Harmonic
Chart Calculator

A harmonic chart takes every position in your birth chart, multiplies it by a whole number and wraps the result around the circle. The number is the harmonic. In the 5th harmonic chart a planet at 10° of Aries (10° of longitude) goes to 50°, which is 20° Taurus; a planet at 82° goes to 410°, which wraps around to 50°. Those two planets were 72° apart, a quintile, and in the 5th harmonic chart they sit on the same degree.

That is the whole idea. Multiplying by N turns every separation that is a multiple of 360°/N into a conjunction, so each harmonic chart gathers one family of aspects into the easiest pattern to see. The 2nd harmonic folds oppositions onto conjunctions, the 4th adds squares, the 5th brings in quintiles and biquintiles, the 7th the septile series, the 9th the noviles. Aspects that most chart readings leave out, because 51.43° or 40° are not drawn on an ordinary wheel, show up as plainly as a conjunction does.

The British astrologer John Addey (1920–1982) developed the method and set it out in Harmonics in Astrology (1976). He had looked for regular waves in the way planetary positions are spread through large collections of birth dates, and he read the whole range of aspects as harmonics of the circle: the opposition as the 2nd, the trine as the 3rd, and so on upward. The charts on this page are his device in its simplest form, the birth chart multiplied out.

Your birth chart comes first: the API turns the birth time into Universal Time and takes every position from the Swiss Ephemeris, as the methodology page describes. The harmonic steps follow:

1. Positions to full precision. Every planet is recomputed from the ephemeris without the four-decimal rounding of the birth-chart data, because multiplying by the harmonic multiplies any error too: that rounding, under a fifth of an arc-second, would grow to about an arc-minute in the 360th harmonic.
2. Multiply. Each longitude is multiplied by the harmonic number and reduced modulo 360°. That includes the exact Ascendant and Midheaven, the degrees rising and culminating at your birth.
3. No houses. House cusps are not multiplied, because the result would not be a house system (the section on houses below shows what happens). Harmonic charts are read for the planets and their conjunctions, and the calculator leaves houses out.
4. Conjunctions. The ten planets, the Ascendant and the Midheaven are compared pair by pair. Any two within 8° of each other in the harmonic chart are listed, with their separation in the birth chart and the aspect that separation is close to. Oppositions in the harmonic chart are not listed: they are conjunctions in the harmonic of twice the number.
5. Groups. Three or more points that all conjoin one another are listed as a group.
6. Range. Any whole number from 2 to 360. Positions show whole arc-minutes, with the seconds dropped rather than rounded.

A conjunction in the Nth harmonic stands for a birth-chart separation of 0°, 360°/N, twice that, and so on up to 180°. Some of those belong to a lower harmonic: the 6th harmonic's 120° is the 3rd's trine, its 180° the 2nd's opposition. So every harmonic contains the aspects of each number that divides it, and adds its own. The table separates the two, worked out from the harmonic number alone.

Prime harmonics, the 5th, 7th and 11th, add only new aspects beyond the conjunction. Composite ones repeat their factors: the 12th holds every multiple of 30°, so nearly every aspect in an ordinary chart reading turns up in it, and its own contribution is the semi-sextile and the quincunx. A conjunction in a composite harmonic is worth tracing back to the harmonic it really belongs to, which the result does for you: it names the aspect in lowest terms.

Barack Obama was born at 7:24 PM (UTC−10:00) on August 4, 1961 in Honolulu, according to his birth certificate. His Sun was at 12°32′ Leo, a longitude of 132.55°. In the 9th harmonic that becomes 132.55 × 9 = 1192.93°; taking away 3 full circles leaves 112.93°, or 22°55′ Cancer. The table gives every point in the 5th, 7th and 9th harmonics, each checked by a second calculation made straight from the Swiss Ephemeris.

The next table runs the calculator on every harmonic from the 2nd to the 12th and on the 16th, and lists each conjunction within 8°. With 12 points there are 66 pairs, and an 8° orb either side covers 16° of the circle, so a chart of randomly placed points would show about 2.9 conjunctions in any harmonic. Barack Obama's charts range from none in the 8th to 4 in the 9th.

