ORIGINAL ARTICLE

Can vocal economy in phonation be increased with an artificiallylengthened vocal tract? A computer modeling study

INGO R. TITZE1,2 & ANNE-MARIA LAUKKANEN3

1Department of Speech Pathology and Audiology, The University of Iowa, Iowa City, IA, USA, 2National Center for Voice

and Speech, The Denver Center for the Performing Arts, Denver, CO, USA, 3Department of Speech Communication and

Voice Research, University of Tampere, Tampere, Finland

AbstractVoiced obstruents and phonation into tubes are widely used as vocal exercises. They increase the inertive reactance of thevocal tract in the 200�1000 Hz range and thereby reinforce vocal fold vibration. But the effect is strong only when theepilarynx tube is also narrowed. The present study focused on the effects of a ‘resonance tube’ (27 cm in length, 0.5 cm2

cross-sectional area, hard walls) on vocal tract reactance and the accompanying economy of voice production (defined asmaximum flow declination rate (MFDR), divided by maximum area declination rate (MADR)). The vowel /u/ andphonation into the tube were simulated with a computer model. Three values were given to the cross-sectional area of theepilarynx tube (0.2 cm2, 0.5 cm2, and 1.6 cm2), which is at the opposite end of the vocal tract from the artificial ‘resonancetube’. The degree of glottal adduction was varied in order to find the economy maximum for each epilarynx tube setting.

Results showed that the ‘resonance tube’ lowered F1 from 300 Hz to 150 Hz and doubled the vocal tract inertivereactance at F0�100 Hz. The largest economy with the ‘resonance tube’ was obtained when the epilarynx tube wasnarrowed (relative to the rest of the vocal tract) and sufficiently tight adduction was used. Most importantly, the intraoralacoustic pressure (calculated at 0.8 cm behind the lips) was tripled with the tube. The results suggest that by optimizing thevibratory sensations in the face that are attributed to increased intraoral acoustic pressure, phonation into a tube may assist atrainee in finding an optimal glottal and epilaryngeal setting for the greatest vocal economy.

Key words: Airflow, breath control, computer modeling, epilaryngeal narrowing, vocal economy, voice training and therapy

Introduction

Voiced fricatives like /v, z, b/, lip and tongue trills,

nasal consonants, and phonation into tubes have

been widely used in voice training and therapy (1�5).

Beneficial effects have also been reported when a

person phonates against a hand nearly covering

the mouth (6). Lessac (7) has proposed the use

of a ‘y-buzz’ as a vocal exercise, which is a closed

front vowel produced with a slight protrusion of

the lips and with so narrow a constriction between

the tongue and the palate that it almost sounds

like the semivowel /j/. This ‘y-buzz’ exercise and

other components of a series of ‘energy’ principles

described by Lessac have been crafted into the

Lessac-Madsen Resonant Voice Therapy method

by Verdolini (8). Also, Stemple’s Vocal Function

Exercises (9) utilize the vowel /o/ as a primary vocal

tract configuration for practice. Collectively, we refer

to all of these exercises as semiocclusive vocal tract

exercises (10).

Some authors have suggested that exercises on

voiced fricatives also increase breath management in

singing (3) and for general improvement of breath-

ing (11,12). Phonation into tubes has been used in

speech therapy for the treatment of hypernasality

(4,13,14), in voice therapy for the treatment of both

phonasthenia and hyperfunctional voice disorder

(4,13�18), and in voice training to improve voice

quality and projection (19).

Phonation into glass tubes (25�28 cm in length, 8�9 mm inner diameter), called ‘resonance tubes’, has

been used in Finnish voice training and therapy

practice (5,13,15�18,20) and in Norway (21). In

Correspondence: Ingo R. Titze PhD, National Center for Voice and Speech, The Denver Center for the Performing Arts, 1101 13th Street, Denver, CO

80204, USA. Fax: �1-303-893-6487. E-mail: ititze@dcpa.org

Logopedics Phoniatrics Vocology. 2007; 32: 147�156

(Received 2 February 2006; accepted 9 February 2007)

ISSN 1401-5439 print/ISSN 1651-2022 online # 2007 Taylor & Francis

DOI: 10.1080/14015430701439765

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Germany, Gundermann (14) and Habermann (4)

mention a method of humming on /m, n, l/ into a

glass tube (B12 cm in length, 1 cm inner diameter)

proposed by Spiess (22) and later recommended by

Stein (23). The name ‘resonance tube’ comes from

the strong sensations of vibrations that are felt in the

lips and face during phonation into these tubes. A

resonance tube is used either so that one end of it is

sunk into a cup filled with water (water resistance

therapy, see e.g. Sovijarvi (20), Rauhala (15)) or so

that it is free in the air, pointing straight out of the

subject’s mouth as a natural extension of the vocal

tract. The other end is kept firmly between the lips.

