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by Jolin Townley

If you ever wanted to understand about arctransform charts, this is the article you should read.

John Townley, with his understanding and experienceof this intriguing subject, masterfully simplifies it to

its common denominators, demonstratinghow it relates to harmonics

and fractuals alike.

v f the plethora of new techniques thatblossomed in the astrological revival ofthe 1970s and 1980s, only a few have

gained truly wide popularity. One of them is the com-posite chart (which I had the honor to introduce); an-other is Astro*Carto*Graphy (Jim Lewis's brilliant ex-pansion of the simple relocation chart), not to mentionharmonic charts (John Addey, et al). Of course therewas the interpretation of the major four asteroids amonglots of other planetary and semi-planetary bodies such asChiron, and now Eris along with a host of other realtrans-Neptunians (as opposed to the hypothetical trans-Neptunians of the Ebertin school). Since then, older andformerly less used methods from classical astrology,including fixed stars and Arabic parts, have come backinto vogue to enliven the mix.

Some of the suggested approaches that were run up theflagpole got shot down or have fallen out of favor (likeDavison time-composites, group composites, and co-alescent charts), though computer programs still makethem available, and others never got saluted sufficientlybecause they were simply not properly understood.Among the latter is the arc transform chart, which israrely used and even more rarely properly understood.

Because there is no widespread general usage on whichto draw and elucidate upon the common and acceptedinterpretation of this method, I will thankfully spare youa long series of example charts that would be nothingbut personal opinion. Instead, I think it more importantto investigate what arc transform charts actually are,

what they physically tell you, and how that might beusefully connected to the mainstream and conceptualbottom line of astrological thought. In other words,this is not a how-to presentation, but more what-is andwhy-to (or not to) look at this interesting technique. Itsimplications about astrological structure are consider-able, and it is a method to dig out details and ap-proaches to astrology that aren't that obvious or avail-able by other methods. It can also be a gallery ofmathematical mirrors and illusions that you need to beaware of and discount or dodge as you examine them.

Wkat Is It, Really?(Theliarmonic Chart)

So what, exactly, is an arc transform chart? It is achart derived from the arc between two planets similarto (in fact, a higher derivative of) a harmonic chart.

So, first then, what is a harmonic chart? It is a reduc-tion of a regular chart by a fractional factor, so that allplanets that have an angular separation of that fractionor its multiples appear as a conjunction. In a 4th har-monic chart, for instance, all oppositions and squares(1/4 steps around the circle) appear as conjunctions(the familiar Uranian 90° dial) and semi-squares andsesqui-quadratures will appear as oppositions. Itmakes it easy to see at a glance what planets are re-lated by a subdivision of the circle by four or its multi-ples. It simply stretches the 360° by a factor of fourand lays the planets over it, restarting every 90° as yougo through the chart, kind of like you folded the circleinto quarters and then stretched it back into a circle,giving a magnifying effect to everything related byfour—a little like origami, if you think about it. Thearithmetic way to accomplish this is to multiply theposition of each planet (in 360° notation, so that, forinstance, 0° Leo is 120, 0° Scorpio is 210) by your har-monic factor, and then successively subtract 360 from

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11

each total until it is less than 360. A clever trick ofprestidigitation, indeed.

Fourth harmonic example:If your Sun is 0° Leo, that's 120 x 4 = 480.

Subtract 360 = 120 (0° Leo)If your Moon is 0° Scorpio, that's 210 x 4 = 840.

Subtract 360 twice and that's 120(0° Leo).

Voila! You have what was once a square, now aconjunction, and that will prove true for any othersquares in the chart (though they may not be at 0°Leo, but somewhere else).

By this method you can derive a chart that will spotany of the finer harmonic aspects in any chart, de-pending on what you're looking for, from obvious5ths and 7ths to obscure 87ths or 137th8.1 Do theymean anything? Well that's another issue, for later.

