# Command: key¶

## 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 estimated key for the passage,
• a coefficient of correlation (Pearson’s “r”) that measures how well the pitch organization of the musical passage conforms to an idealized major or minor key template, and
• a confidence score that indicates how distinctive the key-match is compared with other competing keys. A confidence score of 100% indicates a very strong confidence in the key estimate; low confidence scores indicate that there is at least one other key that is a good alternative candidate.

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:

 -a output correlation values for all keys -f output frequencies for all pitch-classes -h displays 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).

 **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.