Doubling a frequency raises the pitch by exactly one octave

An octave is the interval between a pitch and another at exactly double (or half) its frequency; the two share the same pitch class and sound like ‘the same note higher/lower’. Doubling the frequency raises pitch by one octave, halving it lowers by one octave. Register labeling follows a convention: middle C = C4 (~261.6 Hz), A above it = A4 = 440 Hz, so A3 = 220 Hz and A5 = 880 Hz. In practice, bass lines sit around C1–C3 and leads/pads around C4–C6, so register alone tells you a voice’s role.

Examples

A4 = 440 Hz; A3 = 220 Hz; A5 = 880 Hz. C3 is one octave below C4 at half the frequency. Bass sits C1–C3; leads/pads C4–C6.

Assessment

If A4 = 440 Hz, what is the frequency of A5 and A3? Explain the frequency relationship between two notes an octave apart, and where bass lines conventionally sit.