## Kepler's Music: All Pitches of the PlanetsPutting it all together, we get this table of the min-mean-max pitches of the planets. |

Planet e m M min-pitch mean-pitch max-pitch Mercury 0.2056 0.688008 1.584607 8355.17 12144 19243.47 Venus 0.0088 0.98263 1.017835 3417.586 3478 3540.03 Earth 0.0167 0.967418 1.034256 1934.837 2000 2068.511 Mars 0.0934 0.836454 1.216658 655.7796 784 953.86 Jupiter 0.0485 0.909627 1.104542 60.94498 67 74.00434 Saturn 0.0556 0.897431 1.121213 17.94863 20 22.42426

Here, m is the factor to multiply mean-pitch
to obtain min-pitch, m = 1/(1+e)^{2},
and, M is the factor to multiply mean-pitch
to obtain max-pitch, M = 1/(1-e)^{2}.
Revised 06 jan 2002 by ralph abraham |