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Skyscript Astrology Forum

Kepler's Aspects
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Mark
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Posted: Fri Jun 23, 2006 8:28 pm    Post subject: Kepler's Aspects Reply with quote

I am giving a talk on the history of aspects at my Association in a few months and I am trying to fill in a few missing pieces in the story I haven't quite figured out. I could use some help if anyone out there has some knowledge in this area. Especially around the first use of the semi-square and quincunx.

Most sources I have read attribute Kepler with proposing three new aspects: The quintile, bi-quintile and the sesqui-quadrate. This it pointed out in the excellent articles here on Kepler by Nicholas Kollerstrom and David Plant.

However, in a footnote to his article 'Placido & the semi-arc method of house division' Michael Wackford makes an intriguing additional comment:

Quote:
''Placido followed Ptolemy in his use of the conjunction, sextile, square, trine and opposition aspects. To these he added the parallel, which he considered an aspect in its own right, and the 'new' aspects of 72į (quintile), 135į (Sesquiquadrate) and 144į (bi-quintile). A later thesis by Kepler included 30į (semi-sextile) and 45į (semi-square) but Placido specifically rejected them. The eight geometric aspects he used are related to ratios found in prominent musical resonances. It has recently come to light that Placido also composed music. ''


From my reading of Kollerstrom & Plant's articles I take it that Kepler only used the three aspects above because these fitted in to his Pythagorean philosophy which based his harmonic theory related to musical scales. For example David Plant states:

Quote:
..Kepler proposed the quintile(72į), bi-quintile ( 144į), and sesqui-quadrate (135į). Extending the analogy of the musical scale, the quintile is equivalent to an internal of a major third (4:5), the sesqui-quadrate to a minor sixth (5:8 ) and the bi-quintile to a major sixth (3:5).

Kepler realised that many more aspects configurations were possible , but rejected them on aesthetic grounds. The Ptolemaic aspects and his three new ones gave a pleasing correspondence with the consonances of the musical scale, other aspects ratios produced only discord''


So what was the later thesis referred to by Michael Wackford that proposed the 30į (semi-sextile) and 45į (semi-square) as valid aspects? I assume this was a source written after ' Harmony of the World'' ?
Did Kepler therefore later abandon his attempt to link new aspects to musical scales? Or did he find a way to fit these aspects into his harmonic-Pythagorean scheme?

Another related point I would like to clarify is whether I am right in thinking Kepler's aspects were based on a helio-centric rather than a geo-centric astrology? In which case are those using his suggested aspects through a geo-centric astrology departing from what Kepler proposed?

Oh and can I just add in a question on the quincunx? Deb mentions in her article that in the hellenistic and medieval period this and the semi-sextile were simply an inconjunct or non-aspectual relationship between the planets. However, who was the first astrologer to use the quincunx as an aspect we have recorded?
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Deb
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Posted: Mon Jun 26, 2006 2:57 pm    Post subject: Reply with quote

Hi Mark,

Quote:
So what was the later thesis referred to by Michael Wackford that proposed the 30į (semi-sextile) and 45į (semi-square) as valid aspects? I assume this was a source written after ' Harmony of the World'' ?


Kepler refers to the semi-sextile and semi-square aspects in proposition IX of Book IV of Harmony of the World. He includes these with the Ptolemaic aspects and the quintile, bi-quintile and sesqui-quadrate when he writes:

ďThat these figures are knowable and constructible has been shown in Book 1: that they are also congruent, in Book II Ö that the configurations of arcs expressed by such are influential is in the Axioms I and II previously stated.Ē


Quote:
Another related point I would like to clarify is whether I am right in thinking Kepler's aspects were based on a helio-centric rather than a geo-centric astrology? In which case are those using his suggested aspects through a geo-centric astrology departing from what Kepler proposed?


