This is based on Latin clarus 'bright' with the metaphorical meaning 'diluted'. Its motivation is quite understandable with regard to the watery and less opaque BUTTERMILCH. Analogous forms are documented in FEW, 2, 739 under clarus.

Wartburg, Walter (1922-1967): Französisches etymologisches Wörterbuch. Eine Darstellung des galloromanischen Sprachschatzes , Basel, vol. 20, Zbinden

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