important harmonics
Jun. 16th, 2024 11:28 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
crimsoncurrentI decided to start over with an approach similar to the analysis I used in the 1970's as an astrologer, but with the improved software available now. I looked at harmonic charts 1 (the "normal" chart), the 5th, 7th, 8th, and 64th harmonic charts. The 8th and 64th harmonic charts are particularly important because they are "octave harmonics" or "hard aspects". Hard aspects are harmonics 1, 2, 4, 8, 16, 32, etc. In the harmonic chart wheel are drawn the following aspects: opposition, square, trine, sextile, semisextile, quincunx, semisquare, sesquiquadrate, 1/16, 3/16, 5/16, and 7/16 aspects. A semisquare or sesquiquadrate aspect appears as a conjunction in the 8th harmonic chart, and similarly a semisquare or sesquiquadrate aspect in the 8th harmonic chart appears as a conjunction in the 64th harmonic chart. By looking at the hard aspects in the 1st, 8th, and 64th harmonic charts I can actually see all octave harmonic patterns up to the 1024th harmonic very quickly. I can also see the soft aspects (semisextile, sextile, and trine) as well as quincunx as well.
I also included the 7th harmonic because I associate the 7th harmonic with discipline, chronic situations or determination, sobriety, and deep inner probing, a liking for things that are humble and ponderous, sometimes almost mystical or ancient. From my experience teaching math to children and adults, the 7th harmonic pattern seemed very likely to be strong in the charts of mathematicians. I found some evidence of this in the chart of physicists but not as strong as I had hoped, and other harmonics, like the 17th and 19th were often stronger.
The 5th harmonic is the harmonic of culture, play, dislike of tedium, creativity, and freedom. While the 7th harmonic loves discipline and knows that practice makes perfect,the 5th harmonic excels in creativity and play. The 7th harmonic likes to work and the 5th harmonic likes to play. The 7th harmonic is ponderous and deep, while the 5th harmonic is light and exuberant. I doubted that the 5th harmonic would be strong in the charts of mathematicians but the creative freedom of the 5th harmonic gives it an intelligence which more mundance and steady types typically lack, so it would not be impossible for the 5th harmonic to be important as well.
The first 12 harmonics can be seen in the harmonic charts I constructed as follows:
1st (conjunction): conjuntion in 1st harmonic chart
2nd (opposition): opposition in 1st harmonic chart
3rd (trine): trine in 1st harmonic chart
4th (square): square in 1st harmonic chart
5th (quinitle): conjunction in 5th harmonic chart
6th (sextile): sextile in 1st harmonic chart
7th (septile, biseptile, triseptile): conjunction in 7th harmonic chart
8th (semisquare, sesquiquadrate): semisquare and sesquiquadrate in 1st harmonic chart AND conjunction in 8th harmonic chart
9th: (novile, binovile, quadnovile): cannot be seen, except in aspect grid (not visible in aspect lines)
10th (decile and tridecile): opposition in 5th harmonic chart
11th (1/11, 2/22, 3/11, 4/11, 5/11): not visible
12th (semisextile, quincunx): semisextile and quincunx in 1st harmonic chart.
Many other harmonics can also be seen. For example, the octaves of the 7th (7th, 14th, 28th, 56th etc) appear as conjunction, oppositions, squares, semisquares and sesquiquadrates, etc.) respectively in the 7th harmonic.
I changed the color of Mercury to red in the chart wheel, and left the other planets black, so that I could quickly see Mercury in each chart as I browset through them. My theory was that I would see many aspect lines to Mercury from Mars, Saturn, Uranus, and Pluto. This was what I had found in the study of physicists but there were too many exceptions to the rule to be really impressive. As I browsed through the charts of the mathematicians I was amazed and delighted to see that in almost every 7th and 8th harmonic chart the aspects appeared. Now, at last, the expected patterns appeared conspicuously in almost every chart of mathematicians! However, having spent hundreds of hours of research this year, and countless hours researching before this, I have learned not to jump to conclusions. There are a seemingly endless number of perils in the quest to validate astrological theory!
