Why are the natural notes on the staff special?

Question

I can read music and I also understand how we build diatonic scales on top of the C-D-E-F-G-A-B-C sequence. I also know that intervals between any version of two "letter" notes have the same name, like a C-something to an E-something is always going to be a "third" of some description (major/minor/augmented/diminished/double-augmented).

But I'm still a little puzzled as to why these 7 pure notes are special. Within an octave are 12 equal(ish?) semitones. Yet only the chosen seven are represented by the lines and spaces on a staff. How did we end up choosing these (and these particular ones) to make into the named tones that everything else is based around? (So sharped or flatted versions of these must be notated separately). Or, how did those other semitones end up being second-class citizens, on the staff (on the piano keyboard as well, although I assume the staff came first?).

Another way of asking this is: why don't we use a different kind of staff where each semitone is given a line or space of its own? That would seem, on the face of it, to be a more rational basis for the system.

Is it something about actual tone frequencies or resonance or physical harmonies? Or is this just a convention that arose through specific historical events?

This question on the Math site is asking something very similar, but the answer (although discussing interesting things) doesn't really talk about why we privilege the notes that we do.

Answer 1

This system is the result of the specific historical evolution of Western music notation. The five-line staff was not the first try at writing down the pitches being used in European music. The first systems were just mnemonic, consisting of neumes (squiggles, basically) drawn above the words of a religious text, much like the cantillation symbols that anyone who has ever had a bar-mitzvah remembers being above the Hebrew words in the Torah. They simply stood for melodic formulas, without being linked to any determinate pitch.

These "unheighted" neumes were gradually replaced by "heighted" neumes: a single line was drawn to let scribes record higher or lower pitches, then lines were added to do this more systematically, and so on. The repertory of Gregorian chant in the Catholic Liber Usualis uses a four-line system (example: http://romaaeterna.jp/liber2/lu353.gif). This makes good sense, since there are seven positions on a four-line staff: the four lines, and the three spaces between the lines, and that corresponds to the seven diatonic pitches in any mode.

(Obviously it is possible to use the two outside spaces, which many chants do, to get the note below the final and the note above the upper octave. Much later, some scribes figured out that you could gesture at another line above or below the staff by drawing a line through the neume; these "ledger lines" are now common practice, since many melodies in classical music span much more than an octave.)

If you look at the example I linked to, you can see a little horseshoe-shaped figure wrapped around the top line; this is a "clef" -- that is, a key -- which unlocks the actual pitch information encoded in the system of lines. In the example I give, the clef marks middle C. (You can tell it's C, because there is a flattening sign (the "b") on the space below, and the only place you can put that flattening sign is under the C, for reasons not germane to this little discussion.)

That horseshoe, which actually looks like the letter "C," is thus a "C-clef," because it tells you where "C" is. It is the ancestor of what we today most commonly use as the "alto" and "tenor" clefs. (We put our Cs on the second or third lines of a five-line staff, but they are direct descendants of the one in chant notation.) You can imagine, given the range of men's voices, how convenient that clef is. Most men will be able to sing easily a melody that ranges in the octave below middle C. As vocal music grew more complex and developed multiple parts, some were more easily written around the note F a fifth lower (the "F-clef," or "bass" clef), or a fifth higher (the "G-clef," or "treble" clef).

Only much, much later did it become theoretically possible to put a sharp or flat sign at any place on the staff system, and thus notate twelve chromatic pitches on a five-line staff. At the point where any note could be flatted or sharped, it would have been logical to create a system where each of those notes was given its own line or space, but by then people had been using five-line staves where one line is locked to a given C, F, or G for hundreds of years.

And we still are.

Answer 2

In the history of western music, the 7 notes came first. The twelve arise from adding the necessary notes to play the 7-note scale starting on any note of the 7-note scale.

In the key of C major, no sharps or flats are needed. C D E F G A B C

When you modulate a fourth to F, you need to add the soft B or B♭. F G A B♭ C D E F

And for each further modulation of a fourth you need an extra flattened note for the fourth scale degree ... until you come full circle(*).

The same thing happens if you modulate to the fifth from C major. When you modulate to G, you need to add a Sharp 7th (F♯) for the leading tone. G A B C D E F♯ G

And for each further modulation of a fifth you need an extra sharp 7th ... until you come full circle.

*. Coming full circle actually required the development of 12-Tone Equal Temperament.

Answer 3

Adding to other answers - there are some good physical reasons.

The most consonant interval, apart from octave, is the perfect fifth. Sounds that are perfect fifth apart blend really well, because the lengths of their waves have proportions of 3 to 2, so the basic sound pattern repeats every 6 "basic units" (two vibrations of the lower string take exactly as long as three vibrations of the higher string).

Now if you just stack fifths, one after another, you will get C G D A E H F#, or:

• exactly the material of G mixolidian;
• the first five tones form a major C pentatonic scale;
• roughly the harmonic components (aliquot) heard when G is played.

So while it does not prove anything, it certainly shows that the diatonic sounds are not random, but rather deeply rooted in the whole acoustic system.

Answer 4

I don't think there is really a very good reason why it should be those 7 notes rather than the other 5 as well, except for the fact that writing notes in both the lines and the spaces makes the music much easier to read (if you're playing quickly, the notes can blur into each other as it is, with only 5 lines for them to be on!)

I suppose also it works nicely for me as a trumpeter. "Middle" C, G, and the C,E,and G above that (and a few others) are all played with no valves pressed down, which does seem most natural and least deserving of accidentals