Now available on the web
A growing library of interactive instruments to see, play, and understand harmony.
Free account includes 10 days of every tool. No card required, no automatic billing.
Create your account now to reserve launch ratesBest on tablet or desktop. All tools also adapt to mobile screens.
Scale Studio
Explore 1,815 scales and 346 chord progressions up to extended and altered dominants, with an 88-key piano, circle of fifths and semitone grid.
Scaler
Split the octave into any number of steps, tune every one of them, and hear microtonal scales come alive.
Circle of Fifths
See every key in a circle, find the chords of any key, and move smoothly from one to the next.
Fret Map
Find any scale by name or sound, then take it to the piano or the guitar neck.
Pendulum
Watch the pendulums drift out of step and fall back into a perfect pattern.
Chladni Plates
Change the frequency and watch sand gather along the still lines of a vibrating plate. Each resonance reveals a different Chladni pattern.
Orbital
Explore the cosmos through orbital resonance. Change the ratio between two orbital periods and watch their alignments return in repeating patterns.
Feel it for yourself
Find your interactive tools
Harmony does not stop at the piano's twelve notes.
Lite versions, no account needed. 20 free minutes a day.
Music
Scales, chords and resonance visualizers in one studio
Pick a root and a scale and watch it light up on a piano, on strings and around the twelve-tone circle — then switch to wave-and-staff or Chladni visualizers, fire chord presets, run the arpeggiator and play the synth engine with MIDI input.
Learn how it works →TRY LITE →Music
Keys, chords and modulations in one living wheel.
Explore every key on an interactive circle of fifths: hear its diatonic chords, trace progressions as paths, find pivot chords for modulation, and let MIDI or computer keys reveal the key you are playing in.
Learn how it works →TRY LITE →Music
Scales, modes and intervals across the fretboard
Any tuning, any scale: see where every degree falls on the neck, with correct enharmonic spelling and intervals drawn in place.
Learn how it works →TRY LITE →Music
Divide the octave in any number of parts
Pick a root note or frequency and split the octave into n equal parts, or stack any ratio seed like 3/2 or the golden ratio for open scales that never close the octave. Play every note on a circle or on a set of sweepable strings.
Learn how it works →TRY LITE →Music
Swinging lengths. Shifting phases. Returning harmony.
Release a family of harmonically tuned pendulums and watch their phases weave into waves. Move the sound line to play mellow notes as the bobs cross, then watch the whole installation reunite.
Learn how it works →TRY LITE →Music
Train your ear from semitones to extended chords
Levelled ear training across tones and semitones, intervals, scales and modes, triads through extended chords, progressions and note recognition — with piano and staff diagrams, singing exercises judged by microphone, and an infinite mode that keeps raising the difficulty.
Learn how it works →TRY LITE →Music
Find every note on piano and guitar
Locate all 12 notes on a piano and a guitar fretboard, switch between Do-Re-Mi and C-D-E, and race the clock to find neighbour notes by tones and semitones — with levels that unlock sharps, flats and longer distances as your accuracy grows.
Learn how it works →TRY LITE →Music
A full synthesizer you can see while you play it
Two oscillators, sub and noise through a resonant filter with its own envelope, an LFO and a rack of effects — all drawn live as waveform, spectrum and envelope curves, played from the screen, your computer keys or a MIDI controller.
Learn how it works →Explore →Music
Euler’s Tonnetz and your own note grids — triangular or square.
Play notes and triads on a seamless harmonic lattice of perfect fifths, major thirds and minor thirds. Trace chord progressions, explore their geometry, and play with computer keys or a MIDI controller.
Learn how it works →Explore →Music
A four-track tape sketchpad for harmonic soundscapes
Lay PHI recordings or your own audio files on four circular tape loops, tune each by pure musical intervals, change the tape speed and spread them in space to weave a soundscape in seconds.
Learn how it works →Explore →Music
Handpan layouts you can lay out and play
Build a handpan from its ding upward: choose the scale, the number of tone fields on top and bottom, and hear the layout as you shape it.
Learn how it works →Explore →Music
Three pulses turning at once, drawn as geometry
Set each axis to its own number of beats and watch the polygons rotate against each other — tap tempo, accents, textures and the coincidence points where the cycles realign.
Learn how it works →Explore →Sound & Waves
Resonance drawing its own diagram
Drive a plate at the right frequency and the nodes reveal themselves as figures — resonance you can see rather than derive.
Learn how it works →TRY LITE →Sound & Waves
Sound rendered as a three-dimensional lattice
Interference, superposition and standing waves made visible — the physics behind everything astronomers learn from spectra.
Learn how it works →Explore →Sound & Waves
The geometry of musical intervals
Hear and see the whole-number ratios of just intonation: interfering waves, Lissajous figures and a 3D field that turns stable when the numbers are simple.
Learn how it works →Explore →Sound & Waves
Standing waves inside a room you can resize
Give a room its three dimensions and watch axial, tangential and oblique modes appear as pressure fields — the physics behind why a room colors what you hear in it.
Learn how it works →Explore →Sound & Waves
Tone generators, octave fields, heatmaps and note tables
Three ways into pure tone: faders on a consonance heatmap, multi-oscillator generators with binaural beats, and a full note table tied to your tuning reference.
Learn how it works →Explore →Sound & Waves
Two tones, a space between them
A minimal stereo tone player: tune a base frequency and the difference between your ears, then add soft harmonics, spacious reverb and gentle motion.
Learn how it works →Explore →Sound & Waves
Incoming sound, seen in real time
Microphone, file or test tone analyzed frame by frame: logarithmic spectrum, cascading spectrogram, triggered oscilloscope and a radial view where every octave falls at the same angle.
Learn how it works →Explore →Sound & Waves
Sound turned into living geometry
Leave the microphone on and every sound blooms into mandalas, Chladni fields, harmonographs and radiant rings. Noise stays fluid; stable notes lock the forms into symmetry. Built for full-screen projection.
Learn how it works →Explore →Sound & Waves
Lengths are sound, and every length is playable
A monochord bench with movable bridges, drawn lines that unfold their harmonic series, and figures in 2D and 3D where every edge, run, diagonal, apothem and radius sounds its fraction of the whole.
Learn how it works →Explore →Sound & Waves
Vibrating strings, nodes and the overtone ladder
Twenty harmonics of a single fundamental, each drawn as a standing wave with its nodes and sounded as a pure sine — mute, solo and stack them in 2D or 3D to hear how timbre is built.
Learn how it works →Explore →Sound & Waves
An ultra precise tuner with three living views
A high precision chromatic tuner for any instrument: a luminous string view, a strobe wheel that stands still in tune, and a geometric live view of your sound. Choose your reference pitch, tuning system, sweetened offsets and instrument preset.
Learn how it works →Explore →Number & Form
The five perfect polyhedra, in space
The only five shapes with identical faces, edges and angles — the vocabulary Kepler once used to try to explain the solar system.
Learn how it works →Explore →Number & Form
Classical construction, unlimited canvas
Two tools, no numbers. The instrument astronomy was built with for two thousand years before it had algebra.
Learn how it works →Explore →Number & Form
Basic mathematics with figures, equations and mini games
Equations as balances, drawn fractions, draggable areas and two mini games of calculation and patterns — with saved progress and levels.
Learn how it works →Explore →Number & Form
Every unit, one bench
Move between units of length, mass, energy and time — including the astronomical ones that make big numbers speakable.
Learn how it works →Explore →Number & Form
Pendulum spirographs drawing live
One or several damped pendulums trace their figure frame by frame until they stop: change colors, frequencies and phases, or load presets with just-intonation proportions.
Learn how it works →Explore →Number & Form
Figurate numbers and gnomonic growth in 2D and 3D
Spheres, cubes and tetrahedra that arrange themselves: triangular, square, oblong, root rectangles, cubic and tetrahedral, plus Plato's lambda and the Fibonacci sequence.
Learn how it works →Explore →Light & Matter
Refraction, reflection and diffraction on an optical bench
Move mirrors, prisms, lenses and slits with the cursor and watch light bend, split into colors and interfere with itself — at whatever speed you choose.
Learn how it works →Explore →Light & Matter
From infrasound to gamma rays on a single axis
Pick a frequency and watch it settle into the continuum of waves: wavelength, energy, band, its harmonics and the octaves that turn it into light.
Learn how it works →Explore →Light & Matter
Move color. Discover how light combines.
Add and drag colored circles, mix RGB light or layer ideal color filters, and sample the colors in their overlaps. Save a composition or export an image.
Learn how it works →Explore →Cosmos
The real sky over any place, date and time
Stars down to magnitude 5.6, constellations drawn out, calculated planets, Sun and Moon with their phase: the sky you would have overhead if you stepped out now — or in a thousand years.
Learn how it works →Explore →Cosmos
Moon phases, libration and eclipse seasons
Watch the illuminated fraction turn with the geometry that causes it, and see why eclipses arrive in seasons rather than every month.
Learn how it works →Explore →Cosmos
Periods locked into whole-number ratios
Set two bodies in motion and find the ratios where their orbits start to sing — the same arithmetic that carved gaps in Saturn's rings.
