Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!accuvax.nwu.edu!ferret!sandell
From: sandell@ferret.ils.nwu.edu (Greg Sandell)
Newsgroups: comp.music
Subject: Re: programs that can infer key/meter
Message-ID: <1240@accuvax.nwu.edu>
Date: 10 Oct 89 00:27:22 GMT
References: <15170@netnews.upenn.edu> <125936@sun.Eng.Sun.COM>
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Reply-To: sandell@ferret (Greg Sandell)
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>In article <15170@netnews.upenn.edu> hardt@linc.cis.upenn.edu (Dan Hardt) writes:
>>I'd like to know what programs exist that can
>>infer the key and meter of a melody, just based
>>on the pitch and duration information.  Does anyone
>>know about programs that can do this?

Now that some responses directly addressing Dan's question have come in, let
me suggest an indirect method.  There have been several writings on meter in
music that attempt to list exactly those features which instantiate this or
that time signature.  This theoretical material can (and has, I think) become
the basis for something more computational.  In particular I am thinking about
A GENERATIVE THEORY OF TONAL MUSIC by Fred Lerdahl and Ray Jackendoff (MIT Press,
1983).  Lerdahl (a composer and theorist) and Jackendof (a linguist) use grouping
mechanisms from Gestalt psychology theory to define musical meter.  For example,
given a recurring pattern of two beats and silence, where the silence is longer
than the duration of time separating the onsets of the two beats, the second of
the two beats tends to be heard as a strong beat, or, the first beat of a measure.
If the silence is roughly twice as long as the inter-onset time, then 3/4 meter
will be perceived.  Of course, competing musical elements could contradict that
and create a different meter, but all things being equal, 3/4 time will be heard.
Of course, real music is more complicated than this simple example, but the book
also describes more complicated conditions

Regarding the ability to figure out the key signature of the piece, I'm sure that
what you are concerned with are non-trivial examples where more than seven
diatonic pitch-classes present.  One method uses a rather simple statistical
approach of counting the number of each instance of every pitch-class in the
piece, and comparing it with a prototypical distribution for every possible
major and minor key.  This method grew out of the research described 
by Carol Krumhansl in "Perceptual Structures for Tonal Music" (MUSIC PERCEPTION 1, 
1983, pp. 28-62). (The actual key-finding algorithm has never been published). To 
successfully match C major, for example, the count will have to show a tendency to 
have more C's than any other note, G's running in second place, E's third, and so on.  
I can't remember the exact order of the remaining nine notes, but the remainder of
the 'white notes' follow before any of the 'black notes.'  The actual prototypical
distribution is somewhat more detailed that a simple descending distribution
(e.g., the ratio of G's to C's is not identical to that of E's to G's).  Despite
the seemingly anti-musical approach of a statistical count, I have seen the 
approach work quite well, especially when the pitch classes are weighted according
to their duration and amplitude.  Using MIDI, I once used the algorithm to analyze
the keys of real-time performance using exactly that weighting scheme (key velocity
to measure amplitude), and it had pretty good accuracy.

***************************************************************
* Greg Sandell, Institute for Learning Sciences, Evanston, IL *
* sandell@ferret.ils.nwu.edu                                  *
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'Oh Hey, Look at that: there's a fish on a hat;
 And we'd like to treat everyone here to a cow souvenir.'
	- Peter & Lou Berryman
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* Greg Sandell, Institute for Learning Sciences, Evanston, IL *
* sandell@ferret.ils.nwu.edu                                  *
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