The Air Had Geometry That Brass Could Shape

When I built the theremin circuit back in February, I focused on the audio path — waveshaping, output impedance, that linearization coil that stretches playable range from twenty centimetres to nearly a metre. What I didn’t interrogate was the antenna itself. A brass rod. Vertical. Standard. It never occurred to me that the shape was a choice, not a given.

This week I’m questioning that assumption.

The field is a volume, not a line

A theremin pitch antenna doesn’t measure distance. It measures capacitance — specifically, the capacitance between the antenna and your hand, which together form the two plates of a variable capacitor. Your hand is grounded (through your body’s capacitive coupling to the floor), so as it approaches, the effective capacitance rises. This shifts the variable oscillator’s frequency, which heterodynes against the fixed reference oscillator to produce the audible pitch.

The standard equation for capacitance between two parallel plates:

C = ε₀ × ε_r × A / d

where:
  C   = capacitance in farads
  ε₀  = permittivity of free space (8.854 × 10⁻¹² F/m)
  ε_r = relative permittivity of the medium (≈1 for air)
  A   = overlapping area of the plates
  d   = distance between plates

This is the textbook formula, but it lies by omission. A theremin antenna isn’t a parallel plate — it’s a rod, and your hand isn’t flat. The actual capacitance follows a more complex relationship involving the geometry of both conductors and the electric field distribution between them. For a hand approaching a vertical rod from the side, the field lines curve. The effective sensing zone isn’t a plane; it’s a three-dimensional volume with gradients in every direction.

Here’s what that means practically: moving your hand along the antenna’s axis doesn’t produce the same pitch change as moving it toward the antenna. The field is anisotropic. Different approach angles yield different sensitivity curves.

Antenna geometry shapes the playing field

A straight vertical rod produces a roughly cylindrical field that’s densest near the tip (where the charge concentrates) and weaker along the shaft. This is fine for classical technique — you play in a horizontal plane, approaching and retreating from the rod. But it’s not the only option.

When I was making antenna lobe lanterns — rotating antennas on a turntable to map their radiation patterns — I learned that small geometry changes produce dramatic pattern shifts. A Yagi’s parasitic elements reshape the lobe completely. Bending a dipole changes its polarization and directivity. The physics is the same for capacitive sensing: conductor shape determines field distribution.

Some builders curve their pitch antennas into shallow arcs. This redistributes the field concentration, steepening the gradient in the arc’s focal region while flattening it elsewhere. The result: a “sweet spot” with tighter pitch control, surrounded by less sensitive zones for larger gestures. Others use flat plate antennas instead of rods, which produces a more uniform field but sacrifices the range extension that tip concentration provides.

Measuring what you can’t see

The challenge is that you can’t see the field. You can only infer it from the instrument’s response.

My measurement rig is primitive but functional: an Arduino logging frequency measurements from the theremin’s variable oscillator tap, while I move my hand through a grid of positions marked by a wooden frame with fishing line at 5cm intervals. Each position yields a frequency reading. Enough readings yield a contour map.

The baseline measurement with my standard 30cm brass rod:

Distance from tip	Δf (Hz) per cm
5 cm	847
15 cm	312
30 cm	89
50 cm	23

The nonlinearity is obvious — pitch sensitivity drops off roughly with the inverse square of distance, though the linearization coil flattens this somewhat. The coil creates a series resonant circuit with the antenna’s self-capacitance, and tuning it requires matching the inductance to your specific antenna geometry. Change the antenna, change the coil. There’s no universal value.

What I’m testing

Three antenna configurations, all the same total conductor length (30cm), all using the same linearization coil value (2.2mH) as a starting point:

Straight rod — the control
90-degree bend — a 20cm vertical section with a 10cm horizontal extension at the top
Helical coil — the rod wound into a loose helix, roughly 8cm diameter

Each one will need its own linearization coil value once I understand the baseline response. The helix is the interesting one — coiling the antenna increases its self-capacitance dramatically, which should shift the optimal coil inductance downward. It also distributes the field more uniformly around the coil axis, potentially creating an antenna you can play from multiple angles.

The measurements take time. Moving through the grid, logging each point, trying not to breathe too hard (body movement shifts capacitance — this is why Clara Rockmore kept her thumb and forefinger touching to stabilize her hand geometry). Two hours in, I have half the data I need for the straight rod baseline.

Whether any of this produces a more playable instrument remains to be seen. The ear training from choir work will eventually matter more than the measurement rig — what I can quantify is only useful if it translates to something I can hear and control. But for now, the invisible field is slowly becoming visible, one grid point at a time.