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The top answer on stackexchange is a superb explanation of musical science that most of the finest musicians in history could not give you. They just don't teac

The top answer on stackexchange is a superb explanation of musical science that most of the finest musicians in history could not give you. They just don't teach you these things in music class. Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating. I will add one important point that hasn't really been made: The purpose of equal temperament may have originally been to "change keys without retuning", but it also essentially allows you to play in 12 different keys at the same time. This has been exploited to great lengths as source of musical novelty and is absolutely fundamental to modern music.

alextgordon 16y ago
Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating. This is true, but I think the answer is far more mundane. Musicians operate at a couple of levels of abstraction above that SO answer, so such details become irrelevant to them. Imagine if the standard introduction to programming was a course on Java or PHP. Pretty soon you'd have a plethora of programmers who didn't know a thing about pointers or any of the old tricks programmers used to do with assembly. Wait... that's already happened :)
- levesque 16y ago
  Yeah, and now we argue about whether or not knowing the basic mechanics of your typical language (be it programming or music) can help you achieve a greater global understanding and thus allow you to be a better musician/programmer overall.
- JeremyBanks 16y ago
  I'm not sure I understand. Your argument for why musicians should start at a higher level of abstraction is that starting programmers at a higher level of abstract works out poorly?
seertaak 16y ago
> They just don't teach you these things in music class. Go read "How Equal Temperament Destroyed Harmony". By a musician, for musicians. I would add there are a number of conductors and musicians that insist on playing compositions in their original tunings. > Musical culture seems to resist illumination And I'm sure elsewhere in cyberspace at this precise moment some musician is lamenting the ability of scientists to understand their craft. Plus ca change...
- extension 16y ago
  I realize that some people know this stuff and some places teach it as part of an advanced music education, it's just remarkably uncommon considering how fundamental it is. I would have meticulously qualified my earlier generalization but I foolishly assumed that my hyperbole would not be taken literally. I'm speaking as a musician when I say that we resist illumination. I've raised this topic with many teachers and peers and there is a sort of disbelief in the connection between the artistic experience of music and the underlying mathematics. I don't think this is because musicians are ignorant luddites, I think it's because the emotional response to music is primal and not at all intuitive. Why do we feel so strongly about harmonically related tones? It doesn't sound like anything, in the way a painting or a sculpture looks like something. Abstract art is a relatively recent invention, yet music has been almost purely abstract for as long as anyone remembers.
russellallen 16y ago
Of course they teach those things in "music class". They teach them in music theory class at university level for a start. You're creating a strawman. Just look at the Wikipedia entry on tuning, for example: http://en.wikipedia.org/wiki/Musical_tuning http://en.wikipedia.org/wiki/Musical_tuning Do you think that was all created by non-musicians while 'most of the finest musicians in history' cowered in the corner afraid of the magic being broken?
- jtheory 16y ago
  I remember studying this right near the beginning of freshman music theory in university. It's also at the beginning of a more than one basic music theory textbook. We covered it more deeply (including, gasp, math) in a higher-level electronic music class. It's probably true that many fine musicians won't think much about the mathematical side of music very often at all (practically speaking, this knowledge is not necessary to master an instrument), but certainly anyone who's gone through an academic music education will have covered it, quite possibly more than once.

alextgordon 16y ago

Musical culture seems to resist illumination, perhaps fearing that the "magic" will somehow be broken. The irony is that music is, in a sense, a mathematical illusion, but revealing the trick only makes it more fascinating. This is true, but I think the answer is far more mundane. Musicians operate at a couple of levels of abstraction above that SO answer, so such details become irrelevant to them. Imagine if the standard introduction to programming was a course on Java or PHP. Pretty soon you'd have a plethora of programmers who didn't know a thing about pointers or any of the old tricks programmers used to do with assembly. Wait... that's already happened :)

levesque 16y ago
Yeah, and now we argue about whether or not knowing the basic mechanics of your typical language (be it programming or music) can help you achieve a greater global understanding and thus allow you to be a better musician/programmer overall.
JeremyBanks 16y ago
I'm not sure I understand. Your argument for why musicians should start at a higher level of abstraction is that starting programmers at a higher level of abstract works out poorly?

seertaak 16y ago

> They just don't teach you these things in music class. Go read "How Equal Temperament Destroyed Harmony". By a musician, for musicians. I would add there are a number of conductors and musicians that insist on playing compositions in their original tunings. > Musical culture seems to resist illumination And I'm sure elsewhere in cyberspace at this precise moment some musician is lamenting the ability of scientists to understand their craft. Plus ca change...

extension 16y ago
I realize that some people know this stuff and some places teach it as part of an advanced music education, it's just remarkably uncommon considering how fundamental it is. I would have meticulously qualified my earlier generalization but I foolishly assumed that my hyperbole would not be taken literally. I'm speaking as a musician when I say that we resist illumination. I've raised this topic with many teachers and peers and there is a sort of disbelief in the connection between the artistic experience of music and the underlying mathematics. I don't think this is because musicians are ignorant luddites, I think it's because the emotional response to music is primal and not at all intuitive. Why do we feel so strongly about harmonically related tones? It doesn't sound like anything, in the way a painting or a sculpture looks like something. Abstract art is a relatively recent invention, yet music has been almost purely abstract for as long as anyone remembers.

russellallen 16y ago

Of course they teach those things in "music class". They teach them in music theory class at university level for a start. You're creating a strawman. Just look at the Wikipedia entry on tuning, for example: http://en.wikipedia.org/wiki/Musical_tuning http://en.wikipedia.org/wiki/Musical_tuning Do you think that was all created by non-musicians while 'most of the finest musicians in history' cowered in the corner afraid of the magic being broken?

jtheory 16y ago
I remember studying this right near the beginning of freshman music theory in university. It's also at the beginning of a more than one basic music theory textbook. We covered it more deeply (including, gasp, math) in a higher-level electronic music class. It's probably true that many fine musicians won't think much about the mathematical side of music very often at all (practically speaking, this knowledge is not necessary to master an instrument), but certainly anyone who's gone through an academic music education will have covered it, quite possibly more than once.