The subjects are instructed to produce a vowel-like

sound (/u, y/ are the most natural choices) into the

tube. The aim is the most comfortable, effortless

phonation that produces maximum vibratory sensa-

tions in the lips and face. According to subjective

sensations of many trainees, phonation feels easier

and the voice sounds louder immediately after

exercising with the tubes (clinical observation by

author A.-M. Laukkanen, who has administered the

therapy often). According to Tapani (16) and Sim-

berg (18), patients suffering from functional and

other voice disorders seem to have derived benefit

from the therapy.

Some studies of the instantaneous effects of vocal

tract occlusions on vocal fold vibration have been

carried out on human subjects. Bickley and Stevens

(24), using acoustic analysis in combination with

electroglottography, reported an increase in the open

quotient and a steeper spectral slope in the glottal

source function as a consequence of vocal tract

constriction. These results have recently been con-

firmed with a computer model (10). However,

Laukkanen (19,25) obtained opposite results with

electroglottography (EGG) during and immediately

after phonation on /b/ and into resonance tubes with

subjects that had received training in the use of the

semiocclusive. The relative open time was reduced

during and after semiocclusion with a bilabial

fricative and a tube. Also, the average laryngeal

muscle activity was the same or lower during

phonation into a resonance tube or on /b/ compared

to vowel phonation (26,27). Decreased glottal re-

sistance due to increased flow has been observed

immediately after 1 minute exercising on /b, m/ and

the resonance tubes (28,29). These studies suggest

that vocalists can learn to compensate for the

semiocclusion and perhaps utilize it to their advan-

tage in training the vocal fold adduction and the

related musculature.

All the above-mentioned exercises imply that

semiocclusion of the vocal tract (steady or time

varying as in a lip trill) or an artificial lengthening of

the vocal tract increase the source-vocal tract inter-

actions. Modeling studies have shown that vocal

tract input impedance (and particularly the inertive

reactance) increases with a tube that lengthens the

vocal tract (30), and the glottal flow amplitude and

pulse shape change with increased inertive reactance

(31�33). Furthermore, oscillation threshold pressure

is reduced by increased vocal tract inertance (34). A

study with a singer also suggested an effect of vocal

tract inertance on the oscillatory characteristics of

the vocal folds (35).

Inertive reactance in the vocal tract can also be

increased by narrowing the epilarynx tube area

instead of semioccluding the mouth (36). This also

lowers phonatory threshold pressure and increases

maximum flow declination rate (33), leading to

strengthening of the higher harmonics and even to

an increase in sound pressure level (SPL). This

increase in maximum flow declination rate (MFDR)

would imply a more economic voice production

(more sound output with less mechanical stress

imposed on the vocal fold tissue), provided that the

maximum area declination rate (MADR) in the

glottis does not increase proportionately. We have

suggested the use of the ratio MFDR/MADR as a

measure of vocal economy (33).

Phonation into narrow straws, as opposed to

longer and wider tubes, may add another benefit.

High subglottic pressures are possible without ex-

cessive collision of the vocal folds. Titze et al. (37)

observed lower amplitude and a lower relative closed

time of the glottis on an EGG signal when phonation

into straws was compared to vowel phonation. It was

concluded that, with narrow straws, it is possible to

exercise the use of the high subglottic pressures

needed in singing, while having minimal collision of

the vocal folds. During phonation into a narrow

straw, the intraglottal air pressure rises, causing the

vocal folds to abduct, thereby diminishing the

collision force during voice production.

