Yahoo Tuning Groups Ultimate Backup tuning RE: [tuning] Re: my 'Solar System' piece (was: 'music of the sphe res')

A Google search on "Orbital Resonances" reveals the following (at
http://www.google.com/search?q=cache:gbms01.uwgb.edu/~dutchs/planets/resonan
c.htm+orbital+resonances&hl=en:

>Resonances result when two celestial objects interact with each other
>gravitationally at regular intervals. The regularity of the interaction can
do >one of two things:

>Lock the two objects in step so they repeat the same patterns of movement.
>Perturb one or both bodies enough to break up the resonance.

So Monz and Kraig/Banashphu are both right! But Monz would do well to heed
Kraig/Banashphu's warning, that it's possible to find a simple ratio close
to any proportion, and that alone does not prove that resonance is at work.

Also see:

http://www.treasure-troves.com/physics/OrbitalResonances.html

Also, from
http://www.britannica.com/bcom/eb/article/printable/5/0,5722,119065,00.html:
There are stable configurations in the restricted three-body problem that
are not stationary in the rotating frame. If, for example, Jupiter and the
Sun are the two massive bodies, these stable configurations occur when the
mean motions of Jupiter and the small particle--here an asteroid--are near a
ratio of small integers. The orbital mean motions are then said to be nearly
commensurate, and an asteroid that is trapped near such a mean motion
commensurability is said to be in an orbital resonance with Jupiter. For
example, the Trojan asteroids librate (oscillate) around the 1:1 orbital
resonance (i.e., the orbital period of Jupiter is in a 1:1 ratio with the
orbital period of the Trojan asteroids); the asteroid Thule librates around
the 4:3 orbital resonance; and several asteroids in the Hilda group librate
around the 3:2 orbital resonance. There are several such stable orbital
resonances among the satellites of the major planets and one involving the
planets Pluto and Neptune. The analysis based on the restricted three-body
problem cannot be used for the satellite resonances, however, except for the
4:3 resonance between Saturn's satellites Titan and Hyperion, since the
participants in the satellite resonances usually have comparable masses.

Although the asteroid Griqua librates around the 2:1 resonance with Jupiter,
and Alinda librates around the 3:1 resonance, the orbital commensurabilities
2:1, 7:3, 5:2, and 3:1 are characterized by an absence of asteroids in an
otherwise rather highly populated, uniform distribution spanning all of the
commensurabilities. These are the Kirkwood gaps in the distribution of
asteroids, and the recent understanding of their creation and maintenance
has introduced into celestial mechanics an entirely new concept of
irregular, or chaotic, orbits in a system whose equations of motion are
entirely deterministic.

http://www.google.com/search?q=cache:gbms01.uwgb.edu/~dutchs/planets/resonan
c.htm+orbital+resonances&hl=en:
Certain resonances seem to enhance orbital stability by locking bodies in
step in such a way they avoid conflict. 3:2 resonances seem to be especially
effective. Pluto crosses Neptune's orbit, but its period is 3/2 that of
Neptune, so the two objects never approach closely. Of the 40-plus objects
discovered orbiting beyond Neptune since 1992, an astounding 40% have
periods very close to Pluto's and are also in 3:2 resonance with Neptune.
These objects have been dubbed "plutinos".

🔗Kraig Grady <kraiggrady@anaphoria.com>

Paul!
(As announced earlier I am back and banaphshu is gone for the moment.) That 365.26 divided
by 13 then times 8 is 224.77 is as close as one can get i would imagine to matching the
rotation of Venus. a little over an hour an a half. PHI is over a day off. I believe for the
ancients the relationships that were more interested in were of repeated conjunctions as
opposed to a sidereal measure of rotation. MONZ! do you know how to compute these, I do not
but could use them in deciphering some features of the Anaphorian calendar.

