Spectral Resonance · a journey through the universe's frequencies
the moment
Frequency is drawn on a logarithmic axis: each tick a factor of ten, gold ticks the octaves when there is room. The left wall is the slowest cycle we can name, the age of the universe read as a period; the right wall is the fastest anything can be, one cycle per Planck time. About two hundred and three octaves lie between them, cut into seventeen bands. Every mark is a measurement or a definition with its source, and says which kind of number it is: defined (exact by definition), measured, approx (a typical value of something that varies), or claimed (reported by one group, not established; on the map because it is talked about, and labelled).
Each band is drawn as a world. The measured things in it move at their true rate when the eye can follow them (a heart, a breath, a pulsar's flicker), and otherwise at their true rate divided or multiplied by a power of two, which the corner of the stage always prints. Around them is atmosphere: starfields, haze, particle drift, the glow of a thermal image. That part is a simulation for the eye and is named as one in the same corner. Nothing pretends to be a measurement that is not.
The ear takes about 20 Hz to 20 kHz, ten octaves of the two hundred. In the universe band the beginning is unveiled: the age of the universe brought up 66 octaves is 169.6 Hz. That note is sounded deep, two sub-voices two octaves down beating at 4 Hz, a pulse felt more than heard; its first four partials breathe six times a minute under a vowel that opens from "mm" to "ah" as the veil lifts over twelve seconds and closes again; a hushed minor triad on the note swells voice by voice over it, the way the intro of Shine On You Crazy Diamond voices its drone; a breath of air rises with the swell, and one deep stroke marks the moment. The note is measured; the depth, the beat, the vowel and the triad are choices, and say so. The cursor makes no tone of its own; a phenomenon's transposed note plays only when you press hear it in its panel. Each band carries its own sound, derived from what it draws: the chant in the universe, the slow sky's notes, the chord of the orbits, the day's wind and the Moon's note, the Earth's gravest ring struck as a bowl, the heart and the breath at their marks, the EEG rhythms with the sounds used to entrain them, the storm, the piano, the bat detector and the radios, the caesium second ticking, heat as hiss, rain under the rainbow, and for the bands beyond, their phenomena as a quiet chord, the Planck scale alone with the coin's drips. Every one is either a recording with its credit or synthesized from a measured rate, and the corner says which. Whole line, the default for the cursor's tone, lays the entire line over the ear: 20 Hz at the age of the universe, 22 kHz at the Planck time, each octave of hearing standing for twenty of the line, so sliding the cursor is one sweep of everything the ear can take. The other ways keep the frequency's own octave: a frequency is multiplied or divided by two, whole times, until it lands in the ear, and the panel says by how many octaves. Octave tone plays the note as a stack of octaves at once, so sliding along the line sounds like one endless rise and every octave lands on the same pitch. Transposed plays one sine brought into 110 to 220 Hz. As it is plays the frequency itself when the ear can carry it, and below hearing a click at the true rate. No note is played that is not the frequency, or the frequency by a power of two.
Every sound on the page is either a recording or synthesized from a measured number, and the panel says which. The recordings: a heartbeat (Benboncan, CC BY 3.0); a thunderstorm (RHumphries, CC BY 3.0); a spring meadow at Nagykovácsi, a soft breeze and a few distant birds (rubindaniel, CC0); waves at a shore (Luftrum, CC BY 3.0); a Geiger counter (jo0ls, CC BY 3.0); a blue whale off the Atlantic coast (NOAA, CC0); dolphins whistling and clicking, a bottlenose, Atlantic spotted and common dolphins (NOAA Fisheries, public domain); an elephant rumbling (King, Soltis et al. 2010, CC BY 2.5); the mains hum (public domain); a hoary bat through a detector (Kaldari, CC0); the sea from a hydrophone off Svalbard (Max Eastley, public domain). The piano, the electric piano, the radios' static, the breath, the footsteps, the chant and every phenomenon's own voice are synthesized here.
