John Carlos Baez on Nostr: The red dot moves around once every second. The blue dot moves around faster: log₂3 ...

The red dot moves around once every second. The blue dot moves around faster: log₂3 times as fast. When the time t is an integer and the blue dot is close to the red dot, there tends to be a famous scale with that number of notes in it!

The blue dot comes very close to the red at t = 12. But also at other times:

5: pentatonic scale
7: diatonic scale
12: chromatic scale
17: Safi al-Din Urmawi (1216-1294)
19: Guillaume Costeley (1558), Francisco de Salinas (1577)
24: quarter-tone scale
29: Marchetto da Padova (1318)
31: Christiaan Huygens (1629-1695)
41: Paul von Janko (1906)
53: Jing Fang (78-37 BC), Nicholas Mercator (~1670)