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.”
In: 233
Only musicians seem to be in here. Can we get a math-head to confirm the base-7 part at least ?
it is amazing there has never been a human that was great enough at both music and maths to be able to write a logical, rational system for describing it
Because it’s the eighth note.
The eighth note is an octave.
Sure, there are seven *different* notes in a diatonic scale. But the eighth note is an octave higher.
Don’t overthink it.
I don’t think traditional “counting” comes into play. An octave is 8 notes (as mentioned in the OP). Do Re Mi Fa So La Ti Do. That’s an octave. Just as Mi Fa So La Ti Do Re Mi is an octave. The “counting” doesn’t start over when you get to the 9th note, that would just be naming 9 notes. An octave is just Do-Do or La-La, etc. Doesn’t matter where you start.
>So why is the set of scales called an octave if it’s all based on a base-7 system?
It’s not a counting system at all. I think that’s why you are getting confused. It’s a way of representing a pattern in how the frequency changes between notes. The Ancient Greeks discovered that if you take a vibrating string and add a node in the middle of it, the pitch changes but it sounds “the same.” What’s really happening here is the frequency doubles. They found that if they used that doubling of frequency as the beginning and end of a scale, that they could choose notes in a specific way between them, and then repeat them at higher and lower pitches and everything would sound good together. They used something called a 12-tone equal temperament scale, which means that there are 12 notes in between the root and the octave, and the frequency ratio between any two neighboring notes is the same. They found that to be the most natural way of dividing it up that led to repeatable patterns. They also decided that using 7 different pitches (including the root note) made the nicest patterns, if they followed certain rules about how the notes were spaced. Since there are seven “different” notes, you need seven letters to represent them (this came later, I am not sure how the Greeks labeled notes). If you play a scale without playing the last note, the one where the pitch doubles compared to the root note, it doesn’t sound good. So, a complete scale includes the root note, the octave, and the six other notes in between them. Since that’s 8 notes, we call it an octave.
If they used 8 letters to name the notes, then the system wouldn’t be as useful. As an example, let’s say you had A-H as your numbering scheme. Your scale in the first octave would be:
ABCDEFGH
then in the second, it would be:
HBCDEFG
That’s not a pattern that is easy to repeat. By choosing 7 named notes and repeating it starting a the 8th note, it matches up with the way that scales are defined in Western music.
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
The 8th note is the Octave.
Octo- 8
The scale is called a heptatonic scale. I.e 7 notes in the scale
Hepta – 7
Another scale commonly used is the pentatonic scale
Penta- 5
The naming is off by one because it’s primarily a naming of *intervals*. A “**second**” is the interval from the first to the **second** note in a scale (*), a “**fifth**” is the interval from the first to the **fifth** note, and so an “octave” (octo=**eight**, **) is the interval from the first to the **eighth** note.
(*) For some intervals you’ll see the prefixes “minor” and “major” used because they can have different lengths in semitones. E.g., a minor second is a semitone (such as the interval from E to F) and a major second is a whole tone (such as the interval from C to D).
(**) Many languages are still using the Latin names for the intervals such as a “quinte” for the fifth, but in English we switched to English names for most of them, only “octave” remained (and “second” which is the same in Latin and English).
God everyone’s answering this in a non-5-year-old way.
Imagine each note in a scale is a different colored block, and they’re all lined up. The letters on them repeat, but the colors don’t repeat. There can be any number of them, but let’s say there’s 14 of them. They’re laid out like so:
| C | D | E | F | G | A | B | C | D | E | F | G | A | B |
If I told you to count these blocks, you’d do it like this:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
If I told you to grab the 1st block and the 8th block, you’d end up with two different “C” blocks. They’re both C, but a different color (or tone).
Hence, octave. Music is like counting, less like math. If it started on 0, it’d make this illustration very difficult, and I always use this to teach when I give music lessons.
For the same reason that Jesus rose on “the third day”: the starting point is counted as one. The octave – note VIII – was so named by a culture that had not yet absorbed the concept of zero. (Arguably it still has not; *The Art of Computer Programming*, of all things, almost always counts from one even when counting from zero would make its algorithms much more transparent.)
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