

Math and structure in music: the Circle of Fifths - RiderOfGiraffes
http://en.wikipedia.org/wiki/Circle_of_fifths

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

<http://x31eq.com/lattice.htm>

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.

~~~
anigbrowl
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).

~~~
wgj
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.

~~~
aaronblohowiak
Fiddles are GDAE, all fifths, just like a mandolin

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anon42389475
this is a pretty serious book about music and math
<http://www.musimathics.com/>

~~~
anigbrowl
You just cost me $70, goddammit. Thanks.

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pohl
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>

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teeja
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.

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

~~~
RiderOfGiraffes
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
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.

~~~
RiderOfGiraffes
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.

