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?

  • 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

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
% atonal-util basic 9 3 10 7
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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