Piano pitch detection
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Is there an algorithm for finding a frequency without DFT or FFT?

FFT isn't a particular efficient way of building a tuner. Better (and cheaper) methods include auto-correlation, phased locked loops and delay locked loops, etc..  

One example is to use tracking of local maxima and minima to roughly hone in on the fundamental frequency and then use a local oscillator and phase locked loop to track this frequency precisely. This can track a moving fundamental during tuning quickly, continuously, and with great accuracy even if the frequency is low and if the fundamental is weak.