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Yes, each 7 set is an octave. A scale is 8 notes. To play a scale is 15 notes up and back.
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An octave is seven notes, eight pitches. C and C' are the same note played at different pitches. To play a scale up and back is still seven notes.
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I don't see where anyone answered your qstn about whether or not high notes vibrate to double or triple the frequency the higher a note gets.
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Yes, I did answer it. The frequencies of octaves can only be doubled or halved.