Kepler was a champion for heliocentricity and he argued strongly in favour of adopting the Copernican model in Book 5 of Harmony of the World. But astrologically he was still working from a geocentric perspective in which aspects perfected in the centre of the earth and the influences of the planets descend to us through the sublunar sphere. Although he contradicts or in some places expands Ptolemyís ideas, itís hardly possible to understand the philosophy of his work without a good knowledge of the philosophy set out by Ptolemy. Ptolemy referred to the Earth being in the middle of the heavens Ďwith regard to the senses' which is always the case, so a redefinition of an astronomical centre wouldnít require that the astrological centre should be shifted too.

Quote:
Oh and can I just add in a question on the quincunx? Deb mentions in her article that in the hellenistic and medieval period this and the semi-sextile were simply an inconjunct or non-aspectual relationship between the planets. However, who was the first astrologer to use the quincunx as an aspect we have recorded?


This is more the case with the inconjunct, the semi-sextile was simply considered weak. But interpretative value was taken from the fact that planets 5 signs apart do not connect to each other even in the earliest sources so I think it would be very hard to identify the first astrologer to use them as aspects. I havenít looked for this before but if I find anything interesting Iíll let you know.
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Andrew



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Posted: Tue Jun 27, 2006 6:04 am    Post subject: Reply with quote

The semisextile is equivalent to the lesser undecimal neutral second, the decile to the just minor tone, the semisquare to the septimal major second, the tridecile to the greater septimal tritone, and the quincunx to the septimal major sixth. This, of course, is common knowledge.
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Mark
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Posted: Thu Jul 06, 2006 11:37 am    Post subject: Reply with quote

Hi Deb,

Just a belated thanks for checking that out. Much appreciated.

I must pick up a copy of Harmony of the World though to see how Kepler actually justifies the inclusion of the semi-sextile and semi-square.

In regards Andrew's post..mmmm.. I am blatantly ignorant about music scale theory so I can't determine if thats just a joke or a serious offering. I am going to have a chat to a friend who is an amateur composer and astrology buff.......

I should point out I am not advocating the Keplerian aspects. Still, I think its important to understand why changing the traditional approach to aspects was justified by Kepler and his successors.
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Andrew



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Posted: Thu Jul 06, 2006 6:57 pm    Post subject: Reply with quote

[quote="MarkC"]I am going to have a chat to a friend who is an amateur composer and astrology buff.[/quote]

In regards Mark's post ... mmmm ... Andrew would recommend talking with a professional rather than an amateur ... preferably someone with expertise in the area of musical intervals. Even Andrew could not have made this up (much as he would have liked to).
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Mark
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Posted: Thu Jul 06, 2006 8:32 pm    Post subject: Reply with quote

Hello Andrew,

These posts aren't charged by the column inch! I would genuinely appreciate it if you could elaborate your point in a bit more detail please. You are coming over in quite a cryptic manner ....from my perspective anyway.

In particular, what is your source for the statement above linking these aspects to musical scale?

This might be 'common knowledge' to you but it certainly isn't to me!

Thanks

Mark
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Andrew



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Posted: Fri Jul 07, 2006 1:14 am    Post subject: Reply with quote

Quote:
These posts aren't charged by the column inch!


Just by the column nine inch . . .

Quote:
I would genuinely appreciate it if you could elaborate your point in a bit more detail please.


Absolutely. Please be patient.

Quote:
This might be 'common knowledge' to you but it certainly isn't to me!


Now, that was a joke.
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Andrew



Joined: 31 Dec 2004
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Posted: Fri Jul 07, 2006 1:34 am    Post subject: Reply with quote

Quote:
I would genuinely appreciate it if you could elaborate your point in a bit more detail please.


Here it is:

Thomas VŠczy Hightower

You have to do the spadework yourself: I'm past the point of trying to spell it out.

Have fun!
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Deb
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Posted: Fri Jul 07, 2006 12:39 pm    Post subject: Reply with quote

Hi Mark,

I couldn't understand Andrew's posts either, so I ran a search on the name he just gave. These articles look very interesting.

