Hi Atlantean!

Interesting argument, but I'm afraid I don't agree!

On this basis, it could be argued that the 120th harmonic aspects (eg 3 degrees, 177 degrees) would be more important than either the 24th harmonic ones or the 15th harmonic ones, since they would include not only the conjunction, semi-sextile 10/120ths, semi-square 15/120ths, sextile 20/120ths, square 30/120ths, trine 40/120ths, sesquiquadrate 45/120ths, quincunx 50/120ths, opposition 60/120ths, and Tyl / Reeves 'quindecile' 55/120ths... but also the quintile 24/120ths, bi-quintile 48/120ths, decile 12/120ths, tridecile (a.k.a. sesquiquintile) 36/120ths, quindecile 8/120ths, bi-quindecile* 16/120ths, quadri-quindecile* 32/120ths, and septi-quindecile* 56/120ths, not forgetting the vigintile 6/120ths and its multiples....

This argument fails in my opinion, since the greater the circle division factor, the more major and minor aspects will fit into its pattern, but you are also introducing aspects that are more and more absurdly minor for each further division, and it should be the importance of these base aspects which cannot be derived from a simpler division of the circle that is the standard by which to judge the circle divisor, and not the number of multiples of these aspects that can equally be obtained readily from a simpler division of the circle.

NB: My calculations of fractions above are pure mental arithmetic on-the-fly so if I made any mistakes please forgive them - I'd be glad to put them right.

* for the sake of a working terminology that is more or less consistent with tradition - not definitive terms

To bring some additional elements of the "quindecile" aspects revival, I quote from Ricki Reeves book, The Quindecile: The Astrology & Psychology of Obsession from the 3rd Chapter, the History of the Quindecile:

The quindecile or 165? aspect, was first brought into astrological awareness by German astrologer Thomas Ring (1892-1983). He utilized it in his work on the horoscope of Leonardo da Vinci, noting it in the relationship of Leonardo's Moon in Pisces (the emotional need to merge sensitivity, intuitiveness, and working the intangible) and Neptune in Libra (seeking the illusive, imaginary, and ideal through all to which it relates). Thomas Ring termed this 165? spacial relationship "the separation aspect," denoting its characteristics to be those of disruption and upheaval that divorce the individual from the balance of his or her life, through the nature of the two planets involved.

The use of this aspect then faded into the background of astrology until it was rediscovered by international astrologer Noel Tyl, who came across the work done by Thomas Ring wile researching the horoscope of Leonardo da Vince for his book Astrology of the Famed. Noel Tyl did extensive research, through the use of over 600 horoscopes, and confirmed it to be a most prominant indicator of upheaval and separation in an individual's life. My Tyl included in his work the concept of obsession-compulsion as a factor in the manifestation of this aspect, denoting is as a response to upset and trauma in one's life.

She goes on to discuss Leonardo da Vinci specifically, commenting on his very precise and perceptive mind and then uses his "quindecile" aspect to explain why, even with all of his talents and mental abilities and drive to understand the world and how it functions, that still he was someone who never finished most of his works and how most of his inventive genius never got beyond the drawings and details from his many journals that he kept throughout his life.

Ricki was a student of Noel's so there may be a bias in the Tyl-heavy "history" of the aspect, HOWEVER, he really IS the person most responsible for "bringing the aspect back."

Atlantean

Philip,

Hello

Yes, but by moving to the 120th harmonic, you have cut the 24th harmonic divisions EACH into 5 "pieces", many of which are nonsense aspects. The 24th Harmonic through using only simple fractions contains all the main aspects used in Astrology. (including the ever-more-popular-to-come, quindecile)

From your comments, we should just go straight to the 21,600th harmonic which will include every division possible down to a minute of arc.

The circle...is...of course continuous. The divisions that we use astrologically, extremely discrete for manageability.

Peace

Atlantean

Considering that Noel Tyl in Astrology of the Famed (1996) cites the delineation of Leonardo's horoscope from a book by Ring that was published in 1980, I personally feel that to say the aspect was lost then 'rediscovered' is stretching the truth a little. Ring's work has been popular in Germany continuously. What Tyl did was to discover it for himself, then conduct his own research, and re-present it to the English speaking marketplace. It had never been 'lost'.

This reminds me a bit of the hyperbole surrounding the supposed 'rediscovery' of the 'Law of Attraction' by Jerry and Esther Hicks and Rhonda Byrne, the latter marketing it as 'The Secret'. These ideas have been out there all along in books from the early 20th century. Some people just have a keen eye for marketing in my humble opinion.

I read the history section of Ricki Reeves' book you refer to late last night, hence my comments overnight regarding Tyl's sources in 'Astrology of the Famed' to which Reeves refers.

I still don't agree with your reasoning for the importance of the 24th harmonic, sorry to say. The only base aspects in the 24th harmonic that cannot be derived from simpler divisions of the circle than (2*2*2*3) are 15 degrees, 75 degrees, 105 degrees and 165 degrees. These and these alone are the aspects by which this division should be judged. The same argument you place for the 120th harmonic, that these might be 'nonsense aspects', could equally be applied here and for exactly the same reasons. The multiples of the same base aspect that can be derived more simply are completely immaterial in assessing the base aspect per se and its multiples that can only be derived from a minimum of the circle division factor that was applied (in this case 24) to obtain it.

