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Usually, the acetic acid is produced by a double fermentation, converting simple sugars to ethanol using yeast, and ethanol to acetic acid by acetic acid bacteria.
Reggie Smith's instructions for simple homemade wine vinegar:
Buy any wine and then add 1/2 teaspoon of 3% hydrogen peroxide (standard drug store strength) to the full bottle (standard 750mL wine bottle), shake a few times to mix and wait a couple of minutes. The sulfites are gone!
For best results, cut the wine with 1 part wine to 1 part water; vinegar has difficulty forming over 10% ABV and wine that ferments in-bottle usually has to have a lot of alcohol evaporate out first. Then add about 8 oz of unfiltered vinegar (with live mother), cover with breathable fabric of paper towel, and let sit. In a few weeks, you should have vinegar with a mother on the surface!