Convolution Reverb Calculation
First, you have to extract the Room Impulse Response (RIR) of the space from your sine sweep recordings. You can do this by taking the ratio of the FFTs of the  measured response and sine sweep input and then taking its IFFT, rir = ifft(fft(measured, Nfft)./fft(sin_sweep,Nfft)). I generally use Nfft = 2^nextpow2(length(measured))
You can truncate the RIR to $L$ samples, depending on how long the reverb tail is.
Break your music source into frames of $M$ samples.
For each frame, you want to convolve a signal of length $M$ with the RIR of length $L$. The output of the resultant convolution will be $M+L-1$ samples. So you have to pick an FFT size accordingly. Then multiply the FFT of the current frame of the signal, with the FFT of the RIR.
The final step is overlap add.

Here is some MATLAB style code.
% sig - Input signal
% rir - Room Impulse Response extracted from sine sweep
% M - length of each frame
% L - length of the RIR 

nframes = round(length(sig)/M));
Nfft = 2^nextpow2(L+M-1);
conv_sig = zeros(nframes*M,1);
for frame_no = 1:nframes
    sig_frame = sig((frame_no-1)*M+1:frame_no*M);
    conv_frame = ifft(fft(sig_frame,Nfft).*fft(rir,Nfft));
    conv_frame = conv_frame(1:M+L-1);
    conv_sig((frame_no-1)*M+1:frame_no*M+L-1) = conv_sig((frame_no-1)*M+1:frame_no*M+L-1)+conv_frame
end