The importance of the 7th and 8th harmonic charts was exactly what I expected. In my work with clients in the 1970's I did not expect a great deal of information from the normal astrology chart! I know that this sounds strange, but every astrologer has his/her own unique way to analyze charts, and I rely on a number of harmonic charts and midpoint patterns to analyze the chart. The 8th harmonic chart, in many ways, is more fundamental than the 1st harmonic chart because it reveals the inner dynamic patterns within the person. Each harmonic chart fills in the coloring of the chart; the basic personality is built on a structure of the octave harmonics.
One additional note on harmonic charts: the orbs used are different from other forms of astrology. A 16 degree orb is used for conjunctions, 8 degrees for oppositions, 4 degrees for squares, 5 1/3 degrees for trines, etc. The orbs must be proportionate. If you change one orb, you must change them all. An orb greater than 2 degrees is not very strong because it is above the 8th harmonic level which is a threshold point for digging deep within the core of the person's personality and energy dynamics.
I then created an AstroSignature for mathematical ability. I gave 1 point to a conjunction, opposition, or square in the 7th or 8th harmonic charts for each of the following planetary patterns: Mercury-Saturn, Mercury-Uranus, and Mercury-Pluto. I dropped Mercury-Mars, which was in my original hypothesis, because it did not show up nearly as strongly as the 3 other planetary pairs. I also refined my original hypothesis to be specifically these 3 aspects (conjunction, opposition, and square) in these 2 harmonic charts only. Additional analysis showed that trines, sextiles, semisextiles, and quincunxes also occurred frequently in the charts of mathematicians in the 7th harmonic chart, so these were also added.
Hypothesis reformulated and restated from this exploratory study
An equivalent way of stating the hypothesis, and perhaps an even simpler way of stating the hypothesis is this: Mathematicians are more likely to have conjunctions within a 16 degree orb between Mercury and Saturn, Mercury and Uranus, and Mercury and Pluto, in the following 9 harmonic charts: 8, 16, 32, 7, 14, 21, 28, 42, and 84.
The beautify of this hypothesis, as compared to the hypotheses that I had earlier created for physicists and alcoholics, is that it is very consistent, as described in rule #11 above. I use all traditional aspects (the multiples of 30 degrees or 12th harmonic, or in other words conjunction, opposition, square, trine, sextile, seminsextile, and quincunx) in 2 harmonic charts between Mercury and the planets Saturn, Uranus, and Pluto. This is very consonant with astrological theory. I hypothesized that Mercury would aspect thse planets because this was my observation as an astrologer, in my rsearch with physicists, and the choice of these planetary pairs conforms reasonably with the expectations of most astrologers. The orbs used and harmonics used does not conform with what most astrologers expect but it does conform with my hypothesis.
RESULTS OF THE STUDY:
The results of the study were stunningly more consistent than any other research that I have done. In the table below if the percentage of charts that have each of the 3 planetary pairs conjunct in each of the 6 harmonic charts:
The individual totals for the planetary pairs were not calculated for the 21st, 42nd, and 84th harmonic. These harmonics were added later and by this time it was decided that all 3 planetary pairs would be used, so individual totals were not needed.
https://astrosoftware.com/Proveast.htm
AstroSignature Analysis:
An AstroSignature for mathematical ability was created in the Kepler program. A weight of 5 points was given for the 3 planetary pairs conjunct in the six 7-based harmonic and a weight of 1 point was given for the 3 planetary pairs in the three octave harmonics. Because the 7-based harmonics had stronger results, a stronger weight was given to them. The weight of 5 for 7-based harmonics and weight of 1 for octave harmonics are fairly arbitrary values selected to simply give much more emphasis to the 7-based harmonics.
After the AstroSignature is created, a Mathematical Aptitude score for any person can be produced. The Mathematical Aptitude score for mathematicians using this formula calculated for the 27 mathematicians was 16.37. The average score for the 167 alcohlics was 8.54. The ratio of these scores is 1.92. In other words, mathematicians scored nearly twice as high as alcoholics.
Astrological Conclusions:
The 7th harmonic chart has been used for many hundreds of years in Vedic astrology, and is known as the saptamsa chart. In Vedic astrology it is an indication of your area of training and which teacher or guru should guide you. The 7th harmonic has also been associated with spirituality. I have given my interpretation above, and based on this interpretation, hypothesized its relevance to mathematical ability. The hypothesis was confirmed.