The current study focused on the use of one

specific ‘resonance tube’ used in Finland. First,

the effects of the tube on vocal tract reactance were

calculated. Second, the effects of the tube on self-

sustained vocal fold oscillation were studied with a

computer simulation model.

Methods

The three-mass body-cover model of Story and

Titze (38) was used for simulation. The model

allowed inputs in the form of laryngeal muscle

activation (39). The vocal tract was simulated with

the wave reflection algorithm (40,41), including

frictional air losses, kinetic losses, wall vibration

losses, radiation losses, and glottal losses. The

supraglottal tract was modeled with 44 sections,

148 I. R. Titze & A.-M. Laukkanen

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each 0.398 cm in length, and cross-sections for the

/u/ vowel determined experimentally with magnetic

resonance imaging by Story et al. (42). The total

length of the supraglottal vocal tract was 17.5 cm,

which corresponds to an average male vocal tract. A

subglottal tract (36 sections, 14 cm in length) was

included, with the area function also modeled after

Story et al. (42).

Sound radiation from the lips was modeled as a

circular piston oscillating in a spherical baffle, which

has become a standard in speech simulation (43), but

can be challenged for frequencies above 5000 Hz.

In fact, many aspects of the wave reflection algorithm

as detailed by Liljencrants (40) and Story (41) begin

to lose accuracy for frequencies above 5000 Hz

because they are based on a one-dimensional wave

equation.

Waveforms were simulated with this model, typi-

cally 200 ms in length to show about 20 cycles of

vibration at around 100 Hz. From these waveforms,

the following variables were calculated: peak glottal

area, mean glottal area, MADR, peak glottal flow,

mean glottal flow, MFDR, vocal economy (MFDR/

MADR), and glottal efficiency (acoustic output

power divided by the product of mean airflow and

subglottic pressure) (44). In addition, several values

of peak and mean vocal tract pressures were com-

puted. Results are shown in Table I. Finally, the

combined reactance of the subglottal and supraglot-

tal vocal tract was calculated with and without the

tube, and with three epilarynx tube diameters. The

reactance calculations followed the procedure de-

scribed by Story et al. (30).

It must be pointed out that the accuracy of any

simulation depends on many factors. Some para-

meters in the model are known to better than 0.1%

accuracy (e.g. density of air, sound velocity), but

other parameters are known only to an order-of-

magnitude (e.g. tissue viscosities and elasticities).

Thus, the results that are about to be shown may

have error in an absolute sense, but the relative

changes with parameter variation, which are of

primary importance, are less susceptible to error

because the uncertainties usually cancel out.

Results

The vowel /u/ was first simulated as a control case.

The vocal tract shape is shown in Figure 1 (top left).

This vowel has a small lip opening, making the

radiation losses comparable to those of the tube.

Simulated laryngeal muscle activity (20% thyroar-

ytenoid, 20% cricothyroid, and 50% lateral cricoar-

ytenoid) produced an F0 of about 100 Hz. The

epilarynx tube cross-sectional area was 0.5 cm2 (the

first eight supraglottal sections), and the lung

pressure was 0.8 kilo-pascals (kPa). The value 0.5

cm for Ae is typical on the basis of measurements

made by Story et al. (45). Several studies of how

vocal efficiency and vocal economy vary with Ae

have already been conducted (46�48). Results follow

the basic principles of maximum power transfer in

electrical and acoustic circuits. If Ae is such that the

vocal tract input impedance matches the glottal

impedance (which is a time-varying nonlinear quan-

tity), the output power of the simulator is max-

imized. Efficiency of conversion of aerodynamic

power to acoustic power, on the other hand, is not

maximized when the impedances match. As an

alternative to glottal efficiency, we have been at-

tracted to a quantity called vocal economy, which is

presently defined as the ratio of maximum flow

declination rate to maximum area declination rate

(10). In the current study, the value of Ae allowed

vocal economy to reach a peak with various glottal

adjustments. Values of AeB0.1 prevented vocal fold

oscillation because the input impedance was too high

and values of Ae�2.0 greatly reduced the oscillation

range because no benefit was obtained from vocal

tract coupling.

