This article needs reformatting! Please help tidy it up.--WouterSwierstra 14:14, 9 May 2008 (UTC)
This Article will be about Haskore, which is a Haskell library for describing music. It follows an approach of describing a domain specific language and thus reduces complications of arbitrary language decisions. Imagine, for example, a structure describing Music in any imperative language and compare this to the simplicity of a Haskore representation.
A core of the Haskore system is Score data, which is
stored as a Type called
Music. Score data is usually
represented like this:
This sequence of Symbols, while looking relatively simple to the musician's eye, gives us a lot of information about the music we associate with it. Some of the information encoded here would be the number of notes struck, their lengths, how they overlap or don't.
Implicitly, we assume that we're dividing an octave into 12 "halftones" (look at the numeric values of (12th root of 2)^n for n=0...12 and compare to "simple" fractions to gain understanding of the significance of this number: n=7 is the "fifth" (c-g), n=4 the "major third", n=3 the "minor third" etc.), that a certain note called "a" represents 440 oscillations per second and a few other, even more arcane things.
We shall see that we need to give our computer all this information to reproduce the music that we associate with these notes.
Get [attachment:tmr-Haskore.tar.gz Haskore]. This version of Haskore is ancient but stable. I corrected it slightly to account for features that changed in the meanwhile.
Unpack the file. It provides some documentation and the Haskore sources.
To use Haskore interactively, change to
Haskore/Src and start
hugs (you could also use
ghci, but be sure
to put the file
Haskore/ghc_add/IOExtensions.lhs into the
Haskore/Src Directory before.) Type
:l HaskoreLoader and
:m Basics to initialize Haskore for immediate
:l example will load Haskore, some
declarations in the examples in this text, and import
TestHaskore which will save us some time and brains by
defining reasonable defaults for some features.
Follow-ups of this article will need CSound. Most distributions of operating Software will allow for a relatively easy installation.
1.2 Building blocks of Music
Haskore offers a data type called
Music that represents - as
you might have guessed - music. The "atoms" of music, notes, can be
generated by giving their "pitch class" (This is where the
implicit assumption that our octave is divided into 12 pitches shows
, octave, duration, and a List of Attributes , like in:
Basics> :t (c 1 (1%4) )
c 1 (1 % 4)  :: Music
This snippet would represent a "c4" note, played for a fourth
measure. The infix operator
% is used to create a rational
number. This way we can easily specify triplets, for example, which
are harder in inherently quantized environments.
The names Haskore gives to the "pitch classes" are, as one
would expect, the names used in the Anglo-Saxon languages, that are,
a b c d e f g. Sharp and Flat pitches are available via
af, respectively. Note that this encoding is
an absolute one and does not differentiate in any way among
Now how do we make this single note a music? We will have to combine it with other notes. There are two obvious way to do this.
||<^> attachment:haskore1-ex2.gif ||<#eeeeee>
:+: ||<^> || = ||<^> ||
The sequential composition, expressed by the operator
(:+:) :: Music -> Music -> Music
results in a value that represents both values in temporal
composition (I am tempted to write "played one after the other", but
there is no playing going on for now, so this would be a bad idea)
||<^> attachment:haskore1-ex2.gif ||<#eeeeee>
:=: ||<^> || = ||<^> ||
The parallel composition
:=: has the same type, but composes
both values to one that represents them simultaneously ("played at the
:t, we can see that both Operators take two
and return a
Music value. Using these Features and the rests
hnr etc., for quarter note
rest, half note rest), we can already construct a lot of
Other useful operators (Actually, all the "operators"
mentioned are just infix type
Music values - see
line 34...43. The semantics of the constructed Score is to be added
Trans :: Int -> Music -> Music and
Tempo :: Ratio Int -> Music -> Music. Use them to Transpose
tunes, or to change their speed.
The list at the end of each note does not seem to make much sense
until now. It is intended to hold notewise attributes. For example,
the Volume of a Note can be kept here, since it might be different for
each single Note.
c 4 (1%4) [Volume 50], for example, would
represent a quarter "c 4", played at "Volume 50". While we have a
clear definition for "c 4" and "1%4", we don't have one for
"Volume 50". This will become important now, when we want to make
our music audible.
What is missing now to play that music? Since there is no inherent
support for Music in "Computers" (Turing-Equivalent Machines), we
need to output something that a given synthesis equipment
understands. A canonical choice for score data would be
only information still missing in our
Music Data is
A Haskore abstraction for converting score Data to something closer to
acoustical reality is a "Performance". There is a function
perform :: PMap -> Context -> Music -> Performance that
Music to a
Performance, given a
PMap (a Mapping from player Names to Players) and a
Context (which is not interesting right now, but
can control how various performances will be coordinated).
For example, we can turn an arbitrary
Music Value to a
Performance like this:
Main> perform (\_->defPlayer) defCon example1
Using some default Values we nicked from
TestHaskore.lhs. We see that the
Volume 100 note
attribute was converted to an event volume of
that result, it's questionable if the default values were chosen
all that wisely.
Main> perform (\_->defPlayer) defCon example2
We see that a performance is a flat list of
Events as opposed to a
Score value, which is rather tree-like in structure.
