Every note on this course so far has assumed two things: that A above middle C is 440 Hz, and that the octave splits into twelve equal semitones. Neither is a law of nature. Both were agreed on.
A440
A440 is the tuning standard that sets the A above middle C, A4, at 440 Hz. It took a long time to agree.
| When | What happened |
|---|---|
| 1860s | France set a standard of 435 Hz, adopted by many countries |
| 1885 | Austria recommended 435 Hz |
| 1926 | The American music industry settled informally on 440 Hz |
| 1936 | The American Standards Association recommended 440 Hz |
| May 1939 | Delegates from France, Germany, the Netherlands, Italy and England met at the BBC in London on concert pitch |
| 1955 | ISO took the standard up as Recommendation R 16 |
| 1975 | Formalised as ISO 16 |
Equal temperament
Twelve pure 3:2 fifths do not quite return to the starting note: they overshoot by the Pythagorean comma, as lesson 6 noted. Equal temperament spreads that difference out by making every semitone exactly the same size. Each one multiplies the frequency by the twelfth root of two, about 1.059463, so twelve of them double it: one octave. In cents, every semitone is 100.
The figures for it were worked out by the Chinese prince and theorist Zhu Zaiyu, of the Ming court, and, independently and slightly less precisely, by the Flemish scholar Simon Stevin. Equal temperament has been the main tuning of Western music since the 20th century.
What it costs
The price of playing in every key is that only the octave stays perfectly pure. The fifths and fourths come out almost indistinguishably close to their just ratios; the thirds and sixths are further away. As Europe switched to equal temperament, composers adjusted how they wrote to keep that dissonance down.
Sources
Every date, name, tempo and origin on this page comes from these pages, read on 2026-10-24.