Also as a further piece of information, I plan on using this in musical context, so buffering must be kept to an absolute minimum to avoid delays in the signal.
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Looking at the datasheet you linked, that codec doesn’t support I2C, only I2S. This codec, however, supports SPI.
If you still want to continue to use I2C you might want to check https://communities.intel.com/message/343414#343414 . This thread discusses the I2C performance of the Galileo.