COMMAND

 key -- estimate the key for a Humdrum passage

SYNOPSIS

 key [-af] [inputfile ...]

DESCRIPTION

 The key command estimates the key of a given musical passage using Krumhansl's tonal hiearchy method. The command is restricted to identifying only those keys within the common major/minor tonal system. Modes outside the major/minor system are not recognized.

The input may be either **semits or **kern representations. The program adapts to input having varying numbers spines each with a different interpretation.

Output consists of three items of information:

The algorithm is based on Krumhansl's perceptually-based key-finding method (see references). This method compares a given pitch-class frequency profile with two perceptually-determined prototypes (one each for major and minor modes). The coefficients used for these prototypes are those determined by Krumhansl & Kessler (1982). In order for the algorithm to work properly, durational information ought to be provided. When using **semits format input, best results are achieved when the input has a time-base format. (See the timebase (4) command.)

The key command is poor at distinguishing less common enharmonic keys. For example, it is unable to distinguish the following enharmonic spellings for tonic pitches: C-flat, B-sharp, E-sharp, F-flat. Also, key is unable to distinguish enharmonic spellings involving double- or triple- sharps or flats. That is, G double-sharp major is identified as A major. KEY is able to distinguish the more common enharmonic spellings (such as E-flat versus D-sharp).

There is no special output file-type designation.

OPTIONS

 The key command provides the following options:
-aoutput correlation values for all keys
-foutput frequencies for all pitch-classes
-hdisplays a help screen summarizing the command syntax
Options are specified in the command line.

The -a option will show all of the correlation coefficients for all 24 of the (enharmonic) major and minor keys.

The -f option will output the relative frequencies for each of the twelve chromatic pitch classes (in quarter-note durations).

SAMPLE OUTPUT

 Without any options, typical outputs are of the following form:

Estimated key: B minor (r=0.8442) confidence: 51.3%

With both the -f and -a options invoked, a typical output is given below. The -f option causes 12 pitch-class tallies to be outputted. These values are given in acculumated whole-note durations. For example, the output: "PC[5]: 4.25" means that the enharmonic pitch-class "F" appears in the passage for the equivalent of 4 whole-notes plus a quarter-note duration. If inputs do not include durational information (such as in **semits input), each note is assigned the nominal duration of a quarter-note.

PC[0]: 5.50617
PC[1]: 0.375
PC[2]: 6.1875
PC[3]: 0
PC[4]: 5.625
PC[5]: 4.25
PC[6]: 1.25
PC[7]: 5.6875
PC[8]: 0.5
PC[9]: 4.625
PC[10]: 0.625
PC[11]: 4.40625
Tonic[0] major 0.791744 minor 0.0962456
Tonic[1] major -0.747033 minor -0.337397
Tonic[2] major 0.506935 minor 0.535771
Tonic[3] major -0.404982 minor -0.720203
Tonic[4] major 0.0308014 minor 0.64007
Tonic[5] major 0.475928 minor -0.13113
Tonic[6] major -0.735928 minor -0.157988
Tonic[7] major 0.772586 minor 0.205276
Tonic[8] major -0.574103 minor -0.487743
Tonic[9] major 0.232566 minor 0.66303
Tonic[10] major -0.014411 minor -0.625767
Tonic[11] major -0.334105 minor 0.319835
Estimated key: C major (r=0.7917) confidence: 5.7%
The -a option causes the tonic major and minor correlations to be printed for each pitch-class. Good key matches have a high positive correlation; the maximum value is 1.0.

In the above sample output, notice that the confidence score for the predicted key of C major (Tonic[0]) is quite low. The reason for this is that the correlation coefficient for A minor (Tonic[9]) is rather close to that for C major (0.791744 versus 0.66303) Note that confidence scores may be used as a simple index for estimating the tonal ambiguity or degree of chromaticism for a passage.

PORTABILITY

 DOS 2.0 and up, with the MKS Toolkit. OS/2 with the MKS Toolkit. UNIX systems supporting the Korn shell or Bourne shell command interpreters, and revised awk (1985).

SEE ALSO

 **kern (2), kern (4), **semits (2), semits (4), timebase (4)

WARNINGS

 As noted, key is very limited. When used to find "the key" of a particular work, it frequently produces incorrect results. In particular, for much tonal music, key has a tendency to mistakenly identify the dominant of the key rather than the tonic. See also the discussion under "proposed modifications."

BUGS

 The current version does not handle multiple stops in **kern spines.

NOTES

 Currently the program is sensitive to **semits and **kern interpretations. If no recognizable interpretation is given in the input stream, key assumes **kern compatible input. This may lead to erroneous results.

REFERENCES

 Krumhansl, C. Cognitive Foundations of Musical Pitch, Oxford: Oxford University Press, 1990, Chapter 4.

Krumhansl, C. L. & Kessler, E. J. "Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys," Psychological Review, Vol. 89 (1982) pp.334-368.

PROPOSED MODIFICATIONS

 The key command is likely to appeal to two types of uses: (1) those who are interested in knowing the key of a musical work without having to examine the work manually, or (2) those who are interested in a perceptual characterization of the tonality of a passage. These goals are quite different. The current key command implements the second approach; key is not very good at consistently and correctly identifying "The Key" of typical tonal works. Another command (or variant of the key command) might use contextual heuristics (such as looking at the final chord of a work, or examining cadences) in order to better identify "the key" of a work.