Comparing The Frequency of Two Signals With Periodogram

I have a series of distorted sine waves that I am trying to determine the frequency of. It would appear that the periodogram function should allow me to do this but I am a little confused by the results.

I know my signals should be sinusoidal waves, so I decided to compare the results of periodogram on my 'ideal' and distorted ('turb') signals, both of which are 1x360 vectors, with the following code:

rotation = (0:length(ideal)-1);
[pI,fI] = periodogram(ideal,[],[],length(ideal));
[maxI,i] = max(pI); disp(fI(i));

[pT,fT] = periodogram(turb,[],[],length(turb));
[maxT,j] = max(pT); disp(fI(j));

fig = figure();
subplot(1,2,1); plot(rotation,ideal,'b-',rotation,turb,'k-')
subplot(1,2,2); plot(fI,pI,'b-',fT,pT,'k-');

which produces a figure like this:

I am not sure exactly what the figure on the right showing the output of periodogram should be telling me but as I understand it, it should show a peak at the frequency of my input function. For the ideal function this should be 6 (i.e. there are 6 oscillations over the course of my measurement). However the peaks of both functions are located at 6.3281. I cannot tell if the fact this is almost 6 is coincidental or if I have totally misunderstood what the periodogram function is telling me.

My question is, am I using the periodogram function the correct way to compare the frequency of two functions and if so why is it returning an inexact result for a perfect signal?

I would greatly appreciate any light that anyone could shed on this topic.