Umbra

Pitch

Each moon has one pitch, proportional to how fast it goes around Jupiter, raised by whole octaves until it can be heard. The idea comes from Hans Cousto's The Cosmic Octave.

Moon	Orbit	Resonance	Measured
I Io	1.77 days	440.0 Hz	440.0 Hz
II Europa	3.55 days	220.0 Hz	219.2 Hz
III Ganymede	7.15 days	110.0 Hz	108.8 Hz
IV Callisto	16.69 days	188.6 Hz	186.6 Hz

Io, the fastest, is the A at 440 Hz. Europa takes twice as long, so it sounds an octave lower, and Ganymede another octave below that. Callisto's period doesn't divide evenly into the others; raised two octaves, it sits a septimal sixth above Ganymede, an interval that falls between the keys of a piano.

The real periods are close to 1 : 2 : 4 but not exact. Resonance tuning rounds them to pure octaves. Measured tuning uses the actual periods, which makes Io's octave above Europa about 6 cents wide and Europa's above Ganymede about 13.

Events

A note sounds when a moon does something you could watch through a telescope: it goes behind the planet or comes out, starts or stops crossing its face, enters or leaves its shadow, or casts its own shadow on the cloud tops. Each moon does each of these about once per orbit, so Io, going around in 1.77 days, plays most often and Callisto least. Because of the lock, Io's events come twice for every one of Europa's and four times for every one of Ganymede's, much like the subdivisions of a step sequencer. And because the three never line up, the pattern has no shared downbeat.

The beat

Jupiter turns once every 9 hours 55 minutes, and each turn is a beat. With the clock set to Jupiter's day, notes move to the nearest quarter of a turn; with Free, they sound at the exact computed moment. The delay's echoes are fractions of the same beat. In Primus post Iovem an Earth day passes every 1.5 seconds, which makes Jupiter's day a tempo of about 97 beats a minute; Configurationes Mediceorum starts slower, at 2 seconds a day. Speed runs from 0.75 to 8 seconds per day.

The sound

The voices are soft mallets and round tones: a felt mallet on a wooden bar, a yarn mallet on a metal bar with a slow tremolo, a rounded oscillator, a pure sine, a breathy ocarina, a round low tone, and a soft beat on a frame drum. Each note is played a little by hand, a few milliseconds early or late, a little louder or softer, a few cents off true. That variation is worked out from the moment of the event, so a passage sounds the same each time you come back to it. Everything plays through a long reverb, a delay whose echoes darken as they repeat, and the tape stage from Wind,oh.

Io, Europa and Ganymede are the best-known orbital resonance, but not the only one. The System list switches the instrument to five others, two in our own solar system and three around other stars, picked to show how different a resonance can sound. Each brings its own bodies, beat, skies, mixes and views. The voices, the room and the desk stay as you left them. In Resonance tuning each system's pitches stand exactly in the ratio shown beside its name.

Venus and Earth 13 : 8

Venus goes round the Sun thirteen times while Earth goes round eight. The match is close but not exact, and nothing holds the two planets to it, so astronomers count it a near-resonance rather than a lock. It still shapes the sky: Venus comes back to the same place among the stars every eight years, and its five closest passes to Earth in that time fall at the points of a five-pointed star, which the Resonance view draws as five petals.

Venus sounds at the moments people have always watched it for. It plays at its farthest east of the Sun (the evening star) and farthest west (the morning star), as it passes behind the Sun and between Earth and the Sun, and, in pairs eight years apart with more than a century between pairs, as it crosses the Sun's face. Twelfths plays the 13 : 8 as a rhythm, a note each time a planet moves into the next twelfth of its circle. The beat is the Moon's month. The skies are the transits of 1769, which Cook's expedition watched from Tahiti, 1882 and 2012. The next is in December 2117.

Neptune and the Kuiper belt 3 : 2 · 12 : 7 · 10 : 3

Pluto goes round the Sun twice for every three orbits of Neptune. Its orbit dips inside Neptune's, and from 1979 to 1999 Pluto was nearer the Sun than Neptune was, but the resonance keeps them apart. Whenever Pluto is nearest the Sun, Neptune is far around its orbit, and the two never come within about 17 AU of each other. Orcus is in the same 2 : 3, half a cycle out of step with Pluto, which is why it is sometimes called the anti-Pluto. Haumea is near 7 : 12 and Gonggong at 3 : 10.

