There are a couple of oversimplifications in argumens above:

1. A couple of references were made to "divide the circle into twelve equal arcs." There are 13 notes in the chromatic scale so the division must be triskadecate, not duodecate.

2. In conventional "theory" there's no such thing as a "circle of fifths. Each "movement clockwise" adds one sharp to the key signature, or cancels one flat. Each movement counterclockwise adds one flat or cancels one sharp. For a "theoretically pure" graphic, you must draw a spiral of fifths so that the "keys" of C#, C## etc are properly shown. The notion that you can "fall back an octave and substitute the enharmonic notation" doesn't work accurately except for equi-tempered tunings.

For an equi-tempered scale, a circle suffices, but in just temperament you DO NOT arrive back at the same "C" (or any other) pitch after each transit of the "circle." It is that difference that needs to be shown/understood, and an accurately constructed "spiral of fifths" will show it quite clearly.

Once the concept of the spiral is understood, it can be rendered immaterial whether the octave is encompassed in exactly one turn around the (non-existent) circle, and you can use any "scale" (unit of mensuration) to represent the frequency ratio of adjacent "notes" in some arbitrarily selected "unit of arc/angle" (creating a sort of logarithmic spiral of pitches). Drawing any two "kinds of scales" on opposite sides of the same "curl" of the spiral will accurately show the disagreements between the tunings.

If you can discard the notion that a "circle" has some mystical significance, you can easily create a linear (straight line) slide rule for comparisons between tunings, although for a "complete set" of scales encompassing suffient octaves to show the differences clearly it may be a rather long stick.

John