Introduction to Aspects in Astrology (2)
– written by Philip Graves, 2002;
– revised / expanded 27th-28th Dec 2003;
– slightly corrected, September 30th 2015;
– some aspect names slightly revised, June 1st, 2016
– reformatted for WordPress, June 1st-3rd, 2016


Table of aspects

Name: the usual name for the aspect type*
Angle: the angle between the two factors concerned at which the aspect is exact
Division: the prime number(s) by which the 360º circle was divided to form the base aspect
M*abbreviation for Multiplier: the number by which the base aspect’s angle was multiplied to form the aspect concerned
Orb: the maximum recommended orb of influence within which the aspect will be effective
Range: the near and far limits for angles within which the aspect will take effect.

Name Angle Division M* Orb     Range
Conjunction   0º     1 1 9.00º   0.00-9.00º
Sextisextile  10º  2,2,3,3 1 0.20º   9.80-10.20º
Quartisemisquare  11.25º 2,2,2,2,2 1 0.25º  11.00-11.5º
Quartisextile  15º  2,2,2,3 1 0.50º  14.50-15.5º
Vigintile  18º   2,2,5 1 0.20º  17.80-18.2º
Seminovile  20º   2,3,3 1 0.40º  19.60-20.4º
Quartisquare  22.5º  2,2,2,2 1 0.80º  21.70-23.3º
Quindecile (1)  24º    3,5 1 0.20º  23.80-24.2º
Semiseptile  25.7º    2,7 1 0.30º  25.40-26.0º
Tredecile  27.7º    13 1 0.20º  27.50-27.9º
Semisextile  30º   2,2,3 1 1.50º  28.50-31.5º
Undecile  32.75º    11 1 0.35º  32.40-33.1º
Triquartisemisquare  33.75º 2,2,2,2,2 3 0.25º  33.50-34º
Decile (2)  36º    2,5 1 0.60º  35.40-36.6º
Novile (3)  40º    3,3 1 1.00º  39.00-41º
Semisquare  45º   2,2,2 1 2.20º  42.80-47.2º
Biquindecile  48º    3,5 2 0.20º  47.80-48.2º
Quintasextisextile  50º  2,2,3,3 5 0.20º  49.80-50.2º
Septile  51.4º     7 1 0.90º  50.50-52.3º
Trivigintile  54º   2,2,5 3 0.20º  53.80-54.2º
Bitredecile  55.4º    13 2 0.20º  55.20-55.6º
Quintaquartisemisquare  56.25º 2,2,2,2,2 5 0.25º  56.00-56.5º
Sextile  60º    2,3 1 3.00º  57.00-63º
Biundecile  65.45º    11 2 0.35º  65.10-65.8º
Triquartisquare  67.5º  2,2,2,2 3 0.80º  66.70-68.3º
Septasextisextile  70º  2,2,3,3 7 0.20º  69.80-70.2º
Quintile  72º     5 1 1.80º  70.20-73.8º
Quintaquartisextile  75º  2,2,2,3 5 0.50º  74.50-75.5º
Trisemiseptile  77.1º    2,7 3 0.30º  76.80-77.4º
Septaquartisemisquare  78.75º 2,2,2,2,2 7 0.25º  78.50-79º
Binovile  80º    3,3 2 1.00º  79.00-81º
Tritredecile  83.1º    13 3 0.20º  82.90-83.3º
Square  90º    2,2 1 6.00º  84.00-96.0º
Quadraquindecile  96º    3,5 4 0.20º  95.80-96.2º
Triundecile  98.2º    11 3 0.35º  97.85-98.55º
Quintaseminovile 100º   2,3,3 5 0.40º  99.60-100.4º
Nonaquartisemisquare 101.25º 2,2,2,2,2 9 0.25º 101.00-101.5º
Biseptile 102.9º     7 2 0.90º 102.00-103.8º
Septaquartisextile 105º  2,2,2,3 7 0.50º 104.50-105.5º
Tridecile (4) 108º    2,5 3 0.60º 107.40-108.6º
Undecasextisextile 110º  2,2,3,3 11 0.20º 109.80-110.2º
Quadratredecile 110.75º    13 4 0.20º 110.55-110.95º
Quintaquartisquare 112.5º  2,2,2,2 5 0.80º 111.70-113.3º
Trine 120º     3 1 4.50º 115.50-124.5º
Undecaquartisemisquare 123.75º 2,2,2,2,2 11 0.25º 123.50-124º
Septavigintile 126º   2,2,5 7 0.20º 125.80-126.2º
Quintasemiseptile 128.6º    2,7 5 0.30º 128.30-128.9º
Tredecasextisextile 130º  2,2,3,3 13 0.20º 129.80-130.2º
Quadraundecile 130.9º    11 4 0.35º 130.55-131.25º
Sesquiquadrate (5) 135º   2,2,2 3 2.20º 132.80-137.2º
Quintatredecile 138.45º    13 5 0.20º 138.25-138.65º
Septaseminovile 140º   2,3,3 7 0.40º 139.60-140.4º
Biquintile 144º     5 2 1.80º 142.20-145.8º
Tredecaquartisemisquare 146.25º 2,2,2,2,2 13 0.25º 146.00-146.5º
Quincunx 150º   2,2,3 5 1.50º 148.50-151.5º
Triseptile 154.3º     7 3 0.90º 153.40-155.2º
Septaquartisquare 157.5º  2,2,2,2 7 0.80º 156.70-158.3º
Quadranovile 160º    3,3 4 1.00º 159.00-161º
Nonavigintile 162º   2,2,5 9 0.20º 161.80-162.2º
Quintaundecile 163.65º    11 5 0.35º 163.30-164º
Undecaquartisextile 165º  2,2,2,3 11 0.50º 164.50-165.5º
Sextatredecile 166.15º    13 6 0.20º 165.95-166.15º
Quindecaquartisemisquare 167.75º 2,2,2,2,2 15 0.25º 167.50-168º
Septaquindecile 168º   3,5 7 0.20º 167.80-168.2º
Septendecasextisextile 170º 2,2,3,3 17 0.20º 169.80-170.2º
Opposition 180º    2 1 9.00º 171.00-180º

(1) or quintitrine (2) or decagon / semiquintile; (3) or nonagon; (4) or sequartiquintile / tredecile; (5) or sextaquartiquartile

Note: there may occasionally be some overlap between the range of aspects formed from the division of the circle by different prime numbers. An aspect falling within an ‘overlap’ range combines in its interpretation the prime number properties of both aspect series present.

NB: In order for the final column of figures in the above table to display properly in WordPress, it was necessary to add zeros to some figures after the decimal points. These are not significant figures.

*: Footnote, Nov. 30th 2014, expanded June 1st, 2016: In many cases, no standard name for the minor harmonic aspects existed. I therefore used functional names of my own that accurately described the process by which the aspect was derived in the cases of aspects that lacked a standard name, when preparing the groundwork, in the course of my own private research into harmonics and aspects back in 1996, for what eventually became this article. The functional names are typically a combination of prefix denoting the multiplier, and stem denoting the circle division factor (or ‘harmonic’) used to form the base aspect of the series to which the aspect belongs. Since then, some minor modifications to names have been made chiefly on grounds of seeking closer conformity to convention for the Latinate form of the prefixes, which are now set according to the following scheme: bi = two times; tri = three times; quadra = four times; quinta = five times; sexta = six times; septa = seven times; nona = nine times; deca = ten times; undeca = eleven times; tredeca = thirteen times; quindeca = fifteen times; septendeca = seventeen times.


Orbs of influence

Because angular connections between factors at the time of birth produce an effect on the person born when they are simply close to corresponding to the exact angle of one of the significant aspect types, a system of orbs of influence is applied to the different types of aspect, indicating how nearly the angular relationships between two factors have to match the exact angle of the aspect type concerned to qualify as forming the aspect. For instance, a sextile has to be accurate only to within 3º either side of 60º to produce a significant effect, so any angle from 57º to 63º between two chart factors qualifies as a sextile. The allowable orb of the sextile aspect in general is thus specified as being 3º. 

Historically, orbs allowed were larger or smaller relative to the average importance of the two luminaries or planets being connected; but in the early 1860s an astrologer called Richard Morrison (better known by his pen-name of Zadkiel) introduced the concept that orbs should be consistent between any pair of factors for all types of major aspects, but with aspects to the Sun and Moon given somewhat larger orbs; and most astrologers from the time of Alan Leo and Alfred Pearce in the early 1890s have followed variations on his view. Even today, some still allow greater orbs for aspects to the luminaries, or in some cases to the ruling planet (usually meaning the planet considered by astrologers to have the closest natural affinity with the particular Ascendant sign in the individual’s birth chart). It is generally acknowledged that orbs for aspects to minor bodies such as the asteroids, centaurs and fixed stars should be much reduced.

The conjunction and opposition have been shown to work with broadly equivalent orbs since they are both in effect aspects relating to the division of the circle into two. Beyond this, however, the orbs of allowance for a given aspect decline in line with the circle division factors used to create the base aspect, subject to a variation in slope of orb decline according to the relative obscurity of the aspect’s circle division factors (with ‘2’ being more significant than 3, 5, 7, 11 and 13 in turn); and a shallower decline for all aspects that form multiples of thirty degrees and therefore correspond to the natural zodiac.


Applying vs. Separating Aspects 

Many astrologers distinguish between the effects of applying aspects, where the faster-moving factor was getting closer to achieving the exact aspect with the slower-moving one, and will have reached it after the moment of birth; and separating ones, where the exact aspect had already happened before birth and the faster-moving factor was therefore moving further away from the slower one. Astrologers mostly believe that applying aspects are stronger in their effects than separating ones, and some even allow them larger orbs accordingly; however, one prominent astrologer in the late 19th century took the opposite view. The process whereby a faster-moving planet comes within orb of an aspect to a slower-moving planet or stationary point in the figure and approaches the exact aspect over time is called its application to the slower-moving planet or point.


Dexter vs. Sinister Aspects

A further distinction in perspective is drawn between dexter or lower aspects: those from a specified planet to a point less than 180º after it in the zodiac (anticlockwise from it in the figure), and sinister or upper aspects: those from a specified planet to a point less than 180º before it in the zodiac (clockwise from it in the figure).


Working out what aspects are in a natal figure:

1. Either use a free chart calculation service such as the ones at and, or use the manual calculation procedure detailed in the Calculation article, to determine the positions by signs, degrees (º) and minutes () of the celestial bodies and angles in the birth chart whose aspects you want to look up. If you use an automated service, you should see your sign placements clearly listed beneath the natal figure itself – you can ignore the diagram of the figure; and the signs to which the shorthand astrological ‘glyphs‘ or symbols correspond are labelled. You don’t need to use the glyphs yourself; the words will do fine. Write down all the sign, degree and minute placements on a piece of paper in a list.

2. For the sake of convenience when it comes to calculating the angular separation between all your factors, convert the minutes of degrees into the nearest complete decimal point of a degree: for 0-5 minutes, add 0.0; for 6-11 minutes, 0.1; for 12-17 minutes, add 0.2; for 18-23 minutes, add 0.3; for 24-29 minutes, add 0.4; for 30-35 minutes, add 0.5; for 36-41 minutes, add 0.6; for 42-47 minutes, add 0.7; for 48-53 minutes, add 0.8; for 54-59 minutes, add 0.9. For example, if you have the Sun at 19º46′ of Scorpio, convert it into 19.7º Scorpio.

3. Follow the step-by-step instructions under ‘Calculating the Aspects’ in the Calculation article.

You will be asked to make a note for each aspect you discover of the orb of influence that you are having to allow. The closer to the centre of the allowed range for the aspect type, the stronger the effects of the aspect will be. In the example in the article, 84.6º is 5.4º away from the exact angle of the square, 90º, so you would write down ‘5.4º’ by ‘Sun square Moon’. You can see that this is about three quarters of the distance towards the outer limit (7º) of the allowable orb for a square, so the aspect will not apply at maximum strength but will still be significant, squares being among the strongest aspects in any case.

4. Continue until you have worked out all the aspects in the figure and their orbs of proximity.


Choosing which interpretations to read:

The aspect types typically covered in separate pages for each pair of chart factors in printed astrological delineations are the conjunction; sextile and trine; square and opposition; and quincunx. The sextile and trine are often grouped together, as are the square and opposition, with authors having written one delineation to cover all ‘soft’ or ‘harmonious’ aspects and one for all ‘hard’ or ‘inharmonious’ aspects; but you will also find separate interpretations for the square and opposition and for the trine and sextile by other authors, and should read whichever one of those corresponds to the nature of the aspect you are looking up most closely. For aspect types not specifically covered by printed delineations, I would suggest the following approximations:

For the quintile, biquintile (5), and the septile, biseptile and treseptile (7), consider the entry for the trine, modified in the light of the characteristics supposed of the prime numbers 5 or 7.

For the decile and tredecile, consider the entry for the sextile, modified in the light of the characteristics supposed of the prime number 5. 2*5 is closest to 2*3.

For the semisextile, consider the entry for the quincunx, for which it is the base aspect, modified with reference to the meaning of the semisextile.

For the semisquare, sesquiquadrate, quartisquare, triquartisquare, quintaquartisquare and septaquartisquare, read the entry for the square, but presume a less forceful, more niggling conflict, based on the multiple instances of the prime number 2 in which their base aspects are sourced.

For the novile, binovile and quadranovile, consider the entry for the trine, modified in the light of the characteristics supposed of the novile series (3,3).

Brief dedicated delineations of quintile, septile, novile and semisquare-series aspects are found in a few dedicated books on harmonics in astrology.

Continue to Part Three of Three. . .

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