"Paul H. Erlich" wrote:

> Monz wrote,
>
> >But you have to be careful to make sure that your ideas are
> >reconciled with the physical facts. Astronomers are certain
> >that the Venus/Earth 13:8 ratio (actually, they seem to recognize
> >it more as 8:5, but 13:8 is much more precise)
>
> Monz, that uncertainty between 8:5 and 13:8 underscores Kraig/
> point!!! Astronomers would certainly not claim that the planets were
> _locked_ into an 8:5 ratio if the true ratio was 13:8! Also, both of these
> ratios are suspiciously close to the golden ratio, which is approximated
> better and better by adjacent members of the Fibonacci series: 2:1, 3:2,
> 5:3, 8:5, 13:8, etc.
>
> But I'll have to check on this and get back to you guys as to whether it's
> just revolutionary periods, or in fact also rotational periods, that favor
> simple ratios.
>
>

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

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kraig Grady <kraiggrady@anaphoria.com>

Paul!
Well not exactly, for the inner planets. for instance if we were looking at Venus and the
Sun from our POE after 224 days the earth would have moved and it would take more time for it
to catch up. For the exterior planets we would have a similar phenomenon in that lets say
between Jupiter and saturn the conjunction would be longer because when Jupiter gets back to
where it started (its year) saturn has moved and need to catch up. Even conjunctions with the
outer planets and the sun are always longer than one of our years for the same reason. Pluto
being the closest. These are I believe are referred to as Synodal Periods.

"Paul H. Erlich" wrote:

> Kraig wrote,
>
> >I believe for the ancients the relationships that were more interested in
> were of repeated conjunctions as >opposed to a sidereal measure of rotation
>
> The ratio would be the same either way.
>
>

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

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Monz <MONZ@JUNO.COM>

> [Kraig Grady]
> http://www.egroups.com/message/tuning/11961
>
> Monz and Paul!
> Just ran across this interesting bit Look about half way down.
> I need to look at this more!
> http://www3.bc.sympatico.ca/JNHDA/sbb4d2.htm

Wow, Kraig, this is interesting stuff! Many galaxies (including
the one we're living in) form as spiral accretions of gas and
dust, just like this pattern! So if the solar system followed
the same 'rules', then it happens cosmologically on many different
levels the same way.

I also note the resemblance of this graphic with Erv's 'harmonic
spiral' graph that I love so much (cover of _Xenharmoniko^n_ 6).
Yes, folks, this is about tuning!

I have a longer post on the way discussing much of what you
said; it's amazing how this thread has tapped into so much
of the recent research I've done in the wake of my study of
Sumerian music! It's like I can just sift thru my notes from
this summer and assemble them into posts.

(There ya go, Dan Stearns, for the answer as to why I've been
so absent around here until this week- been busy studying lots
of ancient, and recent, cosmological theories and math.)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗Monz <MONZ@JUNO.COM>

> [Dan Stearns]
> http://www.egroups.com/message/tuning/11975
>
> Cool, quite a vast treasure-trove to mine there...

Yeah - I could spend the rest of my life studying this stuff!

> can't wait to check it all out, as always, I'm sure it will be
> interesting...

I *was* in the process of assembling it all carefully into a
series of webpages, but Troubledoor's appearance here spurred
me into making my recent comments, and more importantly, into
finally beginning my musical 'mapping of cosmic vibrations'.

> Guess I don't have to send you out some sort of Paul Erdos
> motivational speech or something after all!

No, you don't... but thanks for the one you *did* send me
earlier this year! I believe that my 'temperament' (no, here
I'm NOT talking about tuning!) is quite similar to his.
I'm very happy devoting my time to studying patterns in
numbers... and even happier when I can give that study some
sort of musical significance.

-monz
htto://www.ixpres.com/interval/monzo/homepage.html

>
> Dan

🔗Monz <MONZ@JUNO.COM>

Egged on by some of Kraig's criticisms and given a boost by the
astronomy links Paul posted, I decided to hunt down more precise
info on the planets's orbital periods, and to make a more accurate
version of 'Solar System'. Here it is:

http://www.egroups.com/files/tuning/monz/solarsystem/Solar2.mid

There's not a lot of difference, but to my ears, this version is
a bit more strident, and brings out the 'major chord' quality
of the orbital-period ratios even more strongly.

