Yahoo Tuning Groups Ultimate Backup tuning Crunchiness

> > > [me, Monz]
> > > http://www.egroups.com/message/tuning/11867
> > >
> > > this comparision of orbital periods *only of adjacent planets*
> > > is similar to Paul Erlich's comparison of *dyadic* harmonic
> > > entropy among members of a larger set (such as a chord or
> > > scale).

> > [David J. Finnamore]
> > http://www.egroups.com/message/tuning/11894
> >
> > Analogous, yes, but are they really similar in any musically
> > relevant way?

> [Paul Erlich]
> http://www.egroups.com/message/tuning/11907
>
> Well, the cycles of adjacent planets and moons do tend to lock
> into simple-integer ratios,

Which was pretty much my point.

> [Paul]
>
> though they I don't know if they always manage to do so.
> Non-adjacent planets or moons might have very complex
> ratios as a result.

Below I give tables showing all the orbital ratios as decimal
values, to 4 significant digits. I also give the orbital periods
in Earth-days, which means that the values can be calculated
with much greater accuracy by anyone who wants to do it.
(I've done it, but it won't fit here; listen to the piece
to hear the accurate values.)

In the 'addendum' at the bottom of this post, there are two
charts showing how closely these values fit various low-integer
ratios, with the percentage error. In my previous post on this,
http://www.egroups.com/message/tuning/11867
I already pointed out the planetary relationships that had the
closest fit to low-integer ratios (but I used 23-limit there);
here they are quantified, and many other less-good rational
approximations are shown.

> [Paul]
>
> On the other hand, I've been considering dyadic harmonic
> entropy for all the notes in a set, adjacent or otherwise;
> if I only considered adjacent ones, it would be more analogous
> to the solar system.

I was going to add that statement to my original post, but I
guess I thought it was obvious enough for anyone who's been
following the harmonic entropy threads... that's why I used
the emphases that I did.

> [Paul Erlich]
> http://www.egroups.com/message/tuning/11906
>
> But what does this have to do with tuning?

To answer David directly, and you too, Paul: this is
musically relevant because I've suggested a collaboration
on a 'solar system' piece here, and in fact as I was writing
this post, it got so long and involved, and inspired me so
strongly to work on the piece I've been suggesting, that
I just decided to disconnect from the internet and work
on the piece myself. I stayed up all night to write this
post, and here's the piece:

http://www.egroups.com/files/tuning/monz/solarsystem/solar.gif

The basic orbital data
----------------------

Orbital periods of planets (in Earth-units):

days years
Mercury 87.97 0.24
Venus 224.70 0.62
Earth 365.26 1.00
Mars 686.98 1.88
Jupiter 4332.71 11.86
Saturn 10759.50 29.46
Uranus 30685.00 84.00
Neptune 60190.00 164.80
Pluto 90800 247.70

(NOTE: many sources give Pluto's period as 248.5 Earth-years.
I got this data from a NASA website, and assume it to be the
most recent and accurate.)

Ratios of orbital periods of the solar system:

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto
Mercury 1.000 2.554 4.152 7.809 49.24 122.3 348.8 684.3 1028
Venus 0.391 1.000 1.626 3.057 19.28 47.89 136.5 267.9 402.6
Earth 0.241 0.615 1.000 1.881 11.86 29.46 84.00 164.8 247.7
Mars 0.128 0.327 0.532 1.000 6.306 15.66 44.66 87.62 131.7
Jupiter 0.020 0.052 0.084 0.159 1.000 2.484 7.083 13.90 20.89
Saturn 0.008 0.021 0.034 0.064 0.403 1.000 2.851 5.594 8.408
Uranus 0.003 0.007 0.012 0.022 0.141 0.351 1.000 1.962 2.949
Neptune 0.001 0.004 0.006 0.011 0.072 0.179 0.510 1.000 1.503
Pluto 0.001 0.002 0.004 0.008 0.048 0.119 0.339 0.665 1.000

Notice anything familiar? Why, it's nothing other than
an Interval Matrix! We're used to seeing tables like this
filled with fractional ratios (one need go no farther than
Partch's _Genesis of a Music_ for an example); this is the
same thing but in decimal format.

Given the fact that the planetary distances increase
logarithmically, just like our perception of musical ratios,
I have given all numbers to the same number of significant
digits - in this case, 4 digits, so that it would fit here.
6 significant digits would provide pretty reasonable accuracy,
and can be calculated from the table above this one.

