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How Many Notes In an Octave? And How Many Semitones?
An octave interval has 2 notes. You can stuff as many notes as you want between those 2 notes (for example the 12 semitones of the chromatic scale), but you still won’t escape the octave. You can never pry the octave open any wider, because you can’t reduce a frequency ratio to anything simpler than 2:1. It's called an OCTave because the term also can refer to the 7 notes of a diatonic scale, plue the octave, for a total of 8 notes.
Paradoxically, making peace with the smallest intervals of the octave, the semitones (through a bit of fudging called equal temperament), provides more than ample relief, if not escape, from the octave’s tyranny (coming up in Chapter 5).
(Tuning purists will note that some tuning systems slightly “stretch” the octave, such as one used by Indonesian Gamelan percussion orchestras. But such tunings are highly variable and, in any case, unheard of in Western popular music.)