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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The naming is off by one because it’s primarily a naming of *intervals*. A “**second**” is the interval from the first to the **second** note in a scale (*), a “**fifth**” is the interval from the first to the **fifth** note, and so an “octave” (octo=**eight**, **) is the interval from the first to the **eighth** note.
(*) For some intervals you’ll see the prefixes “minor” and “major” used because they can have different lengths in semitones. E.g., a minor second is a semitone (such as the interval from E to F) and a major second is a whole tone (such as the interval from C to D).
(**) Many languages are still using the Latin names for the intervals such as a “quinte” for the fifth, but in English we switched to English names for most of them, only “octave” remained (and “second” which is the same in Latin and English).
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