Math and structure in music: the Circle of Fifths

http://en.wikipedia.org/wiki/Circle_of_fifths

21 16 17 years ago

en.wikipedia.org

wgj2• 17 years ago

The circle of fifths is a by-product of the more generalized lattice theory:

As the Wikipedia article explains the Pythagorean Comma, there are actually many possible commas caused by equal temperament when traversing the lattice in various ways. Most traditional harmonic theory exploits our psychological response to these gaps caused by equal temperament. Music theory based on the circle of fifths is a small subset of that.

anigbrowl2• 17 years ago

There is actually a keyboard based around this theory, though it's a bit pricey ($500, or $700 for one with more features): http://www.c-thru-music.com/cgi/?page=prod_axis-49

Some people love it, though if you have extensive experience with a keyboard then it may actually be counter-intuitive (I learned music on a piano and I still get hopelessly lost on the frets of my bass guitar whenever I try to play something new).

wgj2• 17 years ago

I didn't know about this device. Very cool. I have considered developing an algorithmic software concept based on lattices. This device is a hardware version of what I thought that might look like.

I might as well mention that Robert Fripp's New Standard tuning for guitar is entirely in fifths:

http://en.wikipedia.org/wiki/New_Standard_Tuning

Same side effect of turning seasoned guitarists into beginners, as the tuning is substantially different from other alternate tunings for guitar.

nuba• 17 years ago

Whoa, found many other interesting things there, too: http://x31eq.com/tuning.htm

Thanks!

pohl• 17 years ago

There are some interesting parallels between the CoF and the color wheel, the most obvious of which is that pitches opposite each other anywhere on the CoF are the most dissonant when juxtaposed against each other - similar to complimentary colors opposite each other on the color wheel. (Think orange and blue). Besides that invariant, the tones are permuted in the CoF a bit, which differentiates it from the standard 12-color wheel, which keeps neighboring tones together.

I wonder if one permuted the color wheel to be more like the CoF if it would make the basis of an interesting music visualizer, such that the harmonic relationships between tones correspond to the harmonic relationships to colors shown.

Here's an old visualizer that attempted something like this, but they didn't permute the color wheel in the manner I'm suggesting: http://www.musanim.com/mam/circle.html

anon42389475• 17 years ago

this is a pretty serious book about music and math http://www.musimathics.com/

anigbrowl2• 17 years ago

You just cost me $70, goddammit. Thanks.

Tichy3• 17 years ago

This really is not news. This stuff is taught in primary school.

RiderOfGiraffes3• 17 years ago

Not in any primary school of which I'm aware. I'd be interested to know what area you are in to make such a claim. Is it every primary school?

For information/reference, it wasn't taught to me, or my sister, or my nieces, or my wife, or any of my colleagues at work. I've checked. Or at least, to be more accurate, none of them knew of it when I mentioned it to them recently. Perhaps it was taught - it certainly didn't stick.

rdouble• 17 years ago

It's taught to young music students. I learned it in public school in the middle of nowhere. Probably age 10 or 11. As did both of my sisters, brother and everyone else in the school orchestra. One wouldn't learn it outside of music lessons or a music program. However, it's taught pretty early on if you're doing anything related to classical music.

Tichy3• 17 years ago

I went to school in Germany, where all pupils have basic music lessons. I admit that when I learned it at school, I did not pay much attention, and only really learned it again from taking guitar lessons. Still, it is very, very basic stuff. Not saying it is not interesting, just surprised it makes it here as "news".

teeja• 17 years ago

I can't speak for all accordians, but the chords at the left-hands of piano-accordian players are arranged in circles of fifths. F is below C is below G is below D ...

As a result, buttons for all the (non-chromatic) intervals are within 2 buttons of the tonic ... for every tonic. Once you've got the pattern, it's the same for every key, no matter how remote.

Math and structure in music: the Circle of Fifths

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