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Min's Planetary Awareness Technique Chapter 12

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Daniel Min, Ph.D.

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Nov 21, 2003, 7:10:05 PM11/21/03
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CHAPTER 12

WHICH BRINGS US TO Neptune, compassing the perimeter of
the solar system, further from the Sun than Pluto about
20 years at a time every 247.92 years over Pluto's side-
real orbit. Neptune's orbit is about two-thirds that at
164.79 years. Neptune, whose universal archetype is the
Hermit of the major arcana, has an orbital eccentricity
of only 0.0086, which is barely more than that of Venus.

Compare Pluto's eccentricity at a whopping 0.2488, or a
fourth again greater ratio between major and minor axis.
Combined with Pluto's steep orbital inclination over 17
degrees compared to Neptune's milder 1.77 degrees slope,
and Pluto's mean heliocentric distance of 3,670,000,000
miles or less than a third more than Neptune's distance
from the Sun, and you'll see why these ancient brothers
cross paths every two and a half centuries, therearound.

The third planet beyond the path of his younger brother
Jupiter, Neptune, known as Poseidon in the Greek, there-
fore holds the trident--third also by the element water
which is Pisces, the Hanged Man of tarot, which Jupiter
rules in his inferior aspect and Neptune rules superior.

At 2,796,000,000 miles from the Sun, the temperature on
the surface of this blue gas giant stays relatively con-
stant at -200C or -328F, very nearly the same as Uranus,
as is its composition. Neptune is only a bit smaller at
30,800 miles in equatorial diameter, spinning around at
16 hours 7 minutes per sidereal day, or 6,000 miles per
hour at the surface on the equator. The tilt of Neptune
on its rotational axis is more than 29 1/2 degrees, but
like Uranus, is much too far from the Sun to affect sur-
face temperatures between seasons, at 41.2 years apiece.

Recall from my Tarot Manual chap 3, the 3:2:1 resonance
of Mercury, which rotates on its nearly plumb axis with
its ecliptic exactly 1.5000 times each 360-degree orbit
(87.97046 earth-days) around the Sun, so that one solar
day on Mercury averages exactly two sidereal years, and
three sidereal rotations of Mercury equals two sidereal
orbits, hence its 3:2:1 ratio of day-to-year resonances.

There's a 3:2 resonance between Neptune and Pluto, such
that Pluto's angular momentum achieves equilibrium with
Neptune by slowly librating between steeper orbits with
reduced tangential velocities, then by declining orbits
with elevated tangential velocities, thereby preventing
any possible collision between them--at least in theory.

While a theory can come and go, we can be sure that the
earliest life forms on Earth probably date back several
billion years. So even with all the catastrophic events
of geological antiquity, life has managed to find a way
to survive and thrive through rain, hail, sleet or snow,
through massive crustal displacements, earthquakes, vol-
canoes, meteoroids, famine, pestilence, war, natural se-
lection, etc. Yet through it all, life goes on on Earth.

This is because the universe itself is one vast, living
organism. People argue about the creation of life, when
life has always been the vibrant energy of the universe.
So life has always existed, and will always continue to
exist, since the universe is infinite as the stars that
illuminate it, as darkness that makes the light visible.

Neptune is the sphere of wisdom, of mysticism, of souls
reaching toward the whiteness of Neptune which is Pluto,
who is the white stone at the geocenter of Earth. There
is a verse in Revelation that refers to a "white pebble"
which is hidden from sight, just as Pluton is invisible:

"qui habet aurem audiat quid Spiritus
who is having an ear is hearing what the Spirit

dicat ecclesiis vincenti
is saying to the ecclesias To the conquering

dabo ei manna absconditum et
I shall give to him manna the absconded and

dabo illi calculum candidum et
I shall give also to him a pebble white and

in calculo nomen novum scriptum quod nemo
in the pebble a name new written which no one

scit nisi qui accipit" (2:17)
is knowing except for him who it is accepting.

