Multiple objects

You have a circle. You want two circles. This turns out to be the central problem of the whole medium.

Why summing fails

The obvious move is to add the second shape's signal to the first. It does not work, and it is worth understanding exactly why rather than filing it under "sounds bad".

There is one beam. At any instant it is at one position. Adding two signals does not put the beam in two places — it puts the beam at the vector sum of the two places, which is a third position belonging to neither shape.

What you get is one new figure, related to both inputs and resembling neither. Two circles do not become two circles. They become a single blobby closed curve.

The general form of this is the medium's hardest musical constraint:

You usually cannot play two sounds at once. Adding a second sound does not layer it over the first, it changes the path entirely.

That is why oscilloscope music sounds the way it does, and why "just add a bassline" is not available.

The four solutions

1. Z-axis blanking

Some hardware scopes have a third input on the back that switches the beam off. Gate it while the beam travels between objects and the travel becomes invisible. Real separation, no distortion of either shape.

Two serious problems. A stereo file has two channels, so your third one does not travel — the piece plays back wrong on everyone else's scope. And the gating is inaudible: the picture changes in a way the music does not, which breaks the one-to-one relationship that makes the form worth doing.

2. Square-wave offset

Add a square wave to both channels and the whole figure jumps between two positions. Fast enough, and your eye sees two copies rather than one jumping object.

It works and needs no third channel. It also scales badly:

• Each additional square wave doubles the copies.
• Each must run at half the frequency of the previous one.
• The slowest must stay above the ~30 Hz flicker floor; the fastest is capped by Nyquist.

Four objects is comfortable. Sixteen is not.

3. Fast draw plus a position list

Draw the object rapidly while stepping through a list of positions slowly. Position one, draw; position two, draw; and so on.

The governing rule is arithmetic worth memorising:

drawing frequency = position-change rate × number of positions

Ten objects refreshed 30 times a second needs a 300 Hz drawing rate. Thirty objects needs 900 Hz. This is how swarm and flocking pieces are built.

The cost is fidelity: a high drawing rate pushes the harmonics that sharpen corners above Nyquist, so every object softens as you add more. Ten crisp objects and thirty mushy ones are the same budget spent differently.

4. Phase cutting — the real answer

Take the single phase ramp and cut it into slices. Remap each slice back to a full 0-to-1 range. Draw a different object in each.

Cut in half: the first half of every lap becomes a complete ramp driving object A, the second half a complete ramp driving object B. In one cycle the beam draws A start to finish, then B start to finish, then repeats. Fast enough, and you see two whole, separate, independent objects.

Practitioners describe this as the single most useful technique available, and it earns that:

• Slices need not be equal. Weight them and a complex object gets 70% of the cycle while a simple one gets 30% — which is simultaneously a brightness control, since more beam time means a brighter object.
• You get a frequency hierarchy for free. There is a master rate at which the whole set is traversed, and a rate inside each slice. That is the structure music already has, so the visual arrangement and the musical arrangement stay locked together.
• It is still two channels. It survives being bounced to stereo, uploaded, and played on someone else's scope exactly as you heard it.

Comparison

The last column is the one people underrate. If the way you separated two objects is inaudible, you made a video with a soundtrack.

Doing it in OSC-1

Phase cutting is in the Shape Morph panel:

Two readouts are worth watching. The panel names the musical interval the copies produce — see Harmony, because this is where chords come from. And it shows the per-copy redraw rate, warning you as it approaches 30 Hz: copies divide a fixed beam-time budget, so the flicker floor from method 2 has not gone away, it is just being spent far more efficiently.

Copies, Spread, Focus, and Crossfade are MIDI- and OSC-learnable. Changing copy count live rearranges the chord; switching to FOCUS and sweeping between placements turns the same structure into a clean performance gesture without changing the source shape.

The fly lines

The signal still contains travel between copies: the beam must move from the end of one object to the start of the next, and two audio channels cannot switch it off on the way. OSC-1's Vector Display and Amber CRT presets hide those connector lines automatically while leaving the intended picture and ordinary music intact.

If a different display still makes the travel noticeable:

• Switch presets. Vector Display and Amber CRT suppress the connectors automatically.
• Arrange around them. A ring layout puts the travel around a consistent path; a row makes it a horizontal band. Layout changes where the travel goes.
• Use a laser. A projector has a real blanking channel — see below.

On a laser, you really can lift the pen

This is the one place the constraint genuinely lifts. Laser projectors have a blanking channel, so the beam can be switched off between objects.

Under Laser Output, Auto-Blanking inserts the beam-off moves for you and Jump Threshold sets how large a jump must be before it counts as travel rather than drawing. Separate objects, no connecting lines. See Hardware.

Related

• How to draw two things at once — the illustrated version
• Harmony — why copies make chords
• Fidelity — the budget all of this spends
• Shape tools — the Shape Morph panel