At a sample rate of 96kHz, each "cycle" at 4152 Hz, is 23.121 samples. You can only do integer samples. And 0/0.121 is 8. At 4000 Hz there are exactly 24 samples per cycles. The former has spurs in the FFT at Tone Frequency / 8, the second has no spurs.
As a result, rather than having the last sample used in the FFT being equivalent to the one before the first sample, its somewhere in the middle. And THAT is what the FFT is seeing.
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