The octave harmonics (8, 16, and 32) showed promise of having some significance, but not as strong as the 7-based harmonics. This finding was not expected, but the positive indications of the octave harmonics were consonant with the original hypothesis as well.
Indications for Future Research:
The hypothesis for this study was not articulated as clearly as it is now stated. If the results of this study can be confirmed with another group of mathematicians, this would constitute validation of astrology, and upon repeated duplication and peer review of the studies would constitute proof of astrology.
Current astrological literature consists of an almost endless number of possible variables, and a synthesis of some of the most important variables into a coherent formula that can provide a platform for further research is needed for astrological theory to make a transition from unverifiable hypotheses to supported theories. This pilot study initiates the process of this transition. The synthesis of relevant variables into a supportable theory is a daunting task, but this current pilot study shows great promise of providing this foundation for further astrological research.
Note that the experimental group used in the current study was a group of highly accomplished mathematicians. A study of less accomplished mathematicians or those who work primarily in pedagogical pursuits or applications of mathematical theory may not have the exceptional qualities of mental discipline and mental intensity that these noted mathematicians have, and therefore may not have the strong 7th harmonic patterns that was found in the current research study.
I hypothesize that astrological influences represent a complex web of energetic patterns. These energetic patterns develop in response to environmental stimulation and decisions made by the individual. Each person is endowed with a wide range of capabilities and from this palette of potentials creates a life pursuit. The astrological influences do not magically represent behaviors, but rather represent energetic patterns. We are now at the initial stages of unraveling these complex patterns, and over time the capabilities of astrology may prove as awesome as the advances of other sciences and arts. The interweaving of variables is complex, and the interaction of astrological, environmental, genetic, and possibly other influences involves a system of influences that cannot be fully appreciated by simple methods. Nevertheless, the domain of astrological theory is tractable and amenable to scentific research, and with care and persistence, a scientific pursuit of astrology can lead to successful advances, and this new body of supported theory is applicable to a wide range of human conditions, and can prove to be a benefit to humanity.
No doubt further research would refine and expand the number of harmonics and planetary pairs used. Inclusion of other astrological variables could further refine the formula, and finally a solid basis for further research would begin, and the initiation of astrology as a field amenable to scientific analysis can begin. Huge research group sizes of thousands of charts are not needed. However, all research is time consuming and without the support of academic institutions and publicly funded research projects, progress in astrological research, as with research in any other discipline, will be very slow. Hopefully, a paradigm for future research has been established in this study. Only future studies will clarify the extent to which this pilot study provides a robust and stable platform upon which to build a scientific study of astrology.
I also included the 7th harmonic because I associate the 7th harmonic with discipline, chronic situations or determination, sobriety, and deep inner probing, a liking for things that are humble and ponderous, sometimes almost mystical or ancient. From my experience teaching math to children and adults, the 7th harmonic pattern seemed very likely to be strong in the charts of mathematicians. I found some evidence of this in the chart of physicists but not as strong as I had hoped, and other harmonics, like the 17th and 19th were often stronger.
The 5th harmonic is the harmonic of culture, play, dislike of tedium, creativity, and freedom. While the 7th harmonic loves discipline and knows that practice makes perfect,the 5th harmonic excels in creativity and play. The 7th harmonic likes to work and the 5th harmonic likes to play. The 7th harmonic is ponderous and deep, while the 5th harmonic is light and exuberant. I doubted that the 5th harmonic would be strong in the charts of mathematicians but the creative freedom of the 5th harmonic gives it an intelligence which more mundance and steady types typically lack, so it would not be impossible for the 5th harmonic to be important as well.
The first 12 harmonics can be seen in the harmonic charts I constructed as follows:
1st (conjunction): conjuntion in 1st harmonic chart
2nd (opposition): opposition in 1st harmonic chart
3rd (trine): trine in 1st harmonic chart
4th (square): square in 1st harmonic chart
5th (quinitle): conjunction in 5th harmonic chart
6th (sextile): sextile in 1st harmonic chart
7th (septile, biseptile, triseptile): conjunction in 7th harmonic chart
8th (semisquare, sesquiquadrate): semisquare and sesquiquadrate in 1st harmonic chart AND conjunction in 8th harmonic chart
9th: (novile, binovile, quadnovile): cannot be seen, except in aspect grid (not visible in aspect lines)
10th (decile and tridecile): opposition in 5th harmonic chart
11th (1/11, 2/22, 3/11, 4/11, 5/11): not visible
12th (semisextile, quincunx): semisextile and quincunx in 1st harmonic chart.
