the core & the 3 legs (ripples smacking in)
the sapphire core sits at 000 (the zero). the 3 orange legs are the weight-1 axes {001,010,100}; ripples travel inward and strike the core. the faint purple ring is weight-2 {011,110,101} (leg-pair XORs), the far node is 111. when the three strikes land together (δ=0) the core flares and rings; spread them and the strikes fight — at δ=120° they cancel the breathing mode entirely. drag to rotate the scene.
the song — ring-up & waveform
top: the coherent drive vs timing spread — a Dirichlet (phased-array) curve, peaking at 3× when the taps are in time, zero at 120°. middle: the ring-up envelope (the core answers Q× louder, building over many cycles). bottom: the sapphire\u2019s waveform — a clean tone when driven in time, nothing when nulled.
toddler corner
ELI5: imagine a wine glass that hums a perfect note when you tap it — a sapphire is that, but a MILLION times better; tap it once and it hums for millions of ripples. Now, three friends stand at the three corners of a triangle, each holding a rope that runs to the glass in the middle, and they flick their ropes to send a bump down to the glass. Here\u2019s the whole secret: if all three flick at the exact SAME instant, the three bumps pile on top of each other and shove the glass three times as hard — and because the glass barely loses any energy, those little shoves add up and up until it\u2019s SINGING loud. But if they flick out of sync, the bumps arrive at different moments and shove different ways — they cancel out, and the glass stays quiet. There\u2019s even one exact spacing (a third of a beat apart each) where they perfectly erase each other and the note dies completely — though at that spacing they instead set the glass spinning its sound around the rim instead of pulsing. So "making the sapphire sing right" isn\u2019t about hitting it harder — it\u2019s about all three legs hitting it in perfect time. Rhythm, not force. Tap together, and the zero at the center turns into a bell.