The Arc Transform ChartThe arc transform chart was invented by Englishastrologer, James Williamsen, simply by adaptingthe method of calculating a harmonic chart. It iscalculated by taking the shorter arc between anytwo planets and dividing it into 360 and using thatresult as the decimal fraction (harmonic) to multi-ply all planetary positions, before then reducingeach with 360° subtraction. So, if two planets were100° apart, a bit wide for a square, but not nearly atrine, you would divide 360 by 100 = 3.6 and use3.6 to multiply everything by, and then reduce.What you then would get is all planets 100° apart(or multiples of it, like 200 or 300) shown as con-junctions on the new arc transform chart. Planets50°, 150°, 250° and 350° apart would become oppo-sitions; planets 25°, 75°, 125°, 175°, 225°, 275° and325° apart would appear as squares; planets 33 1/3°or 66 2/3° and their multiples (ones that don't coin-cide with 100, 200 or 300) would show up as trines,and so on. Of course, you could reduce the fraction100/360 and find that arc to be a 5/18, or part of the18th harmonic, but it would be more difficult to re-duce if it were, say, a 97° arc (somewhere between7/26 and 3/11).

But, whether you're deriving a harmonic chart of amore common fraction whose numerator (n) is 1 oran arc transform chart of a perhaps unknown frac-tion, you will pretty quickly run into a number ofarithmetic artifacts that might look meaningful butreally aren't (composite charts have the same prob-lem). Any tight conjunction in the original natalchart will remain so in a harmonic or arc transform,regardless, though it will get less tight the higherthe denominator (d). It doesn't mean they are re-lated to anything, only that any arc you roll over

Uranus and Neptune 100 ApartJul25,19496:00 pm EOT+4:00Sea Cliff, NY73W3843

CkartlNatal Event

KockTropicalGeocentric

Uranus and Neptune 100 ApartJul25,1949 Chart 26:00 pm EOT 18th HarmonicSeaCliti,NY

Oeocosmic Hournal

them that hits one will hit the other. Further, if you castcharts for harmonics where the denominator is the samebut the numerator is different, you will only sometimesget the same conjunctions and other mutual relationshipsand never the same zodiacal degrees where they occur.That's because this is really an arithmetical way to mag-nify the fractional arc into an artificial circle for viewingin horoscope-like form, and nothing more. Thus, a 1/18chart (the 18th harmonic) will keep the relationships thesame as a 5/18 (the 100° arc transform) but a 7/18 or anyother n/18 will not, and instead will have oppositions,trines, sextiles, noniles, or in the case of 7/18 a 36th, de-pending on the relationship of the numerator to the de-nominator. If, however, the original arc was 7/18 (140°)then that chart would share the same relationships (butnot zodiacal positions) of the basic 1/18 harmonic; butnone of the others would.

Note in Chart 1 (the natal'event chart) that Uranus andNeptune are exactly 100 apart (-which is 5/18 oithecircle or a J.Uarc transform).

Chart 2 shows the same na tal da ta as the 18 harmonic.Chart 5 sho\vs the arc transform.

The arc transform paints identical relationships buttotally different zodiacal placements, because thevj aredifferent values of the 18 harmonic; so all three chartstell similar but different stories.

Uranus and Neptune 100 ApartJul25,1949 Chart 36:00 pm EDT Arc TransformSea Cliff, NY

What is important to carry away from all this com-plexity is that you are looking at the same originalchart every time, just from a slightly different win-dow and magnification where one doesn't always fitsnugly on top of the other, especially when primenumbers are involved in the fraction.

Further, the higher and finer the fraction describedby the arc transform, the more wildly it will varywhen the originating factors appear to remain thesame. Although the positions of Uranus and Neptunein the example, remains at 100° apart (within a min-ute of arc) for several hours before and after this ex-act time given, arc transform charts closely on eitherside of it will differ considerably from a simple 18th

harmonic chart. A great deal depends on the totalaccuracy of the orbital elements used to compute theephemeris positions, and that is less exact than youmight think, especially near the stations of the plan-ets. This is also a problem for planetary return chartswith the exception of solar and lunar. All in all,while appearing to be a tool of great exactitude, arctransforms are only as reliable as the absolute datathey derive from; and when that is off, even micro-scopically, they can vary wildly from the actuality ofthe situation, whatever that might really be. Still, thetechnique is certainly an information mine of a sort,but of what earthly good is it? Again more later.

