The Circle of Fifths (COF) is a diagram that brings all the harmonic intervals next to each other enabling us to see the fixed harmonic intervals of the notes. The circle of fifths is a very useful tool in analyzing chords and scales because (in general) notes closer to each other around the circle sound better together than notes further away. Notes can move in an ascending (clockwise) or descending (counterclockwise) manner around the circle. D was used as the starting point of the circle below because all the sharps and flats are symmetrically the furthest notes away from D. Though D was is used as the starting point in this circle, any note can be used to begin the circle as the notes never change position. This is why it is a circle is useful as it can rotate and describe the harmonic intervals between any notes. The frequencies of the notes and how they are calculated mathematically using fractional exponents, and the generally accepted approximate frequency ratios of the intervals can be found on the circle of fifths poster. What is interesting to note is the frequency ratios of the 3 intervals furthest away from A (min2, aug4, and maj7) are more complex than the frequency ratios of the other intervals and require larger numbers to approximate. |