Everything here is slow. The events are each body at its nearest to the Sun and its farthest, and two bodies lining up with the Sun, over a held chord of all five. The beat is Jupiter's year, almost twelve of ours, and centuries pass in seconds. The Resonance view turns with Neptune so that Neptune stands still, and each body loops once for every orbit it makes in the cycle, twice for Pluto and Orcus, seven times for Haumea and three for Gonggong. The skies are 18 February 1930, when Clyde Tombaugh found Pluto on plates taken at Lowell Observatory, and Pluto's nearest pass to the Sun in 1989.

TRAPPIST-1 24 : 15 : 9 : 6 : 4 : 3 : 2

Seven planets about the size of Earth, around a small red star 39 light-years away. Their years run from a day and a half to under nineteen days, and each pair of neighbours is close to a simple ratio: 8 : 5, 5 : 3, 3 : 2, 3 : 2, 4 : 3 and 3 : 2. The period of the outermost, h, was pinned down in 2017 by using the chain to predict it and then finding transits at that period in data from the Kepler telescope's K2 mission. The beat is one orbit of b.

HD 110067 54 : 36 : 24 : 16 : 12 : 9

Six planets between Earth and Neptune in size, 105 light-years away. Neighbours stand at 3 : 2, 3 : 2, 3 : 2, 4 : 3 and 4 : 3, which in music are three fifths and two fourths. When the system was reported in 2023, the periods of the outer planets were worked out from the chain first and confirmed by observing transits when the chain said they would come.

Kepler-223 8 : 6 : 4 : 3

Four planets of roughly Neptune's size, thousands of light-years away, at 4 : 3, 3 : 2 and 4 : 3. As they tug on each other their transits come early and late, and timing those drifts is how the resonance was confirmed in 2016. Chains like this are thought to form as young planets drift inward through the disc they were born in and catch on each ratio in turn.

Around other stars, the instrument plays what a telescope can catch. A planet sounds as it crosses in front of its star and as it passes behind, and two planets sound as they pass each other as seen from Earth. We see all three systems almost edge-on, which is why their planets cross the star at all. The skies are today and the measured transit each system's schedule is timed from.

From above leads, as the plainest picture of what is happening. Each system offers the views that suit it. The notebook and the table are Jupiter's alone, and the light curve appears only for other stars. None of them change the sound.

From abovetoday

The system seen from above Jupiter's north pole, with Earth toward the bottom. The strip between the two vertical lines is the line of sight: a moon in its far half is behind the planet, and in its near half it is crossing the face. The hatched band is Jupiter's shadow. It leans away from the line of sight by the angle between the Sun and Earth as seen from Jupiter, never more than about 12 degrees, and near opposition the two coincide, so going into shadow and going behind the planet happen almost together. A gray line flashes when two moons line up. Around other stars it is the same picture, with the star in the middle. For Venus and the Kuiper belt it is the orbits to scale from above the plane of Earth's orbit, with the Sun in the middle.

Galileo's notebook1610

One small sketch per night, at about 5 p.m. local time, the way Galileo drew them: a plain circle for Jupiter and unnumbered stars, east on the left. Moons too close to the planet are lost in its glare. Two moons closer together than his telescope could split are drawn as one star, and the brighter moons get larger stars. The heavier line is now.

Cassini's table1668

One row per night at 10 p.m., west on the left as Cassini drew it, with the day of the month in the left column and the month in his abbreviations, Octob. or Novemb. Each moon is an asterisk with its numeral. His Latin notes appear under a row when a moon is behind the planet (post Iovem), on its face (in facie) or in its shadow (in umbra), or when its shadow is on the face (umbra Primi in facie, for Io).

Curves1988

Each moon's distance east or west of Jupiter, in Jupiter radii, as a continuous line, with time running down the page and east on the left. The two vertical lines are the planet's edges. A line breaks where its moon can't be seen and turns faint where the moon crosses the face. The line a quarter of the way down is now, and everything below it is still to come, so you can watch an event approach before you hear it. Markers show where the layers that are on will sound. For Venus the line is its angle east or west of the Sun, so the evening star is on the left; around other stars it is each planet's offset from the star, in the star's radii.

Resonancepattern

The shape a ratio draws over time. Lines join neighbouring bodies at regular moments across several orbits of the outermost, and where the orbits are in a simple ratio the lines settle into a flower; Venus and Earth draw the five petals of their eight-year cycle. For the Kuiper belt the frame turns with Neptune instead, so each body traces one loop per orbit in its cycle.

Light curve2017

The star's brightness over time, as a telescope records it, with time running left to right and now a quarter of the way across. Each planet that crosses the star dims it by the share of the star's face it covers, (planet radius / star radius)². This is how all three systems were found. Edges are drawn sharp; real stars are darker toward the rim, which rounds the dips.