In the original Greek, the word for pebble is "psephos",
which means a transparent or white pebble smoothed and
rounded, like those most commonly found in a river bed.
The word psephos is also used for a transparent quartz
lens used to focus sunlight to ignite fires, or to mag-
nify something up close. Its root word "psallo" refers
to singing a melody or hymn, and vibrations of strings
made by plucking or bowing them in order to play music,
to sing hymns by instrumental accompaniment, e.g. harp,
hence to "magnify" the Gods by hymnodic praise in song.

Freedom from bondage is the common theme of every hymn,
as from slavery in Egypt to freedom from sin in Christ,
none of which comes easily, and all of which takes tre-
mendous faith, patience, commitment and responsibility.
To get it, we must give it. To give it, we must get it.
Just as a second prism placed in series with the first
prism reunites a rainbow back into its component white,
the law singing the music of the spheres is transposed
in the iris of Earth--her focus, the eye of the sky in
which the seven modalities splay out into the signs of
the zodiac in Earth's meridian houses which is clearly
made by the planets. The lens is focused on the center
of the Earth by those who reign upon her with dominion.
This focus of the lens is the fixed point of the under-
world, the fixed center of gravity & the fixed sign of
Earth, which is Taurus, the Hierophant, the exaltation
of the Moon ergo Ace of Diamonds in the court of Queen
of Diamonds which is the ensign of Venus-inferior, the
separating force of Venus receding from Earth as symbo-
lized in the old testament by the golden calf of Aaron,
the advocate of worldly living--with all its pleasures
and pains, the sinfulness of Lucifer banished from the
heavens and cast down to the Earth with his angels the
third (the evildoers) who make the gentiles vulnerable.

The exaltation of Venus is Pisces, which is the key of
B-major, the III of Hearts in the court of the Jack of
Hearts, the mutable quality of water and the augmented
fifth which needs resolution, either down to the fifth,
or up to the sixth, i.e. either down to Bb of Aquarius,
or up to C of Aries, respectively--in reference to the
King and Queen of the same element, namely Cancer (Eb)
and Scorpio (G), ergo major-fifth or major-sixth triad.
The exact behavior of Venus in Pisces is charted below:

Pisces - B Ionian
EMPRESS (Venus) - Three of Cups

first decan/destructive water
pisces/violet/b
minus/plus
vii i ii iii iv v vi
bb b db eb e gb ab
ivi vio ror oye yel gbl bin
aqu pis tau can leo lib sag
mer ven sun mar jup sat moo
e e d e

second decan/creative water
cancer/orange-yellow/eb
plus/minus
v vi vii i ii iii iv
bb c d eb f g ab
ivi red ora oye gre blu bin
aqu ari gem can vir sco sag
sat moo mer ven sun mar jup
r r r r

third decan/sustenant water
scorpio/blue/g
minus/plus
iii iv v vi vii i ii
b c d e gb g a
vio red ora yel gre blu ind
pis ari gem leo lib sco cap
mar jup sat moo mer ven sun
f

In the midst of Pisces is Saturn-inferior Mercury in Ge-
mini likewise, Mars in Scorpio & Jupiter in Sagittarius,
their superior ensigns. Venus empowers hope and balance,
appreciation for the fine arts, all beauty both manmade
and natural. Venus is the Empress, beautiful Goddess of
heaven...whose loveliness is in the eye of the beholder.

The accentuation on the tonic pitch key as its modality
is transposed across the chromatic tones of the Earth's
zodiac draws the listener's attention to the uniqueness
between one planet's relative position to other planets
in their diatonic sidereal order, and the transposition
of each planet and its astrological force in the zodiac
right down to the decans and pentads of each sign. Also,
each of the twelve zodiacal signs are bisected into fif-
teen degree arcs, with each consecutive sign continuing
the veritable sinewave of its chromatic vector in three
dimensions. The following charts summarize these forces:

