Temperament and A440
Every piano is slightly out of tune, on purpose. Hear why equal temperament makes all twelve half steps the same size (the twelfth root of two, about 1.0595), what that costs (fifths a tiny bit narrow, major thirds noticeably wide and beating) and what it buys: every key works. Then meet the note the orchestra tunes to, A = 440 Hz, agreed in London in 1939, and learn to tune by ear by listening for beats.
In this lesson you'll
- Explain equal temperament: twelve identical half steps of ratio 1.0595 that make exactly one octave, and why older tunings with pure intervals made distant keys sound harsh (the wolf fifth).
- Hear the difference between a pure and an equal-tempered interval: the fifth is almost identical, the major third shimmers (beats), and compute A in every octave (220, 440, 880) and a half step up (440 x 1.0595, about 466).
- Tell the story of A = 440 Hz (London 1939, ISO 16 in 1955, confirmed 1975; 415 for baroque music, 442-443 in many orchestras) and tune a note by ear against a reference until the beating stops.
Music in this lesson
- The Well-Tempered Clavier, Book 1 (Prelude in C, first four chords)Johann Sebastian Bach · 1722
Remember
Equal temperament spreads the Pythagorean comma evenly: every half step is the twelfth root of two, so every key works equally well.
The price is a small impurity in every interval: fifths are a tiny bit narrow, but major thirds are noticeably wide, so they beat where a pure 5:4 third rings calm.
A = 440 Hz is an agreement, not magic: two close notes beat as many times per second as they differ in hertz, and when the beating stops you are in tune.