The title may refer to a seat used in Scottish Presbyterian churches to shame people who had committed moral crimes such as adultery or becoming pregnant when unmarried. Since the tune is very jolly it may also be a reference to a parlor game of the same name, where participants write or say something about a player that then tries to guess who made each statement. Or, it may refer to Jenny Geddis throwing a stool at the minister of St Giles Kirk in Edinburgh in 1637, in protest of the new Scottish Episcopal Book of Common Prayer. This is said to have sparked the riot that led to the Wars of the Three Kingdoms. An early version of this melody appears in manuscripts in 1733 and 1734. It is also known as Wrights Rant and Joiners Jig.
Ref: https://tunearch.org/wiki/Annotation:Stool_of_Repentance
Ref: https://thesession.org/tunes/1138
Ref: https://en.wikipedia.org/wiki/Stool_of_Repentance
Ref: https://en.wikipedia.org/wiki/Stool_of_Repentance_(game)
Ref: https://en.wikipedia.org/wiki/Jenny_Geddes
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