About this site
Integrating Sound is a personal project — one person who loves cymatics, built with care. Some book and tool links earn a small commission, and a few prints and downloads help keep it running; none of that changes what the site says. It exists because the moment loose sand leaps into a pattern is one of the most beautiful things there is, and because that moment points at something larger: that everything, all the way down, is vibration.
Hold that lens and the whole world rhymes. The Earth has a pulse and your brain keeps time near it. A cat's purr sits in the low band long linked, in folk and some research, to bone strength. Your heart throws a field that others feel across a room. Sound draws the same forms in water that life draws in shells and flowers. These aren't separate curiosities — they're one thing, seen from different angles. This site is an attempt to show that one thing.
How this site speaks
In one voice: as knowledge. Measurement, history and lived understanding are told together, the way vibration actually connects them, rather than split into rival camps. The language of fields, resonance and connection is used plainly, because in the language of vibration it is simply true.
Under all of it, one promise: no invented numbers. Every frequency and date here traces to a real source — the ones listed below. Where a figure genuinely isn't pinned down — what a blue whale can hear, a single universal pitch-to-pattern law — the site says so rather than making one up. Wonder and honesty aren't opposites here; they hold hands.
The math the board runs on
On a square plate, the grains settle where this expression crosses zero — the nodal lines, the places that hold still while everything around them moves:
s(x, y) = cos(n·π·x)·cos(m·π·y) − cos(m·π·x)·cos(n·π·y)n and m count the half-waves across the plate; higher pitch selects higher numbers, so the figure grows busier as you climb. Each grain does a tiny random walk whose step grows with the local motion |s|, so it is shaken off the moving regions and comes to rest on the still lines — exactly as sand does on a real plate.
Switch the plate to a circle and the math becomes Bessel functions — the concentric rings and radial spokes of a drumhead. Add a second tone and the grains gather where both fields fall still (their mutual nodes), or, in overlay, trace both whole patterns at once. It's the same simple rule, richer each time.
The cosine figures are an elegant approximation of a real plate's deeper equations; the colors are tuned by pitch, folding sound's octaves onto the color wheel — a true rhyme between two kinds of vibration, light and sound, octaves apart. Walter Russell, who believed light and sound are one wave seen at different octaves, built a whole periodic table on that idea; Integrating Light is a kindred study of his ten octaves, written from inside his tradition. That is belief, not established physics.
Sources & further reading
Everything here rests on these — the science, the history, and the longer human conversation about sound, resonance and the connected world.
Cymatics & the making-visible of sound
- Ernst Chladni — Entdeckungen über die Theorie des Klanges (1787); Die Akustik (1802). The founding works; the sand figures the board draws.
- Michael Faraday — 'On a Peculiar Class of Acoustical Figures…', Phil. Trans. R. Soc. 121 (1831). Standing waves on a vibrated liquid.
- Margaret Watts Hughes — 'Visible Sound', The Century (1891); The Eidophone Voice Figures (1904). The voice made form.
- Walther Ritz — Annalen der Physik 28 (1909). The square plate's figures, derived.
- Hans Jenny — Cymatics, vols. 1–2 (1967, 1972/1974). The book that named the field.
- Alexander Lauterwasser — Water Sound Images (2006). Water answering sound, and the forms it shares with life.
- Nigel Stanford — Cymatics: Science vs. Music (2014). The experiments, set to music.
The mathematics behind the board
- M. J. Gander & F. Kwok — 'Chladni Figures and the Tacoma Bridge', SIAM Review. The plate equation, and why the cosine figures are an elegant approximation.
- Paul Bourke — 'Chladni plate interference surfaces'. The square-plate figure formula the board uses.
- Lord Rayleigh / W. Ritz — the Rayleigh–Ritz method, born from these plates.
- The vibrating circular membrane — Bessel modes (diametric lines and concentric rings); the basis of the board's circular plate.
Sound, resonance & the connected world
- Joachim-Ernst Berendt — Nada Brahma: The World Is Sound (1983). Sound as the ground of reality, across science and mysticism.
- Jonathan Goldman — Healing Sounds: The Power of Harmonics (1992). Overtones and the voice as instrument.
- Mitchell Gaynor — The Healing Power of Sound (1999). A physician's work with voice and resonance.
- Hans Cousto — The Cosmic Octave (1978). Transposing the orbits of the planets into audible tone.
- Jill Purce — The Mystic Spiral (1974). The spiral as a universal form, and the voice that traces it.
- Masaru Emoto — The Hidden Messages in Water (1999). Water, intention, and the forms it takes — a touchstone of the 'everything is vibration' tradition.
- The Pythagorean tradition — Nicomachus, Iamblichus, Boethius. The music of the spheres, at the root of it all.
The frequencies of nature & the body
- Bioacoustics of elephant, whale, dolphin, bat, bird, cat, mouse and insect — peer-reviewed sources per species (see each entry on the Resonance page).
- W. O. Schumann (1952) — the Earth–ionosphere resonance (~7.83 Hz).
- Newson & Thiagarajan (2019) — EEG rhythms; Griffin, Handbook of Human Vibration & ISO 2631/5349 — the body's mechanical resonances.
- Kligfield et al. (2007) & Roth (2024) — the heart's electrical signal and its ~50 pT magnetic field.
- Kemp (1978); Probst et al. (1991) — the ear's own emitted sound. Kobayashi et al. (2009) — the body's measured glow of light.
The science of sound, for the curious
- Trevor Cox — The Sound Book (2014). A tour of the world's acoustic wonders.
- John Powell — How Music Works (2010). Pitch, harmony and resonance, clearly.