Each row in the chart shows orbital periods from the point
of view of an observer on the planet listed on the left,
in terms of that planet's 'years' or fractions thereof.

Each column shows how many times the planets revolve around
the Sun in terms of that planet's 'year'.

So the numbers less than 1 are the reciprocals of the corresponding
relationship given by the number greater than 1. For example,
Jupiter revolves around the Sun in 11.86 Earth-years, and the
Earth revolves around the Sun in 1/11.86 = ~0.08 Jupiter-years.

Observe how 1.00 (the 1/1) flows diagonally down the center of
the chart. In mapping the orbital frequencies as sounds, we
can show all 36 planetary relationships as either an otonality or
a utonality. The otonality representation utilizes all the numbers
larger than 1, and the utonality all the numbers less than 1.

My 'Solar System' Piece
-----------------------

This piece is going to be a work in progress. I'm starting
it off with a simple demonstration of the orbital periods
of the 9 planets as a sustained 9-note chord. I use a
reed-organ (harmonium) timbre, so as to be free from vibrato;
the beating you hear is caused by slight differences in pitch.

The obvious starting point was to take the frequency values
from the 'Pluto' column, since they give a nice easy 1/1 at
the bottom, and it made sense to me to have the slowest planet
give the lowest note. So I used Pluto's orbital period as the
1/1 and all the closer planets as the higher pitches of the chord.

(I'm using the greatest pitch-bend resolution, 4096 units
per semitone.)

'8ve' + Semitones = MIDI-note + pitch-bend
Mercury 10 0.08 C 10 + 309
Venus 8 7.84 G# 8 - 653
Earth 7 11.43 B 7 +1759
Mars 7 0.49 C 7 +2020
Jupiter 4 4.61 F 4 -1585
Saturn 3 0.86 Db 3 - 569
Uranus 1 6.72 G 1 -1140
Neptune 0 7.05 G 0 + 223
Pluto 0 0.00 C 0 0

Thru *my* speakers, Pluto is inaudible, Neptune can just
barely be heard, Uranus is a low growl, and Mercury can
just barely be heard (it may be beyond the MIDI-note range).
The greater-than-10-'8ve' ratio between Mercury and Pluto
forced me to map each of them at the respective limits of
the human audible frequency range.

What's most surprising is that the overall sound rings out
quite clearly as something resembling a major chord!

Mercury, Earth, Mars, and Saturn all fall fairly close
to '8ves' of Pluto's 1/1 (if you isolate Earth and Saturn
they pretty much give a 'major 7th'); Venus, Uranus, and
Neptune all give something close to the '8ves' of the
3rd harmonic, and Jupiter sounds like an '8ve' of the
5th harmonic.

(see the '8ve'-reduced pitch graph)
http://www.egroups.com/files/tuning/monz/solarsystem/solar.gif

Using Pluto as 1/1 is rather arbitrary. Since the planets and
the Sun all formed together out of a disk of rotation gas, it
would make much more sense to use the Sun's period of rotation
(25.38 Earth-days) as a 'guide tone' (in Fokker's sense),
and calculate all the planet's periods as subharmonics of
that:

Sun 1.0
Mercury 0.288507446
Venus 0.112950601
Earth 0.069484751
Mars 0.036944307
Jupiter 0.005857766
Saturn 0.002358846
Uranus 0.000827114
Neptune 0.000421665
Pluto 0.00028052

Since the relative orbital periods are still the same,
if the Sun is omitted the chord would have the same sound
as the one I used, because the ratio between the Sun and
Pluto is impossible to represent within the human audible
range - either one of them must be given a note beyond
the audible frequency limit to make all the other planets
audible.

Ideas for extending the piece
-----------------------------

I'd also like to include the planetary distance data
in the piece somehow, but since the orbital distances *are*
periodic frequencies, it makes sense to map *them* as musical
pitch frequencies. After a similar experiment, but one which
mapped the planetary *distances* as pitch, David Finnamore
agreed that orbital period made more sense:
http://www.egroups.com/message/tuning/11894

Perhaps the planet's rate of rotation can be mapped as meter,
with the frequency sounding at the rate of one note per day
(of that particular planet's timescale, based on its rotation),
and the precise distance from the sun can be mapped as some
sort of timbral change. ...?

So it would be a La Monte Young-type piece consisting of a
droning chord whose notes have periodic timbral shifts.
Also, one of the parameters should be mapped to amplitude.

