How do you represent music in a data structure?

Question

Hey folks,

How would you model a simple musical score for a single instrument written in regular standard notation? Certainly there are plenty of libraries out there that do exactly this. I'm mostly curious about different ways to represent music in a data structure. What works well and what doesn't?

Ignoring some of the trickier aspects like dynamics, the obvious way would be a literal translation of everything into Objects - a Scores is made of Measures is made of Notes. Synthesis, I suppose, would mean figuring out the start/end time of each note and blending sine waves.

Is the obvious way a good way? What are other ways to do this?

Answer 1

Hmmm, fun problem.

Actually, I'd be tempted to turn it into Command pattern along with Composite. This is kind of turning the normal OO approach on its head, as you are in a sense making the modeled objects verbs instead of nouns. It would go like this:

a Note is a class with one method, play(), and a ctor taking length and tone`.

you need an Instrument which defines the behavior of the synth: timbre, attack, and so on.

You would then have a Score, which has a TimeSignature, and is a Composite pattern containing Measures; the Measures contain the Notes.

Actually playing it means interpreting some other things, like Repeats and Codas, which are other Containers. To play it, you interpret the hierarchical structure of the Composite, inserting a note into a queue; as the notes move through the queue based on the tempi, each Note has its play() method called.

Hmmm, might invert that; each Note is given as input to the Instrument, which interprets it by synthesizing the wave form as required. That comes back around to something like your original scheme.

Another approach to the decomposition is to apply Parnas' Law: you decompose in order to keep secret places where requirements could change. But I think that ends up with a similar decomposition; You can change the time signature and the tuning, you can change the instrument --- a Note doesn't care if you play it on a violin, a piano, or a marimba.

Interesting problem.

Answer 2

My music composition software (see my profile for the link) uses Notes as the primary unit (with properties like starting position, length, volume, balance, release duration etc.). Notes are grouped into Patterns (which have their own starting positions and repetition properties) which are grouped into Tracks (which have their own instrument or instruments).

Blending sine waves is one method of synthesizing sounds, but it's pretty rare (it's expensive and doesn't sound very good). Wavetable synthesis (which my software uses) is computationally inexpensive and relatively easy to code, and is essentially unlimited in the variety of sounds it can produce.

Answer 3

MIDI files would be the usual way to do this. MIDI is a standard format for storing data about musical notes, including start and end times, note volume, which instrument it's played on, and various special characteristics; you can find plenty of prewritten libraries (including some open source) for reading and writing the files and representing the data in them in terms of arrays or objects, though they don't usually do it by having an object for each note, which would add up to a lot of memory overhead.

The instruments defined in MIDI are just numbers from 1 to 128 which have symbolic names, like violin or trumpet, but MIDI itself doesn't say anything about what the instruments should actually sound like. That is the job of a synthesizer, which takes the high-level MIDI data an converts it into sound. In principle, yes, you can create any sound by superposing sine waves, but that doesn't work that well in practice because it becomes computationally intensive once you get to playing a few tracks in parallel; also, a simple Fourier spectrum (the relative intensities of the sine waves) is just not adequate when you're trying to reproduce the real sound of an instrument and the expressiveness of a human playing it. (I've written a simple synthesizer to do just that so I know hard it can be produce a decent sound) There's a lot of research being done in the science of synthesis, and more generally DSP (digital signal processing), so you should certainly be able to find plenty of books and web pages to read about it if you'd like.

Also, this may only be tangentially related to what the question, but you might be interested in an audio programming language called ChucK. It was designed by people at the crossroads of programming and music, and you can probably get a good idea of the current state of sound synthesis by playing around with it.

Answer 4

Many people doing new common Western music notation projects use MusicXML as a starting point. It provides a complete representation of music notation that you can subset to meet your needs. There is now an XSD schema definition that projects like ProxyMusic use to create MusicXML object models. ProxyMusic creates these in Java, but you should be able to do something similar with other XML data binding tools in other languages.

As one MusicXML customer put it:

"A very important benefit of all of your hard work on MusicXML as far as I am concerned is that I use it as a clear, structured and very ‘real-world practical’ specification of what music ‘is’ in order to design and implement my application’s internal data structures."

There's much more information available - XSDs and DTDs, sample files, a tutorial, a list of supported applications, a list of publications, and more - at

http://www.recordare.com/xml.html

MIDI is not a very good model for a simple musical score in standard notation. MIDI lacks many of the basic concepts of music notation. It was designed to be a performance format, not a notation format.

It is true that music notation is not hierarchical. Since XML is hierarchical, MusicXML uses paired start-stop elements for representing non-hierarchical information. A native data structure can represent things more directly, which is one reason that MusicXML is just a starting point for the data structure.

For a more direct way of representing music notation that captures its simultaneous horizontal and vertical structure, look at the Humdrum format, which uses more of a spreadsheet/lattice model. Humdrum is especially used in musicology and music analysis applications where its data structure works particularly well.

Answer 5

Music in a data structure, standard notation, ...

Sounds like you would be interested in LilyPond.

Most things about musical notation are almost purely mechanical (there are rules and guidelines even for the complex, non-trivial parts of notation), and LilyPond does a beautiful job of taking care of all those mechanical aspects. What's left is input files that are simple to write in any text editor. In addition to PDFs, LilyPond can also produce Midi files.

If you felt so inclined, you could generate the text files algorythimically with a program and call LilyPond to convert it to notation and a midi file for you.

I doubt you could find a more complete and concise way to express music than an input file for LilyPond.

Please understand that music and musical notation is not hierarchical and can't be modelled(well) by strict adherence to hierarchical thinking. Read this for mor information on that subject.

Have fun!