Learn how it works →Explore →Cosmos
3D geometry projected onto a rotating globe
Nest polyhedra inside the Earth and see where their vertices and edges land on the surface — geometry as a way of reading a sphere.
Learn how it works →Explore →Cosmos
Build a system of masses and watch it move
Add, move and launch bodies, tune their masses and velocities, follow their orbital trails and watch the gravitational waves the system radiates.
Learn how it works →Explore →Cosmos
One continuous zoom, from a hand to the whole universe
Keep zooming out and never stop. Every step is a multiplication, not an addition — which is exactly why the universe cannot be drawn to scale.
Learn how it works →Explore →Cosmos
A calculator for dates and time spans
Measure the time between two dates, project a date forwards or backwards by years, months, days or hours, and convert any span into days, hours or years.
Learn how it works →Explore →Your favorites and supported settings follow your account. Recordings and exported files stay on your device.
Capture audio inside the instruments and loop it in Loop Multitrack. Your recordings store locally, ready to replay.
Keep your favorite harmonies one tap away. Favorites, color themes, location and settings sync to your account — ready when you sign in on another device.
Connect a MIDI controller to play Scale Studio, KeyPad, Circle of Fifths and Synth in a compatible browser.
Show a scale, a chord or an interval instead of only describing it. Every lesson becomes something students can touch and hear.
Scale Studio · Circle of Fifths · Ear Training
Explore modes, just ratios and 346 searchable progressions. Switch between Standard and Jazz notation, connect MIDI, and loop your ideas.
Scaler · KeyPad · Loop Multitrack
Study proportion, symmetry and geometry where art and mathematics meet the same numbers as music.
Ratios · Platonic Solids · Compass & Ruler
The same complete collection. Choose how you access it.
Prices in USD.
Early-member price protection
Create your account during launch to reserve today’s monthly and yearly rates. Once subscribed, your renewal price stays protected as PHI grows, for as long as your subscription continues.
No card required
Try the full collection and its shared music libraries. No card required.
Protected launch rate
Full access at a protected launch rate while your subscription continues. Yearly is $96 per year ($8 per month). Cancel renewal anytime.
Future interactive tools included
One payment for lifetime web access, including all current and future interactive tools and updates.
After your trial, choose full access or keep exploring the public Lite versions.Public Lite versions also remain available for 20 free minutes a day, shared across Lite apps.
Ten days, every instrument, no card.
PHI · Sound & form
Hear a shape, see an interval, or discover how a pattern returns. PHI brings together interactive instruments for exploring the relationships between number, form, sound, light and the cosmos.
At its heart is an inspiration from the Quadrivium: the four liberal arts of arithmetic, geometry, music and astronomy. Four complementary perspectives for seeking and understanding the harmony of the cosmos through sound and form.
Number and its relationships
Form, proportion and space
Sound, rhythm and harmony
Cycles, motion and the cosmos
PHI carries that spirit into a modern, hands-on space. A scale reveals its geometry; a frequency draws a pattern; a rhythm becomes motion. Move between instruments to listen, build, compare and discover connections for yourself.
Key ideas, practical examples and experiments to explore further. Choose an instrument and discover how to learn with it.
An account is enough to start. If you choose a subscription during your trial, you will not be charged before the trial ends. Joining near the end gives you at least 48 hours from checkout. Stripe shows your first payment date before you confirm.
$10 USD a month, or $96 USD once a year. Plans renew automatically; cancel anytime from your account settings.
Creating an account during launch reserves today’s monthly and yearly rates for your first paid subscription. Your renewal rate then stays protected while that subscription continues. If the subscription ends and you return later, the rates available at that time apply. Lifetime is a single payment for current and future web tools and updates.
If you have chosen a subscription, billing begins when your trial ends. Otherwise, your account remains available and you can choose full access later. Public Lite versions offer 20 free minutes a day, shared across Lite apps.
The complete instrument collection, with shared libraries of 1,815 scales and modes, 38 chord types, and 346 progressions across 12 styles in compatible music instruments. Choose Standard or Jazz chord symbols, connect MIDI in supported browsers, record locally, and use PHI in English or Spanish.
One $249 USD payment for the web version, with every future update.
Yes. Connect a MIDI controller to play Scale Studio, KeyPad, Circle of Fifths and Synth in a browser that supports Web MIDI. Other tools can be explored with their on-screen controls.
We recommend a tablet or desktop for more room to explore. All tools also adapt to mobile screens in a modern browser. App Store and Google Play versions are in preparation.
Cancel anytime before day 10 and you won't be charged.
