copyright 2001, D. Glenn Arthur Jr. Last updated 1996.

# The Circle Of Fifths

The circle of fifths is an observation of a mathematical property of the relationship between the number of sharps or flats in a key signature and the starting note of the key. It's also a useful mnemonic shortcut to remembering key signatures. (It's also useful for understanding why various historical tuning systems were the way they were and how they differ from modern "equal temprament". I won't go into that here, but if you're interested, take a look at Wim Verheyen's Alternate Intonations explanation.)

Here's how it works: transposing up a fifth (seven half-steps) adds one sharp to (or removes one flat from) the key signature. Transposing down a fifth does the opposite.

So we can very quickly work out the following table without much effort:

```C	Am	our starting point	no sharps or flats
G	Em	up a fifth from C	one sharp (f)
D	Bm	up a fifth from G	two sharps (f, c)
A	F#m	up a fifth from D	three sharps (f, c, g)
E	C#m	up a fifth from A	four sharps (f, c, g, d)
B	G#m	up a fifth from E	five sharps (f, c, g, d, a)
F#	D#m	up a fifth from B	six sharps (f, c, g, d, a, e)

F	Dm	down a fifth from C	one flat (b)
Bb	Gm	down a fifth from F	two flats (b, e)
Eb	Cm	down a fifth from Bb	three flats (b, e, a)
Ab	Fm	down a fifth from Eb	four flats (b, e, a, d)
Db	Bbm	down a fifth from Ab	five flats (b, e, a, d, g)
Gb	Ebm	down a fifth from Db	six flats (b, e, a, d, g, c)
```

You can also see a pattern that can be used to figure out which notes are sharped or flatted, but if all you need is the number of symbols in the key signature and can remember which ones are affected from that, then we can stick to looking at this one feature of the circle of fifths.

If all else fails, you can copy this to an index card and clip it to your music stand when you're in a situation where people are likely to shout out a key name and expect you to know the key signature.

When horns are featured, you'll usually see one to four flats in the key signature. When guitarists write songs, you'll usually see from zero to four sharps (once in a while, one flat). Fiddle tunes seem to mostly stick to one to three sharps (occasionally none).

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