With a little more imagination, there are lots of other
data that could be mapped, such as orbital inclination
(above or below the Sun's equator) and obliquity (the
planet's rotational tilt from its orbital plane). To
make things really complicated, one could throw in stuff
like precession and nutation. The list goes on and on...
everything in the solar system (the universe?) that occurs
over long periods of time, repeats at periodic frequencies.

It would be really interesting to include the data about
the satellites, asteroids, and comets too... and how about
planetary impacts? Wow, what a fantastic sound!
Talk about 'music of the spheres'!

This may turn out to be a really useful endeavor, too:
I've mentioned before how mapping data aurally can allow
us to perceive patterns that we might not notice visually.

Perhaps listening to an accurate aural mapping of the solar
system's frequencies would allow us to hear patterns that
would enable us to predict such important things as major
asteroid or comet impacts on Earth.

Addendum
--------

Here is the interval matrix again, converted into semitones,
for easy comparison with common low-integer musical ratios.
(I removed the 'utonal' numbers so that the chart would fit
here; they're redundant anyway, as described above.)

Note the 841 cents (almost exactly a 13:8) of Venus/Earth,
and the 705 cents (extremely close to 3:2) of Neptune/Pluto.
Other relationships between adjacent planets which are close
to musical ratios are Mercury/Venus (fairly close to 18:7,
the '8ve' of the 9:7 'septimal 3rd'), Earth/Mars (just ~6
cents wider than the 15:8 'major 7th'), and Jupiter/Saturn
(~11 narrower than 5:2, the '8ve' of the 5:4 'major 3rd').

SEMITONES:

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto
Mercury 0.00 16.23 24.65 35.58 67.46 83.21 101.35 113.02 120.08
Venus 0.00 8.41 19.35 51.23 66.98 85.12 96.79 103.84
Earth 0.00 10.94 42.82 58.57 76.71 88.37 95.43
Mars 0.00 31.88 47.63 65.77 77.44 84.49
Jupiter 0.00 15.75 33.89 45.56 52.61
Saturn 0.00 18.14 29.81 36.86
Uranus 0.00 11.67 18.72
Neptune 0.00 7.05
Pluto 0.00

For those who want to know some other planetary orbital data:

(time is given in Earth-units; incl.=inclination,
ecc.=eccentricity; obliquity and inclination measured in degrees)

rotation obliquity incl. ecc.
hours days
Mercury 1403.49 58.65 0 7 .206
Venus 5814.99 243.0 178 3.39 .007
Earth 23.93 1.000 23.4 0.00 .017
Mars 24.55 1.026 25 1.85 .093
Jupiter 9.8 0.410 3.08 1.31 .048
Saturn 10.2 0.426 26.7 2.49 .056
Uranus 17.9 0.748 97.9 0.77 .047
Neptune 19.1 0.798 29.6 1.77 .009
Pluto 152.91 6.39 122.5 17.15 .248

Notes:

Because Venus, Uranus, and Pluto are tilted more than
90 degrees, they seem to us to be rotating backwards,
with apparent obliquities of 2, 82.1, and 57.5 degrees
respectively. In either case, Uranus appears tilted onto
its side.

Charts showing percentage error from ratios
-------------------------------------------

The percentage of error I obtained is greatly dependent
on the integer-limit I chose for my rational denominators,
which was 14. Including larger denominators, particularly
primes, would result in some planetary relationships coming
much closer to a low-integer ratio. I leave this as a
project for the reader...

Here is a table showing the smallest errors of rational
approximations from the actual orbital periods, based on
my 14-integer-denominator-limit, and ranked by amount of
error from least to greatest. I chose 2.18% error as
the arbitrary cut-off point.

Note both the very low integers of the ratio as well as
the tiny error for the Venus/Earth synchronicity (astronomers
call it 'resonance', and it happens to be one of my favorite
musical intervals, 13:8), and the very small errors for the
approximations of 2:3 for Neptune/Pluto and 2:5 for Jupiter/Saturn.

Also, even tho it's not a particularly small number, the
Earth/Uranus ratio is so close to 1:84 that multiplying it
by every integer thru 14 did not produce any close approximation.

