A previous article in this series, called mythbusting vocal strain, argued that the term 'strain' conflates two separate phenomena:
Strain as elastic deformation due to stress, something that happens to the vocal folds and is prone to causing microscopic tearing and subsequent vocal injury.
Strain in the sense of pushing for high notes, ie. the felt need to rely on excessive effort to ascend in pitch.
Today, we will address strain in the second sense, ie. pushing, and see how we can use resonance to avoid it.
Central to resonance is a phenomenon known as constructive interference. This happens when two waves line up so that their combination is stronger. Consider for example a playground swing: the initial push puts momentum into the swing, causing it to move. Since it moves in an arc, the movement becomes increasingly vertical as it departs from the resting position, which causes gravity to increasingly slow it down. Eventually, gravity reverses the direction of movement, but by this point the swing has reached its maximum height, so it will pick up momentum during the descent. Thus, the swing does not simply return to its resting position, but instead overshoots, causing it to move like a pendulum. If there were no friction, this movement would simply continue on forever
A swing however is heavy, especially if someone is sitting in it. Therefore, it needs a lot of momentum, and the initial push is not likely to suffice. If you want it to move in a large arc, you will need multiple pushes in succession, but if you push while the swing is coming towards you, you are decreasing its momentum and making the arc smaller. Yet by pushing while the swing is moving away from you, even if it is just beginning its descent and still moving slowly, you can add more momentum and get a wider arc.
This is known as constructive interference. The pushing can be thought of as a kind of wave that interferes with the movement of the swing — which we can also think of as a wave. For this to work, however, the waves need to match in frequency, thus maintaining the same timing — also known as phase relationship. The initial phase relationship need not produce constructive interference — the person doing the pushing can push even when the swing is coming towards him, so long as the timing matches that of the swing, but in this case, the swing will first come to a complete standstill before the pushing starts actually working.
In singing, both the vocal folds and the vocal tract act like the swing, but to make the topic easier to understand, we will consider them one at a time.
The linear source-filter model
The vocal folds act primarily to modulate airflow. Working together, they constitute a valve that periodically opens and closes. As they open, the increase in airflow causes a buildup of pressure above the vocal folds, which then propagates through the vocal tract. As they close, the airflow above the vocal folds continues, but the airflow through the glottis ceases, causing a vacuum. This vacuum pulls on air particles further along the vocal tract, rarefying them and thus propagating the vacuum.
As a pressure pulse reaches either end of the vocal tract, it is reflected. For reasons that go beyond the scope of this blog post, but which are explained here, the waves are reflected differently at the open end (ie. the mouth) than at the closed end (ie. the larynx). Specifically, high pressure turns into low pressure and vice versa at the open end, which means a pressure pulse must traverse the vocal tract four times (twice back and forth) in order to return to its initial state.
By singing at the resonant frequency of the vocal tract, we are effectively timing the movements of the vocal folds to match the reflected waves, much like with the swing, where we time our pushes to when the swing is moving away. This allows acoustic energy to build up in the vocal tract — gradually, though it is fast enough to seem instant to human ears — much like the swing gradually goes higher and higher as we push it.
To accomplish this when singing a predefined melody, we must constantly adjust the shape of the vocal tract. Since the vocal tract is not a uniform tube, we can adjust separate resonant frequencies independently by changing its shape. For example, we can move the tongue, tilt the head, narrow the pharynx, change the shape of the lips, etc. All of these allow us to modify the resonant frequencies of the vocal tract independently, which is what makes it possible for us to enunciate vowels. This, incidentally, is also why vowel modifications are so important in singing.
Nonlinear source-filter interaction
In singing, things are rarely as simple as they appear at first glance. Therefore, we must consider not only how the movements of the vocal folds excite the resonances of the vocal tract, but also how the sound in the vocal tract excites the resonances of the vocal folds. Fortunately, since the vocal folds generally vibrate in a regular (ie. periodic) manner, their resonances are not manipulated individually and we may speak of a single overall pitch with overtones following a standard harmonic series.
In understanding how reflected waves impact the movement of the vocal folds, a key term is phase relationships, which was covered briefly in the case of pushing a swing. Very briefly, we may say that when two waves have their peaks aligned so as to produce constructive interference, the waves are in phase. Conversely, when they are misaligned so that the peak of one wave corresponds to a trough of the other, we may describe them as being out of phase. If the waves are maximally misaligned, we may say that they are 180 degrees out of phase.
Airflow through the glottis is constrained by the movement of the vocal folds; the air can only escape when the vocal folds are apart and the glottis is open. In the case of the incident wave entering the vocal tract from the glottis, acoustic theory shows that the pressure is in phase with the flow. What this means is that the pressure approximately follows the glottal area — if we set aside reflected sound and focus only on the incident wave, that is.
Ideally, we want the reflected pressure from a previous pulse to arrive while the vocal folds are moving apart, and for reflected vacuums to arrive while the vocal folds are coming together. This means we want the reflected sound to arrive a bit early, which means we want to sing a bit below the resonances, or from a more practical perspective, to tune the resonances slightly higher than the sung pitch. In terms of the singer's sensation, this will be experienced as being "on top of the note" as opposed to "reaching for the note" or "pushing".
Pitch ceilings, voice cracks, and pushing
Having reached the practical section of the blog post, it seems fitting to begin with a practical demonstration. Here is a video in which YouTube creator Physics Girl tries to sing sirens through a PVC pipe, and finds that discontinuities — or voice cracks — inevitably appear around its resonant frequencies.
The pattern seen here will probably seem familiar to many beginning singers, especially those who struggle a lot with close vowels like EE (IPA: /i/) and OO (IPA: /u/). There will be these strange pitch ceilings that you run into; it will seem impossible to go higher without a voice crack, and as you go closer to the ceiling you will find yourself having to push more and more.
As Professor Joe Wolfe indicates in the video, these pitch ceilings actually correspond to the resonances of the vocal tract. Because the phase relationships between the vocal folds and the reflected sound differ above versus below resonance, we cannot sing exactly on the resonance. Also, since the phase relationships when singing above resonance are more conducive to falsetto than to modal, we are liable to experience voice cracks when trying to sing through a resonance.
As mentioned earlier, we can modify the resonances of the vocal tract independently, which is not possible with a PVC pipe. Relying on this, we are able to sing through one resonance by compensating using another resonance, which is why we do not necessarily experience a voice crack when singing through a resonance.
Alternatively, we may of course wish to stay in the lower acoustic register, but take it higher in pitch. Perhaps we enjoy the rich open sound that results from keeping the second harmonic just below the first resonance of the vocal tract (ie. yell-timbre or F1/H2 tuning, or perhaps we are singing a dramatic climax and desire a volume that is hard to achieve with a weaker resonance tuning. In such a case, we need to find ways of elevating the resonance as we go up in pitch which typically involves some combination of opening the mouth, raising the larynx, adding twang, moving the tongue, and modifying the vowels.
Seeking to avoid a voice crack, and either wanting to stay in a lower acoustic register or simply not knowing how to transition to a higher one, some singers will try to simply push closer to a pitch ceiling (from a vocal tract resonance), using an increased amount of medial compression and support power. However, in many circumstances, pushing in this manner does not enable singers to simply ignore the pitch ceiling, only to inch slightly closer to it. Even in this approach, it is still necessary to raise the larynx, open the mouth, etc., which is likely the reason why these adjustments have often been associated with pushing and improper technique. Such a singer would be well advised to simply make these modifications before starting to push, instead of making them only after having pushed as close to the pitch ceiling as possible. This has sometimes been described as "singing on the resonance" or "singing on the harmonics", and it is what provides the aforementioned sensation of "being on top of the note".
Good mixed voice and bad mixed voice
Since mixed voice typically features thinner vocal folds and weaker resonance tunings than chest voice, singers will often make up for the loss of intensity by increasing medial compression (ie. squeezing the vocal folds together). This adjustment is also often a necessary component of formant/harmonic crossings (ie. of singing through a resonance), and is even a necessary component of certain mixed voice coordinations that would otherwise go to falsetto.
This limited amount of squeezing is generally harmless, though marginally less efficient than coordinations that rely less on it. It however also has the interesting side effect of decreasing the overall amount of nonlinear source-filter interaction, and since it typically goes along with less narrowing of the epiglottic funnel, the vocal tract resonances are also weaker to begin with.
Some singers wind up using these properties of medial compression to construct a mixed voice that minimises the effect of vocal tract resonances. Since chest voice is more dependent on resonance tuning, these singers will tend to avoid it even when singing loudly, preferring to further increase medial compression instead of relying on the thyroarytenoid muscles to make the vocal folds thicker.
Conversely, a more efficient mixed voice singer will still rely heavily on resonance tunings in mixed voice, and when going from chest voice to mixed voice, instead of wholesale replacing thyroarytenoid activity with medial compression, they will simply decrease the thyroarytenoid activity. In particular, they will not stretch the vocal folds more than is required to produce the combination of pitch and intensity they are looking for.
Though the other approach requires more support power and thus makes loud volumes a lot more tiring, this is still relatively benign. However, we are at this point getting very close to a very troublesome phenomenon: squeezing spirals.
Squeezing spirals and vocal deterioration
Going high in pitch, mixed voice will naturally become belty and dramatic, making it more advisable to transition to falsetto if a mellow sound is desired. Singers who have not learned to make this transition seamlessly, and do not wish to have a voice crack may however simply try to make their mixed voice sound more "heady"by making it even thinner, less twanged, and consequently, more compressed.
Conversely, going low in pitch, mixed voice is liable to become weak and tonally inadequate. This is where it is necessary to switch to chest voice, but singers who are either timid or habituated to relying on medial compression for volume will tend to avoid this switch. In order to achieve a fuller sound, they instead lower the larynx, maintaining the pharyngeal narrowing often characteristic of mixed voice, and simply add a lot more medial compression. This way, they construct a "fake chest voice" that requires them to stretch their vocal folds even further when they go back up in pitch.
A singer singing in this way will notice considerable deterioration in their clarity of tone, dynamic range, etc., throughout a session of voice usage, which they will erroneously attribute to vocal overuse since it seems to subside with rest. If the technique is not adjusted, however, they will become just as squeezed and thin-sounding the next time they sing, and it will likely take less time on each subsequent occasion.
Thus a lengthy deterioration begins, often spanning several years, with the singer sounding increasingly introverted, the vocal folds becoming increasingly stretched and thin, and an increasing amount of support power being required to overcome the ever-increasing medial compression. This marked deterioration will typically make the singer speculate about vocal damage and make an appointment with an ENT. The subsequent laryngoscopy will show atrophied thyroarytenoids, sometimes to the extent of having bowed vocal folds and a total inability to achieve complete closure of the glottis.
I am not suggesting that all cases of laryngeal wasting are attributable to squeezing spirals — there is of course also such a thing as genuine vocal fold paresis — but it is telling that such diagnoses, including that of vocal fold paresis, seem to be much more frequent in schools of singing that demonise the use of chest voice and advocate the use of mixed voice for absolutely everything.
While squeezing spirals may seem scary, they do not have to be. They can be largely prevented by making sure to work on a strong, "unmixed" chest voice once in a while and making sure you return to a relaxed chest voice once in a while when singing, especially when going low in pitch. If you find yourself caught in a squeezing spiral you cannot break out of, being stuck in mixed voice, you need not panic; simply go low in pitch, working on open vowels for a while with a bit of twang, a low-ish larynx, confident onsets, and a relaxed inflection. Once you have found your chest voice again, try taking it up in pitch, at least to the upper half of the third octave or so.
Summary
The vocal tract has resonant frequencies which can be adjusted individually by moving the tongue, lips, etc., which is how vowels are formed.
When singing, especially in chest voice, we tune vocal tract resonances to match the frequency of the sound produced in the larynx (or those of its harmonics)
Acoustic energy from the vocal tract feeds back into the vocal folds and either sustains or dampens their oscillation. To sustain it, we typically need the vocal tract resonance to be slightly higher than the note or overtone we are tuning it to.
The sensation of "being on top of the note", as opposed to "reaching for the note", is caused by good resonance tuning.
Pitch limits and voice cracks are generally caused by getting stuck in a particular resonance tuning and being unable to take it higher.
These effects are less pronounced in mixed voice, especially if there is a lot of medial compression, very little epiglottic constriction, and very little thyroarytenoid activity.
Relying on mixed voice for everything, especially low notes with loud volumes or high notes with low volumes, will tend to cause a "squeezing spiral", ie. a gradual increase in pressing and a gradual decrease in the fullness and clarity of the tone.
Squeezing spirals are easily avoided or reversed by working on chest voice in the lower range, and by returning to chest voice when a song goes low in pitch.