Canon at Any Interval

This canon from 77 Canonic Variations on Twinkle Twinkle Little Star, mvt. 74 squeezes sixty copies of Twinkle Twinkle Little Star into two minutes. By adding two extra rests, the tune can accompany itself pleasingly at any pitch interval (transposition) and time interval (delay). Think of this as the ultimate 1st-species counterpoint exercise.

Above: The illustrious Jihye Chang playing the opening part of the canon. Below: My remix. You can buy the piano score here. Pianists–let me know if you’re interested in performing it.

To cycle through the different combinations, the top part shifts in time, and the bottom part shifts in pitch.

  • The top part shifts earlier by one note at each repetition (phase). Accenting the original length of the tune reveals a long tune (the green bloom in the video), making this a tempo canon.
  • The bottom part shifts down by a step at each repetition (sequence). It actually descends by more than 4 octaves. In this remix, I’ve used Shepard tones (octave cross fade) to keep it in the same octave.

The tune is built mainly out of stepwise descent, and as Scott Murphy mentions in his blog post on “Annie” time or pitch interval canons, a scale is the simplest tune that can accompany itself at all time and pitch intervals. So it didn’t take a lot of tweaking to get this melody to work as a canon; rather, I spent most of my time trying to make it interesting. The tempo canon was a happy accident that grew out of the phasing, and it provided a large-scale focus for the 26 mini canons.