The Harmony of Spheres--Revisited

As is rather well known that Ancient Greeks thought that the
planets (motive bodies: Hermes, Aphrodite, Ares, Zeus, Cronos,
Moon, Sun), were spaced at the proportions of musical intervals.

The Pythagorean placement is derived from the multiples of threes
and twos: 3/2 (the so-called, nowadays, circle of 5ths).

Well, as most people know, this is not the spacing of the planets.

I do note, however, that per Johannes Kepler (1572-1630) that
cubes (^3) of the mean distance of any two planets from the sun
are in the same ratio as the square (^2) of their period of revolution.

The Pythagorean harmony of spheres solves via the factors 3 and
2, multiplicatively. Kepler, same factors, exponentially.

Not granted there are a number of other discrepancies, like
Pythagoras having the earth, and not the sun, as the focal point.

I don't know if anyone has noted this before. Kudos to the
Ancients and to the Harmony of Spheres!

Polychroni

Polychroni Moniodis wrote:

> From: Polychroni Moniodis <upb_moniodis@ONLINE.EMICH.EDU>
>
> As is rather well known that Ancient Greeks thought that the
> planets (motive bodies: Hermes, Aphrodite, Ares, Zeus, Cronos,
> Moon, Sun), were spaced at the proportions of musical intervals.
>
> The Pythagorean placement is derived from the multiples of threes
> and twos: 3/2 (the so-called, nowadays, circle of 5ths).
>
> Well, as most people know, this is not the spacing of the planets.
>
> I do note, however, that per Johannes Kepler (1572-1630) that
> cubes (^3) of the mean distance of any two planets from the sun
> are in the same ratio as the square (^2) of their period of revolution.

I believe this was only one of the ratios between the planets and showed
the rest by other of the geometric solids. This is a unique observation
though. The ancients also used Epimores to describe the gears of the
planets. So mush with their obsession with epimores. Yet they appear in the
best of scales

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

[Moniodis, TD 116:]
> As is rather well known that Ancient Greeks thought
> that the planets (motive bodies: Hermes, Aphrodite,
> Ares, Zeus, Cronos, Moon, Sun), were spaced at the
> proportions of musical intervals.
> <snip: Kepler, etc.>
> I don't know if anyone has noted this before. Kudos
> to the Ancients and to the Harmony of Spheres!

As I've done more and more research into ancient tunings,
and made lattice diagrams to represent them, I've noted
several times the connections between what I'm doing
and how the ancients thought music described the cosmos.

Making one huge lattice to cover all these different
tuning systems would give a model that is not unlike
the patterns found in the model used by astronomers
today to describe how galaxies are clustered together
between immense voids of space.

(Hence the links to "cosmic" stuff on my website)

|\=/|.-"""-. Joseph L. Monzo...................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\ c/o Sonic Arts, PO Box 620027, San Diego, CA, USA
_U//_/-/__/// | "...I broke thru the lattice barrier..." |
/monz\ ((jgs; | - Erv Wilson |

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I have a book of essays I picked up in a New Age bookstore once, called
"Cosmic Music: Musical keys to the interpretation of Reality", edited by
Jocelyn Godwin. Someone named Rudolph Haase wrote three chapters in it on
Keplers World Harmony. Somewhat flaky, but interesting. Somwhere buried in
the mathematical discussion are stements such as 'Most important is the
realisation that the events of the world are governed by a plan, and that
this plan is recognisable even when the events appear as incomprehensible
and harmful ... this makes it clear that the proper way of thinking for
our world is a finalistic one, whereas natural scientific thinking,
necessarily causally oriented, can only conceive of the world in a partial
manner.'

There was a letter to the editor of the New York Times last Sunday,
complaining about a review of Bach recordings which said 'Bach transcended
the limitations imposed by his religious faith' or some such thing. 'Art
tinged with dogma starts out at a disadvantage', I think is a quote. My
personal impression is that art without a solid basis in faith and strong
belief of some kind tends to be really boring art.

Judith Conrad, Clavichord Player (jconrad@tiac.net)
Music Minister, Calvary Baptist Church, Providence, RI
Director of Fall River Fipple Fluters
Piano and Harpsichord Tuner-Technician

Polychroni Moniodis wrote,

> I do note, however, that per Johannes Kepler (1572-1630) that
> cubes (^3) of the mean distance of any two planets from the sun
> are in the same ratio as the square (^2) of their period of
revolution.

Kraig Grady wrote,

>I believe this was only one of the ratios between the planets and
showed
>the rest by other of the geometric solids.

