Working with Midpoints in the 22.5° mode

(16th harmonic)

© Blake Finley, M.A. Linguistics, 3 years post-Masters


As Uranian Astrology has evolved, Master Uranian Astrologer Ruth Brummund has relayed and built upon the observation by her Hamburg School mentor, Ludwig Rudolph (1893-1982), taking special note of the power and significance of the 22.5° angle in the astrology chart.7

In this article, I will explain how Ruth Brummund has taught and explained the method of making 22.5-degree multiples (16th harmonic) rather than the earlier-popularized 90-degree multiples (4th harmonic) the central measuring reference in midpoint analysis.  Ruth has made a special request for me at this point to explain the 22.5° mode in greater detail, step-by-step, so that its central concept and its functions can be more readily understood and applied.

First, you must understand the principles and function of the 90° dial before any of this is likely to make sense.  Therefore, if you do not understand the 90° dial, you should proceed to first read the pertinent article by clicking here.

What is the reason for stepping up from the 4th harmonic to the 16th? ... The answer is: greater precision and more detail.  At the 16th harmonic, we begin to see details, more clearly indicated, that the antique astrological paradigms of houses and signs hinted at but didn't elucidate so clearly.  Midpoints in the 16th harmonic measure the same astrological realities as traditional astrology, but approach them in a more precise and logical manner.

The overall process is in reality simply a matter of taking one step up to the next squared harmonic from 4 (as 4x4=16), and it can be rather easily done, according to the following methods.

First, recall that the 90° dial is in essence the traditional 360° dial folded over itself twice, so that:

00°- 30° 

represent the 30 degrees of the Cardinal signs (AR,CE,LI,CP)

30°- 60° 

represent the 30 degrees of the Fixed signs (TA,LE,SC,AQ), and

60°- 90° 

represent the 30 degrees of the Mutable signs (GE,VI,SG,PI).

These three basic principles are central to use of the 90° chart and traditional Hamburg Astrology and Cosmobiology.   If you are just beginning study of midpoint astrological techniques, and/or are not fully clear on how the 90° chart and dial are formatted and function, then you should return to the article on the 90° dial and study it carefully, now, as you need to understand where the 90° comes from and how it works before the following will make sense.  To return to the article on the 90° dial, click here.

For those of you clearly familiar with the 90° dial and chart, we now proceed.

First of all, we no longer work with a "22.5° dial", which would take us into another harmonic visually, where we might fine-tune too much and lose perspective and connection with the core 1st harmonic and the basic zodiacal measurement system.  Instead, we work with the 90° chart alone (with an appopriate 90° dial), find adequate information about 16th harmonic structures, minimize confusion from "shifting gears" between one visual harmonic and another, and streamline our work and study, without jumping from one device to another.

The ideal tool for working in the 22.5° mode is the Special Uranian program by Aureas Software, a program designed specifically for work with the newer and more evolved Uranian techniques, and including a remarkably clear, clean, and easy-to-use 90° chart with dial compatible with our 22.5°-mode analysis, as well as 22.5° tables designed specifically for work with the newer Brummund Method of Uranian Astrology.

First, I want to present an overview of the principles involved in working with the 22.5° mode, so we have a theoretical and practical understanding of where it comes from and how it works.  Then, I want to show how we can use the 90° dial to work in the 22.5° mode, or simply to verify positions in the 22.5° mode.

It is important to note here that, with this approach, 22.5°-mode positions can be readily inserted into 90°-dial work without any mathematical transformation or translation needed, thus making it far easier and readily convertible than work with 22.5° dials that too easily lead us to lose track of the original, core relationship to the 360° mode -- and at the same time give access to much greater detail in midpoint analysis.  The following examples will elucidate.

First, let's return to the linear graph used to show the numeric correspondences in the 22.5° mode, as presented in the article on the 90° dial.  It is recommended that you either print this lesson out so you can view the illustrations at appropriate points during reading, or have a 90° dial with you as you read, to see the correlations.

The four larger rows of numbers (0 to 90; 90 to180; 180 to 270; 270 to 360) represent the transitional conversion phase from the 360° mode to the 90° mode; i.e. in a sense, folding over the 360° continuum into 4 layers, where, as examples:

0 corresponds to 90 and 180 and 360,

 both in the table, and on the dial, and all have the same value in the 4th harmonic.

40 corresponds to 130, 220, and 310,

 both in the table, and on the dial, and all have the same value in the 4th harmonic.

