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Dodekatamoria
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Deb
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Posted: Wed Jan 13, 2016 10:21 am    Post subject: Dodekatamoria Reply with quote

I've added a glossary entry on dodekatemoria and thought I would bring some attention to it as I have never used the technique much myself, and wonder if others have experiences to share in regard to its value? It seems to me that few astrologers make use of it nowadays, although its legacy and rationale appears to be as strong as that of the antiscia, and its calculation is quite simple (once some sources of confusion are removed):

http://www.skyscript.co.uk/gl/dodekatemorion.html

The glossary item briefly explains why conflicting accounts of the calculation are offered by Paulus and Firmicus and why Paulus is correct:

As to the use of the technique:

Quote:
Paulus and Firmicus both tell us that the dodekatemorion of the benefic planets bring good fortune if they fall upon the position of the Sun, Moon, Mercury, the angles, Part of Fortune, etc; and likewise the dodekatamorion of malefic planets will be expected to bring damage if they fall upon the chart's sensitive degrees.
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Mark
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Posted: Thu Jan 14, 2016 12:05 pm    Post subject: Reply with quote

Deb wrote:
Quote:
Commentators often describe these two variants as being distinguished by multiplication of 12 or 13


Thanks for the glossary update Deb,

We had an interesting forum discussion on the Duodekamoiria a few years ago. We see again there the the point that comes out in your glossary on whether the sources describe two systems (multiplication by 12 and /or 13) or whether this was a result of confusion that arose in the transmission of the technique.

http://skyscript.co.uk/forums/viewtopic.php?t=5202&highlight=

I think this is why so many find this topic confusing and its methodology a bit arcane. The practical question I have is does this lead to a difference with the tables of dwadasama used in Vedic astrology? If not why are these dodekatemoria not just laid out in table format for simplicity like the Indians use? I think they would be a lot more accessible presented in that way.

https://en.wikipedia.org/wiki/Dwadasama

This certainly helps if you want to check which dodekatemorion sign a planet or point falls in although this obviously doesn't offer you an exact degree which it will fall in. The latter clearly has many delineation uses too.

Mark
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Deb
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Posted: Thu Jan 14, 2016 1:33 pm    Post subject: Reply with quote

I didn't see the old thread Mark, or I would have added my notice to that. Reading through it, I notice Astrojin made similar points to those I made myself. The reason I added the entry is because I have been confused in the past by references to a so called- "13th harmonic", etc, and wanted to help others get past the needless confusion generated by that. When you read the ancient sources, this is clearly not in their mind at all. The word dodekatemorion always indicates association with the number 12, which is why it is used, not just for the 12-fold multiplication, but the 12-fold division as well. I note that in Mark Riley's translation of Valens the word dodekatemoria is also used to indicate increments of 12-degree intervals; then there is its general use for referring to the 12 signs or houses as 12-fold divisions of the sphere (though these are usually translated) - everything about the word is 12-fold in its meaning.

Quote:
The practical question I have is does this lead to a difference with the tables of dwadasama used in Vedic astrology? If not why are these dodekatemoria not just laid out in table format for simplicity like the Indians use? I think they would be a lot more accessible presented in that way.


The only difference is one of terminology; these are just the same but referred to as dodekatemoria in ancient Greek texts. It is well worth following the link I give to Francesca Rochberg's explanation of how the techniques are witnessed in cuneiform texts - note her diagram on p.156 shows the pattern in just the same way that the table on Wikipedia does. This is a different way of using the same word (dodekatemoria) but the two uses are united by the principle that since 12 is the number of the cosmos, its divisions and multiplications can be used to explore things at a microcosmic or a macrocosmic level. I find that quite interesting.
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Mark
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Posted: Thu Jan 14, 2016 2:32 pm    Post subject: Reply with quote

Deb wrote:

Quote:
I didn't see the old thread Mark, or I would have added my notice to that. Reading through it, I notice Astrojin made similar points to those I made myself. The reason I added the entry is because I have been confused in the past by references to a so called- "13th harmonic", etc, and wanted to help others get past the needless confusion generated by that. When you read the ancient sources, this is clearly not in their mind at all. The word dodekatemorion always indicates association with the number 12, which is why it is used, not just for the 12-fold multiplication, but the 12-fold division as well. I note that in Mark Riley's translation of Valens the word dodekatemoria is also used to indicate increments of 12-degree intervals; then there is its general use for referring to the 12 signs or houses as 12-fold divisions of the sphere (though these are usually translated) - everything about the word is 12-fold in its meaning.


Thanks. Its good to see an emphatic position like this. As you point out the number 12 is so integral to astrology the idea of multiplication by 12 to get the dodekatemorion degrees does have much more symbolic logic to it. I have always struggled with the idea of multiplication by 13 for that very reason. Moreover, as you point out the multiplication by 12 method goes back to Mesopotamian astrology.

Mark wrote:
Quote:
The practical question I have is does this lead to a difference with the tables of dwadasama used in Vedic astrology? If not why are these dodekatemoria not just laid out in table format for simplicity like the Indians use? I think they would be a lot more accessible presented in that way.


Deb wrote:
Quote:
The only difference is one of terminology; these are just the same but referred to as dodekatemoria in ancient Greek texts. It is well worth following the link I give to Francesca Rochberg's explanation of how the techniques are witnessed in cuneiform texts - note her diagram on p.156 shows the pattern in just the same way that the table on Wikipedia does. This is a different way of using the same word (dodekatemoria) but the two uses are united by the principle that since 12 is the number of the cosmos, its divisions and multiplications can be used to explore things at a microcosmic or a macrocosmic level. I find that quite interesting.


This surely adds great historical weight to the multiplication by 12 method based on Mesopotamian astrology and its mirrored in later Indian astrology. While I knew the Micro-zodiac was used in Babylonian astrology I hadn't appreciated the multiplication method to obtain specific degrees was this ancient! Quite remarkable really to think that this technique must be one of the earliest we have after the development of the zodiac itself into 12 equal signs.

Incidentally, I missed the helpful tables link you also produced to accompany this glossary entry.

Thanks! I now feel a lot more confident to work with this technique with that kind of back up.

Mark
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Deb
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Posted: Thu Jan 14, 2016 3:33 pm    Post subject: Reply with quote

Philosophically, I think it has a lot going for it - I am interested in this idea that if the dodekatemorion of a benefic falls on a sensitive point it brings benefit to it, etc., but I haven't noticed anyone doing much with that in traditional works.

BTW, I use that table of conversion into absolute longitude a lot, which is why I took the trouble to create it and upload to Skyscript years ago - so I would always be able to reference it easily Smile It's surprising how often it comes in handy.

Glad you got some benefit from the entry!
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RegulusAstrology



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Posted: Thu Jan 14, 2016 4:49 pm    Post subject: Reply with quote

Morning

Currently am using Maternus' computation method though I have not conducted any extensive tests comparing Maternus' and Paulus' calculation methods. What appeals to me philosophically about Maternus' approach is that the 12th parts can be viewed as fractals where 30 degrees of a sign are mapped to the entire 360 degrees of the zodiac.

In A Rectification Manual, pp. 6-8, I link the 12th part placement of Franklin Roosevelt's natal Moon 6CA08 - 12th part is in Virgo - genetically to his mother Sara Roosevelt who has a Virgo stellium in her natal. The obvious connections linking FDR to his mother via Virgo do not show any clues - FDR's Lot of the Mother is 20AR51, and FDR's Midheaven degree is 19GE25. No Virgo there. Yes there is a connection as Sara's Virgo stellium is conjunct FDR's natal Ascendant with Sara's Moon virtually partile conjunct FDR's Ascendant. So this is the connection, but there is no theory I am aware of that necessarily links the natal Ascendant to the mother -

Bottom line is there is a connection between the 12th part of FDR's natal Moon and his mother's nativity. I have not tested this on a wider sample but it shows promise.

