Since I have not been part of the Higher Education environment for the last fourteen years, I miss out on a lot of interesting publications. What is interesting is that an article by Ingo Titze in The Journal of the Acoustical Society of America dating back to 2014 corroborates the theories I have shared on this blog relative to the necessity of deeper fold adduction. Titze’s conclusions (a culmination of more than a quarter century of research and shared research with colleagues) are so accepted in the field that they inspired research in surgical procedures to achieve the so-called rectangular glottis in phonation. I will attempt to clarify the basics as Titze explains in his article:
Titze concludes there are three muscle groups responsible for different aspects of glottal adduction: 1) The Lateral Crico-Arytenoid (LCA) pair that bring the folds to midline at the superior aspect (upper portion) of the folds. 2) Thyro-Arytenoid (TA), which includes two muscles, vocalis and muscularis, thicken the folds vertically and brings the folds in contact at the inferior aspect (lower portion) of the folds. Finally 3) Inter-Arytenoid (IA) pairs seal the posterior gap to prevent air leakage (IA is less relevant to this discussion since it only prevents leakage beyond the vibratory edge of the folds)
Titze states:
The LCA adducts the vocal processes of the arytenoid cartilages, which bring the superior edges of the vocal folds together…The bottom of the vocal folds is adducted by the TA.
But Crico-Thyroid (CT), the primary function of which is the lengthening of the folds (also called the pitch muscle) has an adductory function as well.
Titze explains further:
What role does CT activity play in registration? Its main function is anterior–posterior fiber stiffness regulation of the vocal fold tissue layers by vocal fold lengthening, but CT also plays a role in adduction. LCA and CT activity are often highly correlated in speech (Atkinson, 1978). One reason is that, when fundamental frequency is high and governed by tension in the vocal ligament (Van den Berg, 1960; Titze et al., 1988), amplitude of vibration is small. Smaller amplitude requires more adduction at the vocal processes to allow the vocal folds to reach contact in vibration.
Titze confirms what I have attempted to explain here–That shallower glottal posture (i.e. convergent glottis, as Titze refer to it) requires “more adduction.”
Thinner tends to be pressed (my words).
In addition, elongated vocal folds are retracted from the glottal midline because their cross sectional area is reduced. This retraction requires further LCA adduction, which adjusts the glottis toward a convergent shape if TA activity is not simultaneously increased (Hirano, 1975). In other words, bottom adduction may not follow top adduction of the vocal folds when CT is much more activated than TA (Berke et al., 1989). At the opposite extreme, if TA activation is strong and the ligament is lax due to little CT activation, a divergent pre-phonatory configuration can be the outcome. Adduction at the top is then weaker than adduction at the bottom. For mixed registration, it is hypothesized that the two extremes are avoided with appropriate muscle balance so that a near rectangular glottis is achieved and stiffness is balanced in the tissue layers. A small convergence angle is probably not detrimental, but large divergent or convergent angles are not conducive to low-threshold self-sustained oscillation.
Titze concludes (perhaps correctly) that LCA (the primary adductory muscle) approximates only the upper portion of the folds and that TA is needed to adduct the lower aspect. He then correlates LCA and CT. He refers to convergent glottis as related to LCA dominance and divergent glottis to be TA dominant. That is one way of looking at it. Far be it from me to question the research of a top scientist far more fluent in his understanding of such matters than I am. Nevertheless, I have a suggestion purely from the singer’s point of view:
I believe that pre-phonatory postures are a result of the singer’s expectation of vocal timbre. If I imagine myself to be a bass, I will tend to expect a deep sound, which might lead to exaggerated TA activity resulting in a divergent glottis. The sound feels like it is rooted in the chest. This posture prevents the folds from closing at the upper portion, which is related to a lack of CT activity (lengthening). That imbalance results in lax vocal folds and result in a rather dull timbre. This, of course begins with the singer’s desire to sound bassy (this would work for a mezzo as well). The opposite can be said for a tenor (or soprano)–that is a tendency to desire brightness over darkness in the voice, resulting in an excessively convergent glottal posture. Naturally a tenor or soprano can desire to be excessively dark just as a bass or mezzo may seek to be excessively bright.