Two things stand out. The tightest contact anywhere is the Sun and Mars in the 9th harmonic: 40°01′ apart in the birth chart, within 0°01′ of an exact novile, which no ordinary aspect list would show. And the same pair can appear in more than one harmonic when one number divides the other: Jupiter and Pluto, a biquintile (143°52′ apart), conjoin in the 5th and again, with the orb doubled, in the 10th. The 11th harmonic's contacts have no traditional names at all; the calculator gives them as fractions of the circle.

The 5th harmonic collects the quintile (72°) and biquintile (144°), the aspects that divide the circle into five. Addey linked the number five with the artist and with making: he read the 5th-harmonic chart for the kind of work a person produces, and also for marriage. His book reports the 5th as the third-strongest harmonic in the birth dates of 2,875 artists.

Barack Obama's 5th-harmonic chart has 3 conjunctions. Jupiter and Pluto, 143°52′ apart in the birth chart, are within 0°07′ of an exact biquintile and sit 0°35′ apart here; Uranus and Neptune make a wider quintile; and Mars and the Ascendant a biquintile, the one contact that depends on the birth time.

Seven is the first harmonic whose aspects are not a whole number of degrees: the septile is 51.43°, the biseptile 102.86° and the triseptile 154.29°. Addey tied the number seven to inspiration and the readiness to receive it, to creative work that arrives that way, and to religious and contemplative matters, and his book reports the 7th harmonic among the strongest in the birth dates of 1,974 British clergy.

Barack Obama's 7th harmonic has a single conjunction, the Moon and Neptune: 155°14′ apart in the birth chart, 0°57′ from an exact triseptile, and 6°44′ apart in the harmonic chart. A birth chart drawn with the usual aspects would show the two as unrelated.

The 9th harmonic collects the novile (40°), the binovile (80°) and the 160° aspect, and, because 9 is 3 × 3, every trine. It has a second identity. The navamsa of Indian astrology divides each sign into nine parts of 3°20′ and counts them through the zodiac: for fire signs from Aries, for earth signs from Capricorn, for air signs from Libra and for water signs from Cancer, as the Brihat Parashara Hora Shastra sets out. That rule gives exactly the sign of nine times the longitude, so the navamsa is a 9th harmonic chart. Addey gave it a chapter of his book and kept its traditional use, reading it for the marriage partner.

The difference is the zodiac. Indian astrology applies the navamsa to sidereal longitudes, and this calculator works in the tropical zodiac. Multiplying by nine multiplies the gap between the two zodiacs by nine as well. At Barack Obama's birth the Lahiri ayanamsa, the gap used by most Vedic software, was 23°19′; nine times that is 209°51′, almost exactly 7 signs. So each of his navamsa signs is his tropical 9th-harmonic sign moved back 7 signs, and not one of his 12 points has the same sign in both. Someone born decades later, with a larger ayanamsa, gets a different offset, so there is no fixed rule for converting one into the other.

In the tropical 9th harmonic Barack Obama has 4 conjunctions, the most of any harmonic in his chart, three of them among the Sun, Venus and Mars. For his navamsa, use a Vedic calculator set to the Lahiri ayanamsa; for the 9th harmonic in Addey's sense, this one.

A group of planets that all conjoin in a harmonic chart is a pattern in the birth chart: every pair in it is close to a multiple of 360°/N. The calculator lists each such group. In Barack Obama's 9th harmonic the Sun, Venus and Mars form one. In the birth chart the Sun and Venus are 40°45′ apart and the Sun and Mars 40°01′, both noviles, and Venus and Mars 80°47′, a binovile: three planets spaced at 40° steps, a pattern no list of the usual aspects contains.

The same idea covers the familiar patterns. A Grand Trine is a three-planet group in the 3rd harmonic, a T-square a three-planet group in the 4th, a Grand Cross a four-planet group in the 4th. The Chart Pattern Analyzer finds those named shapes with ordinary orbs; the harmonic charts extend the search to any division of the circle.