The octave is a circle of 1200 cents; a frequency's place on it is the fractional part of its base-2 logarithm. Two frequencies within the tolerance share a note in the sense that some power of two brings them within that many cents of each other. Fifths and thirds compare after also dividing by 3 or by 5, the pure intervals of just intonation. With a catalogue this size some coincidences are expected by chance, and the panel says how many.
Positions come from the Keplerian elements JPL publishes for approximate ephemerides (Standish, 1992; valid 1800 to 2050), solved for the moment shown: Kepler's equation, then the orbit turned by its argument, inclination and node into the ecliptic. The Moon is from a short series (Meeus, ch. 47) good to about a third of a degree. Each orbit's frequency is derived from the rate of its mean longitude in the same table. Each planet's pitch is its angular speed around the Sun at the moment shown, the quantity Kepler set to music in 1619, brought by whole octaves into a low register: at their mean speeds Neptune near 53 Hz, Saturn 74, Jupiter 92, Uranus 104, Mars 145, Venus 221, Earth 272, Mercury 283, each bending over its orbit by Kepler's interval (Earth a semitone, Mars a fifth, Mercury a tenth). Every nine seconds the eight are sounded in turn from Neptune inward, half a second apart, as soft bells of three partials placed where the planets stand, so the chord of that moment rings and fades; when the days run, each planet rings again as it passes perihelion. The 1970s realizations of Kepler's harmony (Rodgers and Ruff, Spiegel) let the tones glide continuously in a high register and are remembered as sirens; struck notes at fixed pitches, the way SYSTEM Sounds played TRAPPIST-1, cannot grate against each other, because roughness needs two tones sounding at once within a critical band (Plomp and Levelt, 1965). With the rotations on, each planet's day rings as a second, quieter bell in the octave above its year. A birth moment changes only where the planets stand and how far each has bent: the notes are the solar system's. Nothing here claims they mean anything. They are where the planets were.
The gamma band computes an electromagnetic shower: a gamma ray entering lead converts to a pair after about 9/7 of a radiation length (5.6 mm in lead); each electron radiates a photon after about one radiation length, sharing its energy; each photon converts again; below the critical energy of 7.4 MeV the electrons stop and the photons are absorbed; a field of 1 T bends the charged tracks by their sign. It is the Heitler model with random energy sharing, the textbook picture of what a calorimeter sees, computed afresh every fourteen seconds with the incoming energy set by the live reading. The extreme band's air shower is the same idea in the atmosphere. The bat in the radio band is built from its skeleton, humerus, forearm and four elongated fingers with a membrane between them, and calls at the rates bats use: about ten a second while searching, quickening on the approach, two hundred a second in the terminal buzz.
The Milky Way in the galaxy band is a particle model, 220,000 points sampled from its measured structure: an exponential disc of scale length 2.6 kpc, a thick disc, the bar (5 kpc half-length, 28° from the Sun–centre line, its near end at positive longitude, Wegg et al. 2015), a bulge, and the arms as Reid et al. 2019 fitted them to 199 maser parallaxes (their Table 2: each arm a logarithmic spiral with a kink and two pitch angles, its own width), extended round the Galaxy as the paper's own figure extends them, each with its young blue stars, HII regions and a dust lane on its inner edge. Over the model lies what is measured: the young stars Gaia mapped within about 5 kpc of the Sun (Poggio et al. 2021, the overdensity of upper-main-sequence stars from Gaia EDR3, the authors' public grid), in blue-white, and the masers themselves in gold. Beyond that region no one has measured the disc from outside; the drawing says so. In the universe band the mist is the survey's galaxies smoothed over two megaparsecs: the simplest estimate of where the matter lies, since the galaxies trace the dark halos that outweigh them five to one. Neither is a photograph, and both say so.
