Kashu-do (歌手道): Second Formant, The Foreign Resonance

Vowel recognition is determined by two acoustic energy bands we call 1st and 2nd formants (i.e. F1 and F2). We can identify three other formants that cluster to form what we refer to as the Singer’s Formant. The subject of this particular post is the 2nd Formant or F2 for short.

The following vowel formant chart below gives the center values for the formants of the most common vowels.


A slight alteration of these values, +/- 20 Hz will not change the vowel drastically in terms of recognition. However such a modification may help tune the vowel more precisely to the relevant harmonics of the sung pitch (which are fixed, i.e. unalterable).  As pitch rises or falls, it becomes easier to tune one formant more easily than the other. Sometimes fundamental frequency will rise above F1 and so, F1 can no longer coincide with any of the harmonics of the sung pitch. In such a case, F2 becomes the more viable formant. Such is the case in the female middle voice and in the traditional male upper voice (counter-tenors voices behave similarly to female voices). It is no coincidence that the female middle voice and the male upper voice are the most challenging areas for the average singer.

The primary reason is the following: singers, like everyone else feel a strong attachment to their speaking voices, which is F1 dominant for both males and females. F2 resonance simply feels foreign relative to the speaking voice.

When the F2 area is reached, singers are aware that something must be altered in order for the voice to feel coordinated. There are fundamentally four choices in descending order of efficiency:

1) *Covered tone: Maintain balanced phonation (i.e. excellent closure/weight balance) and slightly modify the vowel to encourage F2. This is the best choice. But the new resonance will feel a little strange at first, as if the singer were abandoning natural speech. In fact, the singer would be abandoning the acoustic pattern of daily speech. However, if the modification is done well (particularly if phonation balance is maintained), the singer does not feel a great difference from F1 dominance to F2 dominance.

*The term covered is deceptive. It is more appropriate to the area of C#4 to E4 and C5 to E5 in male and female voices respectively. The rounding of the lips that define the term, covered, lowers both formants, a strategy that works in the lower passaggio. This is not efficient in that the desired effect at the higher points of the acoustic passaggi, around F4 and F5, is to lower one formant and raise the other. In such a situation, I recommend a smiled schwa as in the inhale before a sneeze.

2) Open tone: Maintain balanced phonation and modify the vowel considerably to follow F1 (maintaining the speaking voice). This may sound slightly awkward because the vowel modification might sound too extreme.  This is however not altogether bad. In this particular case, to maintain F1 dominance beyond the F1 threshold has the bad result of causing the larynx to raise, robbing the singer of natural warmth. The resulting sound will be at best, one-sided (chiaro without enough scuro), and at the extreme, shrill! Still, the resonance adjustment would be viable and would give presence to the voice.

3) Spread tone:  Losing the phonation balance because the resonance adjustment causes the formants to fall between harmonics. In such a case, the acoustics of the vocal tract go against the needs for glottal closure. An  inappropriate acoustic adjustment interferes with efficient glottal oscillation just as appropriate acoustic adjustments encourage efficiency.

4) Loose phonation: There are many singers who produce a slightly breathy tone at the acoustic passaggi, thinking that they are producing a covered tone. When the tone becomes slightly breathy, it takes on a mellow quality that sounds somewhat like a covered tone. The difference is that in a properly covered tone, the glottal efficiency is maintained, while in loose phonation the glottal efficiency is compromised in order to produce a rounder tone. This glotta adjustment is heard frequently in the top of the male voice and in the middle of the female voice.  This inefficient sound has become idiosyncratic among singers today, to the point of being confused for the proper covered tone. This sound does not work well with an orchestra.

I will post example videos and acoustic analysis in the next few days.


10 thoughts on “Kashu-do (歌手道): Second Formant, The Foreign Resonance

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  1. Interesting read as usual!