70 corresponds to 160, 250, and 340,

 both in the table and on the dial, and all have the same value in the 4th harmonic.

What this means is that:

90° (0° Cancer) is the same as 0° on the 90° dial,

that 220° (10° Scorpio) is the same as 40° on the 90° dial,

and that 340° (10° Pisces) is the same as 70° on the 90° dial.

Now, just as 90 is the same as 0, for all general practical purposes, in working in the 90° mode; and 220 is the same as 40; we can apply the same principle to work in the 22.5° mode, and we can do it with a 90° dial.  Let's look again at the dial and graphic showing the 4th and 16th harmonic layers.

Note that the additional 16th harmonic angles are shown in smaller print on the linear table, and on the 90° dial, they are at right angles to the central pointer axis (at 22.5° and 57.5° on the 90° dial).

Ludwig Rudolph pointed out to Ruth Brummund that you "don't have to re-invent the wheel" and use a new 22.5° dial or chart, but simply take note of the midpoints on any given 90° axis, and then turn the dial sideways, manually or visually, at a 90° angle, thus squaring the midpoint axis under study, and you see the remaining midpoints of the 22.5° axis.  Once you realize how this works, it seems so simple.  And yet it has deeply profound impact on the precision of midpoint readings.

Note below that the 22.5° multiples fall in columns under the " V "s in the top line of the linear graphic, and we see that 22.5 is the same as 112.5, 202.5, and 292.5, etc, etc.   What we have done here is to divide the 360° circle into 8 equal segments and then align them in layers.

So much for the underlying mathematical principles.   Let's look at the issue of practical application.  To do this, it is useful to have the Special Uranian program (by Aureas) at hand and running.  The author is aware of no other program that will allow you to implement the following exercises with such facility -- and it has been designed specifically to do so.  If you do not have the Special Uranian computer program, you can emulate these exercises in part with a good, clean, and legible 90° dial.

Alice Bailey  1880.Jun.16  07h32 LMT  Manchester ENG

Let's look at an example chart: that of Theosophist Alice Bailey.  Her birth data are:  1880.Jun.16; 07h32 (am) Local Mean Time; Manchester, England, Great Britain.  The data are from the book "Sabian Symbols" by Marc Edmund Jones.  Ms Bailey taught the ancient wisdom of the Tibetan Buddhist master Djwhal Khul in an attempt to elucidate the world condition and ideological climate during World War 2, and her lessons may be most pertinent again today.  (Her book "Glamour: A World Illusion" is most enlightening.  Note that her astrology methods were those of conservative astrologers of the 1940s and significantly different from what we are using here and now, while the core of her teachings, while also filtered through the Zeitgeist of the 1940s, contain powerful lessons still to be learned by humanity, particularly about the nature and role of materialism in our lives and in our social and political institutions.)

After entering the aforementioned birth data, in the Special Uranian program, we can quickly pull up a chart of natal planetary and astrological point positions in 360°, 90°, and 22.5° mode via the "Natal--Uranian Data" function.  We see the table at the left.  The first column shows longitudes in traditional zodiacal format.  The fourth column shows longitudes in 360° (1st harmonic) format, where 0 Aries = 0; 0 Taurus = 30; 0 Gemini = 60, etc.

The third column shows longitudes in 90° format.  To readily convert 360° to 90° format, we simply subtract 90 from degree number over 90 until we derived a number less than 90.  Notice that in 360° notation, any number less than 90 is identical to the 90° notation.  The 90° dial converts these for us automatically, as does the Special Uranian program.


The second column is where we find the 22.5° mode notation (i.e. 16th harmonic).  Notice that the numeric values are identical to those of 90° and 360° notation whenever they are less than 22.5°.  Thus the MC is at 19°28' in each harmonic notation.

To convert 90° notation to 22.5° (22:30) notation, just as we did when moving from 360° to 90°, we go one step further and subtract 22.5° from any 90° notation greater than 22.5° until we derive a number less than 22.5°.  Now, this can be rather cumbersome to calculate, and therefore we really need the computer program to facilitate the process.  However, we can take the time to calculate these manually, in which case the following conversion table developed by Ruth Brummund will facilitate the process:

Examples from the chart of Alice Bailey: Conversion to 22:30 mode

Position of factors in 90° mode in 90° notation in 22.5° notation

0° to 22:30Where the value is less than 22:30, it remains the same in 22:30 mode notation