To get the 45 degree and 135 degree aspects you do not need 2*2*2*3. You only need 2*2*2. Similarly, to get 30 degrees and 150 degrees you do not need 2*2*2*3. You only need 2*2*3.

For every additional divisor from the whole circle, an aspect becomes naturally more minor by its nature. Aspects derived from 2*2*2*3 will be more minor than those derived from 2*2*3 and those derived from 2*2*2.

In turn, those derived from 2*2*3 will be more minor than those derived from 2*2 and those derived from 2*3, and so on.

In the case of the traditional quindecile, the circle division by 3*5 is a lot simpler mathematically than that by 2*2*2*3. To demonstrate that the 24th harmonic aspects such as 15 degrees and 165 degrees are inherently more major than the 15th harmonic aspects, you are going to have to argue, in my opinion, that the division of the circle by 2*2*2 is a simpler, more natural operation than its division by 5, since both harmonics have in common a division by 3, and we can therefore factor the 3 out when comparing them. So if you believe that the quintile and biquintile are less important in astrological interpretation than the semisquare and sesquiquadrate, then I feel your argument at least becomes consistent according to the principles of how aspects are derived and how their power diminishes as they become more minor with additional divisors applied to the full 360? circle.

Kepler did not believe that the quintile and biquintile were less important than the semisquare and sesquiquare. He believed the quindecile (24?) series was of borderline influence (as per my citation above) and apparently (based on the same source) disregarded the quartvigintile (15?) altogether.

Before Ring (1956) I have found no reference to the use of the 15? aspect in astrology, unlike the several references to that of the 24? aspect. This no doubt in part because Kepler mentioned the latter but not the former.

This brings us into the later 20th century and the harmonic astrologers. Addey, Hamblin and Jay all advocate the importance of the 24? series. At least two of them also give some importance to the 15? series. They are not limited by the limitations imposed by Kepler, since they have taken harmonic theory to a new level of enquiry. Why can we not follow their example and accept both the 24? and 15? series as being of potential importance and study them both with equally open mind?

This brings me back to the whole point of my dissatisfaction with the appropriation of the term quindecile to have a new meaning. It is creating an artificial conflict between two different but theoretically comparably valid series of aspects. There should be no such conflict. Each should be free to be studied. But by giving one of them the name the other already had, Noel Tyl has generated in your mind, if you don't object to my making such an observation Atlantean, the idea that one or the other series of aspects must be cast aside and regarded as relatively insignificant. This need not be the case.

Re: "Considering that Noel Tyl in Astrology of the Famed (1996) cites the delineation of Leonardo's horoscope from a book by Ring that was published in 1980, I personally feel that to say the aspect was lost then 'rediscovered' is stretching the truth a little. Ring's work has been popular in Germany continuously. What Tyl did was to discover it for himself, then conduct his own research, and re-present it to the English speaking marketplace. It had never been 'lost'."

I will give you that one...and I must admit, quite enjoyably!

Re: "Keen eye for marketing..."

Perceptive, though I realized this of course.

Rather than argue back and forth regarding the harmonics, let me present my "case" slightly differently. Peruse the following list and then you'll see my argument devoid of the mathematics that seem to keep leading us astray of each other, even though we both ride the same model high horse.

0 Conjunction
1
2 Semisextile
3 Semisquare
4 Sextile
5
6 Square
7
8 Trine
9 Sesquiquadrate
10 Inconjunct
11
12 Opposition

As the above list could reasonably be said to contain the "common aspects", a point could certainly be made that inspection of "spaces" #1, 5, 7, and 11 MIGHT prove fruitful.

Further inspection of "slot" number 11, the "quindecile" has shown quite conclusively that there IS something going on with space number 11.

Though we don't agree perhaps on the name for the slot, let's not disagree that there is an obvious slot there.

Peace

Atlantean

There is, but the slots are also demonstrably an artifact of your attempt to find the common harmonic that will incorporate both the eighth harmonic aspects (2*2*2) and the 12th harmonic aspects (2*2*3). The eighth harmonic aspects were introduced by Kepler and are non-zodiacal in their intervals. Yet their derivation is still simpler than those of the 24th harmonic because only three rather than four factors are needed.

Similarly, you could seek to find the common harmonic that will incorporate both the 12th harmonic aspects (2*2*3) and the fifth haronic aspects (5) and you will get (2*2*3*5) the 60th harmonic. Does this mean that the six-degree aspect is of importance just because slots appear at 6 degree intervals when we attempt this? I regret I believe not.

All the zodiacal aspects are obtainable by the 12th harmonic. To push beyond that is in my view to admit of harmonic theory as a rational basis for aspects, since the 15 degree aspect, as much as the 45 degree one, does not exist on a 12-fold zodiacal sign basis.