ARC/MODULATION SIG QUA ELE
----------------------------
0 + 15 - 30 Ari Car Fir
30 - 45 + 60 Tau Fix Ear
60 + 75 - 90 Gem Mut Air
90 -105 +120 Can Car Wat
120 +135 -150 Leo Fix Fir
150 -165 +180 Vir Mut Ear
180 +195 -210 Lib Car Air
210 -225 +240 Sco Fix Wat
240 +255 -270 Sag Mut Fir
270 -285 +300 Cap Car Ear
300 +315 -330 Aqu Fix Air
330 -345 +360 Pis Mut Wat
__________________________________________________

|Ari| |Gem| |Leo| |Lib| |Sag| |Aqu|
|15 | |75 | |135| |195| |255| |315|
|/+\| |/+\| |/+\| |/+\| |/+\| |/+\|
0 30 60 90 120 150 180 210 240 270 300 330 360
|\-/| |\-/| |\-/| |\-/| |\-/| |\-/|
|45 | |105| |165| |225| |285| |345|
|Tau| |Can| |Vir| |Sco| |Cap| |Pis|

__________________________________________________

|<---Ari--->| |<---Gem--->|
| | | |
|ari| |sag| |vir| |gem| |aqu| |sco|
| 5 | |25 | |45 | |65 | |85 | |105|
|/+\| |/+\| |/+\| |/+\| |/+\| |/+\|
0 10 20 30 40 50 60 70 80 90 100 110 120
|\-/| |\-/| |\-/| |\-/| |\-/| |\-/|
|15 | |35 | |55 | |75 | |95 | |115|
|leo| |tau| |cap| |lib| |can| |pis|
| | | |
|<---Tau--->| |<---Can--->|
__________________________________________________

|<---Leo--->| |<---Lib--->|
| | | |
|leo| |ari| |cap| |lib| |gem| |pis|
|125| |145| |165| |185| |205| |225|
|/+\| |/+\| |/+\| |/+\| |/+\| |/+\|
120 130 140 150 160 170 180 190 200 210 220 230 240
|\-/| |\-/| |\-/| |\-/| |\-/| |\-/|
|135| |155| |175| |195| |215| |235|
|sag| |vir| |tau| |aqu| |sco| |can|
| | | |
|<---Vir--->| |<---Sco--->|
__________________________________________________

|<---Sag--->| |<---Aqu--->|
| | | |
|sag| |leo| |tau| |aqu| |lib| |can|
|245| |265| |285| |305| |325| |345|
|/+\| |/+\| |/+\| |/+\| |/+\| |/+\|
240 250 260 270 280 290 300 310 320 330 340 350 360
|\-/| |\-/| |\-/| |\-/| |\-/| |\-/|
|255| |275| |295| |315| |335| |355|
|ari| |cap| |vir| |gem| |pis| |sco|
| | | |
|<---Cap--->| |<---Pis--->|

The elemental aspects of the planets in these decanates
and pentades and also in the broader scope of the signs
relative to their meridian cusps at multiples of thirty,
with the midpoints between them at multiples of fifteen,
in alternating positive and negative amplitudes, to wit
Aries, Gemini, Leo, Libra, Sagittarius and Aquarius are
in the plus column, whereas Taurus, Cancer, Virgo, Scor-
pio, Capricorn and Pisces are in the minus column, this
duality and triplicity of the planetary forces to Earth
pertain to the nature or quality of the elements by the
planets who exert these elemental forces upon the Earth.

For example, a planet in the midst of Pisces translates
into the maximum amplitude of that sign's element along
with that planet's sidereal modality. Furthermore, this
chromatically-transposed modality is being modulated in
the elemental triplicity of the sign's decans & pentads.
Thus if Jupiter is found centered in the sign of Pisces,
then Jupiter is ruling therein with Jupiter's expansive
Lydian modality accentuating the reign of Cancer, Virgo,
and Libra in the key of B at maximum amplitude which is
in the minus column of Jupiter's duality--cf. the "plus"
column of Jupiter, i.e., Sagittarius by radial velocity:

Pisces - B Lydian | Sagittarius - Ab Lydian
EMPEROR-Jupiter-Six of Cups |EMPEROR-Jupiter-Six of Wands
|
VII I II III IV V VI | II III IV V VI VII I
Bb B Db Eb F Gb Ab | Bb C D Eb F G Ab
IVi Vio ROr OYe Gre GBl BIn | IVi Red Ora OYe Gre Blu BIn
Aqu Pis Tau Can Vir Lib Sag | Aqu Ari Gem Can Vir Sco Sag
Mar Jup Sat Moo Mer Ven Sun | Sat Moo Mer Ven Sun Mar Jup
R R R R | R R R R
|
1st decan/destructive water | 1st decan/destructive fire
pisces/violet/b | sagittarius/blue-indigo/ab
minus/plus | plus/minus
vii i ii iii iv v vi | ii iii iv v vi vii i
bb b db eb f gb ab | bb c d eb f g ab
ivi vio ror oye gre gbl bin | ivi red ora oye gre blu bin
aqu pis tau can vir lib sag | aqu ari gem can vir sco sag
mar jup sat moo mer ven sun | sat moo mer ven sun mar jup
r r r r | r r r r
|
second decan/creative water| second decan/creative fire
cancer/orange-yellow/eb | aries/red/c
plus/minus | minus/plus
v vi vii i ii iii iv | vii i ii iii iv v vi
bb c d eb f g a | b c d e gb g a
ivi red ora oye gre blu ind | vio red ora yel gbl blu ind
aqu ari gem can vir sco cap | pis ari gem leo lib sco cap
ven sun mar jup sat moo mer | mar jup sat moo mer ven sun
e e d | f
|
third decan/sustenant water| third decan/sustenant fire
scorpio/blue/g | leo/yellow/e
minus/plus | plus/minus
iii iv v vi vii i ii | iv v vi vii i ii iii
b db d e gb g a | bb b db eb e gb ab
vio ror ora yel gbl blu ind | ivi vio ror oye yel gbl bin
pis tau gem leo lib sco cap | aqu pis tau can leo lib sag
moo mer ven sun mar jup sat | mer ven sun mar jup sat moo
r f r | e e d e

Thus Jupiter in Pisces second decan is adding the major
third of cancer above its tonic B, which is the Eb exal-
ting Jupiter therein with the Sun in aries. Essentially,
the rudimentary overtones & harmonic series are layered
as subtones on top of the dominant and fundamental sign
in which the planet's mode is being transposed. The use
of lower-case names for the decans of the elemental tri-
plicities are used to distinguish them from whole signs
of the zodiac & respective whole elemental triplicities.

For those who've already read my Tarot Manual and Light
& Sound, then you'll recognize these musical principles
of the planets & signs as being somewhat redundant--but
this is not really the case. Now we're taking this know-
ledge and applying it in real-world terms of horoscopes
and their astrological portents, as understood by sound
and color. This is the veritable synthesis of astrology
with the psyche, personality, karma and dharma, ourself
in sidereal modes transposed in signs, decans & pentads.

Acoustical physics, the production, transmission, absor-
ption, reflection, control, effect and general behavior
of audible and inaudible sound is a science all its own.
As human beings, especially those with an ear for music
of whatever genre you like, we know what sounds good to
our ears--and conversely what doesn't. Whether occuring
in nature or manmade, most of us know what sounds sweet
or sounds bad and anywhere in between. Dealing with ast-
rology simplifies things for the purpose of this discus-
sion, since we're only concerned with the well-tempered
twelve-tone scale centered on middle C (C4 of the piano)
which is 261.63 Hz by the usual American-standard pitch,
putting A4 (the first A above middle C) at about 440 Hz,
depending on the temperament used to tune an instrument.

Subtle changes in temperament can have a significant im-
pact on the listener. A mere one cycle-per-second delta
to any tone in the scale can make a major difference in
how the instrument sounds when played. Similarly a note
played hard will momentarily attain a higher pitch than
its sustained resolution on most acoustical instruments.
But the softer it is played, the more uniform its pitch.
The standard pitch for the ascending chromatic scale on
C4 up to the C5 octave is tuned to the A 440 as follows:

C 261.63
C# 277.18
D 293.66
Eb 311.13
E 329.63
F 349.23
F# 369.99
G 392.00
Ab 415.30
A 440.00
Bb 466.16
B 493.88
C' 523.25

This is called "equal" temperament, since the frequency
between each neighboring tone is multiplied by the 12th-
root of 2 (1.0594630943592952645618252949463) ascending
and its reciprocal (0.94387431268169349664191315666753)
descending. Of course the accuracy of tuning is no more
than a penny or two sharp or flat at best, given the in-
herent limitations of a stringed instrument and environ-
mental variables in which it is being tuned, and played.

With eighty-eight (sometimes more) keys to tune, pianos
use equal temperament to enable smooth transposition of
music into any of the twelve chromatic tones & diatonic
modalities. Modern electronic keyboard instruments stay
in tune no matter what, and are easily retuned to other
temperament schemes at the mere touch of a button. This
next chart shows equal temperament for the common piano
& for any other chromatically-tuned keyboard instrument:

C0:16.35 C1:32.70 C2: 65.41 C3:130.81 C4:261.63
C#:17.32 C#:34.65 C#: 69.30 C#:138.59 C#:277.18
D0:18.35 D1:36.71 D2: 73.42 D3:146.83 D4:293.66
D#:19.45 D#:38.89 D#: 77.78 D#:155.56 D#:311.13
E0:20.60 E1:41.20 E2: 82.41 E3:164.81 E4:329.63
F0:21.83 F1:43.65 F2: 87.31 F3:174.61 F4:349.23
F#:23.12 F#:46.25 F#: 92.50 F#:185.00 F#:369.99
G0:24.50 G1:49.00 G2: 98.00 G3:196.00 G4:392.00
G#:25.96 G#:51.91 G#:103.83 G#:207.65 G#:415.30
A0:27.50 A1:55.00 A2:110.00 A3:220.00 A4:440.00
A#:29.14 A#:58.27 A#:116.54 A#:233.08 A#:466.16
B0:30.87 B1:61.74 B2:123.47 B3:246.94 B4:493.88

C5:523.25 C6:1046.50 C7:2093.00 C8:4186.01
C#:554.37 C#:1108.73 C#:2217.46 C#:4434.92
D5:587.33 D6:1174.66 D7:2349.32 D8:4698.64
D#:622.25 D#:1244.51 D#:2489.02 D#:4978.03
E5:659.26 E6:1318.51 E7:2637.02 E8:5274.04
F5:698.46 F6:1396.91 F7:2793.83
F#:739.99 F#:1479.98 F#:2959.96
G5:783.99 G6:1567.98 G7:3135.96
G#:830.61 G#:1661.22 G#:3322.44
A5:880.00 A6:1760.00 A7:3520.00
A#:932.33 A#:1864.66 A#:3729.31
B5:987.77 B6:1975.53 B7:3951.07

The newest and best digital keyboards emulate the piano
quite well with inharmonic partials and other subtle im-
perfections through sampled sounds & complex algorithms.
Even so, there's no electronic device that can equal an
acoustic instrument, but they do come closer and closer
herein the 21st century. The chromatic frequency charts
shown above work well in theory, but an actual piano is
dependent on the reality of its design and construction,
its condition and maintenance, its overall quality like
the Steinway or Bosendorfer concert grands, or a common
upright. Each piano behaves slightly different from the
next, hence the skilled piano tuner must employ methods
of counting "beats" between intervals that are suitable
for that particular piano. Basically, this stretches an
octave slightly due to the stiffness of piano wire, and
each octave behaves a little differently. There are two
basic methods for tuning pianos, but ultimately it's up
to the ear of the person tuning the piano which results
in a pleasing and smooth musical sound when it's played.

