Now we come to the fundamental nuts-and-bolts of modern Armanen rune-casting. As mentioned before, the interpretation of the positions of these runes may vary depending on the rune in question. Those which are asymmetric and can be reversed also have a horizontal-negative and a horizontal-positive position, though which is a left (counterclockwise) rotation and which is a right (clockwise) rotation will differ depending on the individual rune.
This is of course the so-called Spiesberger method, which is used by all modern Armanen rune masters (and apparently even others who use systems besides Armanen - we must remember, modern rune-casting techniques as a whole were all but invented by the Armanists in the early 20th century).
Karl Spiesberger is credited with publishing the comprehensive positive and negative Armanen rune positions in his book Runenmagie ('Rune Magick'), published in 1955. However it is believed by many rune practitioners that these positions were already in use by Gorsleben and even Guido von List, far earlier in the 20th century. Since a few of the "merkstave" or negative-horizontal positions published by Spiesberger are not possible with a rune symbol carved on an opaque material like wood, I have had to adjust them from Spiesberger's diagrams, for use with traditional wood casting tiles (or stones). Nevertheless, the esoteric meaning and symbolism of the negative positions is unchanged.
NOTE: all images and interpretations on this post are my own work. ASK before using.
So look below:
You will notice that some of the runes are negative if you turn them 90 degrees left, but others are positive in that same orientation. And the same discrepancy or diversity of meaning happens when you look at how the runes are to be interpreted when turned 90 degrees right. For example, if you look at Fa and Os, they are negative when turned left. But to make Thorn negative, you have to turn it right!
Why is this?
Looking at the structure and shape of the runes provides a critical clue. I found there is a pattern here.
You will notice that the open "cup" runes that have two parallel branches (Fa, Ur, Os) are negative if rotated left. (Fa and Os are 180-degree reversals of each other, and hence each only have one positive and one negative position - rotate them right and they become the negative form of the other rune).
However, enclosing "spike" runes which contain closed triangles (Thorn, Rit, Bar) and "fork" runes with triangle-corners or incomplete triangle-forms and no parallel branches (Ka, Ar, Tyr, Laf, Man, Yr) are negative when rotated right. (Ka and Ar are 180-degree reversals of each other, and hence each only have one positive and one negative position - rotate them left and they become the negative form of the other rune).
And finally, "hedge" runes with radial or diagonal symmetry, which are "non-reversible" - i.e. they look no different if reversed (Hagal, Not, Is, Sig, Eh, Gibor) - are always positive when vertical and always negative when horizontal, no matter which direction you rotate them.
But why these patterns? Why this apparently strange system of the horizontal readings, differing based on the shape of the runes, on cups, forks, triangular spikes and symmetric hedges?
To understand the reasons behind that, we have to look at the runes in a decidedly un-modern way. Although List, Spiesberger and other Armanen rune masters did have to invent a great deal of modern rune-reading practice (as no historical accounts of rune-casting among Germanic peoples - other than than the extremely vague story of Tacitus - survive today), they nevertheless tried to base as much of their method on ancient wisdom and old Norse understandings of the runes as possible. In fact, despite the depredations of organized Christianity against occult and native folk wisdom in the Nordic and Teutonic nations, a great deal of information on runic mysticism did survive in the form of Icelandic grimoires such as the Galdrabók, which cover the uses of many different galdrastafir, para-runic charms and talismans. Other documents such as the Huld Manuscript (which details the symbolic meanings of the various parts of the Vegvísir or 'runic compass') give further clues. While none of these manuscripts date back to the time of the pre-Viking Norse, it is universally agreed that they are copies and compilations of far older works - they draw on far older oral and possibly written traditions of rune-carving and casting handed down by the masters for centuries and even millennia. Some of the Viking sagas, such as Egil's Saga, appear to support the most primitive (and angular) parts of the Icelandic magick-stave tradition.
Based on the knowledge preserved in the Icelandic magickal texts, it becomes clear why some runes are negative when rotated left and others are positive.
The runes (and this can be applied to other systems as well as Armanen) need to be understood, among other ways, as visual representations of catchers and deflectors of the primal energies - both positive/orderly and negative/chaotic - of the universe. (If you are unclear on the reasoning of why a rune is a catcher or a deflector, read the Hávamál verses associated with each of the 18 Armanen runes.) This is exactly the same way the Icelanders and their Norwegian ancestors saw runes and galdrstafir - as devices for gathering, deflecting, converting or storing spiritual energy.
Out of the various galdrastafir stave-modifiers, only the oldest two types (which avoid all curved lines) are primitive enough to be authentically runic in an Odinic sense, rather than later medieval interpolations:
Hence, the runes can also be understood in this way.
The "cup" runes are receivers of energy for the practitioner, i.e. in simplified terms, Fa receives wealth, Ur receives health, Os receives esteem, status and social confidence. Traditionally in Indo-European culture and cosmology, the fortunate one receives with the right hand, the unfortunate with the left, hence when turned left these receiver-runes are negative.
The enclosing "spike" runes and the "fork" runes are deflectors of energy for the practitioner. Thorn, Rit and Bar cancel out the energy of enemies, errors and calamities respectively, while Ka, Ar, Tyr, Laf, Man, and Yr essentially convert negative energies into positive ones and/or redirect them back at their source in some way. Traditionally the warrior deflects attacks with the left hand (the shield hand) hence if turned right these deflectors or shield-runes are vulnerable or negative.
The radial and diagonal symmetric "hedge-runes" (Hagal, Not, Is, Sig, Eh, Gibor) essentially are double-sided clusters of fork-branches. The fact that they are double-sided acts as a substitute for parallel branches, hence these runes can be though of as a combination of the tendencies of both "cup" and "fork" runes, and thus can be either receivers or deflectors of energy, as their Hávamál meanings indicate. These are the only "simultaneous dual-use" runes. Thus, in positive position, Not both attracts cooperation with karma and deflects one's futile discord and resistance to it, as Sig attracts victory and banishes weakness simultaneously. When upright (even if turned upside-down 180 degrees, they remain upright due to their symmetry) the hedge-runes are receivers and refiners of positive energy (as plants receive light and water and perform photosynthesis) - and they also deflect the negative like sharp thorny hedges. But when horizontal (either tilted left or right, again it makes no difference, due to symmetry) they are impotent to catch positive energy or deflect the negative with their shape, and may actually lose or repel good energies and attract bad ones - much as a bush or hedge stunted sideways must fight the wind or fall uprooted, gets less sunlight, is more vulnerable to diseases and parasites, and loses flowers and thus forfeits reproductive potential as a result - no matter if it leans left or right. The symbolism of Hagal, as the Hag-all, the All-Hedge, the all-symmetric defensive hedge-rune and Mother Rune, is particularly telling in this regard. Like the boughs of an overarching hedge, if it is knocked down either left or right, there is no protection from hail or fire.
Also you may notice that there are only three purely "peaceful" runes in the entire sequence. Such is also true of the "Elder" and "Younger" futharks. By contrast there are three times as many "warrior" runes (the deflectors) and twice as many "protection" runes (the symmetrical hedge types). That should make the message loud and clear - runes and Northern paths are not for cowards or weaklings. I am sure this would send a chill up the spine of so many hippie-like "new-age" and "wiccatru" folks who casually use "rune stones" for divination without really knowing their deeper meanings.
So for those of you who want to delve beyond the "what" of the historical reasons for the Spiesberger method being as "odd" as it is, and into the "why" of it all, hopefully this goes a long way towards answering your questions.