Planets ratio % error

uranus/earth 84:1 0.00
uranus/jupiter 85:12 0.01
saturn/mars 47:3 0.02
jupiter/mars 82:13 0.03
venus/earth 8:13 0.03
earth/mercury 54:13 0.04
venus/mercury 23:9 0.05
neptune/saturn 28:5 0.11
mars/mercury 86:11 0.11
uranus/jupiter 78:11 0.12
neptune/pluto 2:3 0.20
uranus/saturn 20:7 0.20
saturn/venus 48:1 0.23
pluto/saturn 59:7 0.24
uranus/jupiter 71:10 0.25
jupiter/venus 58:3 0.28
mars/mercury 47:6 0.31
earth/mercury 25:6 0.35
neptune/saturn 73:13 0.38
uranus/jupiter 64:9 0.40
mars/earth 17:9 0.43
neptune/mars 88:1 0.43
pluto/saturn 76:9 0.43
jupiter/mars 19:3 0.44
mars/venus 43:14 0.46
mars/mercury 102:13 0.47
pluto/jupiter 21:1 0.55
saturn/mars 63:4 0.55
neptune/saturn 45:8 0.55
uranus/jupiter 57:8 0.60
mars/mercury 55:7 0.61
mars/venus 40:13 0.64
saturn/jupiter 5:2 0.64
earth/venus 18:11 0.67
venus/mercury 18:7 0.67
earth/mercury 46:11 0.72
neptune/jupiter 14:1 0.75
neptune/saturn 62:11 0.76
uranus/mars 45:1 0.76
uranus/saturn 23:8 0.83
uranus/jupiter 50:7 0.85
mars/venus 37:12 0.85
mars/earth 19:10 1.02
earth/venus 23:14 1.06
pluto/saturn 17:2 1.09
mars/venus 34:11 1.10
venus/mercury 31:12 1.14
jupiter/venus 39:2 1.15
earth/mercury 21:5 1.15
jupiter/uranus 1:7 1.18
jupiter/earth 12:1 1.18
earth/mars 7:13 1.27
neptune/saturn 17:3 1.30
uranus/saturn 26:9 1.32
mars/venus 31:10 1.40
jupiter/mars 32:5 1.49
mars/earth 21:11 1.50
venus/earth 5:8 1.60
uranus/saturn 29:10 1.71
saturn/neptune 2:11 1.71
pluto/uranus 3:1 1.74
mars/venus 28:9 1.76
venus/mercury 13:5 1.79
saturn/uranus 5:14 1.83
mars/earth 23:12 1.91
venus/mars 1:3 1.91
neptune/uranus 2:1 1.94
saturn/mars 16:1 2.15
mercury/venus 2:5 2.17

------

And here is a more comprehensive table showing all the
significant low-integer approximations to the orbital periods,
within my 14-integer-denominator-limit. Relationships are
ranked by planetary order from the Sun.

Comparisons between widely-separated planets (i.e., between
any of the 'gas giants' and any of the smaller inner planets)
are going to be very close to integer ratios, because one of
the numbers is already extremely large; in most of these cases
I have given only two ratios: the most accurate (within my 14-limit)
and the smallest-integer.

Planets ratio % error

mercury/venus 5:13 -1.76
mercury/venus 2:5 2.17
mercury/venus 3:8 -4.21

mercury/earth 1:4 3.80
mercury/earth 3:13 -4.18
mercury/earth 2:9 -7.73

mercury/mars 1:8 -2.38

venus/mercury 23:9 0.05
venus/mercury 28:11 -0.35
venus/mercury 33:13 -0.62
venus/mercury 18:7 0.67
venus/mercury 31:12 1.14
venus/mercury 13:5 1.79
venus/mercury 26:10 1.79
venus/mercury 5:2 -2.13
venus/mercury 8:3 4.40

venus/earth 8:13 0.03
venus/earth 5:8 1.60
venus/earth 3:5 -2.47
venus/earth 7:11 3.44
venus/earth 9:14 4.50

venus/mars 1:3 1.91

venus/jupiter 1:14 37.71

earth/mercury 54:13 0.04
earth/mercury 29:7 -0.22
earth/mercury 25:6 0.35
earth/mercury 33:8 -0.65
earth/mercury 46:11 0.72
earth/mercury 37:9 -0.99
earth/mercury 21:5 1.15
earth/mercury 17:4 2.36
earth/mercury 4:1 -3.66

earth/venus 13:8 -0.03
earth/venus 21:13 -0.63
earth/venus 18:11 0.67
earth/venus 23:14 1.06
earth/venus 8:5 -1.57
earth/venus 5:3 2.53
earth/venus 11:7 -3.33
earth/venus 7:4 7.66
earth/venus 3:2 -7.72

