Pitch

Frequency and pitch

The faster something vibrates, the higher it sounds. The standard pitch A4 has 440 Hz, the octave above 880 Hz: an octave doubles the frequency. From this anchor every other note is calculated in equal temperament. Each semitone has the frequency of the one before, multiplied by the twelfth root of 2 (≈ 1.0595), and from that follows, for example, C4 at 261.63 Hz.

Many orchestras tune a little higher for a brighter sound, at 442 or 443 Hz. Historically informed performances of Baroque music often use 415 Hz, about a semitone lower.

Accuracy

The deviation is measured in cents: 100 cents equal a semitone, 1200 an octave. As a rule of thumb a tone is often considered cleanly tuned when the deviation is below about ±5 cents. The smallest audible difference between successive tones is about 3 to 6 cents, depending on the listener and register; for simultaneous tones even smaller differences show up as beats. A tuner determines the fundamental frequency and shows how far it lies from the nearest target pitch.

If two tones sound almost equally high, you hear a periodic swelling and fading, the beating. Its frequency is the difference between the two tones: a difference of 2 Hz means two pulses per second.

Pitch and timbre

Two instruments can play the same tone: the pitch is the same, the timbre is not. Tones of the same pitch can also differ in loudness and length; pitch is only one of the four properties of a tone.

Common mistakes

• Confusing pitch with loudness: Loud is not high.
• Following the tuner blindly: It measures against the equal-tempered grid, a compromise. Thirds played in just intonation deliberately depart from it.
• Thinking standard pitch is fixed: 440 Hz is the norm, but many orchestras tune higher.