In the male voice lower and mid ranges, (what has been traditionally called the "chest voice"), the harmonic structure of the sung tone contains many partials - harmonics, which fit nicely into the pattern of resonances for any particular vowel chosen. Throughout this range, the strong, lower harmonics are reinforced by the first vowel resonance corresponding with Formant 1, (F1), midrange harmonics are reinforced by the second vowel resonance from Formant 2 (F2), and higher harmonics are emphasized by the higher "twang" or "singer's" formant resonances. The combination of multiple, powerful low, midrange, and high harmonics present in all vowels is a distinctive characteristic of this section of the male voice.
In contrast with this, in the male high range, (what has been traditionally called the 'head voice'), the harmonics produced by the voice are higher in frequency and more widely spaced. Here, few of the harmonics fit into the vowel resonance pattern. For one particular span of notes in the head voice, there is no significant resonance available to amplify the lowest two harmonics produced.
To achieve vocal power and consistency of tone in the high voice, the male singer uses what he has available, "twang" (singer's formant) and the resonance from F2 strengthening harmonic 3 or 4, depending on vowel.
Between these two resonance strategies is a region of transition, too high for the 'chest voice' strategy, and too low for the F2 alignments of the 'head voice' strategy. This transition region is the passaggio.
Acoustics of the rising fundamental
Throughout the voice, as the fundamental frequency moves, the alignment of harmonics and resonances for a vowel changes. On an upward-moving scale or leap, the fundamental and all the overtones rise in frequency. Since the harmonics are spaced at multiples of the fundamental, the harmonics also get farther apart, too. For most of the chest voice range, this is not an issue, as the resonance from F1 covers a wide frequency range, and midrange harmonics are close enough together for at least 2 or 3 of them to get some benefit from F2. These conditions apply to all the vowels. However, in an upward pitch pattern, as the voice passes middle C (C-F, depending on voice type) eventually the scale reaches a region in the voice where the alignment of harmonics to formants is no longer advantageous. Overall vocal power and tone quality will be lost if an adjustment is not made. The particular point in the male voice where this occurs is as the 2nd harmonic passes F1.
Visualizing harmonics and the /e/ vowel in a spectragraph
As illustration of this, what follows is a series of spectragraphs made with different fundamentals sung to the vowel /e/ (ay), made using my own, baritone, voice. As representative of a lower chest voice tone, the first is of the A natural just a bit more than an octave below middle C , also known as A2. Each vertical blue line represents the intensity of a particular harmonic, where 'up' = louder. Low frequency harmonics start on the left side. The leftmost peak is from the fundamental, and if you look at each peak to the right of that (increasing frequency of harmonic), you can see that the 4th harmonic is the very tallest, and then the peaks become successively shorter.
This peak volume for the 4th harmonic, and the emphasis of those surrounding it, is the result of Formant 1, F1 in its position for /e/ in my voice. Harmonics to the 'left' of the formant center get progressively louder as they get nearer to it, and those to the 'right' of the formant center get softer.
Proceeding to the right is a section of quite harmonics, not so tall in the display, and then there is another build up to the 13th harmonic. This is the area amplified as a result of the location of Formant 2, F2. The spacing of F1 and F2 is what makes this vowel sound like 'ay' to the listener.
After another gap, there are two more areas of emphasis, which are the result of F3 and F4, clustered together. These formants move very little vowel-to-vowel, and form the high frequency 'brightness' resonances of the singer's formant.
The reason we start with this: for any given vowel pronunciation, (like /e/) the formants stay at the same locations even while the fundamental (and the associated harmonics) are moved during the production of different notes. Especially important in the understanding of the male passaggio is the relationship of F1, F2 and how the harmonics align with them.
A2 on /e/ vowel.
As mentioned earlier, for any given sung note, harmonics are always the same frequency distance apart. That frequency spacing is the same frequency as the fundamental... the note being sung. So, if a fundamental is 110 cycles per second (like that A2,) all the harmonics will be 110 cycles apart from their neighboring harmonics. You can see this equal spacing in the picture above. Because of the closeness of the harmonic spacing, you are able to see pretty well the 'shape' of the formant regions.