Separately, in Ben Dykes 'The Search of the Heart,' pp. 198-205, Dykes presents an excerpt from Hephaistio on linking the 12th part of the Ascendant to the 'thought' of the native - this is in the context of developing a significator of thought for a querent as a preliminary step before reading a question.

My interest in this method concerns calculation of the natal 'victor' or 'Almutem Figuris' as Zoller referred to it. I am midway through a multiyear project which will cover 200-250 natal charts. Have hired a programmer to help with some of the testing - and the 12th part of the ASC, MC, Moon, Sun, LOF, and Syzygy will be considered. No preliminary results at this time but just to let you know I am taking the concept seriously.

Best,
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Deb
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Posted: Thu Jan 14, 2016 7:00 pm    Post subject: Reply with quote

Very interesting; thanks for that!
Quote:

What appeals to me philosophically about Maternus' approach is that the 12th parts can be viewed as fractals where 30 degrees of a sign are mapped to the entire 360 degrees of the zodiac.


Yes, I think that is implicit in the use of the technique.
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Mark
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Posted: Thu Jan 14, 2016 9:12 pm    Post subject: Reply with quote

Hello Dr H,

I know you relied heavily on primary directions through the Egyptian bounds to rectify your version of the USA chart for July 4th 1776.

I just wondered if you gave the dodekatemoria any attention in your mundane research?

Mark
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Konrad



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Posted: Fri Jan 15, 2016 7:57 am    Post subject: Reply with quote

Hi Deb,

I have a couple of issues with the glossary entry.

Quote:
Conflicting accounts of the method are offered by Paulus (Introductory Matters, 22) and Firmicus (Mathesis, I.XIII). The method of Firmicus (which is probably afflicted by misunderstanding) projects the result of the calculation from the beginning of the sign in which the planet is positioned, so (starting the count of 120° from 0° Taurus) the dodekatemorion of 10° Taurus would be 10° Virgo. The method of Paulus projects the result of the calculation from the position of the planet, so (starting the count of 120° from 10° Taurus) the dodekatemorion of 10° Taurus is 20° Virgo - another way to get the same result (which is how Paulus describes it) is to multiply the degree position by 13 instead of 12 and then start the count from the beginning of the sign - the multiplication by 13 simply accommodates the fact that the count is including the position of the planet.


First, your calculations are incorrect. Using the Firmicus method, the Dodekatemorion of 10 Taurus will be 0 Virgo (the 120 deg count begins from 0 Taurus). The Pauline Dodekatemorion falls out at 10 Virgo (13*10=130) as this is also counted from the beginning of the sign.

Second, I don't think either is a misunderstanding of the other. Firmicus' method is quite clearly a degree calculation of the method proposed by Porhyry (ch.39) among others. The reason for beginning the count at the beginning of the sign is that this method is one of fractals of space in its purest sense. If we take a planet at 5deg20 of Aries, we count off 2deg30 increments and treat them as signs, we have two full signs plus 20 mins. If we multiply the 20 minutes by 12, we come to 4 deg. So arrive at 4 Gemini. This is the same as if we multiply the whole thing by 12 and count it from 0 Aries (5.333*12=64). These Dodekatemoria are signs within signs and are divisions like the Bounds. As you have illustarted, the Pauline method treats the whole sign as the 360deg circle and finds the planet's relative position starting from itself.

The example in Valens is only definitely a Pauline Dodekaemorion if the Sun is no further into 22 Aquarius than 22deg30. There is an example in Book 9 of Valens in the chapter entitled "Male and Female Nativities; Monstrous or Animal-like Nativities". Here the Moon is in 19 Pisces and is said to fall out in Libra. This is only possible with the Pauline Dodekatemoria if Valens means the 19th degree of Pisces.
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Martin Gansten
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Posted: Fri Jan 15, 2016 8:29 am    Post subject: Reply with quote

I started writing this yesterday, and see now that Konrad has anticipated some of my points. But I'll add this anyway:

There are two systems just as you say, Deb, but the system you favour is not the one Rochberg describes in the book excerpt you link to.