Many other harmonics can also be seen. For example, the octaves of the 7th (7th, 14th, 28th, 56th etc) appear as conjunction, oppositions, squares, semisquares and sesquiquadrates, etc.) respectively in the 7th harmonic.
I changed the color of Mercury to red in the chart wheel, and left the other planets black, so that I could quickly see Mercury in each chart as I browset through them. My theory was that I would see many aspect lines to Mercury from Mars, Saturn, Uranus, and Pluto. This was what I had found in the study of physicists but there were too many exceptions to the rule to be really impressive. As I browsed through the charts of the mathematicians I was amazed and delighted to see that in almost every 7th and 8th harmonic chart the aspects appeared. Now, at last, the expected patterns appeared conspicuously in almost every chart of mathematicians! However, having spent hundreds of hours of research this year, and countless hours researching before this, I have learned not to jump to conclusions. There are a seemingly endless number of perils in the quest to validate astrological theory!
The importance of the 7th and 8th harmonic charts was exactly what I expected. In my work with clients in the 1970's I did not expect a great deal of information from the normal astrology chart! I know that this sounds strange, but every astrologer has his/her own unique way to analyze charts, and I rely on a number of harmonic charts and midpoint patterns to analyze the chart. The 8th harmonic chart, in many ways, is more fundamental than the 1st harmonic chart because it reveals the inner dynamic patterns within the person. Each harmonic chart fills in the coloring of the chart; the basic personality is built on a structure of the octave harmonics.
One additional note on harmonic charts: the orbs used are different from other forms of astrology. A 16 degree orb is used for conjunctions, 8 degrees for oppositions, 4 degrees for squares, 5 1/3 degrees for trines, etc. The orbs must be proportionate. If you change one orb, you must change them all. An orb greater than 2 degrees is not very strong because it is above the 8th harmonic level which is a threshold point for digging deep within the core of the person's personality and energy dynamics.
I then created an AstroSignature for mathematical ability. I gave 1 point to a conjunction, opposition, or square in the 7th or 8th harmonic charts for each of the following planetary patterns: Mercury-Saturn, Mercury-Uranus, and Mercury-Pluto. I dropped Mercury-Mars, which was in my original hypothesis, because it did not show up nearly as strongly as the 3 other planetary pairs. I also refined my original hypothesis to be specifically these 3 aspects (conjunction, opposition, and square) in these 2 harmonic charts only. Additional analysis showed that trines, sextiles, semisextiles, and quincunxes also occurred frequently in the charts of mathematicians in the 7th harmonic chart, so these were also added.
Hypothesis reformulated and restated from this exploratory study
An equivalent way of stating the hypothesis, and perhaps an even simpler way of stating the hypothesis is this: Mathematicians are more likely to have conjunctions within a 16 degree orb between Mercury and Saturn, Mercury and Uranus, and Mercury and Pluto, in the following 9 harmonic charts: 8, 16, 32, 7, 14, 21, 28, 42, and 84.
The beautify of this hypothesis, as compared to the hypotheses that I had earlier created for physicists and alcoholics, is that it is very consistent, as described in rule #11 above. I use all traditional aspects (the multiples of 30 degrees or 12th harmonic, or in other words conjunction, opposition, square, trine, sextile, seminsextile, and quincunx) in 2 harmonic charts between Mercury and the planets Saturn, Uranus, and Pluto. This is very consonant with astrological theory. I hypothesized that Mercury would aspect thse planets because this was my observation as an astrologer, in my rsearch with physicists, and the choice of these planetary pairs conforms reasonably with the expectations of most astrologers. The orbs used and harmonics used does not conform with what most astrologers expect but it does conform with my hypothesis.