What Kepler did with the 15th harmonic (3*5) is really no different to what you are doing with the 24th harmonic in my view. It is an attempt to find the common harmonic between the third and the fifth, just as you were seeking to find the common harmonic between the eighth and the twelfth. Is one of these procedures really any more valid than other in terms of harmonic theory? Both involve looking for the common harmonic between a zodiacal one and a non-zodiacal one. In this case, the third harmonic is zodiacal; the fifth is not.

Thus similarly we get slots:

1 24?
2 48?
3 Quintile 72?
4. 96?
5 Trine 120?
6 Biquintile 144
7 168?

Does that mean that the missing aspects are valid? According to harmonic theory, yes, just as the slots in your list are. There are more slots in this case because there are no 2s in the circle division factor, and finding the common harmonic of larger prime numbers than 2, such as 5, leads to larger numbers of slots. I don't see any difference otherwise.

Must go now - food on, then work! Thanks for the chat!

No, because that list hardly could be considered to contain ALL the common aspects, as the list I presented did...

Atlantean

Philip Graves wrote:Just an historical note since the question of what aspect the term 'quindecile' refers to was raised earlier in this strand.

James Wilson, writing in the first edition of his 'Dictionary of Astrology' (1819), p. 99, under 'Familiarities', expressly attributes the invention of the quindecile to Kepler (p. 99) and goes on to define it (p. 100) thus:

The Quindecile, a distance of 24?, is the circle divided by 15.

Hello

For what it's worth (possibly not much) Fred Gettings in his 'The Arkana Dictionary of Astrology, first published by Routledge & Kegan Paul Ltd in 1985 and published by Arkana in a revised edition in 1990 (which is the edition I am quoting from here) says:-

quindecile An aspect of 24 degrees, derived from dividing the zodiac into 15ths.

That's all he says about it. There are no references for the definition or to any usages of it but in his bibliography he lists the same works of Kepler, Addey and Pearce that have been mentioned in this thread.

He doesn't list the works of Hamblin, Harvey/Harding, Tyl et al.

Regards

H.

Philip Graves wrote:Considering that Noel Tyl in Astrology of the Famed (1996) cites the delineation of Leonardo's horoscope from a book by Ring that was published in 1980, I personally feel that to say the aspect was lost then 'rediscovered' is stretching the truth a little. Ring's work has been popular in Germany continuously. What Tyl did was to discover it for himself, then conduct his own research, and re-present it to the English speaking marketplace. It had never been 'lost'.

My friend Al H. Morrison first wrote to me about the 165 degree aspect in a letter in 1981. He mentioned that he had been using the 165 degree aspect for many years, having been taught about it from Johndro himself in the early 1950's. He wrote that 'It is in the affairs of the houses tenanted by the planets in this aspect that the native has this unending capability of carrying on, continuing, in total disregard of all practical reality. There is nothing like the nagging persistence of the 165 degree aspect, just never say die, never stop trying, never give up on negotiating the non-negotiable.' He termed it the Johndro aspect, for want of a better name, and some people today still call it that.

He suggested at that time that I would find it meaningful if I started looking at charts where Chiron was in a 165 degree relationship with other planets. When I looked at Chiron's discovery chart and found Chiron in such an aspect to Mercury, I was motivated to follow up on Al's suggestion and spent the next three years looking many, many charts of celebrities searching for Chiron in "Johndro aspect" to major planets and angles.

The resulting findings were included as a section in my 1985 book, "Essence and Application: A View From Chiron" specifically devoted to Chiron and the 165 degree aspect. I'd like to quote a small part of that section here:

"The overall pattern I have found, when Chiron is 165^ to any planet, supports Al?s description of persistence. But even more, it seems that the planet in this aspect to Chiron becomes much more active and much more visible as part of the person?s image. This planet is the one that is the vehicle for the persistence. The person pushes, unendingly, with the aspected planet, while Chiron acts to part or overcome the obstacle in the way of the planet. Sometimes Chiron seems to create additional, unusual problems first which the person must resolve---and in so doing, develop more and more persistence in many different kinds of environment. This must be the ?teacher? facet of Chiron showing up."

There is a good bit more, including a brief description of Chiron's influence in Johndro aspect to planet after planet (with the caveat that these were the results of my research, and the reader was advised to to their own research to see if they "come up with similar results."

My book sold several hundred copies before Noel Tyl supposedly 'rediscovered' this aspect around 1996, bringing this aspect to the attention of a great many people who, like myself, had never heard of it previously. But I'd never make the claim that I 'rediscovered' the aspect! (I will always be greatful to Al, however, for bringing it to my attention.)

I do know of at least one software program, Intrepid, that refers to it as the Johndro aspect, and the author of another program, AstroDeluxe for Windows, includes the following statement about this aspect in his users manual, "The research by Al H. Morrison and Zane Stein on the 165 degree aspect appeared in Stein's book, Essence and Application: A View from Chiron, first published in 1985."

Astrologer Bill Meridian is a regular user of the 165 degree aspect, and he has given due credit to learning about the research of Johndro and Brown on this subject from his teacher, the venerable Charles Jayne.

I guess Tyl declaring himself as the re-discoverer of this aspect is the case of an astrologer who just hasn't bothered to explore what other astrologers have been writing about.