First, a closer look at the spacey world of fractionalparts of the circle (often called harmonics, but thatword itself may be misused). If you're looking atwhat numbers to find your 5ths, 7ths, 9ths, 1 lths, 13ths

and up to the 30th part of the circle, on the next pageis a nice table of them, connected in a special way.

Each adjacent aspect is separated with a mutual orbborder based on their denominators, so that higherfractions get smaller orbs than larger ones, directlydetermined by what's next to them and how big theyare. Of course, with this approach, because of theirdenominator size the usual standard, Ptolemaic as-pects take up a larger orb than the smaller, less-explored harmonics—but also because of their de-nominator size, the lesser-used quintile has a biggerorb than a sextile; plus, a septile, nonile, decile oreven an 11th, get a bigger orb than a more traditionalsemi-sextile or a quincunx. The simplicity of it givesone pause for thought about what orbs you shouldreally take. If you added a lot more of the smallerfractions, it really wouldn't tighten things up all thatmuch (unless you went to infinity), as you can seethat as you approach a major aspect, the smallerones dive off the edge toward a infinitely rising de-nominator, like a deep breath, until they reach thebig aspect, both applying and separating. It's a niceimage, really, with larger aspects like black holesabsorbing the smaller ones into their orbs.

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13

Table 1—Fractional Parts of the Circle, often called Harmonics

0* -0* -0/19 44

10 0 - 1 /3610 810 17 - 1 /3510 2610 35 - 1 /3410 4510 55 = 1 /3311 511 15 = 1 /3211 2611 37 = 1 /3111 4812 0 - 1 / 3 012 1212 25 =1/2912 3812 51 - 1 /2813 513 20 . 1 /2713 3513 51 - 1 /2614 714 24 =1/2514 4215 0 = 1 /2415 1915 39 «1 /2316 016 22 m 1 /2216 4517 9 « 1 /2117 3418 0 - 1 / 2 018 2818 57 - 1-/1919 2820 0 = 1 /1820 2220 34 = 2 /3520 46 •21 11 =1/1721 36 '21 49 = 2 /3322 2 '22 30 « i /1622 5923 14 « 2 /31

23* 29'24 0 - 1 /1524 3324- 50 =2 /2925 725 43 - 1 /1426 2026 40 =2 /2727 027 42 = 1 /1328 2528 48 =2 /2529 1130 0 = 1 /1230 3830 51 « 3 /3531 231 1 8 - 2 /2331 3531 4 6 - 3 / 3 432 032 44 - 1 /1133 2933 45 - 3 /3233 5834 17 - 2 /2134 3734 . 50 = 3 /3135 736 0 = 1 /1O36 5537 14 » 3 /2937 3037 54 = 2 /1936 1838 34 * 3 /2838 5540 0 = 1 / 940 5541 9 = 4 /3541 1941 32 • 3 /2641 5142 21 - 2 /1742 5143 12 -3/2543 2743 38 - 4 /3343 54 . ... .45 0 - 1 / 8

46* 9*46 27 -4/3146 4046 57 -3 /2347 2248 0 = 2 /1548 .3949 5 - 3 / 2 249 2449 39 - 4 /2949 5150 0 -5 /3650 1451 2 6 - 1 /752 4152 56 - 5 /3453 .753 20 -4 /2753 3754 0 « 3 /2054 2154 33 = 5 /3354 4755 23 - 2 /1356 056 15 -« 5 /3256 2856 51 - J /1957 17 " ' • ' • '57 36 = 4 /2557 5258 4 - 5 /3158 2360 0 = 1 / 661 2861 43 = 6 /3561 526 2 4 = 5 /2962 1962 37 = 4 /2363 063 32 = 3 /1764 0€4 17 = 5 /2864 3765 27 = 2 /1166 1966 40 -5 /2766 5967 3 0 - 3 /16

68* 6'68 3 4 - 4 /2168 5669 14 = 5 /2669 2969 41 = 6 /3169 5170 0 = 7 /3670 1472 0 = 1 / 573 517 4 7 = 7 /3474 17 .74 29 =6 /2974 4375 0 = 5 /2475 2175 47 = 4 /1976 976 22 = 7 /3376 3677 9 - 3 /1477 5178 16 -5 /2378 3378 45 - 7 /3279 180 0 = 2 / 981 081 17 = 7 /3181 3081 49 = 5 /2282 682 17 = 8 /3582 3083 5 = 3 /1383 4384 0 = 7 /3084 1584 42 = 4 /1785 1685 43 = 5 /2186 586 24 = 6 /25£6 4086 5 4 - 7 /2987 • 687 16. - 8 /3387 3490 0 - 1 / 4

92» 18'92 34 « 9 /3592 4392 54 = 8 /3193 693 20 =7 /2793 3693 55 = 6 /2394 1794 44 = 5 /1995 695 18 = 9/3495 3196 0 - 4 /1596 3596 55 = 7 /26 .97 1798 11 - 3 /1199 099 19 -8 /2999 35

100 0 = 5 /18100 28100 48 - 7 /25101 3101 1 5 - 9 /32101 32102 5 1 - 2 /7104 13104 31 - 9 /31104 44105 0 - 7 / 2 4105 22105 5 3 - 5 /17106 22106 40 = 8 /27107 2108 0 = 3 /1010fi 50109 5 * 10 /33109 17109 3 4 - 7 /23109 50110 0 » -11 /3f110 12110 46 -4/13111 25111 4 3 - 9 /29112 0112 3C -5/16

112- 57*113 9 - 1 1 /35113 20113 4 1 - 6 /19114 9114 33 - 7 /22114 54115 12 - 8 / 2 5115 28115 43 = 9 /28115 56116 8 = 10 /31116 18116 28 -= 11 /34116. 44120 0 = 1 / 3123 10123 26 = 12 /35123 35123 45 = 11 /32123 56124 8 « 10 /29124 22124 37 -9/26124 54125 13 = 8 / 2 3125 35126 0 = 7 /SO126 291«7 4 - 6 /17127 30127 45 - 11 /31128 0128 34 = 5 /14129 14129 36 -9 /25129 50130 0 - 1 3 /36130 13130 5 5 - 4 /11131 43132 0 - 11 /30132 15132 3 8 - 7 /19133 3133 20 - 10 /27133 33133 43 - 13 /35133 57135 0 - 3 /8

136- 13*136 33 - 11 /29136 48137 9 = 8 /21137 28137 39 - 13 /34137 53138 28 = 5 /13139 5139 21 = 12 /31139 35140 0 = 7 /18140 29140 5 2 - 9 /23141 11141 26 « 11 /28141 38141 49 - 13 /33142 6144 0 = 2 / 5145 57146 19- = 13 /32146 26146 40 =11 /27146 56147 16 « 9 /22147 41148 1 4 - 7 /17148 42148 58 = 12 /29149 16150 0 - 5 /12150 42150 58 - 13 /31151 12151 3 5 - 8 /19152 0152 18 -.11 /26152 33152 4 4 - 1 4 /33153 0154 17 - 3 / 7155 41156 0 -13/30156 13156 31 « 10 /23156 55157 3 0 - 7 /16158 3158 24 =11/25

158* 38'158 49 - 15 /34159 4160 0 - 4 /9161 3161 23 -13/29161 38162 0 - 9 /20162 21162 35 = 14 /31162 51163 3 8 - 5 /11164 21164 34 • 16 /35164 45165 0 -11/24165 24166 9 = 6 /13166 50167 9 - 1 3 /281fi*7 O7I O/ e/

168 0 » 7 /151f»ft ' 11I UO J 1

168 45 - 15 /32168 591 US) Jy

169 25 = 8 /17160 4Oi o y *ty170 0 =17 /3617O 111 / w II

170 32 = 9 /19171 0171 26 = 10 /21171 49172 10 « 11 /23172 30172 48 = 12 /25173 5173 20 » 13 /27173 34173 48 =14/29174 0174 12 - 15 /31174 23174 33 - 16 /33174 42174 51 • 17 /35175 6180 0 - 1 / 2

n armomcs ,1-JO, orbs are divided between larger and smaller aspects according to the size of the denomina tor.