Almanacby day

Every event in a calendar, after a weather table in Edward Tufte's Envisioning Information that sets five Februaries of Aomori weather in a grid, a mark for each day and each night. Here each month is a block, with a row for each moon and a column for each day. As the sky reaches an event, its mark drops into its day, filled going in and hollow coming out, the same marks as the log and the mixes. A row under each month counts them. Earlier months stack above the present one, and today is outlined. Venus and Earth fill the months of years, and the Kuiper belt fills five-year cells of centuries.

A mix is a set of layers. The marks beside each name are the layers it plays, and they match the marks in the event log and on the curves.

Galileo

Behind the planet, into shadow, and Jupiter's turning. Each moon sounds a felt mallet note as it goes behind Jupiter and a fifth higher as it comes out, a breathier, lower tone as it enters and leaves the shadow, all over a soft beat once per turn. This is the mix the project started from.

Cassini☾

The nightly reading, behind the planet, and across the face. At 10 p.m. local time each night, every moon in view plays once, west to east, in the order Cassini's table reads. Between readings, moons sound as they pass behind and in front of the planet.

Kepler♪

Melody, turning points, and Jupiter's turning. Each moon's swing from east to west is laid across a pentatonic scale, so as it moves it walks up and down a slow melody, and a soft tone marks the moment it turns back.

Laplace~×

Drone, passing, and into shadow. Each moon in view holds a quiet tone, louder toward the ends of its swing, and the four tones make a slowly shifting chord. Two notes sound when one moon passes another, and the shadow layer marks the eclipses.

Rømer∞

Into shadow, Memory, and Jupiter's turning. These are the eclipses Rømer timed, with Memory keeping a stretch of them on a tape loop that wears away under the live sky.

Full sky

Every layer except Melody and Memory.

Evolve

Every 32 of Jupiter's days (about 20 seconds at 1.5 seconds a day) one layer fades in or out. It keeps between two and six layers on, and always at least one that strikes notes. The choices come from a seed (hover over New seed to see it), so the same seed from the same sky evolves the same way; New seed picks another. Other systems drift at about the same pace at their starting speeds.

Keep this mix

Saves the layers, levels and voices that are on now as a mix of your own, in this browser.

Every event the instrument can detect is a layer. A mix turns a set of them on; the desk lets you turn any of them on or off, give each its own voice, and set its level, reverb, delay and tone. The marks are filled when a moon goes into something and hollow when it comes out. The table describes Jupiter. Other systems leave out the layers that don't apply there and rename the rest for what they do, so Behind the planet becomes Behind the star or Behind the Sun.

	Layer	Sounds when	Voice
	Behind the planet	A moon goes behind Jupiter's disk, and again when it comes out. Going in plays the moon's own pitch; coming out, a fifth above.	Felt
	Across the face	A moon starts and stops crossing in front of the disk, with a higher note for each.	Vibe
	Into shadow	A moon enters and leaves Jupiter's shadow. These are the eclipses Cassini tabled and Rømer timed.	Breath
	Shadow on the face	The moon's own shadow starts and stops crossing Jupiter's cloud tops.	Low
	Turning points	A moon reaches its farthest point east or west and turns back.	Sine
×	Passing	Two moons in view swap places in their east-west order.	Vibe
♪	Melody	A moon moves into a new step of the pentatonic scale laid across its swing.	Felt
☾	Nightly, 10 p.m.	Once each local night, every moon in view, west to east.	Round
	Rotation	Once per turn of Jupiter, at the pitch an octave below Ganymede.	Heart
~	Drone	Continuously. One held tone per moon while it can be seen (Io's a fourth lower, so it doesn't double Europa).	Its own
∞	Memory	When turned on, it keeps the next 16 of Jupiter's days of sound on a tape loop and lets it wear away: the top end fades on each pass, it wobbles, and moments drop out for good. Set its voice to Saturate and each pass gives a little back instead, so the loop thickens into the tape's grain and the gaps fill in. Disintegrate is closer to Basinski's tapes: grainy from the start, wearing more slowly, and flaking in the same places every pass, a little wider each time, until only fragments are left. In every mode it plays back about as loud as it was kept.	Tape, Saturate or Disintegrate

now

Tonight. Your own sky, starting at this moment and running fast.

1610

Galileo, Padua. 7 January 1610, about an hour after sunset, the night he first saw the moons. Opens Galileo's notebook.

1668

Cassini, Bologna. 1 October 1668, just before 10 p.m., the first night of the table in Tufte's book. Opens Cassini's table and plays his mix.

