Squaring the Circle of 5ths

The circle of fifths is a very elegant way of showing a number of things about music very concisely, but only if you understand what those things are. The chart below opens the circle into a square to show what those things are. It relates to two diatonic instruments that I play, the harmonica and mountain dulcimer, but it is actually generic music theory. It shows modes and their relationship to the Major and minor scales as well as the what and why of sharps and flats.

Many people know that as we move clockwise from C on the circle that we add one sharp at each step up to six at F#, and that moving counterclockwise from C on the circle adds one flat at each step, up to five at Db. It helps to understand why.

The top two rows of the small chart above shows the 'C' Ionian Major interval and scale. It has no sharps or flats. When that scale is shifted to line up a new scale, 'G', (lines 3 & 4) so it starts at the 5th position of the 'C' scale, the F which is the 7th position of the 'G' scale does not line up. It is at a flattened 7th position. This change in interval is a change to the Mixolydian mode. To give it the same Ionian Major interval as the 'C' scale we must raise the F by a semitone to F# (bottom row).

Notice on the top chart that the Mixolydian row has a sharp sign (#) to the right of the note that was flattened. Each new row is movement to the next position on the circle of fifths. Each new mode flattens one more note, and the scale for the standard (Ionian mode) Major scale requires one more sharped note. The 7th through 11th harp positions do not have mode names since they start with sharp or flat notes they are out of mode. The 7th position, F#, is unique in that it is shown as having 6 sharps, but that is because the 7th is E# because F has already been named (F#) for the tonic note. The 12th position, 'F' is the Lydian mode which has a raised 4th, so there is a flat to the left of it to tell us that the note must be flattened to make a Major scale interval.

The circle of fifths also shows us which notes are sharped. For 'G' Major, two positions back shows 'F', which is the note that gets the sharp sign. 'D' Major gets the F and C as sharps, etc. If you want to play 'D' Mixolydian, the chart shows that you would not raise the 7th to C#, so the 'D' Mixolydian scale is D E F# G A B C. This works everywhere on the circle.

Many people who play chromatic instruments are only vaguely aware of modes, but people who play diatonic instruments become aware of them quickly when they try to change keys. If all you have is a 'C' harp, and you wish to play in 'A' minor, it's not a problem since 'A' Aeolian minor has no sharps of flats, but if you want to play in 'D' minor the scale starting at 'D' is 3rd position (Dorian). Aeolian minor needs a flat 3rd, 6th, and 7th (see the chart), which means that you need a Bb that is not on the harp. There are three B notes on a 'C' harp. The lowest and highest are available with bends, but the middle one must be overblown which is a somewhat rare skill. For a fretted instrument, notes are bent up, and a 'C' tuned diatonic fretted instrument like the mountain dulcimer does have 'A' notes in spots that can be bent up to Bb. So for the player of diatonic instruments, bending is an essential skill, or having multiple instruments available (harps) of the ability to retune (dulcimer) is required to play in multiple keys. The circle of 5ths tells us which notes must be bent out of mode when playing in multiple keys. I hope that the squared circle helps you to see how the circle of fifths works and it's relationship to modes.

You can find an excellent, and very harmonica oriented, explanation of the circle of 5ths at www.angelfire.com/tx/myquill/CircleOfFifths.html that never mentions modes.

Pentatonics

From Jan 1, 2007