7

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.

11

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.

  • Robert, thank you so much for the history plus that critical last paragraph. So if I'm following you correctly, what happened was this: 1. starting with early recorded vocal music, there were seven diatonic pitches in any scale (without the actual key being necessarily specified early on). 2. eventually, a clef marking ("C" in your example, but later F and G for bass and treble) was used to lock the relative scale to an absolute understanding of pitch. 3. once we broke from purely vocal, diatonic melodies, we added notation for accidentals. [...] – Ben Zotto Nov 23 '14 at 15:59
  • 4. BUT we had already sort of settled on "standard" F and G clefs, so music written in other diatonic keys ends up sort of running a bit roughshod over the "clef"; rather than using some wholly different clef every time we write a piece in (say) F#, we instead mark up the staff to "override" the standard clef. Am I more or less understanding? Finally, the reason why we end up with lines and spaces being the notes of a C major diatonic scale and not, say, the notes of an F# major diatonic scale, is essentially a historical accident derived from the notes used for most early vocal writings? – Ben Zotto Nov 23 '14 at 16:03
  • --- Allow me to clarify that final question: The clefs we've talked about here (C, F and G) all use the notes of the C major diatonic scale for their lines and spaces, even when the orientation is shifted. Is the reason that we settled on those as the primary pitches simply because early vocal music used them consistently instead of, say, the F# major diatonic scale? Thank you! – Ben Zotto Nov 23 '14 at 16:11
5

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.

  • @BenZotto The origin of the scale is in the murky depths of history, but this question gets into it. – luser droog Nov 23 '14 at 17:43
2

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.

-2

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

  • I'm not the downvoter, but I can guess: it's because you reveal a significant lack of understanding of scales and music. Wait until you've played for more than 6 months and you'll see that your comment is invalid. – Carl Witthoft Nov 23 '14 at 13:23
  • I see your point and that's why i didn't downvote you. Apart from the historical reason described above, what you said here (3 white keys being natural to play) actually reinforces why the white keys are considered special. But i do agree that the other 5 notes too are important. Playing pentatonic scales on black keys only (just the melody, not with the chords though) could be interesting. – mey Jan 28 '15 at 1:55

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