Why are they called octaves if there are only seven notes?

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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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Anonymous 0 Comments

The first note of each scale/key is the 1st scale degree. So in a minor:

1(a), 2(b), 3(c), 4(d), 5(e), 6(f), 7(g)……. 8(a)

“8” = “octave” (octavus in Latin)

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