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When you first hear them, a Gregorian chant, a Debussy prelude and a John Coltrane improvisation might seem to have almost nothing in common--except that they all include chord progressions and something you could plausibly call a melody. But music theorists have long known that there's something else that ties these disparate musical forms together. The composers of these and virtually every other style of Western music over the past millennium tend to draw from a tiny fraction of the set of all possible chords. And their chord progressions tend to be efficient, changing as few notes...
Exactly how one style relates to another, however, has remained a mystery--except over one brief stretch of musical history. That, says Princeton University composer Dmitri Tymoczko, "is why, no matter where you go to school, you learn almost exclusively about classical music from about 1700 to 1900. It's kind of ridiculous...
...bius strips math teachers love to trot out to prove to students that a two-dimensional figure can have only one side. Indeed, the simplest chords, which consist of just two notes, live on an actual Möbius strip. Three-note chords reside in spaces that look like prisms--except that opposing faces connect to each other. And more complex chords inhabit spaces that are as hard to visualize as the multidimensional universes of string theory...
Springsteen's known charitable contributions, substantial though they are, amount to only a small fraction of his income. What he does with the rest is a mystery to almost everyone except the staff of Breslauer, Jacobson and Rutman, the Los Angeles accounting firm that discreetly handles many of Springsteen's business affairs. At the firm's elegant quarters on Wilshire Boulevard, a TIME reporter was warned that he would be "thrown out of the office" if he persisted with questions about the Boss's finances...
...attack on the Mehdi Army would be enormously complicated, both militarily and politically. Sadr City is not patrolled by U.S. troops, and except for the occasional Special Forces raid the militia operates freely there...