Hehehe, notice the perfect fifth* in the hum: it's a three phase arc, so the fundamentals and second harmonics cancel out (give or take imbalance between arcs), while the 3rd harmonics add perfectly in phase (because 120 or 240 degrees, times three, is a multiple of a full circle). When one pair of arcs breaks, it reverts to single phase, giving the second harmonic. (The fundamental cancels out anyway, because the arc is approximately square law.)
*An equal-tempered fifth is technically 2^(5/12), i.e., 5 steps on the diatonic scale (an octave divided into 12 pieces by equal ratios). This happens to be very close to 3/2 (i.e., the ratio between 2nd and 3rd harmonics), but not quite equal. Following multiples of 3/2 (up a fifth) and 1/2 (down an octave), you generate the "circle of fifths", which works out evenly on the scale, but ends up a bit out of tune (I think about a half step in total??), because fundamentally, the 12th root of 2 is an irrational number, and cannot ever be represented by a ration number (in this case, a finite product of 3/2 and 1/2 factors). This has been your musical fact for the day.
Tim
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