The Circle of Fifths - a tutorial

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bandcoach

Zukatoku - Mod Scientist
Circle of Fifths
Circle of fifths because you circle around it.

It is the relationship of key signatures as you move through them, pure and simple.

In all there are 21 key signatures. This is because each note can be named as flat (b), natural or sharp (#)


Ab-Bb-Cb-Db-Eb-Fb-Gb
A-B-C-D-E-F-G
A#-B#-C#-D#-E#-F#-G#
If we were to arrange these key names in sequence from Fb to B#, like so:

Fb-Cb-Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#-D#-A#-E#-B#

where each key is a fifth above the previous one, we can see how we can begin to call this a circle of fifths.

We can conceivably bend both ends of this sequence to create a circle that wraps around itself:

circleOf5thsScaled.png


But notice that the two ends are not lined up. In fact, they wrap, spiral like, around to reach the start again at B#.

Generally we only use 14 of keys Cb-C# from the above, as the rest are overkill (you end up with 12# for B#).

Upper and lower tetrads
When we construct major scales we start from the concept that there is a fixed pattern of notes applied to every possible starting note:
T(one)-T-S(emitone)-T-T-T-S.

Let's break that down a bit, because it looks like there might be some symmetry inside of that:

T-T-S
T
T-T-S

Consider the C Major scale

CDEF
GABC

The distance between C and D is the same as between G-A; between A and B is the same as between D and E; the distance between E and F the same as the distance between B and C. Each of these four note scale fragments, called tetrads (literally 4 notes from the Greek tetra - four), has the same pattern: TTS. In any major scale we separate the lower and upper tetrads by a tone, hence our original pattern TTSTTTS.

Now let's go back to the original circle of fifths. Filling in each of the scales, we can see the upper and lower tetrad pattern being continually updated as we move from Fb to C#. Looking more closely, we see that each new key after Fb uses the upper tetrad of the preceeding key as the lower tetrad of the new key, i.e. each scale is prefaced in the upper tetrad of the scale before it in the Circle of 5ths. This is a partial explanation of why there is such a strong link between the dominant (the key a 5th above) and sub-dominant (the key a 5th below) to the main key.

circleOf5thsTable.png


The table is colour-coded to show where the same tetrads (regardless of actual note name) occur.

Looking closely at the table we can also see the following two features
  1. When we move up from Fb-C# the seventh note in each successive scale is sharpened or raised a semi-tone
  2. When we move down from C#-Fb the fourth note of each successive scale is flattened or lowered by a semitone.

Language use
T(one) = Whole-step
S(emitone) = Half-step
 
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bandcoach

Zukatoku - Mod Scientist
I agree! Kind of, I figured I'd use theory as a map instead of rules.

That's a good attitude and the rules (which are really just a synthesis of what has worked before) are simply signposts along the road you want to travel........
 

quantumleap

New member
Hey bandcoach, I was on youtube and stumbled across a wonderful lady by the name of Karen Cuneo Ramirez.. Her videos are pretty informative, much like your posts...But HER circle....is slightly different. I remember in one of her videos, I would link you to it, but I am not even sure which video it was..But she mentioned that the difference does not matter..I would like to hear your opinion on the matter though...

Basically... The circle looks identical to yours..

If you look at it like a clock, the circle Mrs Ramirez made goes:

12:00 = C
01:00 = F
02:00 = A#/Bb
03:00 = D#/Eb
04:00 = G#/Ab
05:00 = C#/Db
06:00 = F#/Gb

and so on...


Whereas your circle, is the opposite..

12:00 = C
01:00 = G
02:00 = D
03:00 = A
04:00 = E
05:00 = B
06:00 = F#/Gb




So, as you can see... 12:00 and 06:00 are the same. C, and F#......but the 2 sides are flipped...Do the same principals still apply? Cuz I know on both circles/clocks.....If you go around in one direction, each note is a perfect 5th apart from eachother. And if you go around in the other direction, they are 4th's apart from eachother....


So I was just curious as to why there are multiple teachings of how to set up the circle?
 

bandcoach

Zukatoku - Mod Scientist
Yep, not a problem on that one at all.

The circle is also mistakenly called the cycle. this is because they are both focused on the relationship of each pair of notes/keys being a 5th apart.

The circle of 5ths is about the tetrad relationship between subsequent keys.

The cycle of 5ths is about the relationship between chords within a key and by extension, the borrowed and exotic chords that can be played within a particular key.

As for which side the sharp and flat keys should go on, it makes no difference. Traditionally it has been set up so that we move clockwise from flat keys to sharp keys - the important thing is that we recognise a movement of a fifth when we do move through the circle. We could just as easily put C at the bottom, defying all tradition.....

btw, Cycle of 5ths tutorial due soon
 

quantumleap

New member
Well that helps me out some...

I've been getting better at picking a scale, and making chord progressions...but sometimes I get stuck on which chords I should continue to use.. Thats when I stumbled upon that lady's videos, and the circle she drew up, I guess would be considered the CYCLE of 5ths, since pretty much..it tells you which chords are played in a chord progression.. Meaning, if C is at 12:00....G and F are to the left and right..So the 3 main chords in the key of C are C, G, and F....and if you go further down the cycle, you find the 3 relative minor chords are E, A, and D........It made a little more sense to me than what I am probably explaining it..

I've tried to get into the Circle of 5ths, but always had trouble comprehending it....But when I came across the Cycle, something clicked....So perhaps I'll understand the circle soon, since obviously I'm beginning to understand more about this stuff finally. Thanks for the reply too....I look forward to your next tutorial
 

InFamE

New member
Even going to school for music, the Circle of Fifths was odd to understand. But useful when you did.
 
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