Now we are ready to write these events out to some musical format, for
midi. We needed some additional information to write out the
midi file, namely a "patch map" to map the instrument name
"piano" to the
midi "Acoustic Grand Piano" (Instrument 1) on
Channel 1. For other instruments, you could just extend the
list. (For a list of instrument names, see
Main> outputMidiFile "example2.mid" (performToMidi (perform (\_->defPlayer) defCon example2) [("piano","Acoustic Grand Piano",1)])
This call gives no visible output. After that, you should, however,
example2.mid in your current directory. Open it with
your favourite (I recommend "Rosegarden"
 on Unix-derivate systems)
Sequencer/Editor tool, or play it back. For ease of use i put all
these bits together to a function in
Main> midiout "example2.mid" example2
1.4 Functional Music
How could functional programming help us specify music? Haskell
variables can of course take
Music values, and build other
values from them, so we can for example
Transpose a given
piece of music.
We could, for example, write a function that converts
a list of intervals (integers) and a
Music value to a chord.
mychord intervals base = map (\n->Trans n base) intervals
minor = [0,3,7]
major = [0,4,7]
0 is the prime, 3 the small third, 4 the large third and 7 the fifth. Now we can specify a simple chord progression:
example3 = (c 4 (1%4) [Volume 100]) :+:
(g 4 (1%4) [Volume 100]) :+: (f 4 (1%4) [Volume 100]) :+: (c 4 (1%4) [Volume 100])
example4 = mychord major example3
As we see,
mychord works with any music value. What
it can't do is building different chords on top of a sequence of
example5 = (mychord major (c 4 (1%4) [Volume 100])) :+:
(mychord minor (d 4 (1%4) [Volume 100])) :+: (mychord major (g 4 (1%4) [Volume 100])) :+: (mychord major (c 4 (1%4) [Volume 100]))
gives us a sequence with different kinds of chords.
1.4.1 Scale Theory
Now as one might know, different "Modes" of (European, traditional)
Music use the same sequence of intervals, just starting from a
different point in the sequence (
Mode) and note (
Tonic). Using the Major scale as the original one:
> maj_skips = [2,2,1,2,2,2,1]
we declare a helper function
runsum, which just sums up numbers
in a list continuously.
runsum = scanl (+) 0
Now we can declare all the scales based on the major scale in one function, and for example, have a look at the intervals of the minor scale.
scale kind = runsum (drop kind (cycle maj_skips))
Main> take 8 (scale 5)
We need cycle because scales repeat all 8 "steps" (every octave). The intervals of the major scale, taken from the sixth (since we start counting with 0: 5), give the (natural or aeolian) minor scale.
We declare a simple melody "step" wise, as in "steps" of a scale (the 8th step being the octave, 12 halftones, and the other steps depending on the exact scale used)
simplemelody = [(0,1%4),(5,1%2),(4,1%8),(3,1%8),(2,1%4),(5,1%2),(0,1%4)]
* Specify a value of type
(Ratio Int->Music)and call it
base(as it will become the base tone (Tonic) of our melody, if we give it an arbitrary length) * Find out how many halftones are between the base of a scale and the "step" wanted:
trans n = (fromInteger (scl !! n))* Transpose the base note, given a length to complete it, about that amount, to get the ultimate result.
realize :: Int -> (Ratio Int->Music) -> (Int,Ratio Int) -> Music realize kind base (n,len) = Trans (trans n) (base len) where trans n = (fromInteger (scl !! n)) scl = (scale kind)
We'll write another helper, that realizes a few notes and puts them in a sequence:
testrealize kind base melody = allseq $ map (realize kind base) melody
1.4.2 Making it Audible
Now we can realize our melody in an arbitrary scale, on an arbitrary base pitch, like for example:
Main> midiout "major.mid" (testrealize 0 (\l->(c 4 l [Volume 100])) simplemelody)
Main> midiout "minor.mid" (testrealize 5 (\l->(d 4 l [Volume 100])) simplemelody)
in c major, and then in d minor. This task (transpose and change mode) makes a nice (and often-cursed) exercise for music students. Thanks to Haskell we were able to solve it in some 20 lines of code.
Now of course we also want to describe music that's not only single-voiced. For example, we could want to describe the a'th three and four note chord in our scale:
tri a = [a,a+2,a+4]
tet a = [a,a+2,a+4,a+6]
and put the chords numbered 1, 5, 4 and 1 after each other (if you ever thought you couldn't tell a I-IV-V-I progression even if you saw one, now you did), putting in a four note chord here and there, and adding an octave to the last I:
test2d:: (Int,Ratio Int)
test2d = [allength (1%2) (tri 0),
allength (1%2) (tet 3), allength (1%2) (tet 4), allength (1%2) (8:(tri 0))] where allength l= map (\a->(a,l))
Now we only need to map realize twice to that, and then fold twice (first in parallel, then serially) to make this a Music value.
rea2d kind base melody = allseq $ map allpar $ map (map (realize kind base)) melody
midiout "iivviprog.mid" (rea2d 5 (\l->(f 5 l [Volume 100])) test2d)
And listen to it.
This would be all for this issue of TMR. If you should feel bored, try Haskore yourself. For example, you could:
* Try to write an own melody, either using
realizeto later change scale, or without. * Put fitting chords along
simplemelody, or put a melody along
test2d* Read in some existing midi files using
readMidiand try to analyze the resulting
Musicvalues. (for example, asking: are all notes in one scale? which ones aren't? what's their harmonic function?) * If you're really bored: get some sheet music and realize it in Haskore.
Anyway, stay tuned for the next Issue of TMR. If you have any questions, join us on freenode (just point your IRC client to irc.freenode.net), channel #haskell, and don't hesitate to ask me.
Bastiaan Zapf (freenode basti_)