earth/mars 7:13 1.27
earth/mars 6:11 2.59
earth/mars 5:9 4.49
earth/mars 1:2 -5.96
earth/mars 4:7 7.47

earth/jupiter 1:12 -1.17
earth/jupiter 1:11 7.82
earth/jupiter 1:13 -8.77

mars/mercury 86:11 0.11
mars/mercury 39:5 -0.12
mars/mercury 109:14 -0.30
mars/mercury 47:6 0.31
mars/mercury 70:9 -0.40
mars/mercury 102:13 0.47
mars/mercury 55:7 0.61
mars/mercury 31:4 -0.76
mars/mercury 23:3 -1.83
mars/mercury 8:1 2.44

mars/venus 43:14 0.46
mars/venus 40:13 0.64
mars/venus 37:12 0.85
mars/venus 34:11 1.10
mars/venus 31:10 1.40
mars/venus 28:9 1.76
mars/venus 3:1 -1.87

mars/earth 15:8 -0.31
mars/earth 17:9 0.43
mars/earth 19:10 1.02
mars/earth 13:7 -1.26
mars/earth 21:11 1.50
mars/earth 24:13 -1.84
mars/earth 23:12 1.91
mars/earth 11:6 -2.52
mars/earth 9:5 -4.30

mars/jupiter 2:13 -2.99
mars/jupiter 1:6 5.10
mars/jupiter 1:7 -9.92

mars/saturn 1:14 11.88

jupiter/mercury 197:4 0.01
jupiter/mercury 49:1 -0.50

jupiter/venus 212:11 -0.03
jupiter/venus 135:7 0.04
jupiter/venus 19:1 -1.45

jupiter/earth 83:7 -0.02
jupiter/earth 154:13 -0.12
jupiter/earth 95:8 0.13
jupiter/earth 71:6 -0.22
jupiter/earth 107:9 0.24
jupiter/earth 119:10 0.34
jupiter/earth 130:11 -0.35
jupiter/earth 59:5 -0.51
jupiter/earth 47:4 -0.93
jupiter/earth 12:1 1.18

jupiter/mars 82:13 0.03
jupiter/mars 63:10 -0.09
jupiter/mars 44:7 -0.32
jupiter/mars 19:3 0.44
jupiter/mars 69:11 -0.53
jupiter/mars 25:4 -0.89
jupiter/mars 32:5 1.49
jupiter/mars 13:2 3.08
jupiter/mars 6:1 -4.85

jupiter/saturn 2:5 -0.64
jupiter/saturn 5:12 3.50
jupiter/saturn 5:13 -4.46

jupiter/uranus 1:7 1.18
jupiter/uranus 2:13 8.96

jupiter/neptune 1:14 -0.75
jupiter/neptune 1:13 6.89

jupiter/pluto 1:14 49.18

saturn/mercury 367:3 0.01
saturn/mercury 489:4 -0.06
saturn/mercury 245:2 0.15
saturn/mercury 122:1 -0.26

saturn/venus 431:9 0.00
saturn/venus 48:1 0.23

saturn/earth 383:13 0.01
saturn/earth 324:11 -0.02
saturn/earth 265:9 -0.05
saturn/earth 206:7 -0.11
saturn/earth 59:2 0.14
saturn/earth 147:5 -0.20
saturn/earth 88:3 -0.43
saturn/earth 29:1 -1.56

saturn/mars 47:3 0.02
saturn/mars 219:14 -0.13
saturn/mars 172:11 -0.17
saturn/mars 204:13 0.18
saturn/mars 157:10 0.23
saturn/mars 125:8 -0.25
saturn/mars 110:7 0.32
saturn/mars 78:5 -0.41
saturn/mars 63:4 0.55
saturn/mars 31:2 -1.04
saturn/mars 16:1 2.15

saturn/jupiter 5:2 0.64
saturn/jupiter 32:13 -0.90
saturn/jupiter 27:11 -1.18
saturn/jupiter 22:9 -1.59
saturn/jupiter 17:7 -2.23
saturn/jupiter 12:5 -3.38
saturn/jupiter 7:3 -6.06

saturn/uranus 5:14 1.83
saturn/uranus 4:11 3.68
saturn/uranus 1:3 -4.96
saturn/uranus 3:8 6.92

