observed as well as the significance of augmented/diminished notes. For triads we have the following: And for seventh chords: Circle of fifths Beginning with a pitch constellation of a chromatic scale, the notes of a circle of fifths can be easily generated. Starting at C and moving across the circle and then one tick clockwise a line is drawn with an arrow indicating the direction moved. Continuing from that point (across the circle and one tick clockwise) all points are connected. Moving through this pattern the notes of the circle of fifths can be determined (C, G, D, A ...). One can also depict non-tempered intervals on a chromatic circle, which allows one to depict commas (small intervals), particularly comma pumps. For example, using a sequence of twelve just fifths (3:2 ratio) does not quite return to the starting point (the size of the gap is the Pythagorean comma), resulting in a "broken" circle of fifths. Technical note The ratio of the frequencies between two pitches in the constellation can be determined as follows. Take the length of the arc (measured clockwise) between the two points and divide by the circumference of the circle. The frequency ratio is two raised to this power. For example, for a fifth (P5, which is located at 7 o'clock relative to the tonic T) the frequency ratio is: References Further reading . . External links Notenscheibe web application - pitch constellations of scales, triads, intervals and the circle of fifths, with basic audio On-line app illustrating pitch constellations ScaleTapper - IPhone app which utilizes pitch constellations. PDF of musical scales Pitch space Post-tonal music theory