Two popular methods are the "Defebaugh F-F Temperament"
in which slower-beating intervals of fourths and fifths
are the dominant tuning reference, using faster-beating
thirds and sixths to make sure the fourths & fifths are
in tune to specification. Or, there's the newer "Potter
F-A Temperament" which essentially reverses the process,
tuning and checking by thirds and sixths, then checking
the fourths and fifths. This latter process extends the
temperament octave to one and a third, and is easier to
hear and count the interval beat of inharmonic partials.
There are, of course, a plethora of variations on these
piano tuning methods but the basics remain true for all.

By counting the number of beats per second between coin-
cident partials of any two fundamental tones, somewhere
in the series of partials we can find one beating suffi-
ciently close to the other as to count the beats by ear.
Provided one of these two tones is properly tuned, then
the other key can be retuned until the proper number of
beats per second can be heard. An expert tuner knows to
set the tuning pins by correct feel of the tuning lever,
while simultaneously setting the strings by playing the
string loudly as the tuning settles to pitch--enough to
equalize the tension across load bearing points of each
string while maintaining the desired pitch. In any case,
the tuner begins by making sure that the A above middle
C is tuned precisely to 440 Hz, and also that the piano
is generally in tune, before attempting any fine tuning.
Ideally, for a piano to stay in tune, it needs to be in
a climate-controlled environment, since radical changes
in temperature will throw even the finest pianos out of
tune. In such cases, tuning near the equinoxes is about
all you can do to minimize the effects of heat and cold.

Before the digital revolution, tuning forks were common-
ly used to tune A4 (440), C5 (523.252), or F4 (349.228).
A-440 is the most popular standard, which is the key of
Saturn-superior, the Mixolydian modality in the sign of
Capricorn. See how Saturn behaves in Capricorn's decans:

Capricorn - A Mixolydian
JUDGMENT (Saturn) - Seven of Pentacles

first decan/creative earth
capricorn/indigo/a
minus/plus
ii iii iv v vi vii i
b db d e gb g a
vio ror ora yel gbl blu ind
pis tau gem leo lib sco cap
moo mer ven sun mar jup sat
r f r

second decan/sustenant earth
taurus/red-orange/db
plus/minus
vi vii i ii iii iv v
bb b db eb f gb ab
ivi vio ror oye gre gbl bin
aqu pis tau can vir lib sag
mar jup sat moo mer ven sun
r r r r

third decan/destructive earth
virgo/green/f
minus/plus
iv v vi vii i ii iii
bb c d eb f g a
ivi red ora oye gre blu ind
aqu ari gem can vir sco cap
ven sun mar jup sat moo mer
e e d

Probably the most important mathematical principle used
for tuning a piano is that the reference pitch, usually
A-440, provides the benchmark by which a piano is tuned,
and that the beats counted between tuning intervals are
the function of the mathematical difference between the
partials being so tuned, e.g., an A-440 played together
with an A-441 would result in a 1 cycle-per-second beat,
since 441 subtract 440 equals 1. An A-440 played with a
A-445 makes 5 beats per second. Lastly, the theoretical
intervals aren't exactly practical, since every partial
above the fundamental pitch is somewhat sharper than it
"sounds" on paper. For example A-440 uses three strings
tuned in beat-free unison, meaning each string is tuned
to 440 Hz, making that key sound bright and strong when
played. Each octave above and below this standard pitch
must be tempered to be slightly wider than mathematical
theory dictates. It's like taking a rubberband and wrap-
ping it lengthwise around a 12" ruler, and marking each
inch-mark on the rubberband with a pen. Holding one end
of the rubberband to the ruler, stretch your rubberband
beyond the other end of the ruler by about a quarter of
an inch, and pay attention to how the increments on the
rubberband are proportionally--cumulatively--widened as
compared with the fixed ruler. The further out that you
stretch the rubberband, the wider each interval becomes,
and these differences are compounded over twelve spaces.
The same thing happens on the well-tempered piano, such
that the highest treble note may be 30 pennies sharp of
mathematical theory alone, while the deepest bass notes
can reach 40 pennies flat--all the while A-440 stays at
exactly 440 Hz. Concert grands have longer bass strings,
which require less stretch than the ordinary baby grand.

