1V/oct pitch is exponential, f = f₀·2^V, with audio oscillators baselined at C4 (261.63 Hz) at 0 V

The 1V/oct standard is exponential, not linear: frequency f relates to control voltage V by f = f₀·2^V, where f₀ is the baseline frequency at 0 V. For audio-rate oscillators in VCV Rack the baseline is middle C, C4 = 261.6256 Hz (MIDI note 60). So at V=0 the oscillator sounds C4; at V=1 it is C5, an octave up (523.25 Hz); at V=−1 it is C3 (130.81 Hz). The exponential law is exactly why the standard is ‘volt per octave’ rather than ‘volts per hertz’: equal voltage steps give equal musical intervals in every register, so a sequencer transposing by a fixed voltage shifts every note by the same interval. Low-frequency oscillators and clock generators use a different baseline — 120 BPM, i.e. f₀ = 2 Hz.

Examples

f = 261.63·2^1 = 523.26 Hz = C5 (one octave up). f = 261.63·2^(7/12) ≈ 392 Hz = G4 (a perfect fifth above C4). f = 261.63·2^(−1) = 130.81 Hz = C3.

Assessment

Using f = f₀·2^V with f₀ = 261.63 Hz, compute the frequency at V = 0.5 and V = −0.5, and state which musical intervals above/below C4 these correspond to. Explain why equal voltage steps give equal intervals in any register.