This piece is based on the “Minuet in G,” often attributed to Johann Sebastian Bach and found in “The Notebook for Anna Magdalena Bach.” This version is a recasting of the original into a new language–basically, translating it from its thirds-based harmony into one based on fourths.
The below illustration can help explain how this conversion was done. The first grouping of eight notes is a series of thirds in C major containing all the natural triads in that key. The first three (C-E-G) form the tonic chord, the group of three starting on the third tone form the dominant (G-B-D) and the final three form the subdominant (F-A-C).
Using that same pattern in the next grouping of fourths, we can define the tonic (C-F-Bb), dominant (Bb-Eb-Ab) and subdominant (D-G-C). Once defined, we can then translate a chord sequence written in a traditional thirds-based major key into a key based on fourths.
Now you may notice and ask why the grouping of fourths is based on the natural minor sequence rather than major. The reason for that is simply to keep the minor second intervals (or major sevenths if you prefer) out of the tonic, dominant, and subdominant chords, resulting in a more consonant resulting translation.
So that takes care of translating the harmony, now how about the melody? For that, it was a matter of interpreting the melody either in terms of chord tones or passing tones. Chord tones were then translated into the corresponding chord tones of the new harmony and passing tones in the thirds harmony were converted into passing tones within the fourths harmony.
Now certainly the new melodic realization was not all black and white decisions–translations are never neat and clean. Decisions need to be made to try to maintain the melodic shape of the original as best as possible–certainly someone else performing this same translation would have made some different choices.
But as it is, that is how it was done. I hope you found listening to it and reading about it enjoyable.
This piece was once included in a 60×60 project, the above recording in fact. While I usually would play this song a bit slower, played at the above tempo the piece conveniently clocks in at just one minute.