What 'élevage' means
Élevage ('raising') is everything between fermentation and bottling: the vessel, the time, the oxygen, the lees. It's where a wine is shaped and stabilised.
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Oak does two jobs
Oak adds flavour (vanilla, spice, toast) and lets in a little oxygen that softens tannins and matures the wine. New oak gives more flavour; old/neutral oak gives mostly gentle oxygen.