Equal temperament — Music, 14–17 years
How modern instruments divide the octave so music can change key without retuning. Music, 14–17 years.
Idea
In equal temperament, the octave is split into twelve equal steps. Each semitone multiplies the frequency by the same amount, about 1.0595. This is not the only possible tuning, but it lets the same keyboard shapes work in every key.
Why it was needed
Older tuning systems made some keys sound beautifully pure but made distant keys awkward or harsh. Keyboard players then had to retune, or accept uneven intervals. Equal temperament is a compromise: it spreads the small tuning errors around the octave so composers can modulate and instruments can play together.
Worked example
Suppose A4 is 440 Hz. One semitone above it is found by multiplying 440 by 1.0595, giving about 466.2 Hz. Twelve such multiplications give 440 × 1.0595¹², approximately 880 Hz, exactly one octave above A4 in this system.
Common trap
A reasonable mistake is to think “equal” means every pair of notes has equal frequency distance. It does not: the steps are equal ratios, not equal differences in hertz. The gap from 220 to 440 Hz is an octave, while the next octave goes from 440 to 880 Hz.
Where it appears
Most pianos, guitars with fixed frets, electronic keyboards and digital instruments use equal temperament or imitate it. A band can change key, and a keyboard can accompany many instruments, without stopping to retune. Some singers and string players still adjust notes slightly for a particular musical colour.
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