[Jun8]

Fascinating read, but definitely not for beginners, at least for people like me, who have difficulty naming the notes (I have to go through "doe a deer..." each time, there are seven of them, right?)

My total music illiteracy really annoys me. However, whenever I try to pick up some knowledge I got held back by lots of questions that the usual music student (or teacher for that matter) has never thought about and no answer can be given. Here are a couple:

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

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

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

Is there a book that explains questions like these?

[alexophile]

People sometimes guffaw at this, but I can't recommend Donald Duck in Mathemagic Land enough: http://www.youtube.com/watch?v=iEVGQKwKeCc They skip over several centuries of shifting and tweaking between the triad and the modern (western) major scale, but it's a great visual answer at least to your second question.

[Jun8]

Funtastic! On behalf of HN, I award you, sir, with the best link posting of the day award!

[ghotli]

I recently went on a crusade to find this and show it to my children. I view it as a turning point in my development and one that influenced my life's path a great deal.

[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.

[cynicalkane]

Modern western music is based on medieval church music, which in turn is based on ancient Greek music. These are two cultures that placed strong value on harmony and mathematical ratios, and it so happens that notes in ratios are harmonious to the ear. Mathematically speaking, the ratios between notes come mostly from low-order ratios in 5-limit tunings: https://secure.wikimedia.org/wikipedia/en/wiki/Limit_%28musi... .

In short, the Western scale is chosen to maximize the harmonic possibilities between different notes while having a reasonably even collection of whole-steps and half-steps between them. The black keys are the "in-between" half steps that do not appear in the C-major scale. The reason the ear likes harmony is probably due to our ears performing a Fourier transform on the incoming sound waves, and our brain blending together collections of multiples of some base frequency into one "note"--this lets us recognize the different characteristics of periodic oscillations from different physical sound sources.

[Jun8]

Thanks for the information. I wonder if there are any "music universals", like the ones for language, i.e. universal grammar. If favoring certain tone ratios is a characteristic of the human auditory system, then there should be.

[cynicalkane]

Like Chomsky's search for universal grammar, the search for music universals has been a failure. Nevertheless, there are some ideas that pop up surprisingly often. Doing a quick mental search, I believe every musical tradition I've heard that emphasizes accurate pitch, and at least one I've heard that doesn't, utilizes the pentatonic scale: https://secure.wikimedia.org/wikipedia/en/wiki/Pentatonic_sc...

[thesethings]

I wasn't aware that either of these quests for universals have been a failure. My friend did a relatively recent music thesis about universals.

I'm not in either field, but a belief in universal "deep structure" has helped me learn both language + music stuff. Even if they don't exist, I'm going to stick with what helps me :D

[cynicalkane]

Well, you could say music must have rhythm, yet there's music with almost no rhythm at all. You could say music is about melody, but there's lots of examples of music with no melody. And as I hinted above, there's cultures where notes don't really have definite pitches.

I can't really think of anything that universally defines "music", other than that it's sound with an aesthetically pleasing structure.

[hasenj]

> Chomsky's search for universal grammar (..) has been a failure

I don't know about Chomsky, but I took a linguistics course and the universal grammar was a major part of the course. It seems you're implying there's no such thing, what makes you think so? The impression I got from the course is that the idea of "universal grammar" is universally accepted (among linguists, of course).

http://en.wikipedia.org/wiki/X-bar_theory

Ironically I don't remember Chomsky's name coming up during the course at all.

[pessimizer]

Chomsky is the first name mentioned in that article.

[hasenj]

Yea, but I don't remember hearing about him in the course I took in the University.

Although to be honest I probably ignored names on purpose because there were so many of them.

[maw]

Interesting question. I think there are some. Does N hz "sound like" N*2 hz and N/2 hz across cultures? I expect the answer is yes, but I don't really know.

Have a look at http://www.youtube.com/watch?v=A13_QGMtlRE. I think Bobby McFerrin would say that there indeed are music universals.

[emillon]

It does. You can view any 2*N Hz signal as a N Hz signal with a doubled period. So two such signals will keep "in phase", and when you mix them it can compose a new coherent sound.

[jtheory]

The "counter-proofs" to music universals is often just presenting an example of music from somewhere that doesn't match the universal in question.

Counter-example don't disprove trends, though, and there are certainly trends (I think "universals" is just not quite the right word).

[kreek]

'Music Theory for Computer Musicians' was very helpful for me. http://www.amazon.com/Music-Theory-Computer-Musicians-Book/d...

There's also a great TV series from England called 'How Music Works' which gives more of a historical background. http://www.youtube.com/watch?v=PnbOWi6f_IM

[krig]

That's basically the questions that music theory answers. As far as I understand things, it mostly relate to frequencies and harmonic resonance. The octaves are exact multiples of the same frequency (so a higher octave is 2x the frequency of the lower octave). The seven notes all fall out from that as well, but it is more complicated to explain and I don't know things well enough to break it down in a way that would be correct and make sense. But basically they resonate with each other.

As to why the human ear finds harmonic resonance pleasing is a more difficult question to answer. Why do we find order pleasing, and chaos frustrating? Speaking generally, the human brain functions as an advanced pattern seeking machine. What we do is take in chaotic and diverse information and make sense of it in some way, piecing individual facial features together into a specific face, and so on. Information that is ordered to begin with requires less work for the brain to process, so perhaps we find it pleasing because it is easy to sort and label mentally?

The intervals of black and white keys relate to the major scale. Basically, the major scale has the property of consisting of two whole steps, one half step, three whole steps and finally one half step. So the piano is constructed based on that scale.

Again, I can't explain it much better than that, but any book on the mathematics of music and signal processing / frequencies would have more information.

But yeah, the reason why you can't answer those questions is because you don't know music theory. That's where the answer to them is. It's not that they can't be answered.

[doki_pen]

Get a list of tone frequencies and do math with them. You will see patterns, called harmonics by musicians. Doubling the frequency (octave) can be thought of as the same tone playing twice, with an even offset. Our brains can pick up on that and notice that 440Hz is the same as 880Hz (only and "octave" higher)

Interesting fact: The tones of the scale aren't exactly evenly spaced, because of math. Some instruments use true tones and are made specifically for a certain key. Other instruments that can play in any key (like guitar) are never truly in tune.

[blahblahblah]

To generate a list of tone frequencies, start with A=440Hz and multiply by 2^(1/12) to get the frequency of the next higher tone or divide by 2^(1/12) to go down to the next lower tone in the chromatic scale. Notice that the octave is 12 of these intervals away, making it's frequency (2^(1/12))^12 = 2 times the initial frequency.