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.”
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I don’t think traditional “counting” comes into play. An octave is 8 notes (as mentioned in the OP). Do Re Mi Fa So La Ti Do. That’s an octave. Just as Mi Fa So La Ti Do Re Mi is an octave. The “counting” doesn’t start over when you get to the 9th note, that would just be naming 9 notes. An octave is just Do-Do or La-La, etc. Doesn’t matter where you start.
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