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Music theory for nerds

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Re: Music theory for nerds

#51

Post by haberman »

lohankin wrote: post #40

The explanation of the origin of major scale in the article is pure voodoo. Minor third is not a simple fraction - is that the reason to exclude it from the scale? How do you explain minor scale then? Maybe it should be excluded, too? Here're my thoughts on the subject. For some reason no one can explain, Western music settled on a system of 12 tones with equal temperament, This system emerged as a result of long evo…

I agree very much with your post's thesis (you have to play AND think; thinking alone won't help. It's an experimental subject.) Just noticed one thing:

> For some reason no one can explain, Western music settled on a system of 12 tones with equal temperament

It doesn't seems surprising to me. If you start from a pitch and go upwards in both octaves and perfect fifths (2:1 and 3:2, the two most fundamental intervals), the perfect fifth sequence will land on 11 distinct tones before (nearly) meeting the octave sequence. Mathematically, (3/2)^12 ≈ 2^7.

So 12 semitones works out nicely because you can follow perfect fifths out in any direction as far as you want and never go outside the set of semitones. And most of the small-ratio'd intervals can be represented with pairs of notes inside this set.

Re: Music theory for nerds

#52

Post by gnaritas »

robbrown451 wrote: post #39
dietrichepp wrote: post #31

Earlier quoted context omitted.

Well, it has to be somewhat arbitrary. But it is nice that the relative minor of C, which is two steps down, is A. Otherwise you would have to go five steps up (from A to F, hypothetically, if A B C D E F G A were a major scale).

If C was called A, that wouldn't be particularly arbitrary. It would certainly make more sense for people learning music. The C major scale is universally agreed to be the simplest, most basic scale, so wouldn't it make more sense for it to be ABCDEFG, rather than CDEFGAB?

No, because that's the A minor scale, which is the same notes as the C major scale but starting at A. A scale should logically always start with its root note.

Re: Music theory for nerds

#53

Post by lohankin »

BurningFrog wrote: post #19
analog31 wrote: post #4

This has got to be some of the worst jargon and notation for anything, ever. Indeed. I'm a musician, and something non-musicians often ask (especially techies, it seems) is why we use such an archaic notation system. The reason is simply that a certain number of musicians have developed the skill of sight reading which is the ability to perform a composition directly from a written sheet, with little or no rehearsal.…

It's a lot like why the QWERTY keyboard remains dominant.

No, it's not the same. Current music notation is a result of long evolution, unlike QWERTY. Try to invent usable alternative - then you will appreciate the convenience of current notation.

Re: Music theory for nerds

#54

Post by undershirt »

ektimo wrote: post #29

I've skimmed a lot of articles on music "theory" but none of them provide anything like what I'm looking for. A music theory should explain: 1. Why do we like pieces when played forward but not backward or inverted? 2. Why do certain sounds evoke certain emotions? 3. How could you write a program to pick out music that people find especially good (versus music that has surface similarities)? In other words, why does…

An aesthetic just seems like a unconscious favorable reaction to stimuli based on genetics and culture. Why our genes and culture have favored certain forms, I suspect there isn't a way to reduce it to something satisfactory.

I used to wonder why I felt good when looking at sunsets, landscapes and clouds. But I figured that our aesthetics probably evolved in response to what was around us. Happier people probably survive better.

The way we hear music seems like such an aesthetic, as it might've occurred within ancient cultures as a form of play and release. I suspect that our random genetic hunger towards different aesthetics might have created an incredible developmental feedback loop. I'm not sure where I'm going with this incredibly complicated topic, but I have a lot of very unrefined thoughts about them, that are probably overly-reductive and wrong.