Returning to Figure 1, the following output wave-

forms of the model are shown on the left panel, top

to bottom: contact area (ca) of the vocal folds in

cm2, glottal area (ga) between the vocal folds in cm2,

glottal airflow (ug) in L/s, and glottal flow derivative

(dug) in m3/s2. On the right panel, we see vocal tract

pressures in kPa from top to bottom: lip-radiated

output pressure (Po), intraoral (mouth) pressure

(Pm) at a location 0.8 cm behind the lips, epilarynx

tube input pressure (Pe), intraglottal pressure (Pg),

and subglottic pressure (Ps). To observe their

relative sizes, all pressures are scaled equally between

�2.0 and �2.0 kPa. Note the relatively small lip-

radiated pressure (top right) in comparison to the

pressures below, within, and above the glottis

(bottom three). The intraoral pressure (second

from top) is also relatively small for the vowel /u/.

Effects of vocal tract lengthening with a tube

Figure 2 shows the same set of simulated waveforms

when a resonance tube is added at the lips, 27 cm in

length and 0.5 cm2 in cross sectional area, the same

as the epilarynx tube. With ordinary speech airflows,

little air turbulence was noted when a subject

phonated through this tube. Hence, no turbulence

was simulated with noise sources. The most out-

standing visible feature in Figure 2 is the large

intraoral acoustic pressure (second from top on the

right). This pressure (Pm) is increased by a factor of

three over the vowel /u/ without a tube. We believe

that this large mouth pressure can be felt as a

Vocal economy study with artificially lengthened tract 149

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Table I. Results for simulations of /u/ in the top row, and with a ‘resonance tube’ in the remaining rows. For each of three cross-sectional areas of the epilarynx (Ae) there are several degrees of

adduction. Vocal economy is defined as (MFDR/MADR) and efficiency as (SPL/mean flow � mean subglottic pressure). In bold: Values for the degree of adduction (in % LCA) giving the highest

economy.

Vocal tract

configuration

Peak area

(cm2)

Mean area

(cm2)

MADR

(cm2/ms)

Peak flow

(L/s)

Mean flow

(L/s)

MFDR

(cm3/s2)

Peak Pg

(kPa)

Mean Pg

(kPa)

Peak Pe

(kPa)

Mean Pe

(kPa)

Peak Pm

(kPa)

Mean Pm

(kPa)

Economy

(cm/ms) Efficiency

/u/; Ae�0.5 cm2;

