

The Circle of Fifths, Part One - dizzystar
http://www.coderedux.com/circle-of-fifths-part-one

======
tinco
The code he wrote for showing how to generate is pretty ugly and left me
confused. I think this shows much better the relation between the 12 notes and
a scale:

    
    
      NOTES = ['c', 'c#', 'd', 'd#', 'e', 'f', 'f#', 'g', 'g#', 'a', 'a#', 'b']
      # 2 is a whole step, 1 is a half step
      MAJOR_STEPS = [2,2,1,2,2,2,1]
    
      # returns the scale in the given key with the given steps
      def scale(key, steps)
        note = NOTES.index(key)
        step = 0
        notes = []
        while step < steps.length
            notes << NOTES[note % NOTES.length]
            note += steps[step]
            step += 1
        end
        notes
      end
    
      scale('d', MAJOR_STEPS) #=> ["d", "e", "f#", "g", "a", "b", "c#"]
    

I think this shows how a scale is just a list of steps applied to the notes
from a certain key :)

~~~
yayitswei
Chris Ford gave an elegant explanation of scales at a Clojure talk in London:
<http://skillsmatter.com/podcast/home/functional-composition>.

He starts with a basic sine wave and builds up abstractions until he has a
Bach canon.

~~~
agumonkey
Only at the first third and already delighted. He's moving between music,
physics, programming in such a simple and pragmatic way, thanks for the
bottom-up dynamic evaluation demonstration. Many many thanks.

links aside, he uses (and is a project contributor)
<http://overtone.github.com/>

ps: they also provide a nice emacs setup <https://github.com/overtone/emacs-
live>

------
haberman
Most musicians aren't aware of this, but an interesting corollary of the
circle of fifths is the Pythagorean Comma:
[http://en.wikipedia.org/wiki/Pythagorean_comma#Circle_of_fif...](http://en.wikipedia.org/wiki/Pythagorean_comma#Circle_of_fifths_and_enharmonic_change)

We generally treat Gb and F# as the same note, but if you actually count
perfect Pythagorean fifths (frequency ratios of 3:2) in both directions from
C, Gb and F# don't actually perfectly meet in the middle!

~~~
jacquesm
That's the cause of that famous piece being called the Wohl Temperierte
Klavier, those little rounding errors add up, once you have settled on a
system that works for everybody by convention Gb and F# have to be the same
notes (since there is only the one key for them...).

<http://www.phy.mtu.edu/~suits/notefreqs.html>

The ratios between subsequent notes differ, but not by much.

Edit: a quickie spreadsheet gives me 0.009502 for the largest difference
between two tones.

See also:

<http://en.wikipedia.org/wiki/Well_temperament>

~~~
fhars
But that again is just a convention, and before western music converged on
some kind of well tempered or chromatic tunings, there were quite some
experiments with keyboards featuring both flat and sharp keys, see
[http://de.wikipedia.org/w/index.php?title=Datei:Cembalo_univ...](http://de.wikipedia.org/w/index.php?title=Datei:Cembalo_universale_Tastatur.JPG&filetimestamp=20111014032521)
or <http://en.wikipedia.org/wiki/Archicembalo>

------
wazoox
Er... something's terribly wrong in this explanation. because the essential
forgotten fact is that, as much as F# is also Gb, C is also B#, F is E#, B is
Cb and E is Fb. So the G# scale exists and is perfectly valid, it reads

G# A# B# C# D# E# F##

And it is a very important point, because each scale on the circle of fifth
has one more sharp than the previous one when turning in one direction, and
one more flat in the other one.

Another point is that there is actually a comma between F# and Gb, and between
F## and G, because the chromatic semi-tone is one comma shorter than the
diatonic semi-tone -- Though of course the distinction isn't done on a
tempered instrument such as a piano or a guitar.

It is all actually quite simple, but not /that/ simple :)

------
stcredzero
Circle of fifths and circle of fourths allows one to algorithmically put
together Irish traditional tune sets that mostly work. (Not exactly as stated,
because Irish trad is really modal, but close enough for trad.)

Basically, take the home chord of a tune and apply one of the following:

If "major" then switch to the relative minor, or vice versa.

Go Round the circle of fifths or the circLe of fourths either direction, but
stay on whichever side of "major/minor."

Go up or down the scale, staying on whichever side of "major/minor."

So for example, a tune set with E minor, G major, A major should work. (Again,
not exactly it, but don't want to explain modes.)

~~~
gnaritas
I bet that all made sense in your head; not so much for the rest of us.

~~~
stcredzero
If you know enough music theory to know what a relative minor is, it makes
sense.

~~~
gnaritas
You might think that, you'd be wrong. I know what a relative minor is, I play
guitar daily. I can play up and down the circle of fifths/fourths and
improvise endlessly over the harmonized major/minor scale playing right
through the changes. None of that knowledge helps decipher the purpose or
meaning of the instructions you gave.

I'll try and walk through it.

> If "major" then switch to the relative minor, or vice versa.

OK, home chord is Em, so we'll use G major.

> Go Round the circle of fifths or the circLe of fourths either direction, but
> stay on whichever side of "major/minor."

OK, that's C or D given G as the starting point.

> Go up or down the scale, staying on whichever side of "major/minor."

So playing the G, C, or D scale over an E minor progression. G makes sense,
same scale as Em; C or D... don't even parse for me. I don't think of chords
and scales as separate, changing the scale changes the underlying chords I'd
play under them, thus changing the key to something other than Em.

> So for example, a tune set with E minor, G major, A major should work.

What? Nothing you just said would lead me to think A major would work over an
Em progression. G major, sure, obvious, it's the relative major of Em and just
another name for G major scale, but A... why A, you haven't explained that
above, your example doesn't match what the instructions seem to say.

~~~
stcredzero
Then what you don't understand is how a trad tune set works. What I'm talking
about is how to put together a set of three tunes that work well as one track
on an album or one "number" in a performance. Each tune internally has its own
progression, which may be different. I'm only talking about the home chord of
each tune. (Which I state.)

~~~
gnaritas
Well that clears up basically nothing; I still don't understand what you're
saying, or where the A major comes in.

~~~
stcredzero
A certain level of density is indistinguishable from trolling.

~~~
gnaritas
True, but I wasn't. You really weren't as clear as you seem to think you were.
If all you're saying is pick as roots nearby notes on the circle of fifths,
you could have been much clearer.

------
jon6
I vaguely remember using this knowledge of the scales to "cheat" on the
violin. If you move your hand into whatever position puts your first finger on
the first note in the scale then you can always move the rest of the fingers
in exactly the same manner - whole whole half, whole whole whole half. My
music theory knowledge is crumbling but what I mean is if you move into 2nd
position on the A string to play a B scale its much easier than starting in
1st position with the 2nd finger.

I did this at a competition once when given some insane scales (like 3 flats
in the clef) without having ever practiced the scale itself and got it right.

------
mrchess
Lots of editorial issues, for example when describing C# and F# some of the
information is incomplete/mixed. Too bad there is no comment section.

------
kenjackson
Looks really good (bookmarked to read later). Although maybe some more
motivation as to why you start music theory with circle of fifths -- as
someone who knows nothing about music, I had never heard of it before.

~~~
dizzystar
That's a really good question. The reason why I started at the Circle of
Fifths is because it's the foundation and it is highly mathematical. It's a
tad bit painful to start with, but I wanted to start from the ground up. This
will make the other stuff far more understandable. I can go on all day saying
"this is how to make a chord" but starting here will let you understand the
later ideas better.

I also started here to demonstrate how logical it all is.

~~~
jblow
You don't seem to provide any context about what the circle of fifths is, or
even what a fifth is for, thus I have no idea why I should care, and in
general it makes it very hard to assimilate the article in a useful way.

~~~
kzahel
Yeah I agree. I think there should be some mention of why a "fifth" is
important (3:2 ratio of frequencies, which is recognizable, and when this is
continued, it eventually "loops back" to the original note (at a 2^n:1 ratio,
where n is the number of fifths up until it repeats)

------
dizzystar
Thanks for all the feedback guys. The links found here are all amazing as
well. I know what to improve in this article and the next article will be much
better.

Thank you so much;

------
aijanai
"Up" this if you read "Cradle of Filth" instead of "Circle of Fifths" lol

