music theory: "There are seven notes in this scale." me: ok music theory: "So we call it an 'octave.'" me, a mathematician: wait
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it's 8 things only if you count the base element for the next scale, too. But then you have overlap and that's uncanny
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I forgot to mention base 8 was also invented slightly differently.
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aww

End of conversation
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8 comes from counting the high tonic along with the low one, yeah, it's a weird mess
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it's a cyclic group with identity element, in a kind of rough and underspecified way
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an octive is the distance (inclusive) between two notes that sound the same.
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Seven notes in a major scale the 8th repeats.
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six if you start counting from zero :trollface:
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