eli5: in music, since there are 12 notes per octave, why are only 7 letters used instead of 12?
In: 15
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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