eli5: in music, since there are 12 notes per octave, why are only 7 letters used instead of 12?
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There are only 7 different notes, so 7 letters : A B C D E F G. An octave goes from one note to the next same note : A B C D E F G A, so 8 notes and not 12.
I don’t know where that 12 comes from.
A scale only has 8 notes (7 distinct notes, because you count the root note twice.)
We named our notes off of the A major scale in the Aeolian mode, the notes of which are A B C D E F G (A)
Other scales include sharps or flats, but any given scale only has 7 different notes in it
Using a guitar sting as an example.
E, F, F#, G, G#, A, A#, B, C, C#, D, D#, E
I used sharps because I don’t know the symbol for flat on a keyboard.
You can make harmonic music with just five notes (the pentatonic scale). Our brains hear different frequencies that are simple ratios to one another as pleasant or “harmonic”. A 2:1 ratio is an octave, but other ratios like 3:2 or 4:3 are great, too. It turns out that when you multiply a base frequency (the “tonic” frequency, like A 440 hertz) by the 12th root of 2, eventually you can create most of these simple harmonic ratios with a close margin that our brains detect as harmonious.
Again, you really only need 5 notes, but musicians discovered that by including two extra tones in the scale they could create music that, while not as harmonious, was more complex and interesting.
It’s a mixture of how the math works, how our brains work, and the tastes of the founders of western musical traditions.
The 12 half steps are an adaption of the fact that a 7 note scale is not created around equal note separations. 7 note scales are different from each other (major vs minor being the two biggest ones), but they are a mix of 5 whole steps and 2 half steps. To make an instrument that can play more than just one scale, a lowest common denominator needed to be found and the 12 half steps work out just right for that.
Other people are doing fine answering this in a specific way. I’ll add that the big picture of music is a mish-mash of many labeling systems that were too simplistic to capture everything.
Scales in “western music” typically have 8 notes. Each scale has different intervals between the notes that split the 12 notes (semi-tones) into the 8 required for that scale – so the intervals (in semi-tones) for a major scale go 2,2,1,2,2,2,1. For a minor scale it goes 2,1,2,2,2,2,1.
Every scale is made up of every letter – A to G once and once only. If the interval lands on either a sharp or a flat, then you choose which to call it based on what letters you need for that scale.
For example, the D major scale goes D, E, F#, G, A, B, C#, D.
Here, the F# is also a Gb, and the C# is also a Db. However D, E, Gb, G, A, B Db, D has 2 Gs and 2 Ds, so isn’t considered “correct”.
So there are only 7 letters because that’s what you need to correctly notate each scale.
I feel like a lot of the answers here aren’t really addressing the question? The reason where are only 7 letters despite there being more notes is mostly due to simplicity and the fact that there are more than 12 notes.
The original western scale was essentially A natural minor, and that is what gave us the notes on the scale: A B C D E F G. This scale had no flats or sharps, so all you needed was the 7 letters.
In terms of the sharps/flats, you also have to keep in mind that on a harmonic level, if you tune your instrument to play a perfectly harmonically accurate Bb scale, you’re going to end up with a bunch of notes that will be out of tune if you try to play a different scale. This is called just intonation: on a harmonic/frequency level the C# in an A major scale and the Db in a Bb minor scale are different pitches, if only slightly (but noticeably!). You can find demonstrations on this with synthesizers and computer programs that give you exact pitches.
So if you get picky with it, there are countless different “notes”, depending on where the note falls in the scale. Back in the early modern period, musicians would literally have to re-tune their instruments when they changed key, otherwise a bunch of notes would be noticeably out of tune.
This was all changed with the advent of something called “equal temperament” — basically designing instruments to “cheat” those differences between C# and Db so that you can play in any key you want without needing to re-tune. It is why even a perfectly tuned piano or guitar will still have some slight wobbly/out of tune notes (particularly the 3rds and 5ths of a chord) depending on the key. Most of us don’t hear this because we’ve grown up with equal temperament in effectively 100% of western music for all our lives and it doesn’t phase us.
All that is to say that the 7 letter formula was the original format and people stuck with it for simplicity — to try and give every possible note a new name would have required countless letters back in the just intonation days, so people didn’t bother. By the time equal temperament comes around and you really only have “12” notes, the standard for musical notation was set across Europe and it didn’t make any sense to change it.
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