31TET Banjo: Cycle of Major Thirds

In 12 tone equal temperament (12TET) the cycle of major thirds is only three notes long and does not generate the entire scale. This is because the 4-semitone width which defines the 12TET major third shares factors with the 12-semitone width octave. In 31 tone equal temperament however, every interval, including the major third, generate the entire scale when stacked. The 31TET octave is defined by the width of 31 diesis and the major third is defined by the width of 10 diesis. Since 31 is prime, no interval can divide the 31TET octave evenly. Ascending/descending by any interval repeatedly will result in each of the 31 tones being visited. In this example, I begin on a major chord. I then play a major chord rooted on the third of the previous chord. I continue to do this until I reach the chord I began on.