Up an Octave
The next picture is of the same /e/ vowel, but singing the A up one octave, the A just below middle C, A3, which is 220 cycles per second. Notice that the peaks are farther from each other than in the prior picture... now they are 220 cycles per second apart.
Looking at the peaks for a moment, you can see that the amplification effects of F1 and F2 are still in the same place (left to right), but now different numbered harmonics are boosted, and fewer harmonics are affected by each individual formant. In the case of F1, the 3rd harmonic is now the most emphasized, with the 2nd harmonic also getting some help, while F2 is emphasizing the 7th harmonic tremendously, but not much else. This excellent alignment of F2 with a harmonic makes it really ring distinctively, and is an example of 2nd-formant tuning, which will get discussed later.
Finding the exact location of F1 for /e/
Are you curious about the exact location of F1? Look at the bottom of this next picture, right beween harmonics 2 and 3. See the blips? All voices have some soft, non-harmonic noise. When that noise falls under a formant, it gets amplified enough to measure. These low blips on the spectragraph are the giveaway to the location of the formant.
A3 on /e/ vowel
Continuing the scale upward
As I continue up the scale from A3, three things happen due to the musical intervals represented by the harmonics:
1) My 2nd harmonic gets closer and closer to F1, strengthing that harmonic. This makes the warmth of the voice 'bloom' in this region, and the resonance makes it possible to oversing some and still get away with it.
2) My 3rd harmonic gets higher above F1, and so it gets progressively softer. In combination with #1, this changes the tone quality somewhat.
3) F2 tunes to successively lower harmonics.
These three trends are very important in understanding the male passaggio.
More on 'What happens when a harmonic rises above a formant'?
As a particular harmonic rises above a formant center, it rapidly decreases in intensity. In this next picture, now singing Bb3 (up just one half step from the A), you can see the effect on the 3rd harmonic. It is quite softer now when compared to the 2nd harmonic. For this note, the principal power of the vowel is being carried by the 2nd harmonic. You may also note that the F2 tuning is emphasizing harmonics 6 and 7 more or less equally. That is because F2 is between them. Harmonic 7 is no longer in the 'ringing' position, and harmonic 6 is not yet high enough to be there.
Bb3 /e/ vowel
The male upper chest voice
My voice is now in the 'fattest' part of the upper chest voice, where most of the vowel power is coming from the 2nd harmonic. This range is just about a perfect 5th wide, because that is the spacing of the 2nd and 3rd harmonics. The region begins as the 3rd harmonic passes F1, and ends as the 2nd harmonic passes F1, in other words, for my /e/ vowel, from the Ab below middle C, to the Eb above middle C. This is what makes my voice a 'low baritone' quality. (Note, you can still see the noise blip.. its getting closer to the 2nd harmonic the higher I sing)
Now, the Db in the following picture. Notice that there are little noise blips on each side of the 2nd harmonic. This indicates optimum alignment of the harmonic with F1, the place where the 2nd harmonic is exactly aligned with F1.
Db4 /e/ vowel
The effects of strong resonance on ease-of-singing
Through the entire compass of my voice, up to this point, lower harmonics have been boosted by F1, which has provided for some cushioning effect for the vocal bands. That situation is about to change significantly as the fundamental rises past this point. A very important challenge to the singer as this happens is to resist the temptation to maintain vocal power via pushing.
And now to the Eb. The 2nd harmonic has just past F1. Its still very strong, but will lose ground very rapidly as I proceed upward. This is the beginning of the tricky section of the passaggio, where the resonance provided to the 2nd harmonic decreases rapidly, and I must, to retain vocal power and tone quality, find another way to shape the vowel.
Eb4 /e/ vowel
My next post, 'Male voice passaggio 102' will discuss the various strategies that can be used to retain resonance through the passaggio.