Music 824: Computer Applications in Music Research
Ohio State University
School of Music

Humdrum Exercise #15 - Answers

All of the following commands assume that you are located in the appropriate score directory.

In Gregorian chant, what is the most common interval following a rising major second?
COMMAND: extract -i '**kern' liber* | mint | context -n 2 -o ^= | grep '^+M2' | sort | uniq -c
ANSWER: 708 instances of +M2 followed by -M2
In Gregorian chant, what is the most common interval following a rising minor second?
COMMAND: extract -i '**kern' liber* | mint | context -n 2 -o ^= | grep '^+m2' | sort | uniq -c
ANSWER: 154 instances of +m2 followed by +M2
In French folksongs, what scale degree most commonly follows the subdominant?
COMMAND: context -n 2 -o ^= france* | solfa -x | grep '^fa' | sort | uniq -c | sort -n
ANSWER: Twenty-four subdominant pitches are followed by the mediant.
In French folksongs, what scale degree most commonly precedes the subdominant?
COMMAND: context -n 2 -o ^= france* | solfa -x | grep 'fa$' | sort | uniq -c | sort -n
ANSWER: Twenty-nine subdominant pitches are preceded by the dominant.
In French folksongs, what scale degree most commonly begins a phrase?
COMMAND: yank -m '{' -r 0 france* | solfa -x | rid -GLId | sort | uniq -c | sort -n

Due to a bug with yank you might have to use the following command:

COMMAND: cat france* | yank -m '{' -r 0 | solfa -x | rid -GLId | sort | uniq -c | sort -n

ANSWER: Twenty-seven phrases begin with the dominant (`so').
For those French folksongs whose phrases begin with the dominant pitch, what is the most common ending pitch of the phrase?
COMMAND: context -b '{' -e '}' -o ^= france* | solfa -x | humsed 's/ r$//; s/ .* / /' | grep '^so' | sort | uniq -c | sort -n
ANSWER: The majority (8) of phrases beginning on the dominant also end on the dominant.
BONUS QUESTION: In Austrian folk songs, what is the most common interval formed by the first and last notes of each phrase?
COMMAND: cat *.krn | yank -m '[{}]' -r 0 | context -b '{' | hint -v | rid -GLId | sort | uniq -c | sort -n
ANSWER: There are 60 phrases that begin and end on the same note (P1 is most common).

A problem with the above approach is that no intervals are calculated when the phrase begins or ends with a rest. A better approach is as follows:

COMMAND: humsed '/r/d' *.krn | context -b '{' -e '}' -o ^= | humsed 's/ .* / /' | hint -v | rid -GLId | sort | uniq -c | sort -n
ANSWER: There are 93 phrases that begin and end on the same note (P1 is most common).
BONUS QUESTION: Consider diatonic intervals only. In Gregorian chant, the most common sequence of intervals consists of repeated unisons. For example, the most common 10-note interval pattern is 9 repeated unisons. How many sequential notes do we have to consider before a string of unisons is no longer the most common diatonic interval pattern?
COMMAND: extract -i '**kern' liber* | mint -d | context -o ^= -n 10 | rid -GLId | sort | uniq -c | sort -n
extract -i '**kern' liber* | mint -d | context -o ^= -n 11 | rid -GLId | sort | uniq -c | sort -n
extract -i '**kern' liber* | mint -d | context -o ^= -n 12 | rid -GLId | sort | uniq -c | sort -n
extract -i '**kern' liber* | mint -d | context -o ^= -n 13 | rid -GLId | sort | uniq -c | sort -n
etc
extract -i '**kern' liber* | mint -d | context -o ^= -n 17 | rid -GLId | sort | uniq -c | sort -n
ANSWER: When -n is 17, a sequence of unisons is no longer the most common interval pattern.
This means that beyond 17 pitches, string of unisons are no longer in the majority.
BONUS QUESTION: In the Polish folksongs (Essen/europa/polska) what is the average number of notes per phrase?
COMMAND: context -b '{' -e '}' -o '[=r]' *.krn | rid -GLId | wc
ANSWER: wc tell us there are 117 lines (i.e. 117 phrases) and 917 words (i.e. 917 notes): 917/117 = 7.8 notes/phrase

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