RESULTS OF THE STUDY:
The results of the study were stunningly more consistent than any other research that I have done. In the table below if the percentage of charts that have each of the 3 planetary pairs conjunct in each of the 6 harmonic charts:
The individual totals for the planetary pairs were not calculated for the 21st, 42nd, and 84th harmonic. These harmonics were added later and by this time it was decided that all 3 planetary pairs would be used, so individual totals were not needed.
https://astrosoftware.com/Proveast.htm
AstroSignature Analysis:
An AstroSignature for mathematical ability was created in the Kepler program. A weight of 5 points was given for the 3 planetary pairs conjunct in the six 7-based harmonic and a weight of 1 point was given for the 3 planetary pairs in the three octave harmonics. Because the 7-based harmonics had stronger results, a stronger weight was given to them. The weight of 5 for 7-based harmonics and weight of 1 for octave harmonics are fairly arbitrary values selected to simply give much more emphasis to the 7-based harmonics.
After the AstroSignature is created, a Mathematical Aptitude score for any person can be produced. The Mathematical Aptitude score for mathematicians using this formula calculated for the 27 mathematicians was 16.37. The average score for the 167 alcohlics was 8.54. The ratio of these scores is 1.92. In other words, mathematicians scored nearly twice as high as alcoholics.
Astrological Conclusions:
The 7th harmonic chart has been used for many hundreds of years in Vedic astrology, and is known as the saptamsa chart. In Vedic astrology it is an indication of your area of training and which teacher or guru should guide you. The 7th harmonic has also been associated with spirituality. I have given my interpretation above, and based on this interpretation, hypothesized its relevance to mathematical ability. The hypothesis was confirmed.
The octave harmonics (8, 16, and 32) showed promise of having some significance, but not as strong as the 7-based harmonics. This finding was not expected, but the positive indications of the octave harmonics were consonant with the original hypothesis as well.
Indications for Future Research:
The hypothesis for this study was not articulated as clearly as it is now stated. If the results of this study can be confirmed with another group of mathematicians, this would constitute validation of astrology, and upon repeated duplication and peer review of the studies would constitute proof of astrology.
Current astrological literature consists of an almost endless number of possible variables, and a synthesis of some of the most important variables into a coherent formula that can provide a platform for further research is needed for astrological theory to make a transition from unverifiable hypotheses to supported theories. This pilot study initiates the process of this transition. The synthesis of relevant variables into a supportable theory is a daunting task, but this current pilot study shows great promise of providing this foundation for further astrological research.
Note that the experimental group used in the current study was a group of highly accomplished mathematicians. A study of less accomplished mathematicians or those who work primarily in pedagogical pursuits or applications of mathematical theory may not have the exceptional qualities of mental discipline and mental intensity that these noted mathematicians have, and therefore may not have the strong 7th harmonic patterns that was found in the current research study.
I hypothesize that astrological influences represent a complex web of energetic patterns. These energetic patterns develop in response to environmental stimulation and decisions made by the individual. Each person is endowed with a wide range of capabilities and from this palette of potentials creates a life pursuit. The astrological influences do not magically represent behaviors, but rather represent energetic patterns. We are now at the initial stages of unraveling these complex patterns, and over time the capabilities of astrology may prove as awesome as the advances of other sciences and arts. The interweaving of variables is complex, and the interaction of astrological, environmental, genetic, and possibly other influences involves a system of influences that cannot be fully appreciated by simple methods. Nevertheless, the domain of astrological theory is tractable and amenable to scentific research, and with care and persistence, a scientific pursuit of astrology can lead to successful advances, and this new body of supported theory is applicable to a wide range of human conditions, and can prove to be a benefit to humanity.
No doubt further research would refine and expand the number of harmonics and planetary pairs used. Inclusion of other astrological variables could further refine the formula, and finally a solid basis for further research would begin, and the initiation of astrology as a field amenable to scientific analysis can begin. Huge research group sizes of thousands of charts are not needed. However, all research is time consuming and without the support of academic institutions and publicly funded research projects, progress in astrological research, as with research in any other discipline, will be very slow. Hopefully, a paradigm for future research has been established in this study. Only future studies will clarify the extent to which this pilot study provides a robust and stable platform upon which to build a scientific study of astrology.