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.
The set of all the notes is not called an octave, it is called a diatonic scale. What we understand in Western music to be scales are all some form of a diatonic scale(major, minor, mixolydian etc.). All diatonic scales consist of 7 intervals, 5 whole steps and 2 half steps. If you think of the scale as a fence, there are 8 posts(notes), with 7 rails(intervals) in between. You need to have the octave to know the length of the 7th interval. Since the octave above the root is the eighth note, its name reflects that.
FWIW, there are 8 interval scales, such as the octatonic scale, which consists of 4 whole steps and 4 half steps. In this scale, the octave is actually the 9th note. These are not used traditionally and would sound pretty jarring to most ears.
Because it starts and ends on the same note. C to C is an octave. C to B is “unresolved”. When you hear C to B, you are just aching to hear that final note, which is the next C. So the octave is the completion of that series of notes.
You assume it’s counting the notes. It’s not. It’s counting steps in a sequence. It’s an octave because it’s the 8th note in a cyclical sequence of repeating 7 notes.
If you measure the distance around a circular track and label the starting line zero meters, you must return to the starting line and count that point again to measure the distance travelled. We don’t call it a 399 meter track.
If you call the starting line “one” and stop when you are at 400, the other racers will pass you as you stand one meter away from the finish line. It doesn’t mean we should call the race the “401 meter”.
Music can be analogous to running around a circular track as the starting line and finish line may be considered to be unique, yet may be the same point and be required to be counted twice.
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