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

There are many reasons this works. I think it comes down to how it makes people feel, though.

If you play just the 7 unique notes of a diatonic (meaning 7 notes before the lettering restarts) scale, the 7th note feels like it needs to go somewhere. It has a feeling of being unfinished, which we call “tension.” Going up to the 1st note again resolved that tension, a sensation we call “release.” Since it doesn’t feel “finished” at the 7th note, we include the 8th one and it feels like a set. So, one way to think of it is how the scale gives us opportunities to experience tension and release.

An even number of notes also helps the last note to give us a sense of release. Another common scale for writing melodies is the pentatonic scale (meaning 5 notes before the octave). These are usually the 5 notes out of a diatonic scale that feel the strongest. It resolves on the octave as well, which in this case would be the 6th note in the sequence. It’s still an even number to resolve.

With just about any scale, that octave being the final note we include in a scale is about tension and release. Since the scale can re-start there, it’s also a sense of returning home, which is the ultimate version of releasing the tension of other notes. Since the scale can restart, it feels like returning home. Many songs end with what we call a “resolution,” which is usually a way to return to the chord built off of the first note in a scale (though sometimes they end on other chords to achieve other emotional effects).

So, the note where the scale restarts is called the octave because we (in the west) like scales with 7 notes before they restart, but we need to include the eighth note that’s kinda the same as the first note because not doing that would feel unfinis

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