The system you support is the one that can be described in either of these two ways:

(a) Multiply the longitude of a planet by 12 and count the result from the planet itself.
(b) Multiply the longitude of a planet by 13 and count the result from the beginning of the sign occupied by the planet.

Both give the same result, which is actually equivalent to a 'microzodiac' of 13 signs (not 12), with the first and last division being the same. Let's take a planet at 2°00 Aquarius and a planet at 28°00 Aquarius:

2 × 12 = 24, which added to the original 2° in Aquarius gives a position of 26° Aquarius

28 × 12 = 336, which added to the original 28° in Aquarius gives 328 + 336 - 360 = 304, or a position of 4° Aquarius

So both the first and the last division of Aquarius belong to Aquarius. If we put the starting points of the divisions in tabular format according to this method, they will look as follows (rounded off):

0°00 Aquarius
2°18 Pisces
4°37 Aries
6°55 Taurus
9°14 Gemini
11°32 Cancer
13°51 Leo
16°09 Virgo
18°28 Libra
20°46 Scorpio
23°05 Sagittarius
25°23 Capricorn
27°41 Aquarius

This is exactly the same thing as the modern '13th harmonic'.

The other system is the prevalent one in India, as Mark says, though both systems have actually found their way into Sanskrit texts (and, if memory serves, both go back to Babylonian sources). It can be described as:

(c) Multiply the longitude of a planet by 12 and count the result from the beginning of the sign occupied by the planet.

This will give a 'microzodiac' like the one Rochberg describes, with 12 divisions beginning with the sign itself. (Incidentally, this will not coincide with any modern harmonic, as there will be a gap or jump between the last twelfth-part of one sign and the first twelfth-part in the next. Harmonics don't have gaps.)

Let's take the planets at 2°00 Aquarius and 28°00 Aquarius again:

2 × 12 = 24, which added to 0° Aquarius gives a position of 24° Aquarius

28 × 12 = 336, which added to 0° Aquarius gives 300 + 336 - 360 = 276, or a position of 6° Capricorn.

So the first division of Aquarius belongs to Aquarius, and the last to Capricorn. If we put the starting points of the divisions in tabular format according to this method, they will look as follows:

0°00 Aquarius
2°30 Pisces
5°00 Aries
7°30 Taurus
10°00 Gemini
12°30 Cancer
15°00 Leo
17°30 Virgo
20°00 Libra
22°30 Scorpio
25°00 Sagittarius
27°30 Capricorn
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Deb
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Posted: Fri Jan 15, 2016 9:47 am    Post subject: Reply with quote

Konrad and Martin, thanks very much for your input. I brought attention to to make sure I haven’t missed anything important, so I am taking your comments very seriously. This is not a technique I have used myself, so I spent some time last week studying descriptions of it in various ancient texts and put together what I thought was a reliable account. I will revise as necessary after checking out all your points.
I had:
Quote:
The method of Firmicus (which is probably afflicted by misunderstanding) projects the result of the calculation from the beginning of the sign in which the planet is positioned, so (starting the count of 120° from 0° Taurus) the dodekatemorion of 10° Taurus would be 10° Virgo. The method of Paulus projects the result of the calculation from the position of the planet, so (starting the count of 120° from 10° Taurus) the dodekatemorion of 10° Taurus is 20° Virgo

Konrad you say:
Quote:
First, your calculations are incorrect. Using the Firmicus method, the Dodekatemorion of 10 Taurus will be 0 Virgo (the 120 deg count begins from 0 Taurus). The Pauline Dodekatemorion falls out at 10 Virgo (13*10=130) as this is also counted from the beginning of the sign.