The universe band draws the 2MASS Redshift Survey (Huchra et al. 2012): 43,507 galaxies at the distances their redshifts give with H₀ = 70 km/s/Mpc, the whole sky, out to about 400 Mpc. Behind them, and again in the microwave band, the sky is the WMAP nine-year map of the cosmic microwave background (NASA / WMAP Science Team, public domain), in galactic coordinates. The same sky in three other lights stands behind three other bands, all in galactic coordinates: at 21 cm behind the radio band (HI4PI, the neutral hydrogen survey of Parkes and Effelsberg, HI4PI Collaboration 2016), in gamma rays above 1 GeV behind the gamma band (Fermi LAT, twelve years, NASA / DOE / Fermi LAT Collaboration), and in soft X-rays behind the X-ray sheet (ROSAT, the all-sky survey's diffuse maps in three bands as red, green and blue, MPE); the HI and ROSAT maps were rendered through NASA's SkyView facility at Goddard. The galaxy band plots the 199 masers with measured parallaxes from Reid et al. 2019, which is how the arms are known, and draws the arms as that paper fitted them; behind the band stands the whole sky as the Gaia satellite measured it, the colour and brightness of 1.8 billion stars in galactic coordinates (Gaia EDR3, ESA/Gaia/DPAC, CC BY-SA 3.0 IGO, acknowledgement A. Moitinho), and over the model the arm map from Gaia young stars (Poggio et al. 2021, GPL-3.0 data release, cited with thanks). The planets band's sky is the Yale Bright Star Catalogue (Hoffleit and Warren 1991), 9,096 stars to sixth magnitude, with the constellation figures from d3-celestial (Olaf Frohn, BSD licence), the zodiac in gold, all turned with the view. The days band asks NASA's GIBS for the true-colour image of the Earth on the date shown (VIIRS from 2012, MODIS Terra from 2000), so its clouds are the weather of that day. Each set is loaded when its band is first entered.
Where the page once drew a typical shape it now draws a real record, cut small and shipped with the page (the sources and licences are listed in the repository\'s tools/spectral-real/SOURCES.md): GW150914\'s strain at LIGO Hanford, whitened and band-passed, drawn (GWOSC, CC BY 4.0), its sound the chirp computed from the measured masses, since the recorded strain is too low for small speakers; the pulse profiles of the Crab, Vela and B1937+21 from the EPN database (CC BY 4.0), repeated at their true periods as the pulsars\' voices; real EEG with the eyes closed and a night\'s deep sleep, one real night\'s hypnogram, a real heartbeat, a chest belt, arterial pressure with its slow wave, and the force under a walker\'s foot, all from PhysioNet (ODC-BY and CC BY); the sea\'s height at the Point Reyes buoy (CDIP); the tide at San Francisco, fetched from NOAA when the page can; three days of the Earth ringing at Albuquerque after the Tohoku earthquake (EarthScope); a day of the grid\'s frequency (NESO open data); a real air shower from the Pierre Auger Observatory (CC BY-SA 4.0); the diphoton mass from ATLAS (HEPData, CC0) with ten real CMS candidates (CERN Open Data, CC0); the giant resonance of lead-208 (IAEA EXFOR); a hematite Mössbauer spectrum (Zenodo, CC BY 4.0). The squid axon\'s spike is computed from Hodgkin and Huxley\'s equations, the threshold of hearing from Terhardt\'s formula; both say so.
Where a photograph is the phenomenon, the page now shows one, with open licences and the credit in the panel: the minerals under ultraviolet (Hannes Grobe/AWI, CC BY-SA 2.5) and a scorpion in UV (CC0); the Sun in its own extreme ultraviolet (NASA/SDO); the aurora from the ISS (NASA); an echocardiogram (Jassal et al. 2007, CC BY 2.0) and a fetal scan (public domain); a 4D CT of the chest (Werner et al. 2017, CC BY 4.0); a panoramic dental radiograph (MartinThoma, CC0); a person in the thermal infrared (CC0); a car radar\'s range-Doppler map (RADDet, CC BY 4.0); a leaf at 614 GHz (Smart et al. 2016, CC BY 4.0) and a banknote in terahertz (CC BY-SA 4.0); remotes firing infrared (Syced, CC0); blue LEDs and a green laser (CC0); the Clam Lake ELF antenna (US Navy); a real FM station on a software radio (CC0); Anderson\'s positron (1932) and a PET scan (Jens Maus, public domain); an antiproton in a bubble chamber (LBNL, public domain); Trillat\'s electron diffraction plate (Wellcome Collection, public domain); an opened watch crystal (public domain); hydrogen, neon, mercury and sodium discharges photographed through gratings (CC0 and public domain); the Crab from Hubble (NASA/ESA) and Vela from Chandra (NASA/CXC); and the crackle of sferics and a whistler recorded on VLF radio (Stephen P. McGreevy, public domain).
