PhD Thesis in music acoustics
FROM AIR TO MUSICAcoustical, Physiological and Perceptual Aspects of Reed Wind Instrument Playing and Vocal-Ventricular Fold Phonationby©1998An ancestral and recurrent dream of humankind is that of flying.
In my ordinary flying dreams,
whenever I inhale, I start levitating in the space;
when I exhale, I immediately return to the firm ground.
Playing a wind instrument may follow the same simple, supernatural rule:
in blowing, one donates life and sound to other beings, and gains the Earth;
in inspiring, one must incorporate spirits and angels.
Contents:Thesis front cover
AbstractThesis back cover (spectrogram of "oh, Susanah" during overtone singing in VVM phonation- see Paper VI)
2.List of abbreviations and conventions
6.Playing a reed woodwind
7.Basic ideas and methods
8.Summaries and comments on individual papers
9.Music continues; a list of possible future investigations
Back to home-page
©1998 by Leonardo Fuks
terça-feira, 25 de dezembro de 2012
This thesis presents an interdisciplinary research on reed woodwind instruments and human voice, focusing on acoustical, physiological and perceptual aspects of sound generation.
The wind instruments studies concentrate on breathing and blowing under realistic conditions and provide a deeper insight on required aerodynamical input parameters. The variation of blowing pressure with loudness and fundamental frequency was measured in professional players of oboe, bassoon, clarinet, and alto saxophone and was found to be quite systematic, though differing between the instruments. Airflow for sustained tones was measured by indirect spirometry, together with blowing pressure and sound pressure level, using extreme reeds, one soft and one hard. Recordings were made in an ordinary room as well as in a calibrated reverberant chamber. Also, tones with an intense vibrato were analysed for the oboe, the saxophone and the bassoon. The results revealed wide variations in blowing pressure, suggesting that a rhythmic modulation of the contraction of expiratory muscles was a main factor, and relatively small variation in fundamental frequency. The players’ perception of self-produced static lung pressures typically used in performances was analysed in a psychophysical experiment, that revealed a quasi-linear relationship between perceived and produced pressures. The respiratory movements during playing were measured by a non-invasive technique, respiratory inductive pletysmography, which offered acceptably reliable data. The results revealed significant participation of the rib cage in all players and also of the abdominal wall in several players. Also, the impact of the continuous changes of O2 and CO2 gases in the pulmonary air exhaled during performance on the fundamental frequency was predicted from theory and compared with experimental data. The effect, smaller than that of temperature variation, still would represent a factor of potential relevance to wind instrument intonation. In addition, the sound production characteristics of a particular type of phonation, perceptually judged as similar to that used in Tibetan chant, were studied by high-speed imaging. Also, it was examined using acoustical and physiological methods. The results revealed a synchronised co-oscillation of the vocal and ventricular folds, which yields a lowering of fundamental frequency due to multiplication of the vocal fold period.
Keywords: blowing pressures, reed woodwinds, oboe, clarinet, saxophone, bassoon, music performance, respiratory inductive plethysmography, perception of blowing pressure, intonation, aerodynamics, Tibetan chant, ventricular folds, respiratory behaviour, airflow, vibrato, music acoustics, physiology of music.
©1998 by Leonardo Fuks
1. Included papers
The present dissertation comprises a summary and the following papers, listed in systematic order. Click to read the abstract of each one. The available papers are undelined, just click to load them.
Paper I Leonardo Fuks & Johan Sundberg (1996): "Blowing pressures in reed woodwind instruments", KTH TMH-QPSR 3/1996, 41-57, Stockholm, to appear in a revised and modified version as "Blowing pressures in bassoon, clarinet, oboe and saxophone", in press for Acustica/acta acustica.
Paper II Leonardo Fuks (1998): "Aerodynamic input parameters and sounding properties in naturally blown reed woodwinds", KTH TMH-QPSR 4/1998, 1-11, Stockholm
Paper IIIa Leonardo Fuks (1996): "Prediction of pitch effects from measured CO2 content variations in wind instrument playing", KTH TMH-QPSR 4/1996, 37-43, Stockholm
Paper IIIb Leonardo Fuks (1997): "Prediction and measurements of exhaled air effects in the pitch of wind instruments", Proceedings of the Institute of Acoustics, ISMA'97 Conference, Edinburgh, Vol. 19: Part 5 (1997), Book 2, 373-378
Paper IV Leonardo Fuks & Johan Sundberg (1998): "Respiratory inductive plethysmography measurements on professional reed woodwind instrument players", KTH TMH-QPSR 1-2/1998, 19-42, to appear in a revised and modified version as "Using Respiratory Inductive Plethysmography for Monitoring Professional Reed Instrument Performance"; in press for Medical Problems of Performing Artists, March 1999
Paper V Leonardo Fuks (1998): "Assessment of blowing pressure perception in reed wind instrument players", KTH TMH-QPSR 3/1998, 35-48, Stockholm, submitted for publication
Paper VI Leonardo Fuks, Britta Hammarberg & Johan Sundberg (1998): "A self-sustained vocal-ventricular phonation mode: acoustical, aerodynamic and glottographic evidences", KTH TMH-QPSR 3/1998, 49-59, Stockholm
The blowing pressures during wind instruments playing have not been systematically measured in previous research, leaving the dependencies of pitch and dynamic level as open questions. In the present investigation, we recorded blowing pressures in the mouth cavity of two professional players of each of four reed woodwinds (Bb clarinet, alto saxophone, oboe, bassoon). The players performed three different tasks: (1) a series of isolated tones at four dynamic levels, (2) the same series with a crescendo-diminuendo tones and (3) ascending-descending musical arpeggio played legato at different dynamic levels (pp, mp, mf, ff). The results show that, within instruments, the players' pressures exhibit similar dependencies of pitch and dynamic levels. Between instruments, clear differences were found with regard to the dependence on pitch.
