Coding with Kulitta

Main Kulitta Page

Last modified: Nov 13, 2016 @ 12:40 pm

This page gives example Haskell code for creating a simple musical phrase with Kulitta 2.2. This is what the top of the file looks like:

> module Examples where
> import Kulitta
> import Kulitta.Foregrounds
> import Kulitta.Grammars.MusicGrammars
> import Kulitta.EuterpeaSpecial
> import System.Random

Let’s start by creating a very simple musical grammar. Kulitta comes with a few built-in, but it is possible to define new ones. We’ll use some of the datatypes defined in MusicGrammars.lhs for Roman numeral symbols.

data CType = I | II | III | IV | V | VI | VII
 deriving (Eq, Show, Ord, Enum, Read)

We’ll encode just a few simple rules and give them probabilities by hand, assuming that duration is divided in half for rules with two symbols on the right:

1. (0.3) I -> V I
2. (0.6) I -> I I
3. (0.1) I -> I
4. (0.5) V -> IV V
5. (0.4) V -> V V
6. (0.1) V -> V
7. (0.8) IV -> IV IV
8. (0.2) IV -> IV

We’ll also use the MP type (“music parameter”) from MusicGrammars.lhs to store the duration for each symbol. We can now write these rules in Haskell as follows.

> r1, r2, r3, r4, r5, r6, r7, r8 :: Rule CType MP
> r1 = (I, 0.3) :-> \p -> [v (h p), i (h p)]
> r2 = (I, 0.6) :-> \p -> [i (h p), i (h p)]
> r3 = (I, 0.1) :-> \p -> [i p] 
> r4 = (V, 0.5) :-> \p -> [iv (h p), v (h p)]
> r5 = (V, 0.4) :-> \p -> [v (h p), v (h p)]
> r6 = (V, 0.1) :-> \p -> [v p] 
> r7 = (IV, 0.8) :-> \p -> [iv (h p), iv (h p)]
> r8 = (IV, 0.2) :-> \p -> [iv p]

The argument “p” to the anonymous function (“\p -> …”, read as “given some value, p, do … to it”) in the code¬†above refers to the parameter associated with the rules. In MusicGrammars.lhs, the function “h” divides the duration of the symbol in half. The file also provides lower-case versions of the Roman numerals that are functions to create appropriately-typed data structures for the grammar.

Now, one problem with using the rules as-is above is that they will exhibit L-System like behavior of unbalanced durations. Kulitta fixes this by allowing conditional rules, such as:

I -> if not enough duration then do nothing, otherwise (normal righthand side)

This results in a more even distribution of durations, since they cannot become infinitely small as generation progresses. We can convert all the rules to this format as follows, making sure that nothing is generated smaller than a quarternote (qn).

> rules :: [Rule CType MP]
> rules = map (toRelDur2 (<qn)) [r1, r2, r3, r4, r5, r6, r7, r8]

Now we can generate some music with the grammar. First, we will create a start symbol and a random generator to work with. The start symbol will be a 4-measure long I-chord (4 times a wholenote, wn) in C-major (written below as “Major” with root pitch class 0, or C).

> startSym = [i (MP (4*wn) Major 0 0 (4*wn))]
> g1 = mkStdGen 42

The “gen” function creates an infinite list of sequential generative iterations. We will call it on the start symbol with a random number seed and then take the 5th generative iteration. This step returns a new random generator, g2, in addition to the abstract structure of the music.

> (g2, absStruct) = gen rules (g1, startSym) !! 5

 

At this point, we just have a series of Roman numerals that each have some duration associated with them. If we were to visualize this as a score of simple triads, it would look something like this:

absstruct

This is pretty boring! We can make it more interesting by choosing more diverse pitches for the chords. To do that, we can map pitches to these chords with a classical chord space (OPC-space to be specific). We will impose no additional search constraints and just use Kulitta’s defaults. This step also returns a new generator, g3, that we can use for the final step.

> (g3, chords) = classicalCS2 g2 (toAbsChords absStruct) []

Now we have something that looks a little more interesting, although it still doesn’t have much texture to it.

chords

And finally, we put a simple foreground on top with chorale-like melodic features.

> (g4, (justChords, finalMusic)) = classicalFG' g3 chords

Note: the foreground function used above returns two things in addition to the generator: a Music value of the chords (justChords) and a Music value with melodies added (finalMusic). The purpose of this is to see the before/after difference as we have done here. This is what we get in the end:

finalmusic

To play the music, we can do this:

> hearIt = playC defParams{strict=True} finalMusic

There will be a bit of a pause before any sound happens, since Haskell is a lazy language – so it will actually only compute the composition when you ask to hear it, write it to a file, etc.

Here are MIDI files of the scores shown above: