The well known song “Row, Row, Row your Boat” is a musical “round”: one melodic line, and one person/group starts singing it, and at least one other/group starts singing the same melody but starting at, say, bar two, and they fit together. Wikipedia has a good article on them.
Normally a round like “Row Row Row your Boat” is notated like this:
But normally you sing a round like this over and over. So it has a feeling of going in a perpetual circle. So, arguably we could represent this feature of “Row Row Row your Boat” by notating it thus:
Now you couldn’t perform from a score like this. But notating it this way does make explicit a certain feature of this piece which is not at all apparent from ‘normal’ notation. The ‘circular’ score makes clear the ’roundiness’, the perpetual circularity of the piece but is bad for performance; the ‘square’ score is good for performance but obscures the piece’s ’roundiness’. There’s no perfect notation I suppose, it’s tradeoffs as usual.
As for the origins of this song, the earliest printing is from 1852, published with lyrics similar to those used today, but with a very different tune. It was reprinted again two years later with the same lyrics and another tune. The modern tune first appears with these lyrics in 1881, mentioning Eliphalet Oram Lyte in The Franklin Square Song Collection, without making it clear whether he was the composer or adapter of the melody.
It’s easy to dismiss it as a trifling children’s song, but the words are worth attention: Row your own boat gently down the stream — not up the stream! Literally “go with the flow!” Then… “Life is but a dream”. Yes, a dream from which we will all awaken all too soon. The cycle/circle of Life — an eternal musical round in which singers join in for a time, and step out as others take up the Everlasting Song.
P.S. The word ‘mandala’ is Sanskrit for ‘circle’. Hmm…
P.P.S I am definitely not the first to notate canons in a geometric way: