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=== Kepler's Aspects=== Collective astrological data along with [[Johannes Kepler]] described 13 aspects in his book ''[[Harmonice Mundi]]''. Astrological data grouped together in five degrees of influentially picked from symbol ratios encountered in geometry and music: 0/2, 1/2, 1/5, 2/6, 1/3, 1/12 along with 1/5, 2/5, 15/5, 10, 10/3, 8, and 8/3. The general names for whole divisors are ([[Numeral prefix|Latin]]) ''n''-ile for whole fractions 1/''n'', and ''m''-''n''-ile for fraction ''m''/''n''. A Semi-''n''-tile is a ''2n''-tile, 1/(2''n''), and Sesqui-n-tile is a Tri-2''n''-tile, 3/(2''n''). All aspects can be seen as small whole number [[harmonic]]s, (1/''n'' of 360°). Multiples of ''m''/''n'' create new aspects where there are no common factors between ''n'' and ''m'', [[greatest common divisor|gcd]](n,m)=1. {| class=wikitable |+ General Aspects !Degree of<BR>Influentiality||colspan=2|First|| colspan="2" |Second ! colspan="2" |Third|| colspan="3" |Fourth||colspan=4|Fifth |- !Aspect|| [[#Conjunction|Conjunction]]||[[#Opposition|Opposition]]||[[#Trine|Trine]]<BR>Bisextile ![[#Square|Square]]<BR>Quartile||[[#Sextile|Sextile]]<BR>Semitrine||[[#Semisextile|Semisextile]]<BR>Duodecile||[[#Quincunx|Quincunx]]<BR>Quinduodecile||[[#Quintile|Quintile]]<BR>Bidecile||Biquintile||[[#Octile|Octile]]<BR>Semisquare||Trioctile<BR>Sesquiquadrate||[[#Decile|Decile]]<BR>Semiquintile||Tridecile<BR>Sesquiquintile |- align=center !Glyph |[[Image:Conjunction symbol.svg|64px]]||[[Image:Opposition symbol.svg|64px]]||[[Image:Trine symbol.svg|64px]] |[[Image:Square symbol.svg|64px]]||[[Image:Sextile symbol.svg|64px]]||[[File:Semisextile symbol.svg|54px]] |[[File:Quincunx symbol.svg|54px]]||<big><big>Q</big></big>||<big><big>bQ</big></big>||[[File:Semisquare symbol.svg|64px]]||[[File:Sesquisquare symbol.svg|64px]]||[[File:Up_tack.svg|56px]]||[[File:Up_tack.svg|56px]]<sup>3</sup> |- align=center !Angle |0°||180°||120° |90°||60°||30°||150°||72°||144°||45°||135°||36°||108° |- align=center !Fraction | '''0/2''' ||'''1/2'''|| '''1/3''' |'''1/4'''||'''1/6'''||'''1/12'''||5/12||'''1/5'''||2/5||'''1/8'''||3/8||'''1/10'''||3/10 |- align=center valign=bottom !valign=center|[[Regular polygon|Regular<BR>Polygon]] |[[File:Monogon.svg|64px]]<BR>[[Monogon]] || [[File:Digon.svg|64px]]<BR>[[Digon]] || [[File:Regular_polygon_3_annotated.svg|64px]]<BR>[[Equilateral triangle|Triangle]] |[[File:Regular_polygon_4_annotated.svg|64px]]<BR>[[Square]]|| [[File:Regular_polygon_6_annotated.svg|64px]]<BR>[[Regular hexagon|Hexagon]] ||[[File:Regular_polygon_12_annotated.svg|64px]]<BR>[[Dodecagon]] |[[File:Regular star polygon 12-5.svg|64px]]<BR>[[Dodecagram]]||[[File:Regular_polygon_5_annotated.svg|64px]]<BR>[[Pentagon]] || [[File:Five_Pointed_Star_Lined.svg|64px]]<BR>[[Pentagram]]||[[File:Regular_polygon_8_annotated.svg|64px]]<BR>[[Octagon]] || [[File:Regular star polygon 8-3.svg|64px]]<BR>[[Octagram]]||[[File:Regular_polygon_10_annotated.svg|64px]]<BR>[[Decagon]] ||[[File:Regular star polygon 10-3.svg|64px]]<BR>[[Decagram (geometry)|Decagram]] |}
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