LCA�50%

0.67 0.23 0.45 0.87 0.33 4.12 4.80 0.48 3.27 0.29 0.48 0.017 9.09 0.0003150

‘Resonance’ tube Ae�1.6 cm2

46% LCA 0.41 0.24 0.09 0.66 0.51 0.23 0.99 0.53 0.59 0.38 0.32 0.080 2.56 0.0000001

47% 0.42 0.23 0.17 0.64 0.43 0.30 1.05 0.58 0.62 0.33 0.55 0.073 2.80 0.0000027

48% 0.40 0.20 0.12 0.61 0.38 0.44 1.08 0.59 0.69 0.30 0.70 0.059 3.85 0.0000057

49% 0.54 0.20 0.29 0.68 0.29 1.65 1.02 0.39 1.02 0.22 0.92 0.040 5.66 0.0000272

50% 0.34 0.15 0.11 0.61 0.31 0.61 1.19 0.68 0.78 0.24 0.75 0.041 5.51 0.0000119

51% 0.48 0.17 0.30 0.67 0.24 1.73 1.10 0.38 1.14 0.18 1.04 0.032 5.77 0.0000471

52% 0.44 0.14 0.29 0.65 0.22 1.69 1.06 0.38 1.11 0.16 1.02 0.030 5.75 0.0000426

53% 0.19 0.057 0.12 0.43 0.15 0.57 1.04 0.61 0.63 0.11 0.60 0.021 4.70 0.0000158

Ae�0.5 cm2

46% LCA 0.43 0.24 0.10 0.59 0.47 0.14 1.07 0.55 0.63 0.44 0.30 0.071 1.48 0.0000007

47% 0.44 0.24 0.12 0.58 0.39 0.44 1.19 0.61 0.74 0.39 0.70 0.057 3.80 0.0000064

48% 0.43 0.21 0.14 0.56 0.33 0.54 1.14 0.65 0.82 0.32 0.81 0.052 3.94 0.0000099

49% 0.61 0.22 0.37 0.56 0.26 2.53 2.74 0.42 1.80 0.25 0.99 0.041 6.93 0.0000484

50% 0.63 0.21 0.36 0.72 0.29 2.76 3.20 0.51 2.17 0.26 1.33 0.029 7.65 0.0000844

51% 0.56 0.19 0.38 0.57 0.21 2.77 3.00 0.39 2.04 0.20 1.12 0.028 7.29 0.0001179

52% 0.26 0.10 0.13 0.49 0.21 0.73 1.16 0.60 1.05 0.20 0.85 0.032 5.67 0.0000250

53% 0.18 0.053 0.12 0.41 0.14 0.61 1.12 0.63 0.82 0.13 0.69 0.019 5.17 0.0000251

Ae�0.2 cm2

51% LCA 0.51 0.15 0.31 0.33 0.16 2.61 5.00 0.59 4.13 0.25 0.78 0.022 8.53 0.0000933

52% 0.46 0.12 0.30 0.33 0.14 2.59 5.24 0.46 4.02 0.22 0.75 0.016 8.76 0.0001388

53% 0.45 0.12 0.35 0.33 0.13 3.09 5.44 0.47 4.30 0.20 0.78 0.014 8.95 0.0001497

54% 0.43 0.08 0.31 0.33 0.11 2.57 4.91 0.51 3.79 0.18 0.76 0.017 8.28 0.0000971

55% 0.45 0.12 0.37 0.33 0.11 3.27 5.60 0.43 4.43 0.17 0.74 0.015 8.92 0.0002841

(56% does not

phonate)

Notes: MADR�maximum area declination rate; MFDR�maximum flow delination rate; LCA�lateral cricoarytenoid activity; SPL�sound pressure level; Pg�pressure in the glottis; Pm�pressure in the mouth (behind the lips); Pe�pressure at the epilarynx tube entry.

150

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.-M.

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‘buzzing’ in the lips and other facial tissues when a

person phonates into a tube.

Effects of combined epilarynx tube narrowing with vocal

tract lengthening on vocal tract reactance

Figure 3(a) shows the shapes for the vowel /u/ again

without a ‘resonance tube,’ but this time with three

different values of epilarynx tube cross-section from

top to bottom: 1.6 cm2, 0.5 cm2, and 0.2 cm2.

Figure 3(b) shows the corresponding reactance

curves of the vocal tract shapes. Reactance is

expressed in units of dyn-s/cm5, where 1 dyn-s/

cm5�105 Pa-s/m3. Thin solid lines are for supra-

glottal reactance, dashed lines for subglottal reac-

tance, and thick solid lines for the combined

reactance. It can be seen that narrowing of the

epilarynx tube area from 1.6 cm2 to 0.2 cm2 (top to

bottom) approximately doubled the reactance at

frequencies below 300 Hz (e.g. from 10 dyn-s/cm5

at 100 Hz to 20 dyn-s/cm5 at the same frequency).

This increased reactance gives rise to greater re-

inforcement of vocal fold vibration due to delayed

feedback from this reactive load (34).

Figure 4 shows similar results when the resonance

tube is added to the vocal tract. The tube lowered F1

from about 300 Hz to 150 Hz. This further

increased the positive (inertive) reactance below

F1. For example, 100 Hz is increased from 20 dyn-

s/cm5 to 40 dyn-s/cm5 (2�106 to 4�106 Pa-s/m3).

But negative reactance occurred from 150 Hz to

about 250 Hz. This is an area where vocal fold

vibration is not enhanced by the vocal tract. The

region of negative reactance can be shrunk, however,

Figure 1. Example of some outputs of the model (vowel /u/, 50% simulated lateral cricoarytenoid (LCA) adduction, 0.5 cm2 epilarynx

tube). Left column from top: Schematic picture of the cross-sectional area of the trachea, glottis, epilarynx tube and mouth cavity; vocal fold

contact area (ca); glottal area (ga), glottal airflow (ug); first derivative of glottal flow (fug, negative peak shows the maximum flow

declination rate). Right column from top: oral radiated air pressure (Po); mouth pressure 0.8 cm behind lips (Pm); epilarynx tube input

pressure (Pe); intraglottal pressure (Pg); subglottic pressure (Ps).

