Ring, chord and sweep: how a wavetable is cut from a shape

A wavetable needs a list of single cycles. The Cymatic Wavetable Pack makes them from the vibration shapes of a drum skin and a square plate. Here are the three ways it cuts a cycle out of a shape.

The pack is calculated, not recorded or measured, and the paths through each shape are my own design.

The starting point: a field

Each table starts with a mathematical field on a shape. For the drum it is the mode shape of an ideal round membrane, written J_n(k r) cos(n theta), where n and m are whole numbers that choose the pattern. For the plate it is cos(n pi x) cos(m pi y) minus cos(m pi x) cos(n pi y) on a unit square. These are standard textbook formulas. The plate formula is a widely used approximation of Chladni figures, not an exact solution for a free plate.

A field gives a number at every point. To make sound you need a single cycle, which is a list of numbers in order. So you walk a path across the field, read the value at each step, and the list of values is the cycle.

One trip is one cycle

One trip along the path is one cycle of the wave. If the path comes back to where it began, the first and last samples match, and the loop has no click at the seam.

Ring

A ring is a closed circle drawn through the field. You walk once around it. Because the circle closes, the cycle loops cleanly with no extra work.

Across the 64 frames of the table, the radius and the centre of the circle move smoothly, so the sound changes continuously from the first frame to the last.

On the drum fields, a ring reads the angular pattern of the mode, so the number of ups and downs in one cycle follows n. A higher n gives a busier cycle.

Chord and sweep

A chord is a straight line across the field. A straight line does not close, so the pack reads it out and then back, tracing the same values in reverse. That makes the end meet the start. The same method is used for the plate and the pack calls that version a sweep. Chord belongs to the drum tables and sweep to the plate tables.

Reading out and back makes the cycle symmetric about its middle. Symmetry in time leaves a mark on the harmonics, so chord and sweep tables differ in character from ring tables. Listen to the two types side by side to hear it for yourself. Nobody has judged these tables by ear yet, and this guide makes no claim about how any single table will sound in your patch.

As with the ring, the line moves from frame 0 to frame 63, so the position control in a synthesizer scans a gradual change.

What the numbers do

Higher n and m: the field has more peaks and valleys, so cycles are busier.
Lower n and m: the field has fewer features. Drum 0-2 Ring starts near a sine, the quietest end of the range.

Every frame in a table is scaled to the same loudness (RMS), so a morph changes tone but not level. Every frame is also band limited: harmonics above 1000 are removed, with a soft taper starting at 700, so very high content cannot create aliasing within the table itself.

Which to try first

Start with a ring if you want the simplest looping behaviour. Try a chord or a sweep when you want to hear the other cut. Then move the position control slowly with a held note, which is the clearest way to hear what the path is doing.

Sixty two candidate tables were built. Drum 0-1 Ring, Drum 1-1 Chord and Plate 4-5 Sweep were left out because their first and last frames were too close to each other.

Limits

The pack has not been tested in a named synthesizer. Check your own synthesizer's file format and frame size. The files use 2048 samples per frame, 64 frames, mono, 44.1 kHz, in 32 bit float and 16 bit.

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