Of course, you are right. I am banging my head as I see that mistake as I had written 0° and 10° Virgo in my notes and have no idea how that got turned into 10° and 20° when I typed up the glossary item! I will change that obvious mistake straightaway, and though I am not sure I agree (or fully follow) your other points yet, I will take out the bracketed remark about Firmicus whilst I look into your other points. So that part of the entry will now read:
Quote:

The method of Firmicus projects the result of the calculation from the beginning of the sign in which the planet is positioned, so (starting the count of 120° from 0° Taurus) the dodekatemorion of 10° Taurus falls at 0° Virgo. The method of Paulus projects the result of the calculation from the position of the planet, so (starting the count of 120° from 10° Taurus) the dodekatemorion of 10° Taurus is 10° Virgo - another way to get the same result (which is how Paulus describes it) is to multiply the degree position by 13 instead of 12 and then start the count from the beginning of the sign - the multiplication by 13 simply accommodates the fact that the count is including the position of the planet.

Thank you for correcting me, and Mark – sorry if this added to your earlier confusion!


Last edited by Deb on Fri Jan 15, 2016 11:32 am; edited 1 time in total
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Deb
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Posted: Fri Jan 15, 2016 11:31 am    Post subject: Reply with quote

Konrad I clearly agree with the above point, which was a stupid mistake on my part; but this part of your post I do not understand:
Quote:
The example in Valens is only definitely a Pauline Dodekaemorion if the Sun is no further into 22 Aquarius than 22deg30.

Even at 23 Aquarius, the result would land in Scorpio:
23 x 12 = 276.
The dodekatemorion of 23 Aquarius would lie 276° ahead of it in the zodiac. 276 = 10 signs and 6 degrees, so the result would be 29 Scorpio.

I am starting to appreciate that (I think) you are expecting the division of the signs by 12 to yield the result of the multiplications, whereas I conceived of these as being two separate techniques, united only by the underlying principle that mathematical manipulation of the number 12 offers symbolic meaning. I find no trace in Firmicus of him regarding the dodekatamoira as “signs within signs” as you suggest; he talks about the Moon sending dodekatamoira (in the actual zodiac) towards other planets. So I don’ think his method is intended to be any different from that described by Paulus, but I have yet to check the text of Porphyry, so will leave it at that for now.

This also makes me realise that I misunderstood Mark’s question earlier, when he asked me to look at the table on Wikipedia. I just noticed that the order was the same and did not mean to suggest that the table on that page gives the result for multiplied dodekatamoria.
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Posted: Fri Jan 15, 2016 12:24 pm    Post subject: Reply with quote

Deb, my point is that at 22deg30, the Firmicus Dodekatemorion also falls out in Scorpio.

My comnent about 'signs within signs' is an observation of my own based upon the description given in Porphyry and the Babylonian Dodekatemorion tablets. I see the 12 and 13 multiplication as two different techniques based upon a similar idea.
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Deb
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Posted: Fri Jan 15, 2016 1:06 pm    Post subject: Reply with quote

Konrad wrote:
Deb, my point is that at 22deg30, the Firmicus Dodekatemorion also falls out in Scorpio.

Thanks for clarifying that, because I misunderstood you to mean that the Pauline method wouldn't work beyond 22deg30. That is actually quite a useful point for me to realise, as my motivation for looking into this matter in the first place was to understand the technique as Valens understood it, and how it impacted on his calculation of the rising sign.

Konrad wrote:
My comnent about 'signs within signs' is an observation of my own based upon the description given in Porphyry and the Babylonian Dodekatemorion tablets. I see the 12 and 13 multiplication as two different techniques based upon a similar idea.


Again, thanks for clarifying that - I also see the 12 and 13 multiplication as two different techniques based upon a similar idea. I have now read the Porphyry description you pointed me to and will refer to it in the reply I am about to post to Martin.
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Deb
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Posted: Fri Jan 15, 2016 1:15 pm    Post subject: Reply with quote

Hi Martin
Thanks for commenting. You start your post by saying:
Quote:
There are two systems just as you say, Deb, but the system you favour is not the one Rochberg describes in the book excerpt you link to.

I’m confused as to why you say that and will write out the part of her text that describes it quite clearly below.
You then (correctly) summarize my understanding by saying:
Quote:
The system you support is the one that can be described in either of these two ways:
(a) Multiply the longitude of a planet by 12 and count the result from the planet itself.
(b) Multiply the longitude of a planet by 13 and count the result from the beginning of the sign occupied by the planet.