So, depending on the piano, the natural harmonic series
of theoretically separating every neighboring tone by a
factor of the twelfth-root of 2 doesn't hold water, but
requires temperament to settle the inharmonics of every
octave, in compensation for slightly sharpened partials.
However, because the natural harmonic series is mathema-
tically perfect, its theoretical overtones are harmonic
across every octave ad infinitum. The chart below shows
the first six overtones in this ideal temperament range:

Pitch First Second Third Fourth Fifth Sixth
----- ----- ------ ----- ------ ----- -----
C3-28 130.81 261.63 392.44 523.25 654.07 784.88
C#-29 138.59 277.18 415.77 554.37 692.96 831.55
D3-30 146.83 293.67 440.50 587.33 734.16 881.00
D#-31 155.56 311.13 466.69 622.26 777.82 933.38
E3-32 164.81 329.63 694.44 659.26 824.07 988.88
F3-33 174.61 349.23 523.84 698.46 873.07 1047.69
F#-34 185.00 370.00 554.99 739.99 924.99 1109.99
G3-35 196.00 392.00 587.99 783.99 979.99 1175.99
G#-36 207.65 415.31 622.96 830.61 1038.26 1245.92
A3-37 220.00 440.00 660.00 880.00 1100.00 1320.00
A#-38 233.08 466.16 699.25 932.33 1165.41 1398.49
B3-39 246.94 493.88 740.83 987.77 1234.71 1481.65
C4-40 261.63 523.25 784.88 1046.50 1308.13 1569.76
C#-41 277.18 554.37 831.55 1108.73 1385.92 1663.10
D4-42 293.67 587.33 881.00 1174.66 1468.33 1761.99
D#-43 311.13 622.25 933.38 1244.51 1555.64 1866.76
E4-44 329.63 659.26 988.88 1318.51 1648.14 1977.77
F4-45 349.23 698.46 1047.68 1396.91 1746.14 2095.37

As long as any one of the first six partials are within
about 15 cycles-per-second of any other tone's partials,
then it can be counted just by listening. You can count
for five or so seconds, then multiply the beats by 5 or
so to increase its accuracy. E.g., the fifth partial of
C3 which is 654.07 Hz, is near the fourth partial of E3
which is 659.26, with a difference of 5.19 Hz, or close
to 26 beats per five seconds. Note the ratio of this in-
terval is 5:4, and is a major third. It should be noted
here that all thirds, fourths and sixths are wide inter-
vals, while all fifths are narrow intervals. The octave
of any key is tempered by the second partial of the bot-
tom note with the fundamental of the octave above, such
that the inherent sharpness of the lower note's partial
causes the well-tempered octave to be stretched thereby
in reference to the compensating-flatness of the bottom
fundamental tone. By comparing all of the partials with
both tones of an octave being tuned, ratios of partials
can be used to fine-tune a specific range, like 4:2, or
6:3, meaning 4th of the lower and 2nd of the higher, or
6th of the lower and 3rd of the upper. Which ratios are
used depends a lot on that particular piano being tuned.

That's because the actual series of partials themselves
are inherently stretched above the fundamental to which
they're referenced so that the higher the partial, then
the greater the delta between theoretical frequency and
actual frequency. The following table shows theoretical
harmonic partials compared to the actual inharmonic par-
tials of the C1 bass string as analyzed in a laboratory
[Piano Tuning etc., A. Reblitz, pub. 1993 Vestal Press].
Note how only the fundamental partial remains identical:

Par. Theory Actual Delta
1st 32.70 32.70 0.00
2nd 65.41 65.52 0.11
3rd 98.11 98.40 0.29
4th 130.81 131.43 0.62
5th 163.52 164.78 1.26
6th 196.22 198.44 2.22

Consider how "one cycle-per-second" is actually defined.
A second of time is referenced to the long-term average
of one solar day on Earth, which day is subdivided into
twelve increments of two hours apiece, ergo twenty-four
increments of one hour each. One hour is composed of 60
minutes, so one solar day equals 1,440 minutes. Minutes
are broken down into seconds, making 86,400 seconds per
mean solar day. Therefore, one second equals 1/86,400th
of a mean solar day. When we think of cycles-per-second,
we're really thinking of equal fractions of a solar day.

There're also sidereal definitions of one mean sidereal
day on Earth, which is similarly subdivided by sidereal
hours, minutes and seconds. The sidereal day is defined
as 23h 56m 04.1s of mean solar time, about 0.9972796759
parts of a mean solar day. A-440 is about 438.803057 Hz
sidereal-to-solar. Middle C at 261.625565 Hz solar time
drops down to 260.9139 Hz sidereal-to-solar time. These
conversions are made relative to solar time, thus A-440
in sidereal cycles-per-second equals only 438.803057 Hz
in solar time. Conversely, A-440 in solar time is equal
to about 441.200 sidereal cycles-per-second. Given that
Earth's meridian houses are sidereal, and are "tempered"
by the approximately 23.439 degree obliquity of Earth's
rotational axis to her ecliptic, attunement with houses
and their planetary signs of the horoscope is analogous
to musical tuning and temperament--exemplary of a piano.
The strings are the planets attuned with their sidereal
orbits, the keys are the ensigns, and the music is life.

Consider also the partials of light, knowing the octave
above red is ultra-violet, while the octave above infra-
red is violet. Humans can't see infrared or ultraviolet,
but we can certainly feel their effects on the body. So
each and every octave of existence can be sensed by the
psyche through attunement with each spiral of vibration,
by listening to the waves within its range of frequency,
listening also for its harmonic and inharmonic partials,
much as the planets form spiral orbits with the Sun, as
the solar system orbits the Milky Way forever spiraling
outward toward the solar apex in this arm of the galaxy.

The archetypal essence of the major arcana places it in
the theoretical harmony category, which is mathematical,
just beyond relativity of force--the impulse for mental
activity as Cayce said. This is the perfect mood, as it
is used in the ancient language. And the imperfect mood
is the essence of the minor arcana which is temporal or
corporeal, demonstrated by the existence of life in the
physical body, subject to the temporal forces of nature
as horoscopic forces are natal portraits in progression.
Think of life as tuning intervals of different partials,
as you listen for inharmonic overtones in sympathy with
inharmonics of other keys, completing a sidereal circle
for each octave of the zodiac which spirals ever onward.

The famous "phaistos disk" that was discovered in Crete
in 1908 at the ruins of an ancient Minoan palace, is an
ancient horoscope complete with planets, signs and lots,
all symbolized by strangely familiar icons. About 6 1/3
inches in diameter, and less than one inch in thickness,
it has 122 glyphs on one side and 119 on the other. The
houses on the perimeter on each side number twelve, and
nearly encircle a spiral path towards the center, which
pathway begins with a small gap between the first house
and the twelfth house, and this's typical of both sides.
The spiral paths form 19 cells on one side and 17 cells
on the other. Accurate illustrations of this are online:

http://www1.primushost.com/~whittet/pspring1.gif
http://www1.primushost.com/~whittet/pspring2.gif

Most experts in ancient languages of this region concur
that the symbols on this disk have a strongly religious
connotation which of course means the planets and signs,
judicial astrology, the past, present and future of man.
The total number of symbols adds up to 241--that is 231
doors or gates plus the 10 planets or vessels of heaven.
I'd say it's 221 gates plus the 10 planets on each side.
You know, like two sides of the same coin...enough said
about this. In the next chapter the ferryman is waiting,
the one expecting payment before you can cross over the
Styx to the other side of oblivion. Pluton-Hades awaits...

End Chapter 12. See Chapter 13 For Completion...
Daniel Joseph Min

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