Re Solar System Chord

Hi Monz,

I've done a first approximation to the solar system chord.

It is intended as first idea, just to get an overall impression of what it will sound like.

Leaves out Mercury and Pluto.

An astronomer friend pointed out that you can use a sine wave added
to a circle as a good first approx. to an ellipse.

So used that, which made it possible to use options already in FTS.

By equal areas rule, fastest and slowest angular velocites are proportional
to inverses of nearest and furthest distances, i.e. aphelion and perihelion.

Joe Monzo's post on the scale data:
/tuning/topicId_11954.html#11995

Data used for MIDI clip:

Headers link to source for aphelion / perihelion data in html version of table MERCURY VENUS EARTH MARS JUPITER SATURN URANUS NEPTUNE PLUTO
Orbital period (years) 0.24084 0.615187 1.0 1.8808 11.8621 29.458 84.01 164.79 248.54

Aphelion (millions of km) 69.8 108.9 152.1 249.2 816.0 1,506.4 3,005.2 4,535.2 7381.2

Perihelion 46.0 107.5; 147.1 206.6 740.6 1,347.6 2,734.0 4,458.0 4445.8

Scale (cents) 12013 10390 9548.8 8455.2 5266.9 3692.1 1877.8 711.42 1/1
Scale step to previous planet as ratios (within 12 cents) 1/1 23/9 13/8 15/8 19/3 5/2 17/6 51/26 3/2
Freq of note. (Hz) 22655 8869.3 5456.2 2901 459.97 185.22 64.948 33.11 21.953
Pitch range (cents) 721.91 22.401 57.867 324.56 167.85 192.85 163.74 29.724 877.7
Time for one orbit 5 secs 7.541 secs 14.792 secs 42.18 secs 1 min 44.76 secs 11 mins 0.72 secs 20 mins 42.69 secs 33 mins 40 secs 85 mins 59.8 secs

Here is the MIDI file:
http://homepage.ntlworld.com/robertwalker/fts/jm_solar_system_chord_no_mercury_or_pluto2_m0.2hz.mid
(5 mins, 165 Kb)
Pitch bends applied only 20 times per second to reduce file size.

As a broken chord, with the orbits speeded up 1000 times:
http://homepage.ntlworld.com/robertwalker/fts/jm_solar_system_chord_no_mercury_or_pluto2_m20hz.mid
Venus is the high cicada like one, and Earth the warbler like one below it.

Times for one orbit in secs:
(50), 20, 12, 6, 1, 0.4, 0.14, 13.2 per sec, (20 per sec)

Notes:

Started all the orbits at the mid position (i.e. descending node - rise in pitch).

Pluto should have its descending node offset relative to Neptune, but since it is left out
that is okay.

By Kronecker's theorem in eight dimensions, the other eight planets will line up
arbitrarily closely every so often (assuming there are no other exact ratios involved).

So this is close to some actual epoch.

Mercury varies in pitch too much for the standard MIDI pitch bend range of + - 200 cents.

It will be possible to handle this by changing the pitch bend range
as I do already for the "joystick theremin" Ok to change pitch bend range
tick box

Mars is okay if it starts within less than 35 cents of concert pitch. To make sure of that, I set
the 1/1 of the scale 10 cents sharp of concert pitch.

Pluto varies too much as well, but since it changes so slowly, it will take a fair while to reach that
point in its orbit.

Calculations (from pluto inwards)

Orbit scale:

248.54/248.54 248.54/164.79 248.54/84.01 248.54/29.458 248.54/11.8621 248.54/1.8808 248.54/1.0
248.54/0.615187 248.54/0.24084
=
1/1 1.5082 2.9585 8.4371 20.952 132.15 248.54 404.01 1032

As cents:
0.0 711.42 1877.8 3692.1 5266.9 8455.2 9548.8 10390.0 12013.0

Pitch range:
69.8/46.0 108.9/107.5 152.1/147.1 249.2/206.6 816.0/740.6
1506.4/1347.6 3005.2/2734.0 4535.2/4458.0 7381.2/4445.8
As cents:
721.91 22.401 57.867 324.56 167.85 192.85 163.74 29.724 877.7

Time for one orbit - set Mercury to 0.2
In seconds:
0.2/1031.96 2.55434*0.2/1031.96 4.15213*0.2/1031.96 7.80934*0.2/1031.96 49.2531*0.2/1031.96 122.314*0.2/1031.96 348.819*0.2/1031.96 684.228*0.2/1031.96 1031.96*0.2/1031.96
=
0.000193806 0.000495046 0.000804708 0.0015135 0.00954554 0.0237052 0.0676032 0.132607 1/5

Or in seconds per cycle:
1/0.000193806 1/0.000495046 1/0.000804708 1/0.0015135 1/0.00954554 1/0.0237052 1/0.0676032 1/0.132607 1/5
=
5159.8 2020.01 1242.69 660.72 104.761 42.1848 14.7922 7.54108 5

My astronomer friend is interested in linking to the piece from his astronomy web site once we have the visuals done
for it too.

Robert

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_18382.html#18382

This is very interesting and, indeed, sound pretty similar to Monz'
efforts, except there seems to be a high pitch that is like a
Neapolitan...

I wonder which planet that is, and why it differs from the Monz
chord...??

Fun stuff

______ ____ ___ ___ _
Joseph Pehrson

Uh-oh.

I didn't receive Robert's original message on this topic, or his reply to
Joseph, but they're there on the archives.

If they don't come through on my e-mail within the next few days, I might
have to change my vote for Yahoo!

P.S. I can't believe so many people are having trouble converting their
account -- it seemed so easy to me -- go to http://groups.yahoo.com/. On the
upper left is says "Sign In". The third line under that says "eGroups
users", and under that is says "Link your accounts here". Click on that and
the rest should be self-explanatory (I hope!)