Sunday, September 12, 2021

Cycle of fifths, not circle of fifths

 Western music has 12 semitones per octave. The strongest ratio, 3/2, is the 7th note above the starting point, out of the 12 notes that take you up to the octave (and thus back to your "starting point" because we consider it the same note). This interval is called the "perfect fifth".

Because 7 doesn't divide evenly into 12, going up 7, and up 7 from there, and up 7 from there (the fifth of the fifth of the fifth) will eventually visit all 12 notes in a scrambled order before returning to where you started. When doing this exercise, it is customary to drop down an octave whenever you get too high, because otherwise you'll go past the highest note your instrument can play.

This is a "cycle of fifths" and the way it interacts with other constructs such as the major scale, note names, and key signatures yields a number of interesting patterns.

However many people use the name "circle of fifths" which leads to endless infographics laid out in a circle. This is unfortunate because it makes it hard to compare between fifths and obscures some of the pleasing patterns that can emerge from seeing e.g. the order in which piano keys become sharped.

So strongly prefer to present information as a "cycle of fifths" in a grid where adjacent fifths can be easily compared.