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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There are generally 12 notes per octave in western music, not 7. Any time the frequency doubles or halves, it is considered to be an octave, regardless of how many notes you are dividing the scale in to, or what scale you’re using.
The major scale and minor scale each have 7 notes, but the pentatonic scale has 5 notes. There are other scales that have different numbers of notes, too, even within our 12EDO system.
Some stuff in music has funny names. You just need to accept it as it is.
Here is some music made with far more than 12 notes in an octave. The composer uses many similar note intervals so it doesn’t sound too unfamiliar, and having more notes per octave means that there are a lot more dissonant intervals, but it also allows for a lot of very different sounds and color shifts, too:
This song was made with 22 note octaves rather than 12 (noting that it isn’t just 24)
There’s a chord sequence found in this song that is a play on the jazzy II-V-I chord sequence. If you listen to the song Giant Steps next to this you might recognize it.
Back to the basics:
So while yes, the major and minor scales may only have 7 different notes – and in many musical cultures around the world there are definitely a lot that are structured in a similar way (Indian music uses a “swari” with 7 notes but they are pulled from a scale with more notes than our 12).
If you made music that only uses those 7 exact scale degrees and never picked a note that wasn’t in that scale, you’d get some pretty boring music. Music becomes a lot more interesting when it breaks our expectations a bit. Music that is all consonant may be a little bit boring. Most children’s music tends to have very few dissonances.
At least most of the time. There are exceptions for everything.
This song does have chord changes but everything was specifically picked to be very consonant. That piece of music was created with a very specific limitation in mind.
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