About the instrument
How the seven bowls are built
The seven bowls on the home page are not a picture of an instrument. They are one, in the sense that matters here: every visible quantity is derived from the same table of seven real bowls, and the seven surfaces genuinely interfere with one another rather than each animating alone.
The seven
Each bowl is a real diameter in inches and a real pitch. Nothing about how a bowl is drawn or how it sounds is set by hand; all of it comes off these two columns.
| Bowl | Note | Hz | Inches | Color |
|---|
| Root | C | 256.0 | 10 to 14 | Red |
| Sacral | D | 288.0 | 9 to 12 | Orange |
| Solar plexus | E | 320.0 | 8 to 10 | Yellow |
| Heart | G | 384.0 | 7 to 9 | Green |
| Throat | A | 426.7 | 6 to 8 | Blue |
| Third eye | C′ | 512.0 | 5 to 7 | Indigo |
| Crown | D′ | 576.0 | 4 to 6 | Violet |
The scale is C, D, E, G, A, C′, D′: a major pentatonic across an octave and a fifth. A pentatonic has no semitone in it, so no two bowls can beat against each other harshly, and any combination struck in any order is consonant. That is why the piece can be left to strike itself at random and never arrive at a chord that needs resolving.
Size
Radius follows diameter, but not in proportion to it. It is raised to the power of 2.1, which exaggerates the taper: the root is not merely larger than the crown, it is a different order of object, which is what the eye reads as a stack receding rather than seven discs in a column.
The scale of the whole stack is not chosen. It is solved: the bowls are placed, their real projected span is measured, the scale is adjusted, and that repeats twelve times until the seven of them exactly fill the frame at whatever size the window happens to be. Measuring the true span rather than estimating it is what keeps the stack centered, because perspective makes the lower bowls project larger and further down than any symmetric guess predicts.
The surface
A singing bowl is not a plate. The profile is a spherical cap, nearly flat through the base and turning up hard toward the rim, then straightening into a short vertical lip. The lip is the part of a real bowl that is actually struck, and the part that reads as a bowl rather than a dish from any angle.
Every sample point on every bowl is displaced by the same sum:
displacement(P, t) = Σj Aj(t) · sin(kj dj − ωj t) · e− λ dj
where dj is the distance in three dimensions from bowl j to that point, and λ is 0.55. Because every disc samples the same sum, the bowls interfere with each other by construction: a ring crossing the heart bowl is the root and the crown arriving there at once, not an animation played on the heart.
The two constants that set the character of a ripple both come off the frequency. The spatial wavenumber is k = f × 0.0142, so a high bowl ripples in tight rings and a low one in wide ones. The rate is ω = f × 0.0024, so the high bowl also ripples faster. The root moves slow and wide and the crown fast and tight, and neither was decided.
The bowls turn as well, one revolution of the root every 96 seconds, with the rate taken from pitch raised to the power of 2.4 and the hand alternating bowl by bowl. Adjacent bowls therefore never turn together, and the set never returns to the same arrangement twice.
Beads, not wireframe
Every sample point is drawn as a bead rather than joined into a continuous line, so the sampling itself is visible and the surface reads as something granular catching light rather than as a mesh. Ring counts follow the bowl's own size, so the spacing between beads is roughly constant across all seven: the root carries a little over two thousand points, the crown a few hundred. Bead size follows the radius and the smaller bowls are inked back up to compensate, because light comes off a bead by its area and thinning alone would have taken the object with the texture.
Sound
Each bowl is a small stack of oscillators rather than one. A struck bowl is not a sine wave: it has a fundamental and a set of inharmonic partials above it that decay at their own rates, which is why a real bowl shimmers as it fades instead of simply getting quieter.
The envelope is a bloom, a sustain and a fade that reaches true silence on time. The bloom is roughly two seconds, which is long: a struck bowl arrives rather than starts, and a short attack on a sustained tone sounds like a bell. Short notes take a shorter bloom, because at half a second a two second bloom never reaches its own peak.
Nothing is struck on a schedule you can hear. The piece waits nine seconds before the first tone, so the page opens in silence, and thereafter chooses a bowl and a moment with the intervals set so no pattern is available to be learned. The bowl that has waited longest is favored, which keeps any one of the seven from going unheard.
No browser will let a page make sound before it has been touched. The control says so by lighting while the audio is held, and a single tap anywhere in the window releases it.
The ground
The warm field behind everything is nine slow pools, six crossing the diagonal from the top left to the bottom right and three running the other diagonal out of the bottom left. Each carries two of the seven colors and crosses from one to the other as it travels, so a hue is always on its way somewhere and no color ever swaps in. Their periods are prime against one another, so the nine never line up the same way twice.
Their strength is not a matter of taste. Text sits on this field, and the alphas are held at the most the page takes while the dimmest ink on it still clears 4.5:1 against the ground at its warmest, measured across a full cycle of all nine periods rather than estimated.
Color
The seven colors above are the traditional chakra hues, but they are never drawn as listed. Each is refitted to whatever ground it is being drawn on, so that it clears 4.5:1 there: the gold reads 1.7:1 on white as given, and a label set in it may as well not be there. The swatches in the table are the fitted values, not the raw ones.
The page also has a day: the ground and the ink shift through a set of grounds, and every color on the page is refitted to each. Nothing carries a second set of values invented for the dark.
Motion, and the choice not to have it
Everything above answers the reduced-motion setting. With it on, the bowls are drawn once in a settled state, the ground holds still, and hover and click still work. The warmth is the point; the drift is the pleasure, and it is the part that can be given up.
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