    I would like to challenge somewhat (well, moderate may be more accurate) what you say about “open tone” in the register of F4-C5, say. Continuing the resonance strategy with a strong H2 throughout certainly yields an “open tone” a la say Florez or Bergonzi. But not all open tones are like this! For instance, the “open” or “white” sound that Pavarotti demonstrate in the how-to-sing-Bel-Canto video is *not* at all open in this sense! The strongest harmonic in his open F4 is H4, so the sound is definitely not first-formant dominant, even though it sounds “open”!

    Pavarotti somehow was able to generate very strong lower harmonics in this register (H2, H3, H4 of increasing strength), and I believe that when he “covered”, he was slightly darkening this very bright basic sound in order to damp the harmonics just right to get a dominant H3.

    So I believe that one of the key issues is to be able to phonate in a way that generate strong lower harmonics (and not just H1, H2 and a singer's formant). If this is not done, there is no chance, I believe, for the voice to “turn” the resonance strategy, since the right harmonics will just not “be there” at all!


  2. Thank you Martin,

    Your moderation is on point. NO disagreement. What I have precised here before on the blog is that we should seek a two-formant strategy (i.e. the relationship between F1 and F2 says a lot about the rest of the spectrum). You might remember in the masterclass in Berlin that I emphasize the importance of the chest voice in balancing the voice as a whole. The lower harmonics that makes the voice “turn” almost spontaneously is due to the strength lower harmonics, which in my opinion coincides with the level chest voice content (i.e. vocalis activity).

    Now a turned voice does not have to be rounded at all (which I explain above in the post). In that sense Pavarotti makes a crucial error in talking about his F4. The one he taught was open was turned and the one he taught was turned was open (in a manner of speaking). I characterize an open tone as F1 dominant and a turned tone as F2 dominant. Rounding the tone in the way Pav explains does not necessarily induce F2 dominance which is the goal.

    In short, F2 dominance in the male high voice or the female middle voice depends in great part on the strength of the lower harmonics you mentioned, which is related to chest voice content. The voices that do not turn lack chest voice (lower harmonics). When we hear Florez or Di Stefano, we hear voices dominated by the higher side of the spectrum. They do not access F2 very well until extremely high in the voice (Bb at least). Even Pavarotti who is overall excellent tends to lack vocalis strength on F4 particularly. This note gave him problems. He could not always sing it softly and he resorted to breathy singing to compensate.

    Caveat: F4 on [a] is not a note/vowel combination that must be turned. We have choices there depending on musical/dramatic considerations. F4# is a different world. That note is better turned.


  3. Mostly, I can follow your line of though here (and it makes perfect sense to me) except perhaps your second paragraph. The one he taught was open was turned and the one he taught was turned was open (in a manner of speaking). Hmm; if I understand you correct, I think I have to disagree.
    He sings one “open” or “white” F4 and one “covered” F4. The covered F4 is *definitely* “turned”: it has a beautiful H3 dominance. And I think it is a fair terminology to call his “open” F4 just that, “open” or “white”. This is how it sounds, even though it is a different open sound than shouting quality of a H2-dominant open sound.

    It is somewhat ironic, though, that Pav in a musical context typically sings F4 open (as you allude to in your last paragraph)!


  4. My memory of the notes in question is that the F4 he calls turned remained H2 dominant and the one he calls open was H4 dominant. But perhaps I remember it wrong.

    The more significant point is that rounding does not necessarily turn the voice unless the lower harmonics are strong. In fact, depending on vowel choice, rounding is not an absolute above E4b in order to access F2 on H3.


  5. The open F4 is indeed H4 dominant, but the turned one is beautifully H3 dominant. See the picture at


    I interpret these spectra as a very strong production of lower harmonics (possibly assisted by some sort of nonlinear mechanism a la the one Titze has proposed) that, in the covered case, is carefully mediated, or filtered, by minute shape changes in the pharynx and/or mouth shape to give the desired vocal color. This “filtering” is what I believe Pavarotti recognized as “covering”.