Three pictures can be yours, on request and never stored: with your position, the Earth\'s field where you stand from the World Magnetic Model 2025 (NOAA NCEI and BGS) gives the frequency at which protons and electrons precess in your own room, and the GPS almanac (US Coast Guard NAVCEN) gives which satellites are above your horizon now; on a phone, its accelerometer draws your own walking; with the microphone, the speech spectrogram is your voice. The grid\'s frequency comes live from Elexon (BSC open data) and the tide at San Francisco from NOAA.
The sounds are recordings with open licences, played at their own speed or sped up by a power of two, which the corner prints: a heart at 61 a minute (Benboncan, CC BY 3.0), a man breathing (hugh, public domain), a blue whale (NOAA, CC0; its 16 Hz calls kept to their band and played eight times faster, three octaves up, as the ocean listeners play them), a hydrophone in the sea off Svalbard (Max Eastley, public domain), dolphins whistling and clicking (NOAA Fisheries, public domain), an elephant's rumble (King, Soltis et al. 2010, CC BY 2.5; one octave up), 50 Hz mains hum (public domain), a hoary bat's calls (Kaldari, CC0), waves on a shore (Luftrum, CC BY 3.0), a thunderstorm (RHumphries, CC BY 3.0), a Geiger counter (jo0ls, CC BY 3.0). The piano and the drone are synthesized and say so. The pictures: NASA's Blue Marble, night lights and cloud cover, and the day's own image from NASA GIBS; the WMAP nine-year map (NASA / WMAP Science Team); the Gulf Stream in the thermal infrared (MODIS on Terra, NASA / SSEC UW-Madison, public domain); the X-ray sheet: Röntgen's radiograph of 1895, a healthy hand, chest, foot and elbow (Mikael Häggström, CC0), a flower (Cadop, CC0), and electron micrographs of sunflower pollen (public domain), a snowflake (USDA, public domain), a butterfly scale (Brandon Antonio Segura Torres, CC BY-SA 4.0), a velvet ant (Janice Carr, CDC, public domain) and diatoms (Mary Ann Tiffany, CC BY 2.5); the heart from the NIH 3D Print Exchange (public domain); the constellation lines from d3-celestial (Olaf Frohn, BSD). The lungs and the bat are modelled, since no measured lung or bat with an open licence was found. The piano, the radio's static and whistle, and the drone are synthesized and say so.
The page carries the site's instrument. Its reading, |z| smoothed on about three seconds and folded by the magnitude law a²/(0.36 + a²), is one number between chaos and order. It drives one thing in every world, always the same thing: the grain of the picture, which clears as the field orders. Where a world has a natural place for it, it drives one more, named in the corner: the swirl of the Earth's storms, the window of the thermal palette, the number of tracks in the chamber, the branching of the air shower. The reading itself is printed at the top right.
CODATA 2018; Planck 2018; JPL approximate planetary elements; NASA planetary fact sheets; IAU nominal solar values; NIST atomic spectra; the ATNF pulsar catalogue; LIGO (Abbott et al. 2016); HITRAN; ISO 226; Cousto, The Cosmic Octave, for the transposition practice only; Sahu et al. 2013 and Hameroff, Bandyopadhyay and Lauretta for the microtubule claim, labelled claimed.