That is correct – either approach will lead to the same result. It is not that I support one approach or another, I am simply basing my understanding on what the authors I have read explain. Keep in mind that (as discussed above) this method means that the dodekatemorion of a planet at 10° of a sign, when multiplied by 12, will fall at 10° of the sign 120° ahead of it in the zodiac (so for one at 10° Aries it falls at 10° Leo; for one at 10° Taurus it falls at 10° Virgo, etc). You suggest this is not what Rochberg describes, saying:
Quote:
The other system is the prevalent one in India, as Mark says, though both systems have actually found their way into Sanskrit texts (and, if memory serves, both go back to Babylonian sources). It can be described as:

(c) Multiply the longitude of a planet by 12 and count the result from the beginning of the sign occupied by the planet.

This will give a 'microzodiac' like the one Rochberg describes, with 12 divisions beginning with the sign itself.

The result of that calculation would mean that the dodekatemorion of a planet at 10° of a sign will fall in 0° of the sign 120° ahead of it in the zodiac (so for one at 10° Aries it falls at 0° Leo; for one at 10° Taurus it falls at 0° Virgo, etc). But the way that I have described it is what Rochberg shows in her book.

In the Babylonian sources they are called zittu and her text (bottom paragraph, p. 157) reads as below (I have omitted her mathematical notations but you can check this on this Google book link):
Quote:
In other sources in which the connection between astrology and magic is documented, incantations are assigned to the twelve zittu of the zodiac. As shown by Neugebauer and Sachs, these two text provide further evidence that the Greek method of computing dodekatemoria was based on the method found in cuneiform material. The method may be formulated in the following way: Given a position in the zodiac expressed in degrees of a zodiacal sign, a second position in the zodiac may be obtained by multiplying the degrees by 12 and adding the result to the first longitude.

Rochberg then gives the interpretation of a few lines from a table in a cuneiform source which demonstrates this (beginning at the top of p.58 ):

Quote:
In line 1, the position given is I 10 (= Ares 10°). Aries 10° is associated with Leo 10°, which is called “Leo of Aries”. Following the abovementioned method of computing dodekatemoria, we multiply 10° (the degrees of Aries) by twelve and travel that many degrees (120°) along the zodiac from Aries to the sign Leo. Adding n degrees of the zodiacal sign [“n degrees” = number of degrees of the planet], here 10, we reach Leo 10° as given … [in the table, she then notes the same procedure yields the rest of the results].


It is pure coincidence (but very handy) that the cuneiform text offers the example of 10° as I did (to make life simple). We can see that it yields exactly the same result as that I described.

Hence, I don’t believe the technique that divides the signs into 2½° sections can accurately produce the results of the technique that aims to multiply the degree positions by 12 (as illustrated here). I don’t doubt your word that they were treated this way in Sanskrit texts and have now followed up Konrad’s reference to Porphyry, where he is aiming to compute dodekatemoria by reference to 2½° divisions of the signs - but this approach simply doesn’t give reliable results for multiplication of the degree point by 12, or show the method described in the Babylonian source Rochberg refers to, or the intention of authors such as Paulus and Firmicus to identify extended points in the zodiac to which planetary connections could be made. Rochberg’s description of the zittu as 2½° divisions doesn’t show this either - it only suggests that the ‘micro-zodiac’ offered symbolic association of these parts with plants, trees, stones, etc.

On the other hand, although I personally believe Firmicus was aiming to replicate the instruction given by Paulus and did so in a clumsy way that simply generated error, I will remove any implication that this was a mistake from the glossary item, because I cannot prove that without going into a major argument, it I don't want the glossary item to contain any unnecessarily controversial points. You have also made me realise that the glossary entry needs some kind of amendment, to give more acknowledgement of what the term dodekatemoria meant when associated with sign sub-divisions rather than degree multiplications. So I am going to give some more thought to that too.


Last edited by Deb on Fri Jan 15, 2016 1:40 pm; edited 5 times in total
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