The circle of fifths

I thought I would draft this tutorial to clarify some misunderstandings about Key signatures and scales in the Circle of Fifths.

If you consider the Circle of Fifths, as you progress around it you increase the root note by an interval of a fifth (C->G->D…).

C5 1

But this does actually create a problem when composing and scoring music because as you move around the circle from C maj then you add one sharp to the key signature. The number of sharps in the key signatures are:

C 0
D 1
G 2
A 3
E 4
B 5
F# 6
C# 7
G# 8
D# 9
A# 10
E# 11 (NB on Scaler this is displayed as F which is a minor bug, I think).

It is worth noting that in theory the Circle does not stop at E#, it continues to B##, F##, C##, and so on ad infinitum adding one sharp at a time!

Obviously scoring a musical piece in the key of G# major with 8 sharps is difficult , and when the musician comes to read the score and play it, " WTF? @@**!!!"

To avoid this most composers use the flat enharmonic keys for the second half of the Circle:

C5 2

Strictly speaking these are intervals of 4ths working anticlockwise from C major, The number of flats is increased b 1 as you work around anticlockwise from C, and are:

C 0
F 1
Bb 2
Eb 3
Ab 4
Db 5
Gb 6

These major scales using key signatures with flats are enharmonic (use the same notes and sound the same as) the equivalent keys using sharps:
C = C
F (1 flat) = E# (11 sharps)
Bb (2 flats) = A# (10 sharps)
Eb (3 flats) = D# (9 sharps)
Ab (4 flats) = G# (8 sharps)
Db (5 flats) = C# (7 sharps)
Gb (6 flats) = F# (6 sharps).

In fact the Circle of Fifths is sometimes called the Circle of Fourths as you move around it in anticlockwise direction because you move up an interval of a 4th from the previous key. And again, in theory it does not stop at Gb but moves on to Cb, Fb, Bbb, Ebb, and so on.

So why is this relevant to Scaler users. Well, if you choose an “odd” key for your composition, say Gb major and you then decide to use modal interchanges in your composition you may get presented with chords based on double flats.

and these chords are technically correct.


I made this graphic to visualize what’s going on with modes. Perhaps it may be helpful. :slightly_smiling_face:
Circle of 5ths Modes