Circle of Fifths Part II: The Inner Circle

by David D. on May 21, 2010

Since our Scales and the Circle of Fifths article has been floating into the top five posts on MMT, we decided it’s time to delve a little deeper.

The Mersenne Star (Click to Enlarge)

On our first visit, we skipped along the outer edge of the circle, which displays the Major keys arranged in intervals of a fifth.  Going clockwise around the circle, each successive key has one more sharp (or one less flat).

With just a straight edge and compass, Marin Mersenne (yes, that Marin Mersenne) produced the drawing shown at right.  The Mersenne Star, from his HARMONICORUM LIBRI XII published in 1648, shows the harmonies and disharmonies between intervals arranged as a circle of fifths.

That’s all well and good for 1648, but today we want more.  And the Circle of Fifths as drawn below delivers.

Here, in addition to a visual display of the sharps and flats, the inner circle shows the relative minor for each major key.  How are they related?  They share the same key signature.  G Major has one sharp (F#), as does E minor.  So they have the same notes in their scales, they just start in different places.

And just like the major scales, all minor scales are made of the same sequence of whole steps (W) and half steps (H).  A half-step, sometimes referred to as a semitone, is the interval between any two adjacent keys on the piano.  A whole step equals two half-steps.  The sequence for a natural minor scale is: W-H, W-W-H, W-W.

The relative minor is always three half-steps down from (or a minor third below) the major key. So the relative minor of C Major is A minor.  Just like C Major, there are no sharps or flats, so it is played on all white keys.  Starting from A, it is a whole step to B, then a half-step to C. Then there are two whole steps followed by another half-step: a whole step to D, another to E, then a half step to F.  Then there are two whole steps to complete the scale: F to G, and G to A.

Got it?  Whole-Half, Whole-Whole-Half, Whole-Whole  Now play that sequence starting anywhere on the piano, and you know all your minor scales.

Fingering: the proper fingering for the A minor scale (and many others) is to start with the thumb of your right hand on A.  Your index finger plays B, middle finger plays C, then cross your thumb under to strike the D key and continue up the scale. You will end with your little finger on A. Reverse the procedure to come back down the scale.

There are 8 notes in the scale, so on the way up, remember 3 + 5 = 8.  On the way down: 5 + 3 = 8. The left hand uses the same sequence, just upside-down.  Try it, you’ll see.  Start with your little finger on the A, and it’s 5 +3 on the way up, and 3 + 5 on the way down.

Drawing from “The Circle of Fifths” by Catherine Schmidt-Jones.

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