The Harmony of the Spheres by Thomas VŠczy Hightower
http://home22.inet.tele.dk/hightower/spheres.htm

The creation of musical scales, part I
http://home22.inet.tele.dk/hightower/scales.htm
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Andrew



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Posted: Fri Jul 07, 2006 11:58 pm    Post subject: Reply with quote

Wrong pages. More spadework. Dig deeper.

Try this:

http://home22.inet.tele.dk/hightower/octave3.htm

See the fourth section, "Sun sign or Zodiacs."

Now look at the diagram to your left: "kepler.gif"

Enlarge it.

Now match the ratios with the intervals (you have to figure that out on your own).

Oh wait, I already did that for you, of course!:

The semisextile is equivalent to the lesser undecimal neutral second, the decile to the just minor tone, the semisquare to the septimal major second, the tridecile to the greater septimal tritone, and the quincunx to the septimal major sixth.

Remember that?

What's not to understand? It can't be much plainer than that. Of course, Hightower isn't an astrologer per se, which may be why he was able to correlate the ratios in the first place. I translated the ratios into intervals (see above).

But this is just the tip of the iceberg.

Speaking of icebergs, Mark, here are links to a couple of articles you might find interesting (philosophical like Hightower but from a deep astrological perspective:)

http://www.khaldea.com/articles/har1.shtml

http://www.khaldea.com/articles/har2.shtml

I think Meyer makes more sense than Hightower, but since he's not a musician . . .
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Gunhilde



Joined: 10 Jun 2006
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Posted: Sat Jul 08, 2006 9:30 am    Post subject: Reply with quote

I don't mean this in a facetious way, but, what's the point in knowing this stuff?
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Mark
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Posted: Mon Jul 10, 2006 6:06 pm    Post subject: Reply with quote

Hello Antiscia,

Thanks for all your input. It will take me some time to try and absorb all this!

One point I have to question though is your suggestion about the origin of the aspects.

I don't think Deb actually stated that the relationship to the ASC was the origin of the aspects. Instead she suggests it relates to the traditional sign rulerships and their position to the Sun. This seems the main counter-theory to the idea the aspects relate back to pythagorean number theory and musical scales. However, Ptolemy seems to use both explanations so perhaps the two ideas are not in contradiction with each other.

Check out Deb's excellent article on sign rulership and the aspects:
http://www.skyscript.co.uk/rulership.html

Undoubtably, the ASC relationship to other parts of the chart was a likely origin of the traditional meanings of the houses. This is set out in Deb's definitive book 'Houses: Temples of the Sky'.

Mark
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Deb
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Posted: Mon Jul 10, 2006 7:40 pm    Post subject: Reply with quote

Quote:
I don't think Deb actually stated that the relationship to the ASC was the origin of the aspects. Instead she suggests it relates to the traditional sign rulerships and their position to the Sun. This seems the main counter-theory to the idea the aspects relate back to pythagorean number theory and musical scales. However, Ptolemy seems to use both explanations so perhaps the two ideas are not in contradiction with each other.


Actually Mark Iím not sure thatís what I was suggesting either. I think aspectual relationships were an important part of the rulership scheme but I wouldnít suggest that they originated out of it; it was more the other way around. (Sorry if Iím misrepresenting what youíre saying BTW, Iím not sure I even understand the question anymore, let alone the answer).

A better article for how I believe aspects are tied to the principles of shape and form is given at http://www.skyscript.co.uk/aspects.html

I wouldnít describe this as a counter-theory to the idea that aspects relate back to pythagorean number theory and musical scales. I think that itís a very important part of the whole issue too, and from what I understand it was used to support the numerological and geometrical principles of aspects rather than contradict them. But Iím simply not qualified to explain that element of the philosophy, being that I donít have a good understanding of it myself! It used to seem to me that the musical associations werenít such a big issue anyway, because most astrological texts fail to dwell upon them or even mention them. But as I said earlier, Iím fairly convinced that to have a good understanding of Keplerís views, we would have to start off with a good understanding of Ptolemyís, because Kepler bases a lot of his theory on either contradicting or expanding Ptolemyís teachings. And we can't overstate the influence of Ptolemy.