Note how finer aspects exponentially bunch up around the larger ones.

What is mainly to be gathered from this comparisonof harmonics with arc transforms is that any arc trans-form represents some multiple of a whole single-fraction (1/d) of the circle (an aspect, but usually afiner one), however small the actual fractional divi-sion may be. Thus, an arc transform chart is an ana-logue of a harmonic chart (which is always 1/d,whereas an arc transform may be 2/d, 3/d ... x/d), aparticular multiple of a higher-than-obvious fractionwhose numerator and denominator are unknown (butultimately reducible to n/d), with the arc transformchart giving you a magnified key to how that arc isinhabited throughout the original horoscope. Like aharmonic chart, it is not a horoscope in itself, just ahoroscope-formatted way of looking at subdivisionsof a fractional division of the circle laid end to end.

Larger vs. Smaller ArcAnother caveat about this technique and its cleverly-simplified arithmetic calculation is that it breaks downif you decide to use the larger arc (over 1A the circle)instead of the smaller. This is because, of course, thelarger arc doesn't repeat itself even once, and apply-ing the usual arithmetic to it will yield a chart witheverything bunched up together into just a few signsand most of the chart empty. Try doing a 0.18 har-monic chart on most computer programs and you'llsee what I mean. Suddenly, you're looking throughthe wrong end of a telescope instead of a microscopicclose up.

Astrological AntecedentsNow, in search of meaning: this may be an interest-ing, modern mathematical approach to twisting ordi-nary data about, but does it have any precedence intraditional astrological theory or practice? Actually, itdoes, in several places.

The idea of turning a limited section of the horoscopeinto an interior, scaled miniature, or fractal, of thewhole has antecedents in the rolling rulerships ofdwads, decanates, planetary hours and lunar man-sions, which are all looked at as whole systems thatlay themselves end to end until they have by repeti-tion covered the entirety of the larger circle of the day,month, year or lifetime. Those are probably the clos-est places to look to, for example, on how to use thearc transform chart. It's the worlds-within-worldspoint of view that highly populates Hindu culture andpops up with considerable regularity in Western phi-losophy as well, also having been rediscovered bymodern mathematics in the exploration of the fractal.Does the arc between two specific planets make up alittle fractal world, which repeats itself over and overaround the circle?

From /7uc/c/sDe Musica Mundana

The Mundane Monochord

with it Proportions and Intervals

In this chart is set forth a summary ofEluddstheory of universal music. The interval between

the element of Earth and the highest heaven isconsidered as a double octave, thus showing the

two extremes of existence to be in disdiapasonharmony. It is significant that the highest heaven,

the Sun, and Earth ha ve the same tone, thedifference being in pitch. The Sun is the Jower

octave ofthe highest heaven and Earth theloweroctave of the Sun. The lower octave (F to G)comprises that part of the universe in which

substance predominates over energy. Itsharmonics, therefore, are more gross than those

of the higher octave (G to g)-wherein energypredominates over substance. If struck in the

more spiritvial part, writes Eludd, the monochord•will give eternal life, if in tke more material part,

transitory life. It will be noted that certainelements planets, and celestial spheres sustain

a harmonic ratio to each other. Fludd advances thisasakey to the sympathies and antipathies existing

between the various departments of Nature.

tOinter Solstice 2008

Cosmic Music

Recent measurements of distant space

objects suggest they are giving of! variouskinds of waves at very low frequencies,corresponding to cosmic music, according to

some fanciful astronomers, including a black

hole emanating the lowest B-f lat in theuniverse. Although there may be a bigB-f lat coming from afar, there may be a

much more local reason for C being socentral as the home tone here on Earth. Ifyou take Earth's yearly cycle, 365.2422

days, convert it to seconds and then divide itby two to reduce it to shorter octave cycles

all the -way to audible Hz, you eventuallyreach 0.005637097 or just 272 Hz, just

bet-ween tempered C and C sharp if A=440.

Trxie C2 is 264 Hz, or expressed in a decimalfraction of a second 0.0037878787—just

the tiniest bit Hat of Earth s tuning.