Input aerodynamic parameters in reed woodwinds - oboe, alto saxophone, bassoon and clarinet - were measured when professionals played different pitches at three dynamic levels. Two reeds were used, one rated as a hard and another as a soft reed. The tasks consisted of playing long sustained tones with and without vibrato. Audio and blowing pressure signals were recorded. Lung volume variations were indirectly measured by a spirometric procedure, which also showed the average air consumption, i.e. the mean airflow. The tones were played in a laboratory room and also in a calibrated reverberant chamber allowing estimation of radiated sound power. Average values for flow resistance, aerodynamical power and mechanical efficiency were computed. Airflow and input power varied con-siderably between instruments and between the two reed types, but generally increased with sound level. For vibrato tones produced on oboe, bassoon and saxophone, wide pressure oscillations were observed, on average 10 cm H2O for the oboe and bassoon, and reaching values of 20 cm H2O in some cases. Possible origins of these pressure variations are discussed.
The effect of carbon dioxide (CO2) exhaled by wind instrument players on the resulting pitch is investigated. A theoretical-numerical approach is applied to determine the dependence of sound velocity on the percentage of CO2 contained in the air. Realistic performance data were obtained from experiments in which a professional musician played a clarinet and an oboe, while the CO2 content of exhaled air was recorded together with the audio signal. By calculating the impact of the variation of CO2 and O2 contents on sound velocity, considerable effects on the fundamental frequency of the tones produced are predicted.
The natural resonance frequencies of wind instruments are dependent on the geometry of the air
column, the dimensions and design of reed/mouthpiece, the placement and size of toneholes and the sound speed in
the gas inside the instrument. Also, this gas continuously changes in composition with respect to the content of
carbon dioxide (CO2) and oxygen gas (O2) due to the player's metabolic activity. These changes should affect the
fundamental frequency to some extent. This frequency is also a function of the embouchure configuration and the
highly varying blowing pressures . The purpose of the present study was to provide an experimental and theoretical
basis for analysis and measurement of the impact of the gas changes in the sounding pitch.
Typical atmospheric air contains a concentration of CO2 ranging between 0.03% and 0.06%, while O2 is found at a percentage of approximately 20.9 %, regardless of local altitude. These are the gases whose percentages change between inhaled and exhaled air. In addition, there is metabolic production of water, which is expelled as saturated vapour. It is also important to note that the respiratory airways comprise a volume defined between the air inlet and the first pulmonary structures, called anatomical dead space, in which the air practically does not change in composition from the ambient values. The anatomical dead space is in average ca. 150 ml. Variations in exhaled CO2 during performance of a solo work with the oboe and sustained tones with the clarinet have been previously documented. The results showed that in wind instrument playing, the CO2 contents in the pulmonary air may vary considerably with time, roughly from 2.5% just after a deep breath up to 8.5% after a long playing period of ca one minute. The O2 contents in the alveolar gas, thus the air to be exhaled, are reported to achieve a minimum value of 14%.
During playing wind instruments such as the oboe and the clarinet, the content of CO2 in the expired air varies between the ambient level and up to 8.5% in extremely long phrases, while for the O2 it may vary from the ambient 21% down to 12%, or even less. The increase in CO2 tends to decrease the pitch and the fall in O2 tends to increase pitch. Even then, due to differences in gas properties and the rate with which the gases vary, the total effect is that of pitch decrease. This effect may account for a fall in fundamental frequency of the tones by more than 20 cents. Although we could presume that the pitch effects induced by gas variation are compensated for by the player by means of varying embouchure, blowing pressure and other playing characteristics, this effect still seems a relevant factor in wind instrument playing.
