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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1. You assume incorrectly that it is a base 7 system, because there is no zero, as in music there is no zeroth degree of harmony. The tonic (root note, or “starting note”) is the first degree.
2. Octave is an **interval** that spans eight diatonic notes. The interval between C4 and C5 is an octave. To illustrate, C D E F G A B C – there are eight notes from C to C.
3. A set of **notes** in a scale is not an octave, because it does not refer to an interval.
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