Skyscript Astrology Forum

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:

''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 72? (quintile), 135? (Sesquiquadrate) and 144? (bi-quintile). A later thesis by Kepler included 30? (semi-sextile) and 45? (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:

..Kepler proposed the quintile(72?), bi-quintile ( 144?), and sesqui-quadrate (135?). 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 30? (semi-sextile) and 45? (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?

Hi Mark,

So what was the later thesis referred to by Michael Wackford that proposed the 30? (semi-sextile) and 45? (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:

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

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 Ptolemy?s ideas, it?s 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 ?with regard to the senses' which is always the case, so a redefinition of an astronomical centre wouldn?t require that the astrological centre should be shifted too.

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 haven?t looked for this before but if I find anything interesting I?ll let you know.

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.

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.

MarkC wrote:I am going to have a chat to a friend who is an amateur composer and astrology buff.

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).

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

These posts aren't charged by the column inch!

Just by the column nine inch . . .

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

Absolutely. Please be patient.

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

Now, that was a joke.

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

Here it is:

Thomas V?czy Hightower

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

Have fun!

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 V?czy Hightower
http://home22.inet.tele.dk/hightower/spheres.htm

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

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 . . .

I don't mean this in a facetious way, but, what's the point in knowing this stuff?

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