I always find it interesting when people say "music is just like math!" and then proceed simply to assign numbers to a scale like that. The relationship between C-D-E-F on a scale is nowhere close to 1-2-3-4. The stuff always ends up sounding like this, which is OK but it still bugs me.
I always find it interesting when people say
"music is just like math!"
It could be a lot more like maths, but for some unfortunate historical decisions.
The scale is frustrating in music. Musicians think about it with the starting number being one, , whereas in maths we think of the starting number as zero.
When you're talking about different arrangements of a triad (example, major chor C-E-G) you can have three positions - root position (C-E-G), first inversion (E-G-C) and second inversion (G-C-E).
Anyone with a math/cs background would wish to express these as 0-2-4, 0-2-5 and 0-3-5 respectively. It would be easier to think about music and maths concurrently theory were it so. But the guys who built the rules of music didn't think like that, so instead it's 1-3-5, 1-3-6, 1-4-6. As a result, it's harder to reuse knowledge.
Timings are the same. First beat in a bar is 1, but it would be better if it were zero. As a result you have to get practiced at doing maths thinking offset by one. It's like having a C for-loop constantly on your back.
Could be a fun geek book geeks - to answer the question, if we redesigned the rules of music based on what we know now, what would we do differently? Interval expression would be top of the list.
Worth considering, I'd be tempted to express the scale as an expression of twelve (including half-tones) rather than what they do at the moment, an expression of 8. Because it gives you better fractions, and avoids conditioning.
I think the western tradition did do an awesome job of the important stuff. For example - the number of notes in the scale. Why twelve notes instead of 15 or 32? The reason is because you get a nice toolbox of frequencies (more than were available in strict pentatonic system, or the cool pentatonic-with-bending), without it getting too complicated. The basics of harmony theory are based around fractions of a halves and (fractional) thirds, which are easy to play with mentally, but give lots of scope for messing around.
I'd be interested from hearing from any Indians or other traditions what they think about the respective compromises. I notice in India that mainstream music has embraced the western scale.
Something like Jazz would be harder in other traditions becaues the internal maths would be harder. But there's still room for hacks like blues.
On youtube there's a great series of music videos by Howard Goodall on music theory. Coventry Carol is one of many Christmas songs that give us a link to the past and times before modern harmony. Say goodby to your Sunday :)
Another thing I've been thinking - there's room for a lot of development in music now that we can have direct manipulation of the waveform. This is a new power - something that has literally only been available for a few decades. Imagine if computer programming had started with high-level languages, and we had only recently discovered assembly language.
When 1-2-3-4 is used in music to show degree, that is an ordinal representation, not a cardinal representation. That's sort of the key difference here.
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I always find it interesting when people say "music is just like math!" and then proceed simply to assign numbers to a scale like that. The relationship between C-D-E-F on a scale is nowhere close to 1-2-3-4. The stuff always ends up sounding like this, which is OK but it still bugs me.
The scale is frustrating in music. Musicians think about it with the starting number being one, , whereas in maths we think of the starting number as zero.
When you're talking about different arrangements of a triad (example, major chor C-E-G) you can have three positions - root position (C-E-G), first inversion (E-G-C) and second inversion (G-C-E).
Anyone with a math/cs background would wish to express these as 0-2-4, 0-2-5 and 0-3-5 respectively. It would be easier to think about music and maths concurrently theory were it so. But the guys who built the rules of music didn't think like that, so instead it's 1-3-5, 1-3-6, 1-4-6. As a result, it's harder to reuse knowledge.
Timings are the same. First beat in a bar is 1, but it would be better if it were zero. As a result you have to get practiced at doing maths thinking offset by one. It's like having a C for-loop constantly on your back.
Could be a fun geek book geeks - to answer the question, if we redesigned the rules of music based on what we know now, what would we do differently? Interval expression would be top of the list.
Worth considering, I'd be tempted to express the scale as an expression of twelve (including half-tones) rather than what they do at the moment, an expression of 8. Because it gives you better fractions, and avoids conditioning.
I think the western tradition did do an awesome job of the important stuff. For example - the number of notes in the scale. Why twelve notes instead of 15 or 32? The reason is because you get a nice toolbox of frequencies (more than were available in strict pentatonic system, or the cool pentatonic-with-bending), without it getting too complicated. The basics of harmony theory are based around fractions of a halves and (fractional) thirds, which are easy to play with mentally, but give lots of scope for messing around.
I'd be interested from hearing from any Indians or other traditions what they think about the respective compromises. I notice in India that mainstream music has embraced the western scale.
Something like Jazz would be harder in other traditions becaues the internal maths would be harder. But there's still room for hacks like blues.
On youtube there's a great series of music videos by Howard Goodall on music theory. Coventry Carol is one of many Christmas songs that give us a link to the past and times before modern harmony. Say goodby to your Sunday :)
Another thing I've been thinking - there's room for a lot of development in music now that we can have direct manipulation of the waveform. This is a new power - something that has literally only been available for a few decades. Imagine if computer programming had started with high-level languages, and we had only recently discovered assembly language.
Actually, those are used somewhat commonly in music. See:
http://en.wikipedia.org/wiki/Degree_(music)
There are much more interesting ways to relate numbers to pitches; see the Pythagorean ratios and tuning before equal temperament.
http://en.wikipedia.org/wiki/Pythagorean_tuning
When 1-2-3-4 is used in music to show degree, that is an ordinal representation, not a cardinal representation. That's sort of the key difference here.
Assigning numbers to scale degrees isn't half as interesting as assigning numbers to each pitch class, then analyzing a composition using set theory.