Re: Kepler

Here is another realization of Kepler's ideas. I posted this earlier, IIRC.

--John

I've tracked down the reference to the original realization of Kepler's
Harmonia Mundi and have found a web page that lists a contemporary CD with a new
version of this realization.

The realization was originally described in "Kepler's Harmony of the World: A
Realization for the Ear in American Scientist 67: 286-292 (1979) by John Rodgers
and Willie Ruff. This early version was created at the Princeton University
Computer Center using Music4BF. I've emailed Prof. Ruff to see if it is still available.

The CD listed on Ruff's web pages at http://www.willieruff.com/menu.html is at
least in part a new version prepared at Stanford and contains 3 tracks.
However, a sample of the first track is available for free download as an mp3
file and I recommend hearing it to compare it to Monzo's and Walker's treatment
of the same material. The liner notes are also downloadable and I've appended
them below. They are a short summary of the 1979 paper without the technical
details of Kepler's laws, the history of the concept of the "music of the
spheres," and some details of the tuning and phasing of the voices. By phasing,
I mean starting the voices in different stages of their cycles to simulate the
orbital positions of the corresponding planets on Dec. 27, 1571 (Kepler's
birthdate).

The liner notes:

The Harmony of the World

A Realization for the Ear of Johannes Kepler's Data from Harmonices Mundi 1619

The main purpose of this record is to present Kepler's Harmony of the World for
a period of several centuries. We decided that the length of time represented
would have to be at least as long as the period of revolution of the slowest
planet, Pluto. Pluto's period is approximately 248 years or, in our terms, 20
minutes and 42 seconds, and we chose a total length of 22 minutes, representing
264 years.

When one listens to the full nine-part Harmony - six tonal and three rhythmic
"voices" - one may find it difficult to sort out the individual voices and
assign them to the planets they represent. Therefore we begin by introducing the
planets one by one, from the innermost to the outermost. The first you hear is
Mercury, which as the innermost is the fastest and the highest pitched. It has a
very eccentric orbit (as planets go), which it traverses in 88 days; its song is
therefore a fast whistle, going from the E above the piano (e""') down more than
an octave to about C# (c#"") and back in a little over a second.

Venus and the Earth in contrast have nearly circular orbits. Venus' range is
only about a quarter tone, near the E next above the treble staff (e"'); Earth's
is about a half tone, from G (g") to G4# at the top of that staff. Together they
drone a sixth, but the sixth is continuously changing from major to minor, or
even down partway to a fifth, as the two planets go through their cycles -
about 3 seconds for Venus, exactly 5 for Earth. Kepler compared Earth's sad
minor second to the first minor second in the standard Do-Re-Mi scale - mi-fa-mi
- and for him it sang of Earth's unending misery-famine-misery. Living into the
period of the Thirty Years War, and indeed dying then, he knew what he was
talking about, and for many millions in our own century, the song has not changed.

Next out from the Earth is Mars, again with an eccentric orbit. Its song is
distinctive, one of the easiest to pick out in the full Harmony. Alone in the
alto, it ranges from the C (c") above middle C down to about F*~ (f4t') and
back, in nearly 10 seconds.

The distance from Mars to Jupiter is much greater than that between the inner
planets (as mentioned above, the asteroids in this gap may represent a missing
planet), and Jupiter's song is much deeper, in the baritone or bass, and much
slower. It covers a minor third, from D to B (D to B) just below the bass staff.
Still farther out and still lower is Saturn, only a little more than
a deep growl, in which a good ear can sometimes hear the individual vibrations.
Its range is a major third, from B to G (B2 to G2),the B at the top being just
an octave below the B at the bottom of Jupiter's range. Thus the two planets
together define a major triad, and it may well have been this concord - in the
ratio 4:5:6, inevitable when angular velocities are equated with
pitches - that made Kepler sure he had cracked the code and discovered the
secret of the celestial harmony. Saturn's cycle is about 2 1/2 times that of
Jupiter (almost 2 1/2 minutes vs. almost 1 minute), and their songs commonly
strike the concordant ratios. This would be even more evident if the speed of
the music were doubled, so that the cycles were half as long and the
pitches were all raised an octave; together they then sing a majestic
counterpoint in the key of G Major.

The outer, post-Kepler planets we have simulated not by musical tones at the
given vibration frequency but by sharp rhythmic beats. Uranus is a rapid
ticky-ticky-ticky changing gradually from less than 9 to more than 10 per second
and back but over a period of 7 minutes, so that the change is not easy to
detect. When the much steadier (because much less eccentric) Neptune is added,
however, at nearly 5 per second, the changes in Uranus' rhythm become more
obvious, because the ratio between the two shifts continually back and forth
from less than to more than 2:1, and the resulting "beats" are readily discerned.

Finally Pluto's bass-drum beat is the foundation of the whole structure.
Although its period is so long - 20 minutes and 42 seconds - its orbit is so
eccentric that the gradual slowing down and even more the speeding up of the
rhythm is manifest. At Pluto's slowest, the ratio with Neptune is almost 1 to 2
1/2, yet near its fastest their rhythms are identical and at the highest
point Pluto is actually a little faster, because in fact at its closest point to
the Sun it is actually closer than Neptune ever comes (lending credence to the
view that Pluto is only an escaped satellite of Neptune's). Thus the relation
between the two rhythms is continually changing, and "beats" come and go as they
come into a simple ratio and then recede from it again. The additional doubled
rhythm of Uranus, ticking away above, adds greatly to the fascination of this cross-rhythm.

We have inserted a part of the Harmony at half speed. The inner planets come
down an octave and are clearer and more readily grasped. Jupiter on the other
hand retreats into the basement, and Saturn is hardly audible. The cross rhythm
of the outer planets proceeds at half pace, and its intricacies become even more apparent.

Part 2 begins with several minutes for the rhythmic planets alone, introduced
one by one from Pluto in to Uranus. Then we add the visible planets, this time
in order from Saturn to Mercuryrepresenting the second half of the full Harmony
of the World, characterized particularly by the steady acceleration of Pluto to
its perihelion and then a minute or so of relaxation beyond.

High fidelity earphones greatly enhance the spatial effect of the general
planetary movement around the Sun. Note that the positions of the planets change
in their orbits in Stereo from side to side. Always play the recording in Stereo.

Since proportion is the key to Kepler's idea of the Harmony of the world, this
recording can be played at slower or faster speeds. Slower speeds will lower the
pitches and allow for a greater harmonic appreciation of the inner planets while
reducing the tonal presence of Jupiter and Saturn. Higher speeds will bring
Saturn and Jupiter into Tonal prominence but Mercury will
climb near or beyond the upper limits of our pitch perception.

This realization of Kepler's data was developed at Yale by Professors Rodgers
and Ruff and recorded at Stanford University by Mike McNabb, Sound Synthesis Consultant.

Produced by Willie Ruff and John Rodgers