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Math and structure in music: the Circle of Fifths (wikipedia.org)
21 points by RiderOfGiraffes on Dec 29, 2009 | hide | past | favorite | 16 comments

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.

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).

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:


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

Fiddles are GDAE, all fifths, just like a mandolin

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


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

You just cost me $70, goddammit. Thanks.

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

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.

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

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.

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.

I took music classes from age 10 through age 16 and was never taught about the circle of fifths. I was taught major/minor, key signatures, time signatures, sight singing (pitch and rhythm), piano, bassoon, harmony, inversion, counterpoint, and more, and I recall most of that, but I recall nothing about the circle of fifths. If I had been taught it then that would be odd, because it so matches my interests as a mathematician. I can only conclude I was never taught it.

YMMV. I don't claim that people weren't taught it, I only say that it isn't taught to every primary school student. I know the claim was "This stuff is taught in primary school." and that may be true, that it is taught in some primary schools. I'm saying it's not taught in every primary school. Maybe it's an American thing.

I thought it was interesting, and that there would be Hackers here who didn't know it and would be something that "... gratifies one's intellectual curiosity."

Hence the submission.

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".

  > just surprised it makes it here as "news".
I appreciate your point, but not everything here is "news" anyway. The guidelines state clearly that things are "On Topic" if they gratify one's sense of curiosity. I, like many others, would be disappointed to see too many things posted here under that banner, and I'd be content to have this item flagged as inappropriate, but it seems to me that many, perhaps most, people don't know it, and I agree that it is interesting.

Hence the submission.

As always, this raises interest in, and discussion of, separating "stuff that's interesting/useful" from "news." Personally, I'm not here for "news" so much as "interesting stuff".

It's an interesting issue.

True, if it was new enough to a sufficient number of people, I guess there is not much to prevent it. I was just surprised.

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