If we take as given that fold posture is primarily influenced by the singer’s imagined sound, then I would explain more simply that LCA is the primary adductory muscle and that the shape of the the glottis will depend on the balance between CT and TA.
Titze concludes that a balanced (or mixed) coordination in the antagonistic relationship between CT and TA will produce a desired rectangular posture that requires less adduction than the convergent (relatively pressed) glottal posture. Ideally, the folds approximate gently along the entire vertical cross-section of the folds.
The rectangular posture gives both richness and brilliance to the tone–In bel canto terms, chiaroscuro.
Titze also mentions that the extreme postures, convergent and divergent, are more stable, which is why more singers tend to find comfort in a one-sided posture (convergent or divergent). The most admired singers achieve a successful tightrope act of balancing CT and TA and regulating breath pressure as to not blow apart the gently adducting rectangular glottis and adjusting vowels in order to achieve acoustic configurations that encourage the dynamic coordination that produces the rectangular glottis.
The singer’s challenge is to figure out how it feels to access the two sides of adduction. How does appropriate TA activity feels such that it produces ideal posture on the lower portion of the folds? And how does one combine that sensation with the sensation of appropriate CT activity to close the upper portion of the folds? That is what we must achieve in voice lessons. The benefits of a mixed (rectangular) posture include an easier, more flexible tone; more dynamic transitions between registers; greater volume control; greater stamina and less wear on the folds. And more!
Lastly, health matters! Our folds’ surface is not always flat and smooth. It is usually somewhat uneven from inadequate sleep or viscosity from inadequate hydration or reflux or allergies or colds, etc. When the surface is uneven, we often compensate by adducting a little more firmly to avoid gaps in the closure (which sounds raspy and produce subharmonics). In so doing, we are creating a chain reaction that results in a more convergent glottis, lacking in depth and causing abrupt register changes. Achieving this balance is the singer’s daily work for a lifetime. Additionally, achieving balance in speaking has a great influence on the ability to achieve a mixed (Bi-stable fold adduction, per Titze’s article) posture in singing.
Copyright 4 December 2020
KASHU-DO 
I’m not sure that’s the case Tee Square. Caruso, Del Monaco and Corelli (add Giacomini) are the most substantial tenor voices we have in the top range. The rectangular model does not necessarily sound dark (as the folds are adequately lengthened). It’s a continuum. Pavarotti in 1961-1970 sounds more (robust) than the later incarnation. Most people prefer the early Pav. Does not sound dark at all, just fuller. When we compare those guys to Kraus or some of the Rossini tenors, the latter group seem to “converge” more. I would argue Corelli, Del Monaco, Caruso and a host of other great tenors are “rectangular”. The divergent tenors sound hollow, lacking in brilliance (I sang like that at the beginning of my change from baritone to tenor). BTW great baritones and basses shouldn’t lack brilliance either. Siepi was revered as one of the greatest basses of all time and sounds almost baritonal compared to many who over-darkened. I will give you this though, Titze recommends a posture that is slightly (1-3 degrees angle) convergent. This makes sense to me. We want to guarantee good closure at the top of the folds, which I believe helps with the clustering of formants 3-5 (the Singer’s Formant).
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Thank you! I’m not a vocal scientist, and to be honest, i haven’t been able to grasp your latest reply entirely. But thanks for the information. Definitely more food for thought. I guess when i have more knowledge, i’ll be able to understand it.
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Neither am I, Tee Square! I’ve just read a lot over the last 35 years. I might get brave and learn physics. What I mean is that convergence (pressing) is our tendency as we go beyond the upper part of the passaggio. It’s not a range we use in everyday life. For most of us, it is difficult at first to maintain a rectangular shape up high (especially if we depress the larynx to achieve it). We’re not machines, right? We should try to fight the tendency to thin out too much by desiring a little more fullness. But let’s say that the natural tendency in the high range is to “converge”. So even the greatest tenors, like you say, would not always achieve a perfect balance and better they go a little thin than lose upper closure. Now I’m making your argument! This is good!
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+> I guess i don’t understand when you say “I wonder if CT is not the key in convergence, which is why convergence tends to occur at higher F0s”. I’m serious. English is not my native language. And i really don’t understand why you are using “I wonder if” and then “which is”, from a language standpoint. But i’m afraid that i might be asking too much. I don’t know if i might be culturally insensitive, to be honest.