Thru my speakers, I can't hear Pluto or Neptune at all, and
can just barely discern Uranus at the bottom and Mercury at
the top when I turn off all the other planets. I'll leave
these four planets out of my analysis.

The 'major chord' effect is due mainly to Saturn, Jupiter, and
Venus, with Mars reinforcing Saturn 4 '8ves' higher. Earth
adds most of the piquancy with a pseudo-'major 7th'.

So the aural effect (at least as I hear it; 'your mileage may
vary') causes Saturn to sound as the 1/1 - it is actually almost
exactly 3 '8ves' and a 135/128 5-limit 'semitone', or what Ellis
called the 'larger limma' (92 cents), above the inaudible Pluto.

Jupiter is 1 '8ve' and 375 cents higher than Saturn - only
~11 cents narrower than an '8ve' + 5/4.

Mars is about 37 cents below the 4th '8ve' above Saturn. It's
also 2 '8ves' and 788 cents above Jupiter.

Earth is 4 '8ves' and 1057 cents above Saturn - pretty close
to one of my favorite intervals, an 11/6 'neutral 7th' (= 1049
cents). To my ears, the more important audible relationship is
that between Mars and Earth: 1094 cents, only ~6 cents wider than
a 15/8 'major 7th'. I think this stands out quite strongly in
the chord. Earth is also 3 '8ves' + 682 cents above Jupiter.

Venus is very high and bright, almost exactly a 13/8 above Earth
(altho to my ears it really sounds a lot like an 8/5 'minor 6th'),
an '8ve' + 735 cents above Mars, 4 '8ves' + 323 cents above
Jupiter (pretty close to a 6/5 'minor 3rd'), and 5 '8ves' +
698 cents (a nice meantone '5th'!) above Saturn.

Here's the more accurate data, which supercedes the tables in
my original post:

Orbital period
days years

Mercury 87.969 0.24084
Venus 224.701 0.615187
Earth 365.256363 1.0
Mars 686.98 1.8808
Jupiter 4332.71 11.8621
Saturn 29.458
Uranus 84.01
Neptune 164.79
Pluto 248.54

The figure given for the Earth's orbital period is known as
the 'sidereal year': the time it takes for the Earth to make
a complete revolution with respect to the stars. It can also
be expressed as 365 days 6 hours 9 minutes 9.76 seconds.
All 'year' values are given in terms of sidereal years.
I really had to hunt for an accurate value for this, and
finally found it at
http://www.treasure-troves.com/astro/SiderealYear.html

This is different from the 'solar' or 'tropical year', which is
the one we're normally familiar with. This is the time it
takes for the Earth to make a complete revolution with respect
to the Sun's position in our sky. The solar year is 365.2421988
days, or 365 days 5 hours 48 minutes 45.9747 seconds. It is
about 20 minutes 23.8 seconds shorter than the sidereal year.

(Our standard system of leap-years gives a solar year 365.2425
days long, as described at the link above. This means that
after 3319 years 10 months, we will lose a day... I don't
think any of us who are alive now will miss it...)

Again, these are also mean values, because they change slightly
over time.

Here is a table of the semitone values of the orbital ratios:

SEMITONES

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto

Mercury 0.00 16.24 24.65 35.58 67.47 83.21 101.36 113.02 120.13
Venus 0.00 8.41 19.35 51.23 66.98 85.12 96.78 103.90
Earth 0.00 10.94 42.82 58.57 76.71 88.37 95.49
Mars 0.00 31.88 47.63 65.77 77.44 84.55
Jupiter 0.00 15.75 33.89 45.55 52.67
Saturn 0.00 18.14 29.81 36.92
Uranus 0.00 11.66 18.78
Neptune 0.00 7.11
Pluto 0.00

Note that this time I accepted the period of 248.54 years for Pluto,
because the majority (and most recent) of the webpages I've found
use that figure. Can anyone verify the correct value for Pluto?

In any case, the pitch I chose for Pluto's 1/1 is so low that I
can't hear it on my system, and most likely neither can anyone else.
Such is the fate of our cold little faraway planetoid...

-monz
http://www.ixpres.com/interval/monzo/homepage.html