Octaves

Middle C vibrates about 261.63 times a second and the C above it about 523.25 times, almost exactly twice as fast.

Same name, higher or lower

An octave is the interval between two notes with the same letter name, eight letters apart counting both ends: C up to the next C. It spans twelve half steps, the whole repeating pattern of the keyboard. Octaves sound so alike that Western music treats them as versions of the same note, a principle called octave equivalence. That is why the letters repeat after G instead of carrying on through the alphabet. Not every culture or era has thought this way; Open Music Theory notes that some ancient Greek theorists did not accept octave equivalence and used more letters.

Twice the frequency

The reason octaves blend so well is physical. Going up an octave doubles the frequency. With the standard tuning A4 = 440 Hz, A5 is 880 Hz and A3 is 220 Hz. Middle C is about 261.63 Hz, and the C above it about 523.25 Hz. When two notes are an octave apart, every vibration of the lower one lines up with exactly two of the upper one, so their waves fit together and the ear hears one fused sound. In equal temperament, used on modern pianos, each half step multiplies the frequency by about 1.0595, and twelve of them multiply it by exactly 2.

Singing in octaves

When a group of men and women sing the same tune "in unison", they are often really an octave apart, because most adult men's voices sit about an octave lower than most women's and children's. The result sounds like one melody, only richer. Choirs, folk singing and football crowds all rely on this. On the piano, playing a melody in octaves with both thumbs and little fingers is a classic way to make it stand out.

Beyond the octave

Intervals larger than an octave are called compound intervals; those up to an octave are simple. To name a compound interval, add 7 to the simple one: a second plus an octave is a ninth, a third plus an octave a tenth, a fifth plus an octave a twelfth. The quality stays the same, so C4 up to E5 is a major tenth. Adding 7, not 8, is the same "count both ends" rule again: the octave's top note is shared with the start of the next interval.

A full piano spans a little more than seven octaves, from A0 at the bottom to C8 at the top. Human hearing covers roughly 20 Hz to 20,000 Hz, which is about ten octaves, since doubling 20 Hz ten times gives 20,480 Hz. Because octaves sound so alike, a tune that is too high or too low to sing can simply be moved by an octave and it remains the same tune, which is exactly what people do when they sing along with a voice in a different range.