Moon = 00:31 00:31 00:31
Mercury = 11:06 11:06 11:06
22:31 to 45:00Where the value is between 22:31 and 45:00, we subtract 22:30
Mars = 38:44 38:44 16:14
Saturn = 26:31 26:31 04:01
45:01 to 67:30Where the value is between 45:01 and 67:30, we subtract 45
Uranus = 65:24 65:24 20:24

Pluto = 57:33



67:31 to 90:00Where the value is between 67:31 and 90, we subtract 67:30
Sun = 85:29 85:29 17:59
Venus = 77:52 77:52 10:22

In summary, it can be said that when a notation in 90° mode is greater than 22.5°, we simply keep subtracting 22.5° until we derive a value less than 22.5°;  and at that point, we have the value for use in 22.5° (16th harmonic) work.

 When converting from 360° to 90° mode, if a value is larger than 90, we keep subtracting 90 until we derive a number less than 90 (degrees).  We can then insert that number into a 90° chart or table and derive identical results for any planet of the same reduced value, as planets at the same degree in 90° notation are all at a 90°-multiple angle (traditionally called "square") to each other, or are conjunct.

Likewise, when converting from 90° mode to 22.5° mode, if a value is larger than 22.5°, we keep subtracting 22.5° until we derive a number less than 22.5 (degrees).  We can then insert that number into a 90° chart or table and derive idential results for any planet of the same reduced value, as planets at the same degree in 90° notation are all at a 22.5°-multiple angle (traditionally called "semi-octile") to each other, or are conjunct.  (Semi-octile designates half (semi) of one-eighth (octile), i.e. sixteenth harmonic.)


What preceded was theoretical background, along with mathematical underpinnings.  Now, let's look at practical application in work with the 22.5° mode using the 90° dial.

We can insert a 22.5°-position of a planet into a 90° chart and find 22.5° midpoints by looking for midpoints along the main axis, and then for midpoints at a right angle to the main axis.  To illustrate, let's continue with Alice Bailey's chart.  And let's find a planet where the notation in 360, 90, and 22.5 mode are each different.  Since the original source of the chart data is not specified, and we haven't rectified the chart, let's skip the MC and AS as we aren't sure they are precise.  The first planet we come to that is notated differently in the 3 modes is Mars at 128:44 or 38:44 or 16:14.  (For the mathematically interested:  just by looking at these numbers together here, in context and in relation to each other, it should be clear which mode is which.  128:44 has to be in 360 notation, since it is greater than both 90 and 22.5.  38:44 has to be either 360 or 90 notation, since it is greater than 22.5.  That leaves 16:14 in 22.5° notation.)   Each of these defines the longitude of Mars, notated in different harmonics.  If we were to look at a 360° dial, and set the dial pointer to 128:44, we would find 38:44 (Mars in 90° notation) at a right angle, and thus could find 90° midpoints by noting the midpoints directly on the midpoint axis of 128:44, and then noting those on the 38:44 axis, which is at a right angle to 128:44.

Likewise, we can follow the same principle with the 90° dial for 22.5° work:

First, let's set the dial to 38:44, the longitude of Mars in 90° notation.  Notice right away that if we look at a right angle to the smaller arrow at 22.5°, we find 16:14, which is Mars in 22.5° notation.  We could just as easily set the dial to 16:14 and find 38:44 at a right angle.  Either way, we are able to derive the same results.  (Unlike more traditional approaches, we generally do not make a distinction between 1st-, 4th-, and 16th- harmonics, as prioritization of importance of factors proves that the nature of the planets and points themselves far outweigh the significance of the [significant] harmonic of their interrelationship.)

To measure the midpoints at a right angle, we simply turn the dial at a right angle to Mars, or in the Special Uranian program, we can do this with two clicks of the mouse, and have the dial set almost instantaneously at a right angle, precisely 22.5° away from the previous setting, with no worries about wobbling dials, paper charts off center, or the other obstacles to precision in manual paper-and-dial work.

In the same manner as indicated for Mars, any 22.5° notation can be inserted into the 90° chart, and the same results will be derived as when using the 90° notation, with this method.

In the 21st Century Uranian Astrology e-group lessons, we will be working with the 22.5° mode.  Those interested in serious study of serious astrology, and not motivated by competing commercial interests, are welcome to join.  Simply do a web-search for "21st Century Uranian Astrology."

-- San Francisco, 2004.May.10

The only software program which effectively calculates the examples printed in these lessons is the 'Special Uranian' astrology program by Aureas Software of Paris, developed in cooperation with Ruth Brummund and Blake Finley  (Click here for further information.)