Additional aspects used, though not commonly, in astrology. The following are 7th-Harmonic, 9th-Harmonic, 10th-Harmonic, 11th-Harmonic, 14th-Harmonic, 16th-Harmonic and 24-Harmonic Aspects which are based on the division of the circle of the Zodiac by seven, nine, ten, eleven, fourteen, sixteen and twenty-four.

Septile

The septile (abrv. Sep) is an angle of 51.428571°, or approximately 51°25'43", one-seventh of the circle of the zodiac. It is supposed to be aspected to have irrational relations between its constituent components but confer the hidden underlying nature and deeper destiny of them.

Bi-Septile

The biseptile (abrv. BSp) is an angle of 102.857143°, or approximately 102°51'26", 2/7 of the zodiac circle. This aspect is considered the externalized septile.

Tri-Septile

The triseptile (abrv. TSp) is an angle of 154.285714°, or approximately 154°17'09", 3/7 of the zodiac circle.

Novile

The novile (abrv. Nov), also known as a nonagon, is an angle of 40°, one-ninth of the circle of the zodiac. The novile is said to represent a constriction between the aspects that can be unlocked and used as a catalyst to self-enhancement.

Bi-Novile

The binovile (abrv. BNv) is an angle of 80°.

Quadnovile

The quadnovile (abrv. QNv), also known as a quadrinovile, is an angle of 160°.

Decile

The decile, also known as a semi-quintile, is an angle of 36°, one-tenth of the circle of the zodiac. This aspect is said to impart ability to help others.

Tridecile

The tridecile, or sesquiquintile, is an angle of 108°, which is supposed to confer a social creativity or the need for withdrawal and introspection needed for external originality. This aspect is also known as the quintile-and-a-half.

Vigintile

The vigintile, or semi-decile, is an angle of 18°, one-twentieth of the circle of the zodiac, or half a decile.

Undecile

The undecile (abrv. Und), also known as the undecim, is one-eleventh of the zodiac circle or an angle of 32.727272° (32°43'38"); in addition there are the biundecile (aka biundecim, 65.454545°, or 65°27'16"), the triundecile (aka triundecim, 98.181816°, or 98°10'55"), the quadriundecile (aka quadriundecima, 130.90909°, or 130°54'33") and the quinqueundecile (aka quinqueundecim, 163.636363°, or 163°38'11"), representing, respectively, two-elevenths, three-elevenths, four-elevenths, and five-elevenths of the zodiac circle. The undecile is said to be associated with social consciousness and the ability to reach beyond oneself for help.

Semi-Septile

The semiseptile (which has also been called quattuordecimal, from the Latin word for fourteen, quattuordecim) is an angle of 25.714286° (or, in degree-minute-second format, 25°42'51"), one-fourteenth of the circle of the zodiac, or half a septile. It is said to have to do with giving up what one has completed in order to move on to the next cycle of activity.

Tresemiseptile

The tresemiseptile, also known as the sesquiseptile, is an angle of 77.142858° (77°08'34"), three-fourteenths of the circle of the zodiac.

Quinsemiseptile

The quinsemiseptile is an angle of 128.57143° (128°34'17"), , five-fourteenths of the circle of the zodiac.

Semioctile

The semioctile is an angle of 22.5° (22°30'), one-sixteenth of the circle of the zodiac.

Sesquioctile

The sesquioctile is an angle of 67.5° (67°30'), or three-sixteenths of the zodiac circle, or a semisquare (octile) and a half.

Quattuorvigintile

The quattuorvigintile is an angle of 15°, one-24th of the zodiac circle.

Squile

The squile is an angle of 75°, 5/24 of the zodiac circle, considered a hybrid between a square and a sextile.

Squine

The squine is an angle of 105°, 7/24 of the zodiac circle, considered a hybrid between a square and a trine.

Quindecile

The quindecile (also known as the johndro or contraquindecile) is an angle of 165°. It is supposed to be associated with an unrelenting headstrong determination, with disruption and upheaval.