I also think that we probably have a very incomplete appreciation of what Ptolemy really had to say about astrological philosophy because so many of his works have been lost or are not easily available to us. Like Kepler, Ptolemy was very interested in both the structure of music and the mechanics of optical phenomena. (He wrote a 3 volume book on music called Harmonica, and a 5 volume book on optical phenomena called Optica, neither of which Iíve seen). Both music and the theory of optics are important concepts in Keplerís philosophy on aspects Ė optics were relevant because much of his theory rested upon the impressions of light and he believed that the meaning of aspects are revealed to us by the way that their images are received by the eye and impressed upon the mind. The translators of his Harmony of the World point out the little known fact that Kepler was the first person to give a correct analysis of the eye as an optical instrument, explaining the inversion of the image on the retina, etc.

I personally think that Kepler was one of the greatest astrological theorists of all time, and his Harmony of the World, one of the most important texts on astrological philosophy of all time. But it's not an easy read. If I ever come close to understanding half of it Iíll be very pleased with myself. Hmm, I canít find the reference for it now but Iím sure I remember one of his comments where he says he wrote the work, knowing it might take 1000 years before someone would be capable of understanding it properly and developing it further. So my advice would be that itís probably hugely ambitious to try to understand all these concepts in preparation for your upcoming talk, but itís a great idea to take on Kepler as a long term project Ė it will give you a lifetime of philosophical challenge.

Deb

PS Ė Yes Iím always grateful for promotion of the book, and remember, no publicity is bad publicity. Of course itís not perfect or anything Ė I mean, I donít imagine it will ever take someone 1000 years to understand my meagre offering Smile

Dee wrote:

Quote:
Deb stated her aspect explanation in relation to 'Classical Astrology', do we know if classical astrology was the origin of all astrology?


I'm not suggesting that Dee. I don't believe that myself. And on the subject of aspects the Mesopotamians are known to have developed and utilised the concept of triplicities before the rise of classical astrology. But I suppose that's another thread.
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granny_skot



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Posted: Mon Jul 10, 2006 7:50 pm    Post subject: Reply with quote

Just an odd note, the oldest currently KNOWN mathematical system was a 60 base system from the Mesopotomian Region, city of babylon, and was created, it seems to deal with astrological movement.

it would lead me to wonder if classical astrology is not indeed the mother of all philosophy and science.

I sometimes wonder if we dont get to close to the subject to see it clearly, after all how can you look at the sky and planets and not see the geometrical relationship?? it seems an odd arguement?

Oh well breaks over back to the matresses... Wink Granny
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Mark
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Posted: Mon Jul 10, 2006 8:34 pm    Post subject: Reply with quote

Hello Dee,

Ok fair comment. I was perhaps getting a tad carried away in describing Temples as 'definitive'. Clearly all such works are provisional. However, it does seem to be the most substantial piece of published material on the origins of the houses that at least I am aware of. Moreover, better
informed people than I seem to concur. I note the Astrology Center of America are also listing this as the best available book on the houses.
Thats not to say your manuscript will not totally transform our current understanding of the houses. I wish you well in that endeavour. Indeed I would be very interested to hear your views.

As for my comments I can only state I was presenting things as I understood them (or misunderstood them!)

My position was oversimplistic and it appears fundamentally incorrect!. Still I don't post on skyscript just to show what I know (or don't know!) I also do it as a learning experience. This thread has certainly given me that!

Incidentally have you seen Maurice McCann's book The Sun & the Aspects? He does suggest the origin of the aspects may be linked to the Sun although more on its observational relationship to the planets. Not the same as sign rulerships I admit.


Last edited by Mark on Mon Jul 10, 2006 9:26 pm; edited 1 time in total
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