Johannes Kepler took things a bit further. He assigned musical intervals to the five astrological configurations called aspects. For instance, the interval called the perfect 4th spans 4 notes—say, C D E F—and does so in 5 half-steps (C-sharp, D, D-sharp, E and F). If one were to shorten the C string to 3/4, it would play at F, a perfect 4th higher. Likewise, if the C string were lengthened to 4/3, it would play a perfect 4th lower (which would be G in this case). One can also divide the frequency of C by the frequency of F and get a 3/4 ratio. So we say the perfect 4th is represented by the ratio of 3:4 or 4:3.

In astrology, there is a planetary aspect called a square when two planets are 90 degrees from one another using the sun as the focus. So 3/4 of the circular orbit is left over and so Kepler equated the astrological square with the perfect 4th.

The superior conjunction or opposition occurs when two planets are in line on opposite sides of the sun which leaves half the circular orbit which corresponds to the octave higher which is half the frequency of the octave lower and is represented by the ratio of 1:2 or 2:1.

The musical interval called the prime, which spans no notes in no half-steps, corresponds to the aspect called a conjunction (or inferior conjunction) when both planets are in line on the same side of the sun leaving the entire circle.

The aspect called the sextile, when two planets are 60 degrees apart (leaving 5/6 of the circle), corresponds the minor 3rd interval which has a value of 5:6.

The aspect called the trine, when two planets are 120 degrees apart leaves 2/3 of the circle and so corresponds to the perfect 5th interval of 2:3.

Kepler also went on to define more aspects of his own invention and corresponded them to various harmonious intervals.