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From John Gruber:

Old (non-retina) favicons are 16 × 16 px; a retina favicon is thus 32 × 32 px. The lazy way to support retina is to replace your old 16 px favicon.ico file with a 32 px file, and allow non-retina browsers to scale the image. The proper solution, however, is to create a single favicon.ico file containing two icon resources: one 16 × 16, the other 32 × 32. ICO files support other resolutions as well, but I see no practical utility in doing so.