Hi AlexT_Intel.
The timer period that I need is 1/44100 that is ~22.675 us. In the original arduino sketch (find attached a simplified version) is done by setting the timer to produce an interrupt with a rate very close to that number (22.675 us). At every interrupt the arduino transfer the audio data to the codec via SPI. One of the problems of not sending the data on time to the codec is that the sound can have 'clicks'.
The attached file contains the main program and part of the AudioCodec.h file (that is #included by the main file).