For the "Hanning" windowing, with no discontinuity until the second derivative, the tails of the first peak that fall off more rapidly (actually as the fourth power of the frequency difference) than for the other window functions, so that smaller magnitude harmonics are evident:
This uncovers the phenomenon of aliasing: the peak at a frequency of about 6.25, that does not appear harmonically related to the fundamental, is actually the 9th harmonic that has benn "folded back" into the Nyquist range by reflection across the Nyquist frequency /(dt x Interval). This type of artifact can be reduced by increasing the Nyquist frequency, so that only neglibly small harmonics suffer this fate. This is done by increasing the sampling rate, i.e. decreasing dt or Interval:
The cost, of course, is that the resolution of the peaks is reduced, unless more points are used, which in turn takes more data.
Changing the number of points changes the resolution, but not the frequency range covered: