Tuning and pitch

In short: Pitch depends on frequency: the faster the vibration, the higher the note. The A above middle C (concert pitch) is today usually tuned to 440 Hz.

In more detail: An octave means doubling of frequency. Between two octaves lie twelve semitones, in equal temperament all in the same frequency ratio.

In detail

• Concert pitch: A = 440 Hz is the usual standard; some orchestras tune slightly higher.
• Equal temperament: Divides the octave into twelve equal semitones. Pianos are mostly tuned this way so all keys are playable.
• Just intonation: Uses simple frequency ratios (e.g. 3:2 for the fifth), sounds pure in one key, less in others.
• Tuner and apps: Show the deviation in cents (1 semitone = 100 cents).
• Beats: Two similar frequencies create beating; it vanishes when tuning (obertoene-und-klangfarbe).
• Temperature: Instruments go out of tune with warmth and cold (schall-und-dezibel).