Tightening of the thyrovocalis only influences (to a certain degree) the frequency of vocal folds vibration. It might also influence the harmonics of the sound produced.
It does certainly NOT influence the format - you probably mean -formant frequency. Formant frequencies are related only to the vocal tract and have nothing to do with the fundamental frequencies and harmonics of the produced sound.
A harmonic frequency - as you mention - is something I don't understand in this context.
I agree with Harm. Vocal cord/fold action affects Fundamental action; Fo action generates the harmonics; their relative strength is determined by state of folds; thicker, shorter has stronger more numerous harmonics that are filtered by vocal tract.