Milton Babbitt was positively thrilled with the riches he found
as he explored music grounded in something other than its
traditional grounding in scale degrees (the 7-note scale,
roughly based on the overtone series). He created the vocabulary
that is still used to discuss this music-that-avoids-scale-
degree-orientation. I will mention two terms he coined--"pitch
class" and "set class". Perhaps think of them as the high 20th
C. modernist way of thinking about pitches and chords. Musicians
learn how to hear any pitch in relation to any major or minor
scale-- A as the 4th scale degree in E major; B as the altered
(Lydian-inflected) 4th scale degree in F major. The regrounding
of music that arose giddily in the 19th & 20th centuries came
first through the implications of symmetrical harmonies--notably
diminished 7th chords, as in Wagner's Tristan Prelude; later,
music was based on highly chromatic tunes that continually
bewilder our scale-degree oriented ears, keeping us confused
about the key at any given mome