The Non-Traditional Aspects:the Quintile, Septile and Undecile Aspect FamiliesThe Traditional AspectsMost astrologers use only the traditional aspects based on a division of the 360 degree horoscope circle into twelve 30 degree sections. Understanding the conjunction, opposition, square, trine and sextile aspects are crucial in reading any chart, and the secondary aspects associated with them, the semi-sextile, quincunx and semi-square are also worth considering. But these are not the only aspects of significance. The Non-Traditional AspectsThe QuintileThe quintile is based on dividing the horoscope circle into five equal parts of 72 degrees each. Two quintiles form a biquintile. Half a quintile is a decile. Three deciles form a tridecile. If five planets were all positioned in a series of exact quintiles (very rare), the biquintiles linking each of them would form the familiar five-pointed star pattern. The septile is based on dividing the horoscope circle into seven equal parts of slightly less than 51 and a half degrees each. Two septiles form a biseptile, and three form a triseptile. 
Many cultures have associated the number seven with religion and the spirit world, and the septile family of aspects is associated with religion, spirituality and idealism. Famous people with patterns of linked septile-family aspects in their birth charts include Pope Benedict XVI, the Dalai Lama, Martin Luther King Jr., George Bush, Emily Dickinson, John Lennon, Bob Dylan and Joni Mitchell. While we recognize religious callings in several cases, others are not associated with conventional religious beliefs. Most, however, had or have a strong desire to reform society.
The undecile is based on dividing the horoscope circle into eleven equal parts of slightly less than 33 degrees each. Two undeciles form a biundecile, three a triundecile, four a quadriundecile and five a quinqueundecile. I find it easier to refer to them as the undecile, the undecile-x-2, the undecile-x-3, etc. Astrologer Robert P. Blaschke, who has done pioneering work in understanding the undecile family of aspects, points out that the number eleven is associated with disruption. The U.S. bankruptcy laws, which allow people crippled by debt to make a fresh start, were codified as Title 11. Jesus had twelve disciples until Judas betrayed him and the number was reduced to eleven until Pentecost when Matthias became the new twelfth disciple. Undecile aspects seem to be associated with disruption and healing. They are common in birth charts, but patterns of linked undecile-family aspects occur more rarely and can be quite significant. Transits by Quintile, Septile and UndecileJust as transits by square, trine and the other conventional aspects bring a special energy into a person's life, transits by quintile, septile and undecile bring their own energy. If you have an aspect between two planets in your birth chart, a planetary transit that affects one of them will also affect the other. For example, someone born with the Sun and Mars in square aspect is likely to have an abundance of energy and, until he or she learns to handle that energy, is also likely to be rather short-tempered. If Uranus transits in opposition to that person's natal Sun, it will simultaneously be transiting in square to Mars, and the freedom-loving, often surprising Uranian energy is likely to create some fireworks—or perhaps a sudden discovery of how to use the boundless Sun-Mars energy in a much more positive way than in the past.Transits by quintile, septile and undecile work similarly, but because their energy of each of these aspect families flows through a different division of the horoscope, a quintile pattern in the birth chart is activated only by a conjunction or another quintile-family transit, a septile pattern only by a conjunction or another septile-family transit, and so on. For example, an artist with four planets in his birth chart linked by quintile aspects may begin work on an especially beautiful or meaningful painting when a planet transits across the point that temporarily completes the "missing" fifth point of the quintile star. 
The horoscope of Martin Luther King Jr. (born Jan. 15, 1929, in Atlanta, Georgia, at 12:00 p.m.) is especially rich in non-traditional aspects: a pattern of quintile/decile-family aspects linking his Midheaven/Sun conjunction, Mars, Chiron and Neptune; two septile-family triangles, one linking Venus, Mars and Jupiter, and the other linking Mercury, Uranus, Pluto and the Moon's North Node, and a pattern of undecile-family aspects linking the Midheaven, Moon, Jupiter and Uranus. On August 28, 1963, when he gave a powerful speech during the March on Washington that he organized, four planets (the Moon, Sun, Venus and Neptune) were transiting the quintile/decile pattern in his birth chart, and three planets (the Moon, Mars and Pluto) were transiting the undecile pattern in his birth chart. As one might expect from the impressive set of quintile-family transits to the quintile-family pattern in his chart, the gathering of 200,000 people King led to Washington and the ideas and aspirations he put into words that day had very definite and powerful effects, leading to a permanent change in the way the U.S. treated its black citizens. The undecile transits of the undecile pattern in his chart relate to the healing process he set in motion. A septile transit of the Moon to his natal Mercury increased the emotional power of his communication, and it's especially notable that the septile energy is related to dreams, imagination, ideals and spirituality, all reflected in the content of his speech, known today as the "I have a dream" speech. If one were to consider only the transits to his chart by the traditional angles, it might seem surprising that he was involved in anything of particular significance that day: Neptune was opposite his Ascendant, the Sun and Uranus were transiting in trine to his natal Chiron, and the Moon was squaring his natal Moon. One can certainly see how these energies were in tune with what happened that day, but there was not a single major traditional transit to his Sun, Mars or Midheaven, something we might normally expect on a day someone made history. Top of Page
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Looking at a diagram, it's easy to see how the traditional aspects echo the twelve zodiac signs. Except for the semi-square, whenever a traditional aspect is exact, each of the planets in it will be at the same degree position in its own sign as the other is in its sign. This makes the aspects very easy to calculate. Anyone familiar with the basics of astrology can see almost at a glance which of the planets in a chart form traditional aspects to each other. This is not true of the non-traditional aspects, which are not based on the division of the horoscope circle into twelve.
The quintile aspect family is associated with an ability to translate thoughts and visions into tangible form. Most people have at least one or two of these aspects in their birth charts. Patterns of linked quintile-family aspects are often connected with artistic talent. Some famous people with quintile patterns in their charts include composer Wolfgang Amadeus Mozart, artist Leonardo Da Vinci, and poet William Blake.
Famous people with patterns of linked undecile-family aspects in their birth charts include Florence Nightingale, Edgar Cayce, Franklin Roosevelt and Barack Obama. While each of these people experienced significant disruptions in their lives, they were gifted healers at a physical or sociological level. Florence Nightingale was an invalid during the last 50 years of her life because of an illness contracted during her nursing work in the Crimean War; Edgar Cayce and members of his family suffered bouts of serious illness but were healed through his visionary abilities; Franklin Roosevelt was crippled by polio but led the U.S. out of the Great Depression; Barack Obama met his father only once and was partly raised by his grandparents while his mother lived and worked in Indonesia. His election has already gone a long way toward healing racial divisions in the U.S., and beyond this has given hope of a brighter future to millions in the U.S. and around the world.