+> And also from your reply, i just realize something. When i sing my low notes, i can sing it thin and pressed but then i’m able to gradually add more depth to it, (by trying to lower the larynx without the tongue). But then when i get to higher notes and try to do the samething, singing thin and trying to lower the larynx to get more depth, it’s not that easy. And from titze’s conclusion, it means that the higher we go the more CT gets active, which makes adding more TA adduction difficult.
+> Here’s my opinion. Just because CT activity increases with pitch, doesn’t mean it only dominates the high range. You said that you only extrapolate from titze conclusions, right. Maybe CT gets dominated at pitch below the passagio? There’s 1 study that challenged this TA dominant low range and CT for the high range. You can read it here:
https://ir.uiowa.edu/cgi/viewcontent.cgi?article=4994&context=etd
Even though this study only has few participants, who are not trained singers, it’s still an interesting one i think. But all of this is just my opinion. What are your thoughts? Thanks.
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I fluent in 7 languages and conversant in a couple others. I write in English because it was the language of my higher education. So no offense taken. Beyond that English grammar is evolving. I could present the thought as a question? “Since convergence occurs at higher frequencies, is it possible that CT (the pitch muscle) is primarily responsible for it (convergence)? I know the paper very well. The measurement of muscle activity is also a bit of a red herring (meaning impossible to confirm any conclusion). Muscular stress depends on the strength of the muscle in question and it’s “at-rest” influence on the system. The passaggio area relies on increased TA activity to counter the natural CT activity. Does that measured increase means greater work is being done by TA at that juncture? Not necessarily. What it does mean is that both muscle groups are active in achieving balance, that TA is not passive in the upper range. That paper and the many conversations that lead to it are very important. What I’m saying is that in the tug-o-war between CT-TA, it might be practical to define dominance in terms of excess in one direction (convergence) or the other (divergence). Thank you for this wonderful discussion! I don’t need to be correct. I hope to learn more!
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Thanks for the explaination and the discussion too! And also thank you for your positivity. It would be great to be able to conduct the same or more experiment on old and great singer. I’m looking foward for your next posts!
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The problem in operatic singing is that we’ve lost objectivity. People always had preferences, but there were criteria to what was considered operatic. Today, the science goes backwards (e.g. “I like this sound. How can I spin the science to support my preferences?”). Beauty and viability in the hall with an orchestra don’t need to be mutually exclusive. The voices of the greats are called old-fashion and schools are more interested in teaching pop techniques, claiming opera is obsolete. But I will continue researching the old and greats! We must build on what they did. To do that we must become at least as good as they were, not abandon their model. These are challenging times!
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Yes, i see at least one voice teacher like you described. He forced people and themselves to believe in what they think is right (two of the ways are showing just enough scientific information to be persuasive and dismissing people with different ideas). Actually, it reminds me of “this is opera” channel. I think you, I and this is opera crews all agree that generally old opera singers are better. But i really don’t like the way they dismiss other opinions without even considering it. To me that’s a sign of subjectivity. I think the first step to become more objective is to admit that we still have to learn, not to fall prey to our assumptions. And some people, like you said, purposely use assumptions and reputation to spread their belief and influence people. It would be a great to find a way to make of all the people and experts (scientific voice teachers and empirical body sensations voice teachers), who genuinely love opera, sit down and have a professionals discussions on vocal techniques.
And i agree with you on that we should be able to do better than the olds did. Now we have more equipments but we don’t do as good, so that’s an interesting problem there. And i support you on your quest. I guess by keep reading your blogs, since i can’t do any further. Don’t forget that i care about your blogs. There’s still people out there who loves opera and its past. And i hope you can find more of those people so it makes this tough time easier. Good luck!
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i mean great “singers” (plural). And looking foward “to”. Sorry 🙂
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I have to come back here because this specific post have sparked so many ideas in my mind. And mixing and matching those give me some new theories. Just theories, you know. The post might be long but please bear with me. Thank you!
So do you remember last time i asked you whether TA inferior adduction fuction and thickening are the same? And you said yes. And from that i assumed that these 2 functions happens at the same times when this 1 TA muscle is activated. At that point, i thought that was pretty much it.