Respiratory movements and lung volume variations during natural performance of wind instrument playing have been scarcely documented in the literature, but may provide a deeper insight into performance techniques, players' physiological characteristics as well as into the physics of the instruments. Using Respiratory Inductive Plethysmography (RIP) respiratory movements of eight professional players (oboe, clarinet, alto-saxophone, bassoon) were measured during playing of exercises and orchestral solo voices. Calibration of the relative contribution of abdominal wall and rib cage regions was achieved from isovolume manoeuvres. Pneumotachometry was applied for absolute calibration of the RIP. Flow through a standard aerodynamic resistance at constant pressure was used for assessing the method of measurement under dynamic conditions. Different possible artifacts are described and discussed. The method yielded linear and accurate results, provided that significant body movement is absent, appeared to be non-disturbing to the musicians, accurate and robust. Depending on instrument and piece the players initiated the breath groups at 55% - 87% and terminated them between 14% - 52% of their vital capacity. Unlike what has been found for singers, the players generally showed simultaneous and in many cases equally important contributions from rib cage and abdominal wall during playing. In extreme cases, inhalations were achieved in approximately 300 ms and reasonably synchronised with the RIP signals.
Perception of blowing pressures in eight reed instrument players was assessed by means of a psychophysical production method. The aim of the study was to investigate how the players judge mouth pressures independently from playing conditions, i.e., without embouchure effort, reed vibration, airflow or auditory feedback. Reference pressures were established by relaxation at three lung volume levels ranging between just above functional residual capacity (FRC) to nearly full lungs. Successive doubling estimates were employed to assess the relationship between pulmonary pressure - a physical variable, and perceived pressure - a psychophysical variable. Regression analysis was applied to the data under four different models - linear, logarithmic, exponential and power functions. Generally, the linear model was the one that presented a highest correlation with the experimental data (r2=0.943), while the logarithmical model (Fechner Law) corresponded to a lowest correlation (r2= 0.869). The power function exponents (Stevens Law, r2=0.924) varied considerably among subjects, with a global average of 0.94, and among the three increasing lung volume levels, 0.79, 0.92 and 1.13, respectively. The method provided consistent data from the subjects and the results provided information about this rarely studied modality.
This investigation describes various characteristics of a particular phonation mode, vocal-ventricular mode (VVM), as produced by a healthy, musically-trained subject. This phonation mode was judged as perceptually identical to that used in the Tibetan chant tradition. VVM covered a range close to an octave, starting at about 50 Hz. High-speed glottography revealed that the ventricular folds oscillated at half the frequency of the vocal folds thus yielding a frequency of f0/2. Phonation at f0/3 was also possible. Presumably, aerodynamic forces produced by the glottal flow pulses sustained the vibrations of the ventricular folds. Complementary aspects of this type of phonation were compared to phonation in modal and pulse registers by acoustical analysis of the audio signal, by inverse filtering of the flow signal and by electroglottography (EGG). In addition, oesophageal pressures were measured. These analyses revealed that every second flow pulse was attenuated because of the ventricular fold vibrations and that the laryngeal contact area alternated between two minimum values. The spectra of VVM sounds contained clear harmonic partials up to about 4 kHz. Oesophageal pressure tended to change when phonation switched between VVM and modal phonation. Examples of periodic pulse register, another case of voice period multiplication, produced patterns of EGG waveform differing from those of VVM. The possibilities of using VVM in contemporary music, whether in a purely vocal form or during to wind instrument playing, are discussed.
©1998 by Leonardo Fuks
2. List of Abbreviations and Conventions
The papers will be henceforth referred to by their Roman numerals.
Figures and Tables will be referred to by the same way as they appear in their respective papers.
Note name convention: the real note names, rather than the transposed ones are adopted throughout the thesis.
For example, in the alto saxophone, A4 stands for the standard A 440 Hz, rather than C4 as it would sound from a score.
D Pmouth amplitude of mouth pressure variations during vibrato
AW abdominal wall
c velocity of sound
ERV expiratory reserve volume
FRC functional residual capacity
IC inspiratory capacity
Irev sound intensity as estimated in the reverberant chamber
IVM isovolume manoeuvre
jnd just noticeable difference
p0 , Pmouth or Pm pressure in the mouth, blowing pressure
PFE power function exponent
RC rib cage
REL resting end-expiratory level
RIP respiratory inductive pletysmography
RV residual volume
SPL sound pressure level
TLC total lung capacity
Tr reverberation time
airflow through the reed/mouthpiece
VC vital capacity
Vt tidal volume
VVM vocal-ventricular (phonation) mode
©1998 by Leonardo Fuks
Respiration and breathing are keywords in this thesis, since they play a central role in wind instrument playing as well as in voice production. In wind instrument playing and in singing the performer shares the vital metabolic air with the sound-producing organ. In a more general perspective, respiratory pauses and sometimes even respiratory sounds contribute significantly to music performance, also in the case of some non-wind instruments. For instance, in the playing of bowed string instruments, western classical performers frequently employ the sounds and gestures of respiration to enhance expressiveness and also to mark musical phrases. Thus, breathing and the associated pauses serve as structural elements in musical performance, often possessing a significant esthetical content.
This study comprises a suite of papers conceived with the intention to examