math & music
Western music theory is a system of music that has been used to create all of the genres and pieces of music that we are normally familiar with including classical, jazz, rock, popular, and blues, all the way from the past to the contemporary.
This system is based on the 12 note chromatic scale: A, A#(Bflat), B, C, C#(Dflat), D, D#(Eflat), E, F, F#(Gflat), G, G#(Aflat)
Think about the keys on a piano. In one set of keys (period or octave), there is seven white keys and five black keys (the sharps and flats) to give the 12 note scale that is repeated or periodic.
This system is based on the 12 note chromatic scale: A, A#(Bflat), B, C, C#(Dflat), D, D#(Eflat), E, F, F#(Gflat), G, G#(Aflat)
Think about the keys on a piano. In one set of keys (period or octave), there is seven white keys and five black keys (the sharps and flats) to give the 12 note scale that is repeated or periodic.
The interval or distance between any consecutive note on this 12 note chromatic scale is called a semitone.
The perfect fifth is an interval of seven semitones. Perfect fifths are very important in music, because any two notes which are related by a perfect fifth interval will be harmonic. In other words, it is one of only a few intervals between any notes where the pitch sounds the same and the result is highly pleasant to the ear.
To construct a circle of fifths, let us start at note C and count upwards one perfect fifth or seven semitones to arrive at G. Now count a perfect fifth from G to arrive at D. This sequence can be repeated until every note of our 12 note chromatic scale is ordered only once when we will then arrive back at the beginning (C in this case). The order becomes: C, G, D, A, E, B, F#, C#(Dflat), G#(Aflat), D#(Eflat), A#(Bflat), F.....repeat.
To represent this mathematically as a sequence now with numbers from 1 to 12 using intervals of seven we get the sequence or pattern: 1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6.
Note that a repeating pattern like this will only work for some intervals. How come? Try making a pattern using intervals of five (five semitones in music).
The circle of fifths is often arranged on a 12 point circle like a clock. It gives us all our information about scales and key signatures. Furthermore, it gives a sequence of notes to play that sound particularly amazing. Baroque and classical composers like Bach, Vivaldi, and Mozart used circle of fifths progressions such as VI-II-V-I, which would be A, D, G, C when playing from a C major scale. Circle of fifths progressions are used across all musical genres of past and popular music for incredible auditory effect.