≈ Harmonic Chart Calculator: Any Harmonic, With the Working Shown
Put in a birth date, and a time and UTC offset if you know them, pick a harmonic from 2 to 180, and this free calculator shows where every body lands in it with the working beside it: the birth-chart longitude, multiplied by the harmonic number, less whole turns of 360 degrees. It names the pairs that stand together in that harmonic and the birth-chart gap that puts them there, and says plainly what the harmonic does and does not mean.
Runs in your browser.
MODERNA twentieth-century technique. The reading of each number is one tradition's; the arithmetic is not, and the page shows it.
- Date onlyEvery planet's harmonic position, with noon used for the time. The Moon and fast bodies are left out of the clusters, because a day moves them too far.
- Date, time and UTC offsetA firm Moon and firm clusters. The offset matters: it is the difference between two moments up to a day apart.
- Time and placeThe harmonic Ascendant and Midheaven, traced the same way.
- Any number from 2 to 180Presets for 5, 7, 9, 11 and 12; the box takes any whole number.
- Tropical or siderealTropical by default. Sidereal makes the 9th harmonic match the Vedic navamsa sign for sign.
What a harmonic chart is
A harmonic chart multiplies every longitude by a whole number and reduces the result back into the circle. In the 5th harmonic everything is multiplied by 5, in the 7th by 7, in the 144th by 144. Every aspect built on dividing the circle by that number becomes a conjunction, which is why a quintile that is hard to see on an ordinary wheel stands out in the 5th harmonic.
The 4th harmonic gathers the squares, the 5th the quintile family, the 7th the septiles, the 9th the noviles. Each harmonic chart is a table of arithmetic and has no houses or horizon of its own. Umbriel draws it with 0° Aries at the left, as a plain ring.
The working, by hand
One placement: the Sun at 14°10′ Gemini in the 5th harmonic. Round the circle from 0° Aries the Sun is at 74.1667°. 74.1667° × 5 = 370.8333°, less 1 × 360° = 10.8333°. That is 10°50′ Aries. Nothing was rounded before the multiplying.
One pair: the Sun and Venus. The Sun is at 14°10′ Gemini and Venus at 26°10′ Leo. Sun and Venus are conjunct in H5 because they are 72°00′ apart in the birth chart (72.0000°), and 5 × 72.0000° = 360.0000°, which is 1 × 360° − 0.0000°. The leftover 0°00′ is the orb in the harmonic (0°00′ in the birth chart). It is primitive: no lower harmonic of 5 already brings this pair together.
One error: the Moon in the 9th harmonic. The Moon travels about 0.55° an hour, so an hour's error in the birth time moves it 0.55° in the birth chart and 9 × 0.549 = 4.9° in the 9th harmonic. Every body is multiplied by the same number, so the more slowly a body moves, the longer its error takes to matter.
Show which birth-chart gaps meet in each harmonic
| Harmonic | Step (360° ÷ N) | Together when the gap is | Opposite when the gap is |
|---|---|---|---|
| H5 | 72°00′ | 72°00′, 144°00′ | 36°00′, 108°00′, 180°00′ |
| H7 | 51°26′ | 51°26′, 102°51′, 154°17′ | 25°43′, 77°09′, 128°34′, 180°00′ |
| H9 | 40°00′ | 40°00′, 80°00′, 120°00′, 160°00′ | 20°00′, 60°00′, 100°00′, 140°00′, 180°00′ |
| H11 | 32°44′ | 32°44′, 65°27′, 98°11′, 130°55′, 163°38′ | 16°22′, 49°05′, 81°49′, 114°33′, 147°16′, 180°00′ |
| H12 | 30°00′ | 30°00′, 60°00′, 90°00′, 120°00′, 150°00′, 180°00′ | 15°00′, 45°00′, 75°00′, 105°00′, 135°00′, 165°00′ |
The 9th harmonic and the navamsa
Both multiply a longitude by 9 and keep what is left after whole turns. The navamsa is cast on the sidereal zodiac and counted by sign; the 9th harmonic is usually drawn on the tropical one, as a continuous longitude. On the sidereal zodiac the two agree sign for sign and degree for degree. On the tropical zodiac they differ by 9 times the ayanamsa, which is about 213 degrees for a modern birth, so this page does not call one the other.
What this calculator answers
Where every body lands in any harmonic from 2 to 180, which birth-chart longitude each place came from, and which pairs stand together or opposite in that harmonic and why.
