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Premium · Discover lessons In development

Ancient questions. Measured answers.

Discover is what Premium is for: interactive lessons on the science behind sound’s mysteries, from Pythagoras’ whole-number ratios to Chladni’s sand and the evidence on 432 Hz. Each lesson keeps its units visible, states its assumptions, and ends with what the model leaves out. Premium also includes full-length video export and live listening.

Status
In development. No release date yet.
Where
The native app for Mac, iPhone and iPad, coming to the App Store.
Price
Premium, $4.99 a month, $39 a year or $89 once, as an in-app purchase. It also includes video export and live listening. See pricing
Today’s app
The free web and Mac apps do not include Discover.

How we keep it honest

Sound attracts big claims. Discover takes the questions seriously and lets you check every answer, whatever you believe going in.

Every equation shown

Each interactive shows the formula it computes, with units you can check by hand.

Sources cited

Claims point to the paper, book or measurement they rest on, with its date and its limits.

What the model leaves out

Every lesson ends with its assumptions and what a real instrument, room or ear adds.

Predict, then test

Commit to a guess first, then hear and measure the answer with your own ears.

An evidence lab

Popular claims, such as 432 Hz tuning and the solfeggio frequencies, are graded supported, untested or contradicted, with the evidence for each.

No healing claims

Xymatics describes sound. It makes no health, healing or wellness claims, and neither do its lessons.

Illustrations computed from the equations under them. They are not app screenshots; Discover’s interface is still being built.

Illustration: beats between two nearby tones The sum of a 40 hertz and a 44 hertz sine wave over half a second. The combined wave swells and fades twice, following a dashed envelope that repeats 4 times per second. 0 0.25 s 0.5 s +2 0 −2
Illustration · Beats

Tones at 40 Hz and 44 Hz add to a wave whose loudness swells f₂ − f₁ = 4 times a second. Slowed down so each cycle is visible.

x(t) = sin 2πf₁t + sin 2πf₂t
Illustration: driven resonance curves Steady-state amplitude of a driven, damped oscillator against drive frequency, for quality factors 1, 3 and 8. Higher Q gives a taller, narrower peak near the natural frequency; for Q equal to 8 the peak reaches about 8 and its half-power width is about one eighth of the natural frequency. bandwidth ≈ f₀/Q Q = 8 Q = 3 Q = 1 0 f = f₀ 2f₀ 1 4 8
Illustration · Driven resonance

Less damping (higher Q) gives a taller, narrower peak near the natural frequency f₀, and a bandwidth of about f₀/Q.

A/A₀ = 1 / √((1 − r²)² + (r/Q)²), r = f/f₀
Illustration: harmonic series of a sawtooth wave Twelve bars for the partials of an ideal sawtooth wave on 110 hertz. Partial n sits at n times 110 hertz and its amplitude is 1 divided by n, so the bars fall from 1 to one twelfth. 1 2 3 4 5 6 7 8 9 10 11 12 1 ½ 0 aₙ = 1/n
Illustration · Harmonic series

The first 12 partials of an ideal sawtooth on 110 Hz. Each sits at a whole-number multiple of the fundamental.

fₙ = n × 110 Hz, aₙ = 1/n

Planned lessons 21 lessons in four modules

Module 01

Waves & resonance

6 lessons
  1. Wave sandbox Frequency, amplitude, phase, wavelength and speed, each with visible units.
  2. Superposition studio Add waves and compare the sum with its parts, from reinforcement to cancellation.
  3. Traveling vs standing waves Moving energy and fixed nodes side by side, with boundaries and reflection made explicit.
  4. Driven resonance explorer Sweep a drive through a damped oscillator and read amplitude, phase lag, bandwidth and Q.
  5. Damping and ringdown Long and short decays after a pluck: stored energy, dissipation and perceived sustain.
  6. Beats under a microscope Nearby frequencies and their envelope, kept separate from musical tempo.
Module 02

Fourier, timbre & tuning

6 lessons
  1. Fourier building blocks Build a waveform from sine waves and compare its trace with their amplitudes and phases.
  2. Time–frequency tradeoff Why a short analysis window locates events and a long one separates nearby pitches.
  3. Harmonic series microscope Partial frequencies and amplitudes, from harmonic instruments to inharmonic bells and plates.
  4. Tuning systems comparison Equal temperament, just intonation, Pythagorean and historical temperaments, in numbers and in sound.
  5. Timbre and consonance explorer Change the partials with the interval held fixed; compare predicted roughness with your own rating.
  6. Commas and near coincidences Why chains of simple ratios do not quite close after octave folding.
Module 03

Scales, units & loudness

4 lessons
  1. Frequency scale ladder Audible sound, ultrasound, infrared, radio and slow cycles, each on its own physical scale.
  2. Sound pressure and loudness Digital level, calibrated pressure, decibels and perceived loudness, kept distinct.
  3. Tempo-to-frequency bridge Beats per minute as events per second, not as an audio pitch.
  4. Unit and scale audit Check units, conversions, logarithmic scales and range limits before trusting a connection.
Module 04

Evidence lab

5 lessons
  1. Claim and source ledger Each claim with its source, evidence type, date, limits and review status.
  2. Mechanism map Lay out a proposed causal chain and mark which links are measured and which are missing.
  3. Correlation and confounding Alternative explanations, and what different study designs can actually establish.
  4. Evidence revision history Corrections and changed interpretations recorded without erasing how a conclusion evolved.
  5. Analogy boundary cards What musical, mechanical and quantum examples share mathematically, and where the physics differs.

Lesson names and contents may change before release.

Built into every lesson

  • Plain-text descriptions Nothing depends on hearing, colour or motion.
  • Pause, step and reduced motion Move through a model at your own pace.
  • Keyboard and screen-reader paths Every control and result is reachable.
  • Beginner, maths or method depth Choose how far each explanation goes.
  • Units and glossary close at hand Every number keeps its unit and its scale.
  • Quiet listening examples Sound plays only when you start it.
  • What this model leaves out A summary of assumptions and limits.
  • Experiment passport Export settings, units and model version so a result can be reproduced.

Start with the free app

Everything in it stays free. Add Premium for the lessons when it launches.

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