saturn/neptune 2:11 1.71
saturn/neptune 1:6 -6.77
saturn/neptune 1:5 11.88

saturn/pluto 1:9 -6.58
saturn/pluto 1:8 5.10

uranus/mercury 1395:4 -0.01
uranus/mercury 1046:3 -0.03
uranus/mercury 349:1 0.06

uranus/venus 1502:11 0.00
uranus/venus 273:2 -0.03
uranus/venus 137:1 0.33

uranus/earth 84:1 0.00

uranus/mars 134:3 0.01
uranus/mars 357:8 -0.08
uranus/mars 223:5 -0.14
uranus/mars 89:2 -0.36
uranus/mars 45:1 0.76

uranus/jupiter 85:12 0.01
uranus/jupiter 92:13 -0.08
uranus/jupiter 78:11 0.12
uranus/jupiter 99:14 -0.16
uranus/jupiter 71:10 0.25
uranus/jupiter 64:9 0.40
uranus/jupiter 57:8 0.60
uranus/jupiter 50:7 0.85
uranus/jupiter 7:1 -1.17

uranus/saturn 37:13 -0.18
uranus/saturn 20:7 0.20
uranus/saturn 17:6 -0.63
uranus/saturn 23:8 0.83
uranus/saturn 31:11 -1.16
uranus/saturn 26:9 1.32
uranus/saturn 29:10 1.71
uranus/saturn 14:5 -1.80
uranus/saturn 11:4 -3.55
uranus/saturn 3:1 5.21

uranus/neptune 1:2 -1.90
uranus/neptune 7:13 5.64

uranus/pluto 1:3 -1.71
uranus/pluto 5:14 5.31
uranus/pluto 4:11 7.23

neptune/merc. 2737:4 0.00
neptune/mercury 684:1 -0.04

neptune/venus 2411:9 0.00
neptune/venus 2679:10 0.00
neptune/venus 268:1 0.04

neptune/earth 824:5 0.00
neptune/earth 165:1 0.12

neptune/mars 701:8 0.00
neptune/mars 263:3 0.05
neptune/mars 175:2 -0.14
neptune/mars 88:1 0.43

neptune/jupiter 139:10 0.03
neptune/jupiter 125:9 -0.05
neptune/jupiter 14:1 0.75

neptune/saturn 28:5 0.11
neptune/saturn 67:12 -0.19
neptune/saturn 73:13 0.38
neptune/saturn 39:7 -0.40
neptune/saturn 45:8 0.55
neptune/saturn 50:9 -0.69
neptune/saturn 62:11 0.76
neptune/saturn 17:3 1.30
neptune/saturn 11:2 -1.68
neptune/saturn 6:1 7.26

neptune/uranus 27:14 -1.70
neptune/uranus 2:1 1.94

neptune/pluto 2:3 0.20
neptune/pluto 9:14 -3.38
neptune/pluto 9:13 4.06
neptune/pluto 7:11 -4.35

pluto/mercury 2057:2 0.00
pluto/mercury 1028:1 -0.05

pluto/venus 805:2 -0.04
pluto/venus 2013:5 -0.01
pluto/venus 1208:3 0.00
pluto/venus 403:1 0.09

pluto/earth 2477:10 0.00
pluto/earth 248:1 0.12

pluto/mars 1317:10 0.00
pluto/mars 395:3 -0.02
pluto/mars 132:1 0.23

pluto/jupiter 188:9 0.02
pluto/jupiter 167:8 -0.05
pluto/jupiter 125:6 -0.25
pluto/jupiter 104:5 -0.41
pluto/jupiter 21:1 0.55

pluto/saturn 42:5 -0.10
pluto/saturn 101:12 0.10
pluto/saturn 59:7 0.24
pluto/saturn 67:8 -0.39
pluto/saturn 76:9 0.43
pluto/saturn 92:11 -0.53
pluto/saturn 17:2 1.09
pluto/saturn 25:3 -0.89
pluto/saturn 8:1 -4.85

pluto/uranus 41:14 -0.69
pluto/uranus 38:13 -0.87
pluto/uranus 35:12 -1.09
pluto/uranus 32:11 -1.35
pluto/uranus 29:10 -1.66
pluto/uranus 3:1 1.74

pluto/neptune 3:2 -0.20

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

Crunchiness

🔗Keenan Pepper <mtpepper@prodigy.net>

🔗Monz <MONZ@JUNO.COM>

🔗Monz <MONZ@JUNO.COM>

🔗Monz <MONZ@JUNO.COM>

🔗Joseph Pehrson <josephpehrson@compuserve.com>