How it calculates
Umbriel casts the birth chart, takes each full-precision longitude, multiplies it by the harmonic number and subtracts whole turns of 360 degrees. Two bodies meet when their birth-chart gap times that number is whole turns, within 3 degrees in the harmonic.
When the result is uncertain
With no birth time, noon is used, and a body that would move more than 6 degrees in the harmonic across that day is left out of the clusters. The Moon and the angles go first, and the number multiplies every error.
Common questions
What is a harmonic chart?
Your birth chart with every longitude multiplied by a whole number and reduced back into the circle. Two bodies whose birth-chart gap is a multiple of 360 degrees divided by that number then stand at the same place, so aspects built on dividing the circle turn into conjunctions you can see.
How is a harmonic position worked out?
Take the body's longitude in degrees round the circle from 0 degrees Aries, multiply by the harmonic number, and subtract whole turns of 360 until the answer is under 360. The Sun at 14°10′ Gemini is 74.1667 degrees; times 5 is 370.8333; less one turn is 10.8333 degrees, which is 10°50′ Aries. Umbriel multiplies the unrounded longitude, because rounding first would move a body by up to half the harmonic number in arcminutes.
Which pairs meet in the 5th harmonic?
Pairs whose birth-chart separation is 72 or 144 degrees, within 0°36′ for a 3 degree orb in the harmonic. Those are the quintile and biquintile. In the 7th harmonic the separations are 51°26′, 102°51′ and 154°17′; in the 9th, 40, 80, 120 and 160 degrees.
What is the 5th harmonic used for?
Harmonic astrologers read it for creativity, talent and style. That is a tradition's reading of the number, not a measurement, and it does not say whether a person has any such talent.
Is the 9th harmonic the same as the navamsa?
They run the same sum, longitude times 9, on different zodiacs. The navamsa is a Vedic divisional chart on the sidereal zodiac; the ninth harmonic is usually drawn on the tropical. Choose the sidereal zodiac here and the signs match the engine's navamsa body for body. On the tropical zodiac they differ by 9 times the ayanamsa, so one is not the other.
Do harmonics need an exact birth time?
More than the birth chart does, and more as the number rises. The Moon moves about 13 degrees a day, roughly 0.55 degrees an hour, so a one-hour error moves it about 5 degrees in the 9th harmonic and about 20 in the 36th. The Ascendant turns about 15 degrees an hour, so four minutes is a degree in the birth chart and 9 degrees in the 9th harmonic.
Does it use the tropical or the sidereal zodiac?
Tropical unless you choose sidereal (Lahiri), and the answer says which it used. The sidereal choice subtracts the ayanamsa from each longitude before multiplying, so the harmonic positions change, not only the sign names.
Does a cluster in a harmonic say anything about me?
Not by itself. Chance alone produces some: among eleven bodies at a 3 degree orb about 0.9 pairs would stand together in any harmonic. The page prints that count beside the real one. A cluster is arithmetic about angles in the birth chart, to think with, not a verdict, and the harmonic chart has no houses or horizon of its own.
What does primitive or inherited mean for a contact?
A contact is inherited when a lower harmonic that divides the number already brings the pair together at the same birth-chart orb: two bodies 72 degrees apart meet in the 10th harmonic because they already meet in the 5th. Primitive means no lower harmonic of that number does, so the contact first appears here. Each contact on the page says which, and gives its orb in the birth chart as well as in the harmonic.
Is the harmonic chart calculator free?
Yes: any harmonic from 2 to 180, with the working shown, and no account.
Does it send my details anywhere?
No. The calculation runs in your browser, nothing you type is stored or sent, and the birth place is only a latitude and longitude you type or pick. Planet longitudes do not need a place; the Ascendant and Midheaven need a place and a time.
Go deeper
Each of these is a page in its own right.
Related free tools
Prints in the head of this page, all public domain except where stated: The Angel of the Ninth Sphere, or Primum Mobile, plate 49 from Planets and Spheres, Master of the E-Series Tarocchi Italian, active c. 1465, c. 1465, Art Institute of Chicago; The Angel and the Eighth Sphere, plate 48 from Planets and Spheres, Master of the E-Series Tarocchi Italian, active c. 1465, c. 1465, Art Institute of Chicago; Claude Mellan, the head of Time with an hourglass, vignette for the Imprimerie Royale, 1639-1643, Rijksmuseum; two knights jousting, bottom margin of a manuscript, c. 1325-1335. Ground: Andreas Cellarius, Harmonia Macrocosmica, 1661, Wikimedia Commons.
Umbriel offers every system here as a set of prompts to think with, never as a statement of fact about who you are. Take what's useful, leave the rest.