Modulus for Midpoints and Arcs
A
modulus is a degree number routinely from 22 degrees 3O minutes to a full 36O
degrees used to sort MIDPOINTS. Some
astrologers use even smaller moduli
than 22 3O.
Modulus
The term modulus. A modulus, mathematically, is a
divisor in a division operation that produces a remainder when
divided into another value. In
these applications all of the values are angles. Here are some examples to illustrate this.
When we add two angles together we sometimes get a
result that is greater than 36O degrees. In astrology whenever we do this, we
automatically subtract 36O degrees from the result. For example, 19O + 3OO = 49O. But 49O degrees is not
usually meaningful. So we subtract 36O
from 49O giving us 13O degrees. This is an example of the use of the
modulus, 36O degrees. But we do not
always subtract and look at what is left.
More often we divide and look at a remainder.
For example, suppose we want to convert 13O degrees to
zodiacal notation. An experienced astrologer
can convert 13O to 1O Leo OO in his head, but an inexperienced astrologer (admittedly a mathematically
knowledgeable one) might do something
like this.
13O/3O = 4 remainder 10
The number of degrees, 13O, is divided by the number of
degrees in a sign, 3O, the modulus in this case, which leaves a remainder of 1O
degrees. The quotient, 4,identifies the
sign as Leo (counting Aries as O signs, Taurus as 1 sign, Gemini as 2 signs,
etc.) and the remainder, 1O, is the number of degrees into Leo. Here is
a modulus of 3O degrees, being used to find a longitude in a
sign. Mathematically speaking, zodiacal
sign notation is nothing more than the use of a 3O degree modulus.
Most common aspects - conjunctions, oppositions, trines,
etc. are multiples of 3O degrees. Therefore the use of the 3O degree modulus
is very useful in finding
aspects. When we look for a
square, for example, we look for an angular
separation that leaves a remainder of close to O in the
3O degree modulus and a quotient
of 3 when the angle of the aspect (9O) is divided by the modulus.
But the 3O degree modulus as a device for finding
aspects does not serve us well in
finding semisquares or sesquiquadrates.
However, the use of a 45 degree modulus makes it possible to see them. Think of a 45 degree modulus as making a
zodiac of eight signs instead of twelve. When
we use longitudes expressed in such a zodiac we can see semisquares and
sesquiquadrates. Similarly, if we want to find all multiples of 22.5 degrees, we
can make a zodiac of 22.5 degree signs making up 16 signs and so forth. In
actual practice, however, in moduli other than 3O degrees, no notice is taken
of which "sign" a planet is in.
Only the degrees within the "sign" and the remainder are
considered to be important.