The musical scales are A B C D E F G A, or Do Re Mi Fa So La Ti Do. If you do it that way, yes, there are eight. But the last note is the same as the first but at a higher pitch. If this were math, we’d basically be dealing with a base-7 system, with A or Do playing the part of zero.
So why is the set of scales called an octave if it’s all based on a base-7 system?
EDIT: Many of the first answers from when I originally asked were helpful but now I’m getting a lot of wrong answers from people who don’t seem to understand how numbers work. In a base-8 system, there are eight unique numbers, 0 through 7, after which it goes to 10. If you translate the notes into numbers, you don’t get 0 through 7, though. You get 0 through 6, after which it goes to 10 at the second Do. That’s why I was trying to reconcile that with the term “octave.”
In: 233
Language and maths combined sometimes seem counterintuitive, and bringing music too… Phew…
If you think about it the same way as days of the week, Monday to Monday is 8 days but there’s only 7 days in the week. So note A to note A is 8 notes in the major or minor scale, which is what the term is based upon, but there’s only seven notes in the scale.
There may be other terms for the same intonation in other cultures that don’t traditionally subscribe to the major/minor scale, however for your question it’s based on the classical scale that you hear in almost all music in the western world
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