eli5: in music, since there are 12 notes per octave, why are only 7 letters used instead of 12?
In: 15
The letters correspond to the [white keys on a keyboard](https://www.smackmypitchup.com/smpu/content/img/MT/mtp01.gif) which are whole notes and there are 7 of them. The black keys are sharps and flats which are half steps between the whole notes.
Notice in the linked diagram, the black key between C and D is both a C sharp or a D flat and the pattern holds for the rest of the black keys.
Musical nomenclature is a total mess because it’s evolved slowly during a time when we were still learning how sound actually works. At first it was just “well, these notes seem to sound nice for some reason, let’s label them.” and “Hey, if I play higher or lower notes outside the range some of them end up sounding like they’re ‘the same’ in some way to these notes. There’s some kind of repetitive cycle here.” Then it was “Hey, if I tune one or two of these notes a little bit off deliberately so it’s sort of halfway between where it was and the next note up, it alters the mood of the music in an interesting way.” Musicians had a good intuitive artistic feel for “what works” long before science really understood what was *actually* going on. Like the fact that the cyclical sensation where a “C” note has a sort of cousin that also sounds like “C” a bit higher, and another one that also sounds like “C” higher than that, and so on, being because those higher versions of “C” have frequencies that are at exactly 2x, 4x, 8x, and so on, while the lower versions of “C” have frequencies that are exactly 1/2, 1/4, 1/8, and so on. The idea that every doubling causes the cycle to repeat was not understood – just that you can hear that it “sound the same” for some reason.
In the end, it turns out that the originally chosen notes of A,B,C,D,E,F, and G weren’t *actually* scaled evenly (or at least evenly on a logarithmic scale). Some of them were “skipping” a step in between and some weren’t. If you map out all the notes between and actually make the notes “equidistant”, then you get the 12 notes of the scale you mention. It turns out the ‘flats’ and ‘sharps’ that had been inserted “in between” the 7 named notes were there specifically because those are the ones where there was twice as wide a gap between the adjacent letters. At that point it would have been possible to rename all the notes so they go from “A”
to “L” with no flats or sharps. You could still have had the idea of “keys”, but then a “key” would be a chosen subset of 7 out of these 12 notes. And the places where you are going half a step up or a full step up would be more explicit and clear that way.
But by then the nomenclature was stuck. It was too ingrained in culture. So we got the utter mess we have today where it LOOKS like, say, E and E# are only “half” as far apart as say D and E are, but they’re not, not really, because in the original letters, D and E already were a half step apart to begin with and had no “sharp” in between them, but we didn’t really pick up on that until later. Again, it’s an evolved nomenclature that dates back to a time when things weren’t as well understood, so it’s kind of a confusing mess today.
In true ELI5 fashion I’ll make it as simple as possible.
It’s because of music theory. Western music is based on 12-tone equal temperament, which means we split wavelength into 12 almost equal increments between each octave, and octave being when a wavelength doubles or halves from the origin. Because of this, western music is generally based on scales that use 12-TET which means they are 7 notes in length. (Ex. C major is C D E F G A B). 7 note scales, 7 note names. It seemed the most logical course of action. From there you could determine which notes are sharp or flat by the key of the music, and thus easier to sight read than if we had NO such musical notation and had to read 12 individual notes. So it was designed quite literally so a 5 year old could read it
If you think that’s complex, Arab music notation (which predates western music) uses 24 Tone Equal Temperament, meaning their octave is divided in 24 almost equal increments.
A simple explanation is that western music is based on musical scales that have 7 steps to them. The familiar “do-re-mi-fa-so-la-si-do”. If you look at the increase in sound frequency at each step, they’re not quite equal. The step from ‘mi’ to ‘fa’, and from ‘si’ to the next ‘do’, is only half as big as the other steps. So the 7 steps go “whole-whole-half-whole-whole-whole-half”. We won’t go into why, except to hand-wavingly say that this “sounds good”. So the scale looks like this:
do re mi fa so la si do+
where ‘do+’ refers to the same note we started with, but an octave higher. (Incidentally, an octave is actually a doubling of the sound frequency, and we perceive such a doubling as creating a note that, while higher, is in some way “the same” as the original frequency. This has to do with harmonics, but I won’t say more about it here.)
Now, you can start this do-re-mi scale from any sound frequency you like. If you want to have a coherent system of notes, then it makes sense to try and start a new scale from one of the notes in your first scale.
That is, let’s take some arbitrary sound frequency and call it “do1”. Then our first scale goes “do1-re1-mi1-” and so forth. Now I want to add a new scale, with the same 7 steps, that starts at re1. So this second scale starts at do2, but do2 is the same frequency as re1.
Okay, so I’m at do2. To go to re2, I need to go one whole step higher. That’s fine, I can re-use ‘mi1’ for that:
do1 re1 mi1 fa1 so1 la1 si1 do1+
do2 re2
Ah… do you see the problem? Now I want to go another whole step to get to mi2. But that lands me squarely in between fa1 and so1. So I can’t re-use an existing note from my first scale there. In fact, this is what my new scale ends up looking like, relative to the old one:
do1 re1 mi1 fa1 so1 la1 si1 do1+ re1+
do2 re2 mi2 fa2 so2 la2 si2 do2+
As you can see, two of the notes in my new scale don’t line up with the notes in the old scale. But that’s okay, we can just add new notes for them. At this point, maybe we should use a different, universal naming system to distinguish it from the do-re-mi’s of the different scales. Let’s first label the notes that were in our first scale, using 7 letters.
do1 re1 mi1 fa1 so1 la1 si1 do1+ re1+
do2 re2 mi2 fa2 so2 la2 si2 do2+
C D E F G A B C D
I won’t go into why we started at C – there’s historical reasons for that which are beyond this answer. In any case, note that we still have more notes to add, to accommodate the 2nd do-re-mi scale. Let’s do that:
do1 re1 mi1 fa1 so1 la1 si1 do1+ re1+
do2 re2 mi2 fa2 so2 la2 si2 do2+
C D E F F# G A B C C# D
There, I’ve labeled the new notes with a ‘#’ or ‘sharp’ sign, to indicate that they are a half-step higher than the letter-note they refer to (so e.g. F# is a half-step higher than F). So now we’re up to 9 distinct notes, A-G plus two sharps, and that’s enough to let us play in two musical scales.
Now, we’ll want to play in more than two scales. If we add a third, starting at ‘mi1’, or ‘E’, then we’ll run into trouble again, because again we sometimes land in between two existing notes. So we’ll have to add a few more notes (G# and D#). And with the fourth scale, again we need more, until finally we’ve added “sharps” to split every whole-step in our ABC-scale into half-steps. So it goes A, A#, B, C, C#, D, D#, E, F, F#, G, G# (and then back to A) for a total of 12 half-steps.
So these 12 notes allow you to play in any 7-tone do-re-mi scale using the same system of notes, and that’s why we have them.
(Now, the true story is even more complicated, because as it turns out, a “true” do-re-mi scale doesn’t really have equal steps between the notes. Do-re is not the same as re-mi, and so forth. So actually, the notes between two do-re-mi scales don’t line up at all, even if you start one from an existing note of the other. So our twelve-tone “equal temperament” system is an approximation of “true” musical harmony, where we fudge the notes a little so that they’re “close enough”, with the great benefit that now you can play in any scale on the same instrument.)
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