Re: Music theory for nerds

#55

Post by lohankin »

haberman wrote: post #51
lohankin wrote: post #40

The explanation of the origin of major scale in the article is pure voodoo. Minor third is not a simple fraction - is that the reason to exclude it from the scale? How do you explain minor scale then? Maybe it should be excluded, too? Here're my thoughts on the subject. For some reason no one can explain, Western music settled on a system of 12 tones with equal temperament, This system emerged as a result of long evo…

I agree very much with your post's thesis (you have to play AND think; thinking alone won't help. It's an experimental subject.) Just noticed one thing: > For some reason no one can explain, Western music settled on a system of 12 tones with equal temperament It doesn't seems surprising to me. If you start from a pitch and go upwards in both octaves and perfect fifths (2:1 and 3:2, the two most fundamental intervals)…

Interesting idea indeed. I need to think about it.

Edit after thinking: still, it doesn't explain the number 12 IMO. It could be 17 or something else. Probably, it's a long chain of coincidences at play: Western music settled on 7-note scales long time ago (long before equal temperament was invented), and we should start looking for explanations from here.

Another edit: one of the important coincidences is that number 12 makes possible the existence of diminished scale, which serves as a "universal glue" due to 2 tritones. (There's not enough space here to elaborate, but you probably know what I mean). And maybe tritone itself is one of factors leading to number 12.

Re: Music theory for nerds

#56

Post by Ericson2314 »

Ericson2314 wrote: post #49
nazgul17 wrote: post #9

Earlier quoted context omitted.

I would love something like that. Any pointer?

A large part of it hasn't been researched very mathematically, to my knowledge. If you google music+grammar you can get some stuff with a linguistic approach, which may be less empirically grounded but certainly a richer theory than the alternatives. And don't get me wrong, science is good but as musician mathematician a richer theory that overreaches reality is much more fun, and besides most of this stuff is cultur…

To reveal my biases (if they aren't already clear) I most enjoy Baroque and Renaissance music; and Jazz, its Cuban and Brazilian equivalents, and their direct descendants (e.g. R&B).

Re: Music theory for nerds

#57

Post by quadrangle »

The author and anyone else who understands correctly that traditional music notation is shitty in lots of ways and is trying to understand how music really works should go get the book "Music and Memory: An Introduction" by Bob Snyder. It uses no music notation and explains music in terms of psychological principles of perception of time. It's not a complete theory of everything, but it shows the way you should be understanding the nature of music.

Beyond that, check out Sweet Anticipation by David Huron, and Tuning Timber Spectrum Scale by William Sethares (and his other Rhythms and Transforms, see http://sethares.engr.wisc.edu/ for web versions of first chapter of each). These sorts of resources are where real understanding of music comes from. Not from the "theory" stuff us music professionals had to deal with that fails to explain anything well.

Re: Music theory for nerds

#58

Post by PeCaN »

BurningFrog wrote: post #19
analog31 wrote: post #4

This has got to be some of the worst jargon and notation for anything, ever. Indeed. I'm a musician, and something non-musicians often ask (especially techies, it seems) is why we use such an archaic notation system. The reason is simply that a certain number of musicians have developed the skill of sight reading which is the ability to perform a composition directly from a written sheet, with little or no rehearsal.…

It's a lot like why the QWERTY keyboard remains dominant.

Yeah, it would be really hard to change all the millions of documents written with QWERTY.

Re: Music theory for nerds

#59

Post by ngneer »

The interested reader is referred to "Mathematics and Music" by David Wright, published by the American Mathematical Society. The realization that the circle of fifths is really there because 5 and 7 (aka -5) are co-prime to 12 was worth the entire thing! Together with 1 and 11 (aka -1) they generate the group Z_{n} for n = 12...

Re: Music theory for nerds

#60

Post by theseoafs »

theseoafs wrote: post #46

> It completely obscures the relationship between the pitches, though. It doesn't actually obscure the relationship between the notes -- it makes them clearer. For example, I see the notes C, E, and G on some sheet music, maybe with some accidentals on some of those notes. I know that I'm therefore supposed to play a C triad. Now, there are multiple kinds of triads, but once I know I'm supposed to play a triad, it's…

Reading this over again, it seems like the author's not yet fully wrapped their mind around "big picture" stuff like keys, chords, basic compositional structure, etc. It's an... interesting choice to write a piece proclaiming that musical notation is absurd when you're only a beginner.
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