A conjunction in a harmonic chart is read the way an aspect between the same two planets would be, with the harmonic number standing in for the kind of aspect. Four habits keep the reading grounded in what the numbers show:

• Start with the distance from exact in the birth chart. The orb in the harmonic chart grows with the number, so compare contacts by the “off exact” column. Barack Obama's Sun–Mars novile, 0°01′ from exact, is a closer contact than any aspect in his ordinary chart list.
• Send inherited aspects home. A trine that shows up in the 9th harmonic, or an opposition in the 4th, belongs to the 3rd or the 2nd. The calculator names each contact in lowest terms, so you can see which harmonic it really comes from, as with his Mercury–Jupiter opposition in both the 2nd and the 4th.
• Compare with chance. About 2.9 conjunctions per harmonic chart is what scattered points produce. A harmonic with 4, his busiest, is only modestly above that; one very tight contact says more than a count.
• Hold the angles to the birth time. A contact with the Ascendant or Midheaven is only as good as the recorded minute of birth, as the next sections show.

An orb in a harmonic chart is the birth-chart orb multiplied by the harmonic. The calculator allows 8° in every harmonic chart, so in the birth chart the allowance shrinks as the number grows: 4°00′ for the 2nd, 1°36′ for the 5th, 1°08′ for the 7th, 0°53′ for the 9th, 0°30′ for the 16th. David Hamblin's Harmonic Charts (1983) scales orbs the same way, by dividing a conjunction's orb by the harmonic number: allow 12° for a conjunction and the opposition gets 6°, the trine 4°, the square 3°.

8° is the base conjunction orb of the site's birth charts, used here without the adjustments for luminaries and outer planets. It is a convention, not a measurement; the result lists each contact's distance in both charts so you can apply a tighter limit of your own.

An earlier version of this calculator multiplied the house cusps along with the planets, and used the first cusp as the harmonic Ascendant. Under Whole Sign houses, which the page requests, the cusps sit at 0° of each sign, so the products sit at multiples of 30° as well. For Barack Obama the twelve cusps times 12 all came out at 0° Aries; times 9 they fell on 4 points; times 5 they were only shuffled among the sign boundaries. The 9th-harmonic “Ascendant” the API used came out at 0°00′ Libra and the 5th at 0°00′ Gemini. The true ones, his Ascendant of 18°03′ Aquarius multiplied out, are 12°27′ Pisces and 0°15′ Virgo.

The angles are the points most sensitive to the birth time, and multiplying makes them more so. Barack Obama's Ascendant was moving 17.5′ a minute at his birth and his Midheaven 14.5′. In the 9th harmonic his Ascendant therefore moves 2.6° a minute, and a birth time 3 minutes out moves it through the whole 8° orb. The Moon, at 0.53° an hour in the birth chart, moves 4.8° an hour in the 9th harmonic. Read harmonic contacts with the angles, and with the Moon in high harmonics, only if the birth time is recorded to the minute.

Addey came to harmonics through statistics. Instead of asking whether a planet fell in a particular sign, he treated the distribution of a planet's positions in a large set of birth data as a wave around the circle and broke it into harmonics, as a sound is broken into its tones. His book works through samples such as the Sun positions of 1,023 children who had paralytic polio, 972 people who lived past 90, drawn from Who Was Who, 7,302 doctors whose birth dates Rupert Gleadow and R. C. Firebrace had collected, and Michel Gauquelin's data on 3,647 physicians and scientists. He also helped found the Astrological Association of Great Britain in 1958 and was its president from 1961 to 1973.

The harmonic chart is the practical side of that work: once the number seven or five was thought to matter, the chart multiplied by seven or five shows which planets in one person's chart take part. The calculator does not depend on the statistics; it applies the arithmetic. Whether the research holds up is a separate question, and the book should be read with that in mind.

• John Addey, Harmonics in Astrology: An Introductory Text-book to the New Understanding of an Old Science (L. N. Fowler, 1976): the method, the meanings of the 5th, 7th and 9th harmonics quoted here, the chapter on the navamsa, and the samples named above.
• David Hamblin, Harmonic Charts: A New Dimension in Astrology (The Aquarian Press, 1983), for orbs scaled by the harmonic number.
• Brihat Parashara Hora Shastra, chapter 6, for the navamsa rule.
• Every position comes from the Swiss Ephemeris (Astrodienst); the sidereal positions in the navamsa table use its Lahiri ayanamsa (SIDM_LAHIRI), with nutation.

The calculator gives positions and conjunctions; the readings of the numbers are those of the authors named, and the page makes no claim beyond them.