Vocal economy study with artificially lengthened tract 151

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by narrowing the epilarynx tube, as is shown in the

lower panels of Figure 4. Due to second formant

lowering with the tube, positive reactance also

increased in the 400�600 Hz region. This effect on

higher (singing) fundamental frequencies and their

harmonics will be left as a follow-on study. Here we

are concerned only with reactive effects at normal

speaking fundamental frequencies.

Effects of epilaryngeal narrowing and the resonance tube

on vocal economy in voice production

As stated earlier, vocal economy is still in the process

of being developed. Our current definition is

MFDR/MADR, based on a simple glottal geometry

that does not include anterio-posterior variation

(33). MFDR is the maximum flow declination rate

and MADR is the maximum area declination rate.

As it presently stands, the ratio MFDR/MADR has

dimensions of velocity (m/s), which has no strong

physical interpretation. It does, however, relate

abruptness of airflow change to abruptness of tissue

velocity change, the first being desirable for acoustic

excitation and the second being undesirable for

tissue stress. Thus, the higher the ratio is, the greater

the economy of production (in theory). As more

sophisticated vocal fold models are used, three-

dimensional glottal kinematics may be needed to

refine the definition. For the present investigation,

the definition is adequate.

It has been shown that vocal economy (however

defined) is likely to be a function of vocal fold

adduction (10,49). Hence, a third experimental

variable, vocal fold adduction, was included in the

simulation. For each value of epilarynx tube area, as

well as for the tube versus no-tube condition, a

group of values for simulated lateral cricothyroid

(LCA) muscle activity was chosen to find the

optimum value of adduction. The highest value of

vocal economy was the function to be optimized.

Figure 2. Outputs of the model for the vowel /u/ with a 27-cm tube attached (top left). All waveforms are comparable to those of Figure 1.

152 I. R. Titze & A.-M. Laukkanen

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Table I summarizes the results obtained for

selected variables calculated from the waveforms.

These variables are labeled across the top. The rows

are divided into four groups, the /u/ vowel being in

row 1 as a control case (with 50% LCA and 0.5 cm2

epilarynx tube), followed by three groups of ‘reso-

nance tube’ cases for different epilarynx tube cross-

sections Ae. Each group of Ae contains several

simulated LCA activities. Simulated LCA activity

was varied such that a peak value in vocal economy

was established, with values dropping off on either

side. The row with bold numbers shows the max-

imum economy case. Note that for Ae�1.6 cm2, the

peak economy value is 5.77 cm/s, while for Ae�0.5 cm2 it is 9.65 cm/s, and for Ae�0.2 cm2 it is

8.95 cm/s. These optimized economy cases yield the

primary numbers for comparison. When the opti-

mum economy cases with the ‘resonance tube’ are

compared to the /u/ vowel, both peak and mean

glottal areas (first two columns) and glottal flows

(fourth and fifth columns) generally declined

slightly, suggesting greater steady back pressures on

the vocal folds and smaller vibrational amplitudes

when the ‘resonance tube’ is attached. MADR and

MFDR are also lower with the ‘resonance tube’.

Acoustic pressures along the vocal tract (Pg�intraglottal pressure, Pe � epilaryngeal tube pres-

sure, Pm�mouth pressure behind the lips) are

likewise generally lower with the ‘resonance tube’.

There is one major exception: Pm. This mouth

pressure behind the lips increased dramatically for all

cases with the ‘resonance tube’, which is perhaps the

most significant result of this study.

The highest economy value with the ‘resonance

tube’ (8.95 cm/s) was obtained with the narrowest

epilarynx. It was very close to the value for /u/, 9.09

cm/s. Efficiency is more difficult to compare because

the tube radiates energy differently than the lips.

Figure 3. (a) Vocal tract shape for the /u/ vowel and (b) with the corresponding reactance curve for three epilaryngeal settings: 1.6 cm2

(top), 0.5 cm2 (middle), 0.2 cm2 (bottom). Thin solid line�subglottic reactance, dashed line�supraglottic reactance, thick line�total

vocal tract reactance (1 dyn-s/cm5�105 Pa-s/m3).

