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Why do we write music the way we do and is it actually the best method?
Dare we ask?
Harmony was something philosophers liked to refer to long before there actually was any--in music. It existed as a concept for many eons before music began to feature it. It thus became the last of what we consider basic elements of music to develop. Before that, it was just rhetoric, like peace on earth.
At least, when musicians began to use it, they already had a name for it.
One of the reasons for this single-note-at-a-time approach to music for so many centuries is that it requires a bit of coordination to make two or more notes sound together and sound like they ought to be that way. In fact, it wasn't until music became a written thing that harmony began to flourish.
(If by 'flourish' we mean every couple of centuries somebody would add another simultaneous event to the mix, lots of conservative voices would protest, and music would lay low for a while to let all the controversy die down. Once people got sort of used to it, they could safely assume it to be the divine order of things, and then the next crackpot musical innovator would try something else and upset the apple cart again.)
Something that is curious about that system of lines and blobs that Guido developed is that it is really quite adept at adjusting to the need for simultaneous pitches. It wasn't designed for that, and for a while, even when different voices sang together, they tended to get their own staves, which meant that each note got its own quarters, and nothing changed. During the Renaissance (1400-1600) musicians often sang together from enormous part books with the various parts facing different directions so everyone could gather around and sing. Otherwise there was little physical evidence that the lines were part of the same composition.
Combining staves wasn't necessarily the problem--put several on a page, one below the other, and draw a line on the left to join them together. But that would require that composers think in terms of the simultaneous combinations of sounds, and that, apparently, required just as much of a mental revolution as getting used to the idea that the earth didn't hold still after all. Until then, composition manuals instructed the would-be scribbler to write pleasing parts individually, without worrying about the vertical alignment of the notes. If the result sounded aesthetically pleasing, all the better, but it wasn't through trying!
It wasn't until keyboard instruments got into the mix that it became necessary to place multiple notes on one staff. Most other instruments can't play more than a note at time, and several don't want to! But a keyboard instrument is perfect for a guy with 10 fingers that like to exult in their individuality. The problem, of course, is fitting all those notes somewhere. At first, this would have been easy, since the only acceptable harmonies were fifths and fourths, notes which are reasonably far apart.
But a few centuries later (don't rush us!) triads came into view. On a keyboard, these conglomerations of sound appear to be every other (white) note. And on the staff, it can be represented by putting the notes in the consecutive spaces, or on the adjacent lines.
Fortunately Guido left room for this innovation by deciding that notes should go on lines and in the spaces between them, so that an ascending scale alternated between notes with lines through the middle (musical shiskabob!) and those bounded by them. [Actually, it occurs to me since I wrote that line that, had Guido decided to only put notes on lines, we would have the opposite problem--that of a three-note chord taking the entire span of a modern staff. However, half-step conglomerations would be easy to represent--put them in the spaces. In which case we wouldn't need accidentals!]
However, you can always get a modern composer to muck it up. As forward thinking as this accident was, it only lasted about a thousand or so years. In the nineteenth century, harmonies, however complicated, mainly stuck to chains of thirds--notes still two notes up or down from their neighbor. But by the twentieth, composers began trying things a little spicier. Now, trying to place a note on a space and the one on the line immediately below it means that there is not enough room for the circles without them mashing into one another. This problem was solved by placing the note-heads on opposite sides of the note-stems, like so:
Some composers decided they liked the mashed-ness pretty well, and the tone-cluster was born, in which every possible note that can be played should be within the span of a certain area. Usually this is done with the flat of the hand, or in the case of a large cluster, the forearm, or, in the case of one piece by American composer Charles Ives, a two by four!
This can be modified, by instructing the player (usually in written instruction) to play all the black keys or all the white keys within the range shown.
That ought to settle things, if you are being all-inclusive; however, if playing every note in the vicinity is not your style, producing a very specific clash may present still more problems. The closer together the notes are, the harder it is going to be to accommodate them. Say we want an A and and A-flat in the same chord. Let's further complicate things by putting in an F and an F-sharp.
That's what that little number is for, with the very creative stem. Now where stems were once simple lines, composers in recent centuries have found all kinds of things to do with them. For instance, there is the issue of the double stem, which goes back before Bach:
The reason for this has to do with its position as a separate voice in the cacophony. We've been discussing harmony as if it were a block of sound, meant vertically, and indeed, all of those sounds that go together have made written music grow very tall, as if it were a bunch of skyscrapers in Manhattan.
But as I mentioned above, musical simultaneity was at first viewed as the product of happenstance--it was the forward flow through time that was most important. If a keyboard instrument allows several parts to be combined on one staff, that doesn't mean they cannot be thought of as several parts, several 'voices.' Bach was very conscientious about giving the separate parts separate stems, even if they formed a chord (and even if it made the music look more cluttered). If the notes could be drawn with notes going in separate directions, well and good. If not, the note was moved over ever so slightly to make sure that it didn't have to share a stem with another note:
Thus, in a situation where one note happens to be shared by two voices, it is logical to give it two stems. And, in music before the middle of the 18th century, it was rare that note-heads would share the same stem. This, of course, is one of those things that is confusing to piano students, and seems to be taking the long way around. From the point of view of the 17th century (and earlier), it was necessary to justify each note as a part of a melodic line; not to do so, treating it like a mass of sound, rather than as a harmonious accident, was still a new and contentious innovation. To us, it no longer seems like any big deal, anymore than a car is a car and does not need to be described as a kind of carriage that doesn't need horses to power it, or a piano no longer goes by its full name (fortepiano, or 'soft-loud', because it could do both). It all depends on the place (before or after) from which you are viewing the musical universe.