Quantum theory came out of the work of Louis de Broglie who discovered that the electron shells around an atom are structured like a musical note with a fundamental frequency accompanied by harmonics or overtones. Perhaps that was why all Pythagorean initiates had to master the lyre (as did the druids).

In Greek mythology, the Fates produced the 5 notes or vowels of the lyre but Apollo added 2 more to make a diatonic scale. Pythagoras (whose name means ¡°Apollo speaking¡±) was said to have added an 8th, which completes the octave. The Greeks did not use our 12-tone equal-tempered (or 12-TET) scale of today. A Chinese musicologist of the 16th century, Zhu Zaiyu, first calculated the value of an equal-tempered half-step to be the 12th root of 2 or about 1.0595. Shockingly enough, the name of Apollo in Greek, Apollon, adds up in Greek isopsephia (where every letter in the alphabet has a corresponding number) to 1061. One of his titles, Pythias, from whence "Pythagoras" is derived, adds up to 1059. And Apollo, let us remember, was the god of music.

Apollon is Thrice-Great Hermes or Hermes Trismegistus¡ªwho gave us music among other things. In isopsephia, Hermes¡¯ name adds up to 353, which totals to 1059 when multiplied by 3--Thrice-Great Hermes. His name multiplied by 2 totals out to 706 which is very close to 0.707 which is the inverse of the Logos--¡Ì2 (1.414)--and also half of it. 706/1059=2/3=the perfect 5th. In Greek mythology, Hermes invented the lyre and presented as a gift to Apollo, his older brother.

Some might determine that the Greeks must have known the about 12-TET since that seems far too close to be coincidence, yet in the 19th century, a Western musicologist developed a system that enabled values between two intervals to be converted into a linear scale for comparison. This was useful because, in the Pythagorean scale (the actual ratios with no tempering), the interval ratios are not intuitive. The difference between the interval called a tritone (6 half-steps) and a perfect 5th (7 half-steps) is only a single half-step but it is hard to know that simply by comparing their ratios¡ª729/512 to 3/2. So a linear scale was developed to better illustrate this. It utilizes the following formula:

1200 log2 a/b, where a/b represents the two ratios being compared. Hence:

1200 log2 1.5/1.42383 or 1200 x log2 1.053496555 = 90 and the units used here are called ¡°cents.¡± So a half-step in the linear system is 90 cents (but generally rounded off to 100 cents). A whole step equals 204 cents (1200 x log2 9/8)but rounded off to 200 cents. The octave is 1200 cents. Oddly, the ratio for the full Pythagorean octave is 531441/262144 which converted into cents is 1223.46 or thereabouts. So we subtract the 1200-cent perfect octave to see how far the untempered octave drifts from say C to C¡¯ and we can see that the amount of drift is 23.46 cents.

What is astonishing is that 23.46 is extremely close to the actual tilt of the earth on its axis! The tilt is responsible for our zodiac. The octave is a circle of 12 notes that is off-kilter by 23.46 cents while the zodiac is a circle of 12 constallations that result because the earth is off-kilter by 23.44 degrees as it rotates. There is no way this was deliberate. Yet, it works out somehow.