Musical Information (Mus 253/CS 275A)
Musical Dice Games
Several 18th century composers such as Mozart and Haydn composed
music which is performed by rolling dice to determine the sequence
of measures in the music.
The table below contains one of these dice-game compositions:
Musikalische Würfelspiele (Musical Dice Game), Kontre-Tänze (Contra-Dance), K6 Anh. C30.01 (K3 Anh. 294d)
by Wolfgang Mozart.
The piece is generated by rolling a pair of dice. The outcome of the
dice roll is a number between 2 and 12. For each measure in the composition
there is a set of 11 possible measures which are chosen by the dice roll.
For example, if a 9 is rolled for the first measure of the piece, pre-composed
measure #142 will be the first measure of the generated composition.
If a three is rolled for the second measure, then measure #64 will be the
second measure of the generated composition. You can view the individual
measures in Humdrum text format or in MIDI file format in the table below.
To generate a composition, you would roll the dice 16 times, and choose
a measure for A1 through A8 and B1 through B8.
The table below gives a list of 100 random realizations of the contra-dance.
The set on the left contains the music in Humdrum format, and the set on the
right contains the music as MIDI files.
To combine the individual measures, use the humcat command.
This command will join two or more Humdrum files into a single data
stream. For example, with these two files:
humcat file1.krn file2.krn
will generate the following composite data:
humcat can join any Humdrum files which contains
the same number of spines and matched exclusive interpretations
at the join points.
Suppose the you roll dice with this pattern: "2 5 10 6 3 8 9 9".
Then, you can generate the A section of the contra-dance with the
humcat cda000.krn cda070.krn cda114.krn cda086.krn cda071.krn \
cda149.krn cda125.krn cda023.krn cda089.krn > partA.krn
If you use the same dice rolls to generate the second section, this
is the command which would be run:
humcat cda155.krn cda157.krn cda029.krn cda019.krn cda031.krn \
cda080.krn cda096.krn cda127.krn > partB.krn
To generate the final composition, combine partA.krn and
humcat partA.krn partA.krn partB.krn > full.krn
- First, download the individual measures
to your local computer. Or, alternatively go to the kernscores website and download a zip file of the
source material. Click on the "Z" button on the page:
- Generate an example composition by rolling some dice and using
humcat to combine the individual measures into a single
Humdrum file. Then convert that file to MIDI and listen to it.
Repeat until bored. To generate a large number of variants,
download and run this PERL script.
If you do not have real dice, you can borrow my pair of
virtual dice, by typing the command (BASH shell version):
NUM=$RANDOM; let "NUM %= 12"; let "NUM += 1"; echo $NUM
Or a PERL language version:
perl -e "print 2+int(rand(6))+int(rand(6))"
For example, if you roll a 7 and then an 11, then the combining command would be:
humcat cda000.krn cda165.krn cda085.krn
Which will start the composition with these two measures:
- Combine some of the measures in a non-proscribed way.
For example, paste the measures together in reverse order.
What does the music sound like?
- Examine the musical key of each individual measure in the composition.
In particular, choose a row from the A or B columns and measure the key
in each measure listed on that row. For example, the key of measure 060
which is for roll 11 in the B8 column is in the key of C Major:
The best key is: C Major
What is the pattern of musical keys for measures in a particular row?
What is the pattern of keys in measures in a particular column?
- Create a set of realized contradances, then identify the musical
key of the dance by using the Humdrum command
or the Humdrum Extras command
Are all of the compositions in the same key or different keys accoring to the