The wikipedia article shows note frequencies with six significant digits. In the low notes that's a resolution of 0.0001 Hz. To get that resolution at 9,259 samples per second you would need an FFT size of 92.5 million samples (185 megabytes). That is not going to happen on an Arduino in any reasonable amount of time.
Perhaps you can use zero crossings to measure the frequency. Have you looked at any frequency counter sketches?
http://interface.khm.de/index.php/lab/experiments/arduino-frequency-counter-library/