I perform some tests where I run cepstrum pitch detection algorithm over polyphonic sound. Result shows that there is almost always occurrence of lowest frequency of tones played simultaneously. I think this is because the lowest frequency has the longest period. But I do not know if it is true or why it is so. Can you somebody explain this or why there is lowest frequency? Or suggest some publications?
The lowest pitch in a chord is likely to have a large number of its possible overtone frequencies match the actual overtones of other notes in a harmonious chord, leading to a good cepstral magnitude, which looks for spectral periodicity (overtone series's).
However a cepstrum might also find more overtone sequence periodicities at pitches lower than the lowest pitch in a chord.