Very high precision zero crossing detection
You'll likely want to measure the total of many zero crossings (and divide by 'many' before taking the reciprocal).. or average many measurements.. otherwise noise in the signal will unduly affect your measurement, and you don't need the answer that quickly. 

You can measure easily to a couple hundred nanoseconds with a typical 8-bit micro (so 200ns in a 5kHz note would give you 3 digits) but that doesn't translate necessarily into results anywhere near that stable or accurate.