Is there an algorithm to get the Scale and Key of a song from a series of notes? [closed]

Question

From a series of MIDI notes stored in array (with MIDI note number), does an algorithm exist to get the most likely key or scale implied by these notes?

Answer 1

If you're using Python you can use the music21 toolkit to do this:

import music21
score = music21.converter.parse('filename.mid')
key = score.analyze('key')
print(key.tonic.name, key.mode)

if you care about specific algorithms for key finding, you can use them instead of the generic "key":

key1 = score.analyze('Krumhansl')
key2 = score.analyze('AardenEssen')

etc. Any of these methods will work for chords also.

(Disclaimer: music21 is my project, so of course I have a vested interest in promoting it; but you can look at the music21.analysis.discrete module to take ideas from there for other projects/languages. If you have a MIDI parser, the Krumhansl algorithm is not hard to implement).

Answer 2

The algorithm by Carol Krumhansl is the best-known. The basic idea is very straightforward. A reference sample of pitches are drawn from music in a known key, and transposed to the other 11 keys. Major and minor keys must be handled separately. Then a sample of pitches are drawn from the music in an unknown key. This yields a 12-component pitch vector for each of 24 reference samples and one unknown sample, something like:

[ I,        I#,      II,       II#     III,       IV,      IV#,   V,     V#,    VI,     VI#,   VII    ]
[ 0.30,  0.02,  0.10,  0.05, 0.25,  0.20,  0.03, 0.30,  0.05,  0.13, 0.10  0.15]

Compute the correlation coefficient between the unknown pitch vector and each reference pitch vector and choose the best match.

Craig Sapp has written (copyrighted) code, available at http://sig.sapp.org/doc/examples/humextra/keycor/

David Temperley and Daniel Sleator developed a different, more difficult algorithm as part of their (copyrighted) Melisma package, available at http://www.link.cs.cmu.edu/music-analysis/ftp-contents.html

A (free) Matlab version of the Krumhansl algorithm is available from T. Eerola and P. Toiviainen in their Midi Toolbox: https://www.jyu.fi/hum/laitokset/musiikki/en/research/coe/materials/miditoolbox

Answer 3

There are a number of key finding algorithms around, in particular the ones of Carol Krumhansl (most papers that I've seen always cite Krumhansl's methods)