shuffle 3 "a b c"` could return `"a b c"`, `"a c b"`, `"b a c"`, `"b c a"`, `"c a b"`, or `"c b a"`. But it will **never** return `"a a a"`, because that is not a permutation of the parts.

`scramble n p` is like shuffle but randomly selects from the parts of p instead of making permutations. For example, `scramble 3 "a b c"` will randomly select 3 parts from `"a"` `"b"` and `"c"`, possibly repeating a single part.

spaceOut xs p repeats a pattern p at different durations given by the list of time values in xs