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Mathematical explanation of music and white/black notes in a piano

math.stackexchange.com

11–20 of 31 posts

Re: Mathematical explanation of music and white/black notes in a piano

#12
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.

Re: Mathematical explanation of music and white/black notes in a piano

#13
The piano to me feels like an iPhone, it does a lot of things well, and it hides many details from you. I don't know if real pianos are tunable/adjustable, but the electronic one we have at home certainly isn't (except in its ability to sounds as different instruments).

I recently bought a Oud[1], a classical stringed middle eastern instrument, it's not fretted, it's portable, and adjustable. To me, when I compare it to the piano, the Oud feels like the Unix of musical instruments. It's a bit hard to get used to at first, but it's designed to be lite-weight (portable) and adjustable, allowing power users to be very creative and expressive. Most other users will stick to a standard tuning and placement of fingers.

I'm not super-bothered by the way the piano is layed out, to me it's just a simplified instrument that works for 95% of the cases.

What I don't understand is why do all the middle eastern scales (maqam[2]) have 7 tones. The fact the western C major scale also has 7 tones is just another example of yet another scale with 7 tones (and it happens to correspond to the Ajam maqam[3]).

There are some middle eastern scales not really playable on a piano, like the Rast[4], unless the piano is somehow adjustable.

[1]: http://en.wikipedia.org/wiki/Oud

[2]: http://en.wikipedia.org/wiki/Arabic_maqam

[3]: http://en.wikipedia.org/wiki/Ajam_(maqam)

[4]: http://en.wikipedia.org/wiki/Rast_(maqam)

Re: Mathematical explanation of music and white/black notes in a piano

#14
I'm glad folks are finding this interesting. However, this is pretty much common knowledge to anyone who has taken music theory. It's usually not given a great deal of attention as most musicians using the standard 12 tone don't care much about what's going on under the hood. They're a bit like programmers who use a high level language and an IDE and don't know how a compiler or assembly works.

Just a bit funny to come across it here, it'd be a bit like finding out musicians were talking on a forum going 'wow, computer programs are written using structured text files!' or something of the like. Not trying to be rude..

Re: Mathematical explanation of music and white/black notes in a piano

#16

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.…

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 :)

Re: Mathematical explanation of music and white/black notes in a piano

#18
post #13

The piano to me feels like an iPhone, it does a lot of things well, and it hides many details from you. I don't know if real pianos are tunable/adjustable, but the electronic one we have at home certainly isn't (except in its ability to sounds as different instruments). I recently bought a Oud[1], a classical stringed middle eastern instrument, it's not fretted, it's portable, and adjustable. To me, when I compare it…

> I don't know if real pianos are tunable/adjustable, but the electronic one we have at home certainly isn't (except in its ability to sounds as different instruments).

An acoustic piano cannot be easily tuned (it takes a couple of hours to a trained specialist, because there are more than 200 strings to adjust). However "serious" electronic keyboards have been fine-tunable for more than 20 years. Many of them can play any microtonal scale you may imagine, and many different classic temperaments are pre-programmed.

Re: Mathematical explanation of music and white/black notes in a piano

#19
post #8

12 tones is not the only possibility. there is also a 19 tone scale: http://en.wikipedia.org/wiki/19_equal_temperament there are also some mp3 files using 19 tone scale: e.g. http://www.harrington.lunarpages.com/mp3/Jeff-Harrington_Pre...

Sounds great, thanks for the music link :)

Re: Mathematical explanation of music and white/black notes in a piano

#20
post #18
post #13

The piano to me feels like an iPhone, it does a lot of things well, and it hides many details from you. I don't know if real pianos are tunable/adjustable, but the electronic one we have at home certainly isn't (except in its ability to sounds as different instruments). I recently bought a Oud[1], a classical stringed middle eastern instrument, it's not fretted, it's portable, and adjustable. To me, when I compare it…

> I don't know if real pianos are tunable/adjustable, but the electronic one we have at home certainly isn't (except in its ability to sounds as different instruments). An acoustic piano cannot be easily tuned (it takes a couple of hours to a trained specialist, because there are more than 200 strings to adjust). However "serious" electronic keyboards have been fine-tunable for more than 20 years. Many of them can pl…

Yea I've seen a Youtube video of someone adjusting a Yamaha keyboard to play notes on middle eastern scales.
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