But Kepler didn't stop there! The truth is, he hated traditional astrology. He thought it rank and superstitious. He developed many of his own principles while doing away with much of the traditional practices and beliefs of astrology. Among his changes, Kepler wanted to cover more musical intervals. So he added three more celestial Aspects to the mix: the quintile where two planets are at 72 degrees relative to the sun; the bi-quintile where two planets are 144 degrees relative to the sun; and the sesqui-quadrate where two planets are at 135 degrees relative to the sun. To Kepler, the quintile is the major 3rd interval because it leaves 4/5 of the zodiacal circle; the bi-quintile leaves 3/5 of the circle and so corresponds to the major 6th; and the sesqui-quadrate leaves 5/8 of the circle and so corresponds to the minor 6th. Why didn't Kepler create, say, a name for the 45-degree relationship? It would have corresponded to the whole step of 8/9. Kepler simply didn't like the other correspondences and found them aesthetically displeasing. The five traditional arrangements along with his new three, he said, covered the most consonant and pleasing intervals. The rest would only introduce discord.

That, however, did not stop others who heard of Kepler's work from adding more. In 1647, William Lilly wrote a work called Christian Astrology in which he introduces Aspects as the semi-quadrate of 45 degrees (a whole tone). But in addition, he introduced the semi-sextile of 30 degrees, the semi-quintile of 36 degrees, and the sesqui-quintile of 108 degrees. These last three, however, have no correspondences to musical intervals although the sesqui-quintile is close to the tritone ratio of 5/7.

By the 18th century, vowels were combined with astro-musica. In 1716, Thomas Gale wrote a work called Rhetores graeci in which he talks of Demetrius and the Egyptian symbology of 7 letters distributed upon two fingers was indicative to them of music. He concluded these 7 letters were the same vowels written of by Demetrius. The writers that followed, such as Barthélemy and Kopp, expanded on this idea but each differed widely from the other.

From highest pitch to lowest, along with the Greek vowels each represents, Barthélemy's scheme was as follows:

1. Saturn, omega, A
2. Jupiter, upsilon, G
3. Mars, omicron, F
4. Sun, iota, E
5. Venus, eta, D
6. Mercury, epsilon, C
7. Moon, alpha, B

Kopp's scheme was:

1. Moon, alpha, A
2. Mercury, epsilon, G
3. Venus, eta, F
4. Sun, iota, E
5. Mars, omicron, D
6. Jupiter, upsilon, C
7. Saturn, omega, B

But equating vowels with music is appropriate since both are dependent on sound for their meaning. Moreover, the Greek vowels and the musical note system seemed to parallel one another. Originally, the Greeks had only 5 vowels before upsilon and omega were added to them in 403 BCE. Strangely enough, Greek mythology names Apollo as having added 2 more strings to the lyre through the addition of 2 more vowels. Pythagoras was said to have added an 8th, completing the octave.

Apollo was the god of music to the Greeks. His younger brother was the roguish Hermes. One day, Hermes rustled some of the Apollo's cattle. Although he denied his guilt, no one believed Hermes. To make it up to Apollo, Hermes fashioned a lyre from a tortoise shell and presented it to him and Apollo gratefully accepted the gift. Here, a musical relationship was being explained in myth language. In the Ancient Greek alphabet, each letter had a numerical value. "Hermes" is 353 and "Pythias" (another name for Apollo) is 1059. We now know who Thrice Great Hermes is of the Hermetic and alchemical traditions: 353 x 3 = 1059. Pythias or Apollo is Thrice Great Hermes. The gift of the lyre represented the perfect 5th interval—the basis of all harmony, of all music—since its ratio is 2/3. 353 x 2 = 706 (very close to the inverse of the mystical square root of 2 or 0.707) and 706/1059 reduces to 2/3.