Male and female voices do not function in the same way for notes above their highest passaggio. The primary reason for this difference is the fact that the female voice is singing pitches in E5 to C6 range and male voices are singing pitches in the E4 to C5 range. The male voice is an octave lower than the female voice.
That is so obvious it would seem redundant to mention it. However it is easy to forget that the harmonics are a numerical expressions of the lowest harmonic (which is also called the fundamental). Thus A4 has a fundamental of 440, its 2nd harmonic is 880, its 3rd harmonic is 1320, etc. A4 is a high note for a male voice but it is within the middle range of a female voice. A5 (880) is a high note for a female voice. Its 2nd harmonic would be 1760. Its 3rd harmonic would be 2460, etc.
Notice that as the fundamental gets higher and higher the harmonics get farther and farther apart. The distance between the Tenor A4 (440) and its 3rd harmonic is, of course, 880. The distance between the Soprano A5 (880) and its 3rd harmonic is 1540.
This spreading of the harmonics as the pitch rises requires a different resonance strategy for the female voice when compared to the male voice.
The female voice tunes the second formant of the vowel to the second harmonic in middle voice (F2:H2). Above about E5, however, the second harmonic is too high to maintain this F2:H2 resonance strategy and the singer must now tune the first formant to the fundamental (F1:H1). (Remember that the fundamental is also named harmonic one)
How does the singer get the first formant space high enough to tune it to the fundamental. Two things are needed. First she must choose a vowel that has a high first formant and the vowel /a/ has the highest first formant. Second she must open her mouth by dropping the jaw because that raises the first formant even higher. Another benefit of tuning the first formant to the fundamental is that it will boost the intensity of the singers voice up to a ten fold increase,
This is the reason that the female voice is really unable to produce a quality tone on pitches above G5 with any vowel except /a/. All the other vowels have lower first formants and it is not possible to raise their first formants enough to tune to the fundamental.
The male voice tunes the first formant to the second harmonic (F1:H2) in chest voice and middle voice. Above about E4 the second harmonic becomes so high that maintaining this strategy produce a yelling quality in the male voice and an eventual disconnect or crack in the tone. To avoid this the male voice must tune the second formant to either the second harmonic or the third harmonic. (F2:H2 or H3). To do this a vowel must be selected that has a high second formant The vowel /i/ has the highest second formant, the vowel /e/ has the second highest second formant. Both of these vowels are preferred by male voices when singing above E4 for tenors, (approximately C4 for bases and D4 for baritones) It is the selection of vowel that makes this transition into the male head voice easier. As one goes through the vowels from /i/ to /I/ to /e/ to /E/ to /a/. the second formant is lower for each succeeding vowel. If you say these vowels expelling air through the mouth without phonation, you will hear the second formant pitch descend as you silently pronounce them in the order given.