Tempered C2 is 261.626 Hz or 0.00382250,

the tiniest bit flatter still. So, Earth s own f re-quency might appear to be between C and

C sharp (and if you use A=444, it's closerstill to true C).

After discovering the pitch of Earth, a littleabove C, it s worth calculating the rest of theplanets. Quite curiously, Venus (most associ-ated with music) is smack on A at just 442

Hz. Of the rest, the inner and oviter mostplanets, Mercury and Pluto, are multipleoctaves of each other at just above C sharp

(C#), and all put together the tones E, F,G, B-f lat, B, E-f lat (E-b) are lacking. Here's

the list, all compressed to the same octave,although some others (like Mars and Saturn)are actually also octaves or so apart:

Earth =272 =C, a trifle sharp

Mercury =282.5 = C#, a trifle sharpVenus =221.22, or 442.44 = AMars =289.44 =D, a trifle flatJupiter =367.15 = F#

Saturn =295.69 =D

Uranus =414.71 =G#Neptune = 422.86 = G#, a trifle sharp

Pluto =281.34 =C#, a trifle sharp

There is another similar usage, and that is Arabic parts.An Arabic part is determined simply by applying the arcbetween two given planets outward from a third point (orfrom one of the original two) to see where it winds up(which place becomes the part of whatever)—whichyields one (though not the only) set of places whichwould become a conjunction in their arc transform chart.Arabic parts only do that once, however, and not stepwiseuntil the whole circle is covered, unlike an arc transformchart.

So, in all these earlier methods, the ancients have consid-ered important the kind of data that an arc transform chartyields. Why did they do this, how did they interpret it,and is it about dividing space, time, or both? The answersaren't easy to pin down, but they likely lie in two princi-pal areas: natural resonance and learned repetition.

Natural ResonanceThere are reasons, probably quite physical, that astrologyhas traditionally leaned on the so-called major aspects andlarger minor aspects (in essence, the larger harmonic divi-sions or simple multiples of prime numbers under 12).Primary among these is the observation that the naturalworld seems to resonate according to these divisions,especially musically. The natural octave and its wholetones and semitones are determined by ratios described by

a

The fundamen talproportions of the larger numbers

and their fractional proportions determine pitch

and harmony, and on the cosmic scale have

been considered the determiners of

the music of the spheres.

Seocosmic H'our

16

these numbers. Indeed Pythagoras and later Renais-sance astrologers like Fludd (see sidebar, page 15) andKepler conceived of the planetary ratios as fundamen-tally musical. If we simply step up their relative or-bital periods by octaves until we get into the audiblespectrum, we get many of the fundaments of the musi-cal scale (see Cosmic Music and the illustration of theguitar to the left).

What's interesting is that the ratios of all the planetcycles are very Pythagorean, indeed, and seem to putthem in distinct musical families, not surprising aftereons of settling into their mutually resonant orbits.

It s GravityWhen you get beyond mere musical metaphor, how-ever, you find that the laws of gravitation tend to rollplanets into just these kind of natural harmonic rela-tionships. The Lagrange points of orbital stability andinstability virtually define the fundamental largest as-pects of conjunction, opposition, trine, and sextile.2

Astrologers should probably take note that they arefundamentally dealing with some very physical phe-nomena, and our behavior and psychology which weconnect with the planets has been driven by evolution,itself driven by environmental cycles powered byplanetary cycles. Thus, we do not project our mythsupon the planets, but rather derive our innermost setsof growth, timing and mythology and symbolismyromthem, around which our character structure, both asindividuals and as a species, forms as part of life evo-lution in general. The fundamental resonances of thesolar system are integral to what we do—they predateus and we formed ourselves around them as resonantattractors with intractable momentum over time. It's apicture painted simply by the step-down effects ofresonant gravity, and the continuing lock it has on allexistence, as the planets inexorably entrain and rein-force these rhythms from the top down and the ground(our environment) up.

Individual ResonanceBut if that was all there was to it, we'd be living in acrystalline universe, totally locked in to a perfect, sta-ble resonant chord. Ultimately, we may become so,but for the moment the fact is we're not. We are notsolely tuned to and timed by the external timing fac-tors stepped down from above, from diurnal, solar,lunar, tidal and less obvious, but equally as stronglonger-period cycles. There is a wiggle factor.