Vocal economy study with artificially lengthened tract 153

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Vocal efficiency, traditionally defined as the ratio of

radiated power from the mouth to aerodynamic

power at the glottis, has limited use because it is so

highly dependent on mouth opening. Every vowel

has a different efficiency. Vocal economy, as defined

here, is less sensitive to vowel because the computa-

tion involves glottal variables only.

Discussion

It is known on the basis of earlier results (33) that a

relatively narrow laryngeal vestibule (epilarynx tube)

can increase the maximum flow declination rate

(MFDR) while simultaneously lowering the mean

glottal airflow. Since a narrowed epilarynx tube

causes some steady backpressure in the glottis, it

also diminishes the maximum area declination rate

(MADR) and thus leads to higher economy. This

increase in vocal economy can be linked to an

increase in vocal tract inertive reactance, which

assists the vocal folds in self-sustained oscillation.

In this study, a ‘resonance’ tube added to the vocal

tract at the lips in and of itself increased the inertive

reactance in the 100�200 Hz region, which could

then be further increased if the epilarynx tube was

also narrowed. But the economy was not greater

than that of an /u/ vowel, which has a lip opening

comparable to the tube diameter (between 0.2 and

0.5 cm2). Thus, the tube seemed to offer no more

than any other oral semiocclusive. In particular,

there was no new resonance at speaking pitches.

Remarkable, however, was the finding that the

mouth pressure just behind the lips was three times

higher with the tube than with an /u/ vowel. There-

fore, it seems plausible that the rationale of using a

tube with vocal exercising is that it guides the trainee

to the sensation of facial tissue vibration, which is

sensitive to impedance matching between the glottis,

Figure 4. (a) Vocal tract shape for the /u/ vowel combined with a resonance tube and (b) the corresponding reactance curve for three

epilaryngeal settings: 1.6 cm2 (top), 0.5 cm2 (middle), 0.2 cm2 (bottom). Thin solid line�subglottic reactance, dashed line�supraglottic

reactance, thick line�total vocal tract reactance (1 dyn-s/cm5�105 Pa-s/m3).

154 I. R. Titze & A.-M. Laukkanen

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epilarynx, and the vocal tract. It is likely that the

most beneficial epilaryngeal setting cannot easily be

found without this ‘lip buzz amplifier’.

Regarding the concept of narrowing the epilarynx

tube, a note of caution is offered. If not carefully

conceptualized and executed, epilarynx tube nar-

rowing may be interpreted as hyper-adduction of the

false folds. The opposite is true. Narrowing of the

epilarynx tube should take place only by anterio-

posterior movement of the epiglottis, not by medio-

lateral movement of the ventricular folds, which

could easily be set into vibration. This vibration

would be rough, with a strained voice quality.

Traditionally, voice coaches and singing pedagogues

have stressed the importance of a wide pharynx (e.g.

Appelman) (50). The mental image of a yawn (or, at

least, an anticipation of a yawn) is promoted as a

means of freeing up the voice. Widening the pharynx

(and perhaps the entire vocal tract) effectively

narrows the epilarynx tube, if held constant. Acous-

tically, narrowing and widening are relative concepts.

What matters from the point of view of impedance

matching is the relative size between the mean cross-

sectional area at the entry of the glottis and the cross-

sectional area of the vocal tract. This can be obtained

in a variety of ways.

Conclusion

Phonation into a so-called resonance tube, although

not providing any new resonance conditions other

than what is predicted from an artificially lengthened

vocal tract, appears to have therapeutic value in that

it provides acoustic pressure feedback from the lip

area. Relatively strong pressures are felt at the lip-

tube junction, which increase when the epilarynx

tube area above the glottis effectively narrows. Thus,

as has been claimed in earlier studies (10), altering

the acoustic load at the mouth with a tube may

facilitate a better impedance match at the glottis.

It remains to be shown whether specific length-

diameter combinations of the tube can optimize the

process of impedance matching. Future studies will

focus on the laryngeal and epilaryngeal settings of

human subjects during and immediately after vocal

exercising with tubes and other occlusions of the

vocal tract.

Acknowledgements

This study was supported by funding from the

National Institute on Deafness and Other Commu-

nication Disorders, grant number 1R01 DC04347,

and grant numbers 32879 and 106139 from the

Academy of Finland.

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