    I absolutely agree with your second point. The F2 will be there, the question is whether there is any strong harmonic content in that region.


  6. We are getting into the interdependency of the source tone and the filtering mechanism. Traditionally in science-based vocal pedagogy (new information notwhitstanding)we have been made to believe that we should more or less leave the source alone and that we have greater control of the vocal tract than we do the glottis.

    You are right when you say:”The F2 will be there, the question is whether there is any strong harmonic content in that region.”

    We have to be able to create a tone strong enough in all harmonics to have subtle control over the vocal tract adjustments.

    The Pavarotti clips are fascinating. The covered one yields the F2 on H3 as we see traditionally in good tenors. For my money this is a better sound because of the balance between F1 and F2. They should both be strong with one slightly dominating. In my experience (and this a theory only), when both F1 and F2 are strong, the balance between fold depth and closure is almost optimal.

    In the open clip, F2 is dominant but but on H4. To do this, the low harmonics have to be sacrificed. I believe the folds become less deep to accomplish this. Not enough vocalis activity. The tone would be also borderline pressed. It is also not necessary to round the vowel the way Pavarotti did to achieve F2 on H3. I believe he knows the resonance sensation that produces this adjustment and just does it. Unfortunaly, it is associated with rounding, a concept attached to the idea of a covered tone. This rounding might be interesting as a vocal coloring in certain contexts but not necessary for the F2/H3 adjustment.

    A question: On the Gedda “m'ama” how is the distribution of energy between F1 and F2? Is it that both are strong and F1 on H2 is slightly stronger than F2 on H3? Without doing the analysis, that would be my guess!


  7. My hypothesis was that the difference between Pavarotti's open and covered F4 was primarily in the “filter” and not in the “source”, whereas you seem to argue that there are major differences in the source productions as well. OK, after a re-listening (from How to Sing Bel Canto I on YouTube), I realize that you may be right; the source production does sound “fatter” in the covered case.

    Regarding Gedda (for other readers: this regards a section of him singning M'ama si m'ama from Una Furtiva Lagrima in a recording where the register shifts are unusually audible), he turns the voice very clearly precisely on Gb4. I cannot really see support for your hypothesis in the spectra: comparing the Gb4 with the F4 before and after the audible register shift on m'ama, the difference is about 6dB between H2 and H3 in both cases (H3 6dB stronger than H2 on Gb4 and H2 6dB stronger than H3 on F4). The difference in the spectra is mainly in H4, which is stronger on the F4 plus a somewhat stronger singer's formant on the F4.


  8. So this is article focuses exactly on what I am working on. Thank you.

    I have just a couple of questions: please, what does “turning the voice” mean?

    Also, about lip rounding, Titze is one of the vocologists who encourages lip rounding, saying that a narrowing of the Vocal Trakt and the lip rounding are “additive”,and encourages the impedance of the Vocal Trakt and supra glottic pressure (Titze, Vocology)

    I am a little confused, because I did believe a gentle lip rounding (not forced) would help pharyngeal resonance and help phonation thanks to the impedance.


  9. HI Math Flair, “turning the voice” or “girare” in Italian is used to indicate the change from F1 dominance to F2 in the mail passaggio and female lower passaggio. Some like to use the terrm “cover” especially when lip-rounding is used.

    Although lip rounding has impedance properties, the effect is too global in a one-sided way. All formants are lowered, when in most cases we want “divergent” effects on the two lower formants. Impedance can be accomplished without lip-rounding when the larynx is low enough. The increased room and vowel shaping can create impedance effects based on acoustic adjustments. This gives more independence to articulators (tongue, lips, laryngeal-migration, jaw). Rounding feels nice to singers and it's an easy control. If you look at the majority of top singers, they do not use lip rounding. Impedance through the deepening of the pharyngeal space requires a vocal fold posture that encourages flow. It is all inter-dependent.


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