We also have individual internal clocks that keep usgoing relatively in sync with our environment, onwhich we rely when fundamental cues may be tem-porarily absent and which we reset as driver rhythms

reassert themselves. This is where the temporal factorbecomes as important as the spatial one. It is likelythat much of the effects of any natal chart comes fromits reinforcement by continual transits (cycles) tweak-ing it in regular fashion. If there are certain kinds ofevents that repeat within a given time segment, we be-come attuned to them and they in fact add to, if notmostly create, our expectations and hence our innerstructure. The fundamental cycles that we all share,give us joint character, and the ones we don't share (orthe unique combo that is our nativity) give us our indi-vidual natures as they vary from the average. It is amatter of repeating the same experiences over andover until they become us, starting at extreme infancyand building into full adults over the years, varyingfrom slightly to markedly different for everyone.

This approach might indeed be labeled behavioristastrology, and in relation to the natal chart is hard toprove, since it's hard to document and so utterly sub-jective (especially since the most important parts areestablished in early childhood, entirely unrecordedand unremembered, quickly-relegated, to the subcon-scious and autonomic parts of our personalities). Butthe principle becomes much more obvious when wetake another type of astrological chart in which theprocess can be watched to work as the obvious deter-mining factor. That would be the composite chart. Acomposite chart is not a chart of a beginning, but of anacquired process, and its strength and influence on thetwo people involved increases as they remain in con-tact and it absorbs more repeated transits, gainingever-stronger definition by accretion. As events causeeach person to meet at the set of dynamic mutualshores that define a composite chart, it becomes a vir-tual individual in itself, created by evolving circum-stance. That's why when we see a bad one, we can runwhile it's still weak and relatively unmanifested be-fore it gains strength and eats both individuals alive.

Here, indeed, we may find the very mechanism of anymeaning to be found in an arc transform chart (or, forthat matter, Arabic parts, or any system that primarilyexploits a particular arc that is subject to reinforce-ment by multiple transits and progressions). For in-stance, the arc between the Sun and Moon marks out acertain length of time between when we get hit bysomething and then the next one takes the same hit—diurnal rhythms mark that in hours, lunar in days, so-lar in months, and so on. The more it happens, themore we absorb (and then internalize and forget) thattiming factor, until it becomes a part of us. Thus,while everything at large may be resonating in gravi-tationally-resonant major aspects, you, yourself, aremarching to a different, more fragmented drummer,but it's yours alone, and the longer you live, the morefamiliar the beat.

If) inter Solstice 2008

The Sun-Moon arc is naturally the strongest (it'sthe easiest to feel, being the environmentally mostinfluential), and not surprisingly, the Part of For-tune is the most-used and familiar Arabic part, be-ing the first and primary projection of the Sun-Moon arc transform. From there, it's a step-downto the rest of all possible planetary pairs. You havean internal clock ticking out the set of time spansbetween them, and it is these rhythms that helpshape your expectations and innate timing in life.

That, I believe, is what is uniquely useful aboutarc transform charts—they accentuate the eccen-tricities of any one given natal chart, the extra setof non-standard rhythms that make for the vaga-ries of the individual existence. The overall ten-dency, over time (over the ages) is for systems tostabilize and resonate in the major harmonic rela-tionships, the bigger aspects. Thus, the solar sys-tem was pretty chaotic until the current state of theplanet's orbits settled in and adjusted to eachother, in general equilibrium, even though neverquite the hypothetically ideal, perfectly-lockedresonance. A great deal of our own individuallives are about coming into some sort of the sameequilibrium while having to live with our ownuniquely different separations from it. A majorharmonic chart will tell you how well you fit intothat overall equilibrium, and an arc transform willtell you how your planets match up on their own,much finer sets of what are, essentially, just higherharmonics, overtone series of the more fundamen-tal drivers.

A Tool for Tuning,

orBeijond...With that in mind, I personally use are transformsfor just that—fine-tuning. When I see no obviousharmonic at all between two planets, they bringotherwise unavailable insight. When I see two thatare close, but not quite exactly on a major har-monic, they give me an idea as to whether thewhole chart resonates better with the major har-monic or whether there is actually a tighter picturein the arc transform. An example would be myMoon-Sun, which are in a bi-septile aspect to eachother. A 7th harmonic chart shows some interestingresonances around the board, a grand trine. AMoon-Sun arc transform, however, ties everythingtogether much more precisely, actually making theaspects tighter, especially the Venus-Chiron-Plutorelationship with the Jupiter-Neptune-Mars-Uranus cluster, showing that it rings of itself evenmore and slightly differently than just in the basicharmonic. That's partly because the fundamentalSun-Moon relationship is close to bi-quintile (2/5)

John TownleijAufll7,19450151:00 am EWT+4:00Walter Reed DC77W010038N5500

Ckart4Natal

KockTropicalGeocentric

John TownlevjChartS

0151:00 am EWT +4:00Walter Reed DC

7th Ha

Oeocosmic Tournal

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and the harmonic chart by nature gives a single-quintilereduction (1/5), changing the Venus position from oppo-sition to square.

Sometimes choosing between the two can put you in to-tally different worlds, however. In her excellent bookInsights Into Astrology;' Nona Press spends many pageson her well-reasoned take on both harmonics and arctransforms, using her chart and those of her family asprimary familiar examples. Her Sun and Moon, however,are within a 2°14' conjunction, so when she leans on aSun-Moon arc transform, that's super-magnification of atiny arc to an almost magical degree, somewhere aroundthe 161st harmonic. Anyone else would have left it as atight conjunction (1/1 harmonic, the natal chart itself)and not bothered to fine-tune it further, but she findsmeanings both by transit and progression as that tiny arcrepeats and divides itself in sub-cycles around her chart.Her interpretations, lending planetary assignments to

Note tha t Chart 4 is m y na tal chart.

Chart 5 is the 7 harmonic of my natal chart.Chart 6is the Sun-Moon arc transform.

An arc transform can both tighten and rearrange the

view of a close-btj harmonic, as -with the relative

Venus position shown in Chart 6.

John TownleyAugl7,19450151:00 am EWT+4:00Walter Reed DC

ChartOSun-Moon Arc Transform

particular harmonics and meanings to them withwhich I would not necessarily agree, still seem tocome out all of a piece when all is said and done.She uses both harmonics and arc transforms tocreate whole new super-magnified worlds of in-dividual existence, whereas I would use the tech-nique simply as a fine-tuning adjunct of what isto be seen through more traditional methods.

In summary, regardless of how you use arc trans-forms or whether you use them at all, they bringup fundamental questions as to what astrologyreally is, physically and experientially, and whatis and isn't legitimate within that framework. Inthe end, I don't think they will see much moreuse among practitioners than they already have,except for the few who devote themselves to thetechnique, mainly because of the massive amountof fine data they present, even with a computer tokeep track. Still, they can be of use both as apractical and a philosophical tool to see how con-sistent and effective your overall viewpoint is,and they reveal a window into the enormity of thefractal environment which is our moment-to-moment, totally personal experience ofexistence.*

Endnotes1 http://www.astrococktail.com/minoraspects.html.2 http://www.astrococktail.com/Lagrangepoints.html.3 Press, N. Insights into Astrology. CA: ACS Publications,

1993.

All Rights Reserved.

Early in his astrological career, John Townleyintroduced the composite chart technique for ana-lyzing relationships in his book, The CompositeChart, and twenty years later wrote the definitivework on the subject, Composite Charts: The As-trology of Relationships. He has been the presi-dent of the Astrologers' Guild of America, andwas the editor of The Astrological Review. Formore on the author, visit his website: www.astrococktail.com. He can be reached attownley@astrococktail.com.

Editor's Note: If you would like more individualinterpretive text on what smaller harmonicsmean, you will find such on http://www.astrococktail.com/minoraspects.html. Describedis the meaning of some of the minor aspects-harmonics based on John Townley's experience.The harmonic list included in this article worksquite well with the definitions on the above citedweb page.

IDinter Solstice 2008