1676

Rømer, Paris. 9 November 1676, twenty minutes before the model has Io leave Jupiter's shadow, so the first sound you hear is the eclipse he predicted. Plays the Rømer mix.

2015

Three shadows. 24 January 2015, when the shadows of Io, Europa and Callisto crossed Jupiter at the same time.

any

Any night from 1600 to 2200, starting at 9 p.m. your time.

other

Other systems have their own skies, listed with them above.

live

Live plays the real sky in real time. Io goes behind Jupiter when it really does, Jupiter's day lasts 9 hours 55 minutes, and the line under the sky tells you what comes next and how long until it does. Left playing in a room with Galileo's mix, it makes six or seven sounds a day.

Under the sky, the desk folds out. It holds the layer table, one row per layer, with a switch to bring the layer in or take it out, its voice, the note it last played, and its level, reverb, delay and tone. Layers that are off are dimmed, and a switch lights while its layer sounds. Beside it are the master controls (reverb, delay, the tape stage with its wow, flutter, age and drive, volume, and MIDI), the clock and speed, the tuning, and the moons (or the planets or bodies of another system), each with where it is now. Any of them can be turned off to take its notes out of the music.

MIDI, under the volume, sends the music to a synth or a recording program. Each layer plays on the channel of its number in the desk, at the moment it sounds, and each body's place east or west of its planet goes out as a controller on channel 16 (CC 20 for the first body, 21 for the second, and so on). It needs a browser with Web MIDI, such as Chrome or Edge.

Listen, above the sky, hides everything else and leaves the view and one line of what was just heard. Beside it, PNG and SVG save the view on screen with the title, the sky's time and the layers playing: a picture at three times the screen's size, or clean vectors to print or edit.

space play   v view   m mix   1 to 0 and - layers   [ ] speed   e evolve   r real time   l listen   d desk

Positions come from the lower-accuracy method in chapter 44 of Jean Meeus's Astronomical Algorithms. Each time the code changes, the model is checked against Galileo's nights of 7 and 13 January 1610, Cassini's notes for 8 and 9 October 1668, and the triple shadow transit of 24 January 2015.

It simplifies in a few places. Jupiter's shadow is treated as a cylinder the width of the planet, without the slight narrowing of the real cone or the soft edge of the penumbra, so eclipse times can be off by a few minutes, most of all for Callisto. Moons eclipsing each other, which happens in some seasons, are not modelled. For planning an observation, use a full ephemeris such as JPL Horizons.

Venus and Earth come from JPL's approximate elements for the major planets, good from 3000 BC to AD 3000. The model is checked against the transits of 2004, 2012 and 2117 and Venus's greatest elongation of March 2012. It times a transit from the centre of Venus crossing the Sun's edge, so it starts about fifteen minutes after the first contact an observer would see.

The Kuiper belt bodies are plain two-body orbits from the JPL Small-Body Database, which leave out the planets' pull on each other. Over centuries they drift, and the model has Pluto nearest the Sun five weeks late in 1989. That is close enough to hear the resonance, but not to point a telescope.

The planets of other stars run on published linear schedules, a measured transit time and a period, from the Extrasolar Planets Encyclopaedia. Real transits wander from these by minutes to hours (in a resonant chain the planets pull each other early and late), and a small error in a period adds up over years, so a transit predicted far from the measurement can be hours out. Orbits are taken as circles.

Callisto's orbit is tilted enough that for years at a time it passes above or below Jupiter and its shadow, and then it plays none of those events. The view from above says when this is happening.

• Galileo Galilei, Sidereus Nuncius (Venice, 1610).
• Giovanni Domenico Cassini, Ephemerides Bononienses Mediceorum Syderum (Bologna, 1668).
• Johannes Kepler, Harmonices Mundi (1619).
• Edward Tufte, Envisioning Information (Graphics Press, 1990).
• Jean Meeus, Astronomical Algorithms, 2nd ed. (Willmann-Bell, 1998), ch. 44.
• Hans Cousto, The Cosmic Octave (1978).
• Orbital resonance, Wikipedia.
• E. M. Standish, Keplerian Elements for Approximate Positions of the Major Planets, JPL.
• JPL Small-Body Database, for Pluto, Orcus, Haumea and Gonggong.
• The Extrasolar Planets Encyclopaedia, for the three other stars.
• S. M. Mills et al., A resonant chain of four transiting, sub-Neptune planets, Nature 533 (2016).
• R. Luger et al., A seven-planet resonant chain in TRAPPIST-1, Nature Astronomy 1 (2017).
• R. Luque et al., A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067, Nature 623 (2023).