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For many / most compositions, the composer sticks to one pitch class set. For example, {C,C#,D,D#,EF,F#,G,G#,A,A#,B} where A = 440 hz would be an example. But let's suppose instead I picked a set of frequencies like {440, 10000,948,230,25} or something like that. This would be a random set of frequencies.

Are there examples of musicians who have made music using pitch class sets like this? If so, what are some prominent ones?

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  • I can't imagine that someone did it, since the necessity to produce pitches by frequency entry excludes all non-electronic instruments; why then bother to set up a score, if one could simply deliver the sound.
    – guidot
    Aug 17 '16 at 14:57
  • Is the point of random frequencies to avoid a tuning system? I ask because some microtonal systems have fixed, regular tunings, and so not random frequency-wise. That's different that random order which is the basic concept in aleatoric music. Dec 15 '20 at 15:14
  • I would just note that the first example isn't sufficiently specified, since only the frequency of A is given. You also have to specify a temperament. The second example implies that you do not wish to consider octave equivalence, but the term "pitch class" exists because of octave equivalence. If you allow for octave equivalence then the second set might more helpfully be defined as {440, 460, 474, 625, 800}
    – phoog
    Dec 15 '20 at 16:00
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The answer depends on how the question is interpreted. If the focus is on random pitches, then aleatory music is the place to look. If the focus is on pitch-class sets, then serialism gets primary focus.

Random music (a.k.a. Aleatory music; a.k.a. Chance music)

John Cage is particularly famous for attempting to create unpredictable music. Karlheinz Stockhausen also worked in this area.

Among notable aleatory works are Music of Changes (1951) for piano and Concert for Piano and Orchestra (1958), by the American composer John Cage, and Klavierstück XI (1956; Keyboard Piece XI), by Karlheinz Stockhausen of Germany. (SOURCE; Links added.)

Microtonal serialism

Once one leaves the realm of the familiar 12 chromatic pitches, one enters the realm of microtonality. Microtonality embraces the use of frequencies that occur "in between" the more familiar ones.

The most prominent example I know of that combines serialism with microtonality is Karlheinz Stockhausen's Gesang der Jünglinge (1955-56)

Compositions based on pitches (frequencies) selected at random

I'm not aware of any significant experiments is using randomly selected pitches to create music.

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There are a lot of musicians who have experimented with alternative techniques and electronic techniques. Starting around mid 20th century to probably today. I don't know about the specific technique you mention, but try checking out Pierre Boulez. French composer and conductor. I believe he started an institute for experimental music as well. One of the pioneers was Karl Stockhausen.

If you want it to still sound tonal, you might check on the Internet for the history of tuning. A 440 has not always been the standard, and tuning wasn't always strictly tuned equally between the twelve notes. Look up "Just tuning" or "Equal temperament" or "Well tempered".

Another thing to maybe look up would be micro-tuning. This was another modern technique that also took cues from folk music of other countries like. Some Asian countries like China have choirs that sing melodies that incorporate notes that wouldn't fit into the western system easily. Also India has its own complex music system and I believe has scales that incorporate notes outside of the western system.

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Convert the various frequencies back to pitches (I am unaware of a "frequency set class" or what that would even mean), here in the Standard Tuning(TM), then lookup that pitch set class:

% perl -MMusic::Scala -E '$s=Music::Scala->new;say for map { $s->freq2pitch($_) } @ARGV' 440 10000 948 230 25 | while read pitch; do expr $pitch % 12; done
9
3
10
10
7
% atonal-util basic 9 3 10 7
c,des,ees,g
111111
4-z29   All-interval tetrachord
c,e,ges,g   half_prime
% 

This is a popular pitch set among 20th century musicians, so examples should be easy to find.

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