Kraig, Kepler's constructions using Platonic solids were an exercise in
sheer Platonic numerology and in any case could have nothing to do with
the observation in question since the periods of revolution were not
determined by those constructions. The observation in question was one
of Kepler's three laws of planetary motion, which were obtained from
compiling vast amounts of observational data. The other two laws are
that the planets revolve in an elliptical path with the sun at one
focus, and that the line connecting a planet to the sun sweeps out equal
areas in equal times. These results led Newton to discover the universal
law of gravitation, which can explain all three of Kepler's laws.

In any case, there are no particular ratios between planets specified
here, as one can put the planets at any arbitrary set of distances from
the sun and they will still follow Kepler's laws.

Paul H. Erlich wrote:
>Kepler's constructions using Platonic solids were an
exercise in sheer Platonic numerology

I seem to remember both Helmholtz and Carl Sagan (Helmholtz
in "On the Sensation of Tone," and Sagan in "Cosmos") using
the example of Kepler while discussing the pros and cons of
the Pythagorean tradition. (Both obviously arguing in favor
of empirical observation and experiment at the expense of
'numerology.')

Dan

"Paul H. Erlich" wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Polychroni Moniodis wrote,
>
> > I do note, however, that per Johannes Kepler (1572-1630) that
> > cubes (^3) of the mean distance of any two planets from the sun
> > are in the same ratio as the square (^2) of their period of
> revolution.
>
> Kraig Grady wrote,
>
> >I believe this was only one of the ratios between the planets and
> showed
> >the rest by other of the geometric solids.
>
> Kraig, Kepler's constructions using Platonic solids were an exercise in
> sheer Platonic numerology and in any case could have nothing to do with
> the observation in question since the periods of revolution were not
> determined by those constructions.

Kepler along with being a brilliant astronomer was also an astrologer. In
fact many of the aspects between planets were introduced by him. He wrote
over 200 books on astrology most of which access is denied. He showed how
the periods of revolutions did not follow a plan as you said. He goes on
though to see the distances as being related via the enclosure of one
platonic solid inside another. This was an attempt to solve the harmony of
the spheres question as stated by Ptolemy. That these relations are more
in the family of irrational numbers. We understand now why this would have
to be the case or certain repeating resonances would destroy the orbit of
one if not all of the planets.Still it does not diminish my admiration of
his attempt to preserve the sentiments and concerns of the astronomer who
work would take 1500 years before it would be updated.

> In any case, there are no particular ratios between planets specified
> here, as one can put the planets at any arbitrary set of distances from
> the sun and they will still follow Kepler's laws.

Somehow you have not read the same document as me. Its filled with ratios
and notes even. In fact, I use the text in a performance a few years ago.
Various instruments scattered in an outdoor hallway near a coffee shop. A 4
way conjunction was in the sky. Each instrument had a rhythm pattern that
reflected its rotation period. Kepler stood on a soapbox and was preaching
this as people walked by or stood and listened. As most raving, no one
could follow him. The truth sometimes come in such form.
BTW have you played any of his temperments. I have never had the chance
but always suspected that their might be more to them that meets the eye.
My interest in alot of this is to understand why the ancients chose the
ratios they did. It is apart of our tuning history that our roots are in
sacred geometry. If Art has become as Mircea Eliade pointed out" the
secularization of sacred objects", what is this. These days,like the
alchemists, have an keen interest in the opposite

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

> From: "D. Stearns" <stearns@capecod.net>
>
> Paul H. Erlich wrote:
> >Kepler's constructions using Platonic solids were an
> exercise in sheer Platonic numerology

I wish I had time to pelt you with imformation on this topic, but I don't
-- too many concerts.

However I will point out that the numerology didn't seem as meaningless in
Kepler's time as it may in ours -- he put a lot of time and effort in his
adulthood into defending his mother from a charge of witchcraft!

>
> in "On the Sensation of Tone," and Sagan in "Cosmos") using
> the example of Kepler while discussing the pros and cons of
> the Pythagorean tradition. (Both obviously arguing in favor
> of empirical observation and experiment at the expense of
> 'numerology.')

Arthur Koestler wrote a book about Kepler called 'The Watershed', which I
gather was an abridgement of a very long book called "the Sleepwalker" in
which he showed Kepler and Galileo (whose father Vincenzo was a lutenist
and Lute builder who wrote on temperament topics) on opposite sides of a
divide, older world view from modern one. Older one being a good deal more
palatable to my view.

I have seen Kepler credited with being the first to use the terms 'major
and minor modes', by the way.

Judy