But then i read these 2 studies below and star questioning things, thus leading to some new ideas. But anyway here are the 2 studies:
1. https://search.proquest.com/openview/458a6dec16b25fa2/1?pq-origsite=gscholar&cbl=5383
2.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1550351/
The first link:
I know you mentioned that there are two TA muscles in your past blogpost several years ago, but at the time i read those, for some reasons i chose to dismiss this information. But i digress. Anyway, we can agree that there are two TA muscles: Thyrovocalis (TAv) and Thyromuscularis (TAm). And they are close to each other (medial one and lateral one). That’s what is established in the first link.
The second link:
In this link, if you scroll down to the Results and then section C (Posturing observations and insights) you will see Titze reported that the TAv has 2 functions: SLIGHTLY ABDucting the vocal folds AND shortening/thickening them (Yes, you read that right, TAv slightly ABDuct vocal folds). The TAm has 1 function which is to ADDuct the fold (Yes, TAm ADDuct the fold)
I would say the TAm properly adduct the inferior part of the folds, since top adduction is responsible by most LCA and IA. So the bottom part of the fold is adducted by specifically the TAm, (not TAv) let’s be clear on that.
But also from the first link, the author suggested that the TAv can work independently of the TAm. This is just a suggestion. i don’t know if they have the same nerve that control them or not. In fact, I could interpret the author’s statement in 2 ways
1. I can change the activity of TAv without changing the activity of TAm (opposite of 2)
2. I can change the activity of TAm without changing the activity of TAv (opposite of 1)
According to Titze paper above, for example if we increase the activity of TAv, we might make the fold slightly more abducted. And this might weaken the adductive tension of TAm. But i’m not sure here. So i’m not sure about statement 1.
But i can’t refute statement 2. In fact i believe that statement 2 is very likely to be correct. You’ll see why when i bring this up later.
Anyway, you might be asking what do all of the aboves have to do with convergent, divergent and rectangular glotal posture?
Let’s use the information on 2 TA muscles that we established earlier to talk about all the 3 postures and how i would fix the 2 extreme ones
Let’s start with Convergence. From your point of view you said that the lack of enough TA against CT and LCA will cause convergence. So what should we do to “cure” covergence?
Answer number 1: Start with convergent posture, increase the activity of the thyrovocalis or TAv muscles. Or in other words, increasing the thickening/shortening action of the system. However, to make sure the system doesn’t convert to divergent due to massive increase in thickening action, we need to at the same time increase the CT and LCA action. (Assumingly we can do these thing by inserting electrode needles into singers muscles like scencetist often do to precisely control the activity of muscles). We do that over and over again but the system will always remain convergent. Why?
If you look at Titze’s yellow diagram of a convergent posture, the root problem is actually the lacking in the bottom adduction. Not the lacking in thickening action. And the TAv doesn’t adduct the bottom part of the folds like i said earlier in the post! TAv job is to shorten/thicken the folds lengthwise, but it doesn’t adduct the bottom part depthwise. Adduction is simply not the job of TAv. That’s why no matter how much we increase the action of TAv and then increase LCA and CT, (maybe through repetitive training) we will always end up with a convergent posture. So increasing TAv activitiy at all is not very useful. And that leads me to answer number 2
Answer number 2: So how to adduct the bottom part of a convergent posture? If TAv cannot do the job, What can? (Drum roll) It’s the TAm – Thyromuscularis! Of course! We already established that earlier! We ONLY need to increase the action of the thyromuscularis to a degree that the adduction at the bottom follow the adduction at the top. Adduction at the bottom is the job for TAm like i said earlier. And i believe there is no reason for CT and TAm to oppose each other, since CT correlated very well to other adductor like LCA for example. And woa la, convergence is solved! Not by increasing TAv action, but TAm action instead.
And from all this Divergence is solvable too. Divergence is just too much TAv without any increase in LCA and CT. i would solve divergence by turn it into convergence (a light cough help sense the influence of LCA to strenghthen it again, with CT) and then increase the activity of TAm to achieve rectangular glottis.
So the overall solution is when we have a convergence, we don’t make TAv more active. Adding more TAv just makes it more convergent (if we grind our LCA and CT harder) and if we keep increasing TAv at one point we’ll flip to divergence (too much thickness that make CT and LCA just give up).
All we need to do when we have convergence is: we try keeping the TAv activity the same, but try to increase TAm instead…Wait a minute!
Do you remember the statement 2 i made earlier:
“I can change the activity of TAm without changing the activity of TAv”
In order for us to be able to correct convergence, we need to increase TAm activity without increasing TAv activity. In other word, you have to have to “change the activity of TAm without changing the activity of TAv”
If the rectangular is possible in a person’s voice, than it it possible to train that person from singing convergently to singing with rectangular glottis. And that means that person also can develop the skill to increase TAm activation without changing the activity of TAv. And here’s the big argument. all the people who can sing out there can learn to control this manuever with the TAm. So my statement 2 should be correct with most of us who can sing and have no disorder that affect singing.
-》Most of us can “change the activity of TAm without changing the activity of TAv”
So how do we acquire the independence control of this TAm muscle? How to control TAm independently of TAv?
This is where i’m still looking into the research.
This research
https://www.researchgate.net/publication/322488704_Oblique_thyroarytenoid_muscle_in_humans_An_independent_muscle_or_an_accessory_belly_Oblique_Thyroarytenoid_Muscle_in_Humans
have this section that talked about the TAm:
“The lateral muscularis compart-
ment contains a high proportion of fast-contracting mus-cle fibers that may be specialized for the rapid vocal-cord adduction necessary to protect the airway, respond-ing to the stimulation of the laryngeal mucosa”
So the only thing i can say now is the activation of this TAm muscle needs to be learned through some sort of quick and innate reflexes. Bit i’m not sure.
The last thing is imagery. i guess that when you’re singing as a bass, you might activate more TAv then you should . That made CT and LCA weakened, thus preventing you from your true tenor sound. i believe that our true voice only appears when we learn to use TAv in right amount and TAm to adduct the bottom to truely deepen the fold contact( instead of using too much TAv to make an artificial darkness). That’s all of my opinions.
Thank you for reading all of these! It means a lot! Thank you once again!
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Well done Tee Square. I stand corrected. The issue is how do you deal with this proprioceptively. Like you said, do we have independent control of the the two TA muscles? So far in my experience, I believe the two muscles both have a shortening/thickening function. The function of LCA will have an effect on lower adduction (I believe) even if its function focuses on the superior extreme of the folds. I’ll acquiesce to TmA doing the inferior closure. The singer deals with this from proprioception: desiring a clear full tone. Developing the lower extreme of the range (Low F0s) requires greater mass and will have a positive effect on complete vertical closure. Maintaining this posture higher in the range (without over-adducting) is crucial. In such a flexible (not pressed posture) deep closure can be maintained and the necessary reduction in vibrating fold mass can occur by the muscular portion of the folds remaining still. 4th dimension (cube within a cube or more exactly hyper-rectangle inside a hyper-rectangle. AKA a Tesseract.
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This is a very carefully prepared comment Tee Square! Bravo and thank you for a great contribution. I love your analysis of the two parts of the TA!
If you noticed, I refer to TA as a muscle group in my posts. In previous posts I have also mentioned the slight angle of TAm contributing to “Adduction”. Naturally the opposite is true of the countering muscle, TAv.
The adductive property of TAm is that it “bulges” the folds. I believe both muscles are necessary and extreme closure of the inferior mass of the folds is not necessary. I’ve seen some MRIs that suggests that complete adduction of the inferior mass is not necessary for the desired acoustic effect. It is enough that they are close (but that’s not formally researched. It’s plausible though).
From a sensory experience, the singer needs to identify sensations relative to LCA closure, IA closure and TA fullness and closure. They can be isolated for clearer experience and combined for organic singing. No one can perform while trying to control a bunch of muscles. I like to guide singers to components of “singing” that lead to the desired functions, such that their experience remains artistic. I find that the cardinal vowels /i/, /a/, /u/ lead to approximation of LCA, IA and inferior fold aspect (TA) respectively. Achieving this 3-way closure and having a sense of balance between them is the singer’s steering system. The concepts of chest and head voice plays into this. I, personally, am aware of a full sensation in the chest (solar plexus) I relate to inferior fold posture. It feels strongly active in the lower voice up to the passaggio. A lighter sensation is also always present and it becomes more present in my mind as I go through the passaggio upward. Yet, the full sensation, at best, does not diminish or rise. It simply relaxes a bit allowing the superior closure to be more active in the upper range. The singer can experience the upper sensation (lighter mechanism) as a “lean, clear tone” and vocalic clarity, such that the experience relates more to artistic expression than mechanical action. The singing process must relate to a need for expression and a recognization of the balance of the singer’s vocal posture at its most efficient and flexible. Naturally, we must understand the anatomy to address issues of balance. We must always be careful not to be just mechanical because the breath can become “static” (not dynamic) and hinder the continuity of fold oscillation.
Thanks again for an insightful post!
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Yes thank you!
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I’ve been thinking about this lately and i think the “strap muscles” in the neck might also play a very important role in singing. And i also never see you talking about strap muscles so i want to have this chance to ask you about those.
I think all of us can sing an F1/H1 tone (first formant reinforcing first harmonic) cleanly with almost no opposition from the TA. And this tone, at face value, seems like a convergent tone. But when i sing this F1/H1 tone cleanly, firmly (fully adducted, not breathy nor pressed) and gently my larynx actually lower a little bit and the tone sounds like a small full voice. So is my interpretation of titze theory wrong? Or the theory itself is wrong(or maybe incomplete? Or other possibilities? I’m not sure.
From the F1/H1 tone, with a specific pitch, if we want to cresendo to a more intense sound, TA will be more engaged, thus shorten the fold and might weaken the CT and lowering the pitch. But if we want to keep the same pitch, the fold length should not decrease, i think. I think this is where strap muscles help the CT to keep stretching for the same pitch, or in other words, to keep opposing TA without being weak. So i think when doing cresendo, TA activities increase, but at the same time strap muscles activities increase to keep the same pitch.
What do you think? Thank you!
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Interesting questions! The strap muscles’ main function is lowering the larynx, either by pulling the structure towards the clavicles (points of origin) or depressing the Hyoid bone. The vector of the thyrohyoid is oblique and does not have a direct effect on fold lengthening as far as I understand. As laryngeal depressors, they assist in lowering the larynx which would lead to a lowering of all formants especially the first. They would help around the passaggio areas in particular. As for F1/H1, that can occur with lower formant vowels like /I/ and /u/ at low pitches. It’s also a characteristic of female/high treble males voices beyond F5. There is a phenomenon that H1 is unusually strong when the tone is very breathy. That is one way to determine falsetto in acoustical analysis. What is the point of F1/H1 for you? And are you attempting to produce it throughout your range?
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Thanks for the reply! When i looked back at my own comment, i didn’t know why i brought up that F1/H1 concept in the first place. I guess it’s not relevant now.
I think when we sing pianissimo we have little TA. But when we cresendo, TA will be more active, and has the tendency to shorten the folds and might lower the pitch. To counteract that tendency, or in other words, to keep the the folds length the same, i think the sternothyroid or sternohyoid will aid CT in stretching for the same length. Not the thyrohyoid. Sorry for not being clear earlier.
Also i have a question, since you mentioned formants. We all agree that male singers have 3 resonance strategies:
1. F1/H2 or F1/H3,4… ,
2. F2/ H3, H4
3. Cluster (F3, F4, F5)/H5 or H6
Do you think we can do 1 and 3 at the same time in the low range? Or 2 and 3 at the same time above? (No 1 or 2 at the same time for sure) I noticed that the cluster is vowel independent and F1 or F2 is vowel dependent so i ask these question. The only connection between cluster and F1 (or F2) is the position of the larynx. So i’m not sure if we can have both a strong F1 (or F2) and strong Singer’s Formants though. Again, just my guess. I might be incorrect.
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Hi Tee Square, very late responding to this. The chiaroscuro dynamic is based on the idea of combining the dominant low formant F1 or F2 with the cluster F3-5. Björling did this particularly well. At his best he maintained a balance between the SF (F3-5 cluster) with the dominant lower formant (F1 or F2). This is the strategy I follow but the source must be trained to achieve this.
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