[msluyter]

  Why are there seven notes? Is this due to an property of the ear?

The 7 tones that make up a major scale are basically a cultural artifact of western music (which goes back to gregorian chant). Other cultures have more/fewer tones.

  Ditto, for the octave concept, why should it be multiples of two?

Can you clarify this question? Octaves result from the natural harmonic series: http://en.wikipedia.org/wiki/Harmonic_series_(music)

  Why are there black keys between some white keys on the piano and not between 
  others?

Well, IMHO this is a purely arbitrary cultural artifact resulting from the evolution of the keyboard (first in pipe organs). Since the octave is divided into 12 chromatic tones, you could in theory devise a keyboard with alternating white/black keys. However, the organ keyboard evolved in the middle ages, when chromaticism wasn't fully developed, hence, it appears the "white notes" of the keyboard appeared first, then later, the black notes added at the appropriate positions within the chromatic scale. See this, along with the accompanying picture, which clearly shows a small keyboard with the white keys only:

http://en.wikipedia.org/wiki/Pipe_organ#Keyboards

[jerf]

"The 7 tones that make up a major scale are basically a cultural artifact of western music (which goes back to gregorian chant). Other cultures have more/fewer tones."

It's difficult to draw the line between culture and biology, but that's probably too far to the "cultural" side. There is a basis for those, which is that if you start on the base tone of C and run around the circle of fifths you'll get the white keys first: C -> G -> D -> A -> E -> B -> F#, and you get F by going down from the base tone. The importance of the fifth itself comes from the fact that the first harmonic of the base tone is one octave up, and the next harmonic is very close to an octave and a fifth with equal temprement. This seems more than coincidence.

I also find this a better explanation for why so many cultures pick this up once they are exposed to it. (Which is not to say they give up all their old harmonies but this tuning+scale has certainly gone global.) I really have a hard time imagining the mechanics of the Western Global Harmonic Imperialist Conspiracy; it seems much more likely that it so happens that people we call Westerners found this local optima first and it spread because humans in general like it, and it belongs to all humanity, not "the West", just like "perspective" and mathematics.

[msluyter]

I once asked an ethnomusicologist if any common factors existed across all musical cultures and he said that about all he could point to was: a) some concept of a tonal center and b) the interval of the 5th remained fairly constant, despite whatever scales/tunings might exist.

So, I'd grant that much, but beyond that, I don't see much evidence for the diatonic scale as being somehow inherently inevitable. The harmonic series isn't much help, since you get to the flat-7 or flat-five before various other diatonic notes (plus, it's not particularly in tune at the higher partials).

And the circle of fifths rationale seems to be a just so story: http://en.wikipedia.org/wiki/Just-so_story (why stop at 7 notes? why not include G# or even C#? why not just C-G-D-A-E? (incidentally, a pentatonic scale) etc...?)

But this debate could go on ad infinitum, because the issue lacks empirical grounding. Which is to say, how could one falsify either the nature or culture thesis?

[jerf]

I answered a slightly different question than I think you think I did. You said "Well, IMHO this is a purely arbitrary cultural artifact resulting from the evolution of the keyboard (first in pipe organs). Since the octave is divided into 12 chromatic tones, you could in theory devise a keyboard with alternating white/black keys." I gave you a plausible non-arbitrary answer for why that particular pattern was chosen. Not why equal temprement is inevitable or why "7" notes in a scale are special, just why the white keys are ABCDEFG as we know them and not some other pattern. You can put more or fewer notes in your scales in stuff we still would call "Western" music without anybody caring or even noticing. (Much good Western music uses all 12 tones pretty freely.)

As for whether it's a Just So story, sometimes that's all you get. However, if it is just coincidence it's a mighty coincidence.

[Jun8]

I think an octave up (down) means double (half) the frequency of the tone. The usual explanation, I think, is that the Pythagoreans who invented it found this to be the "most pleasing" ratio.

I wonder if there are user studies to back this claim.

I am also at such a low level, that part of your explanation just goes over my head, i.e. what is chromatic scale? Wikipedia says: "The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones." Now very helpful. I thought there were 7 notes! And I don't know any other terms in that sentence (checking their Wikipedia entries doesn't help either, leads to a loop)

[te_chris]

"The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones."

basically what this is saying is that in western music we have divided an octave (the space between a frequency and exactly double that frequency) into twelve "pitches" that we call notes. non-diatonic refers to the fact that it has no basis in any of the western minor or major scales (the two fundamental western scales) as it covers every note of the octave, thus is circular and beyond definition.

Hope that helps

[krig]

The chromatic scale is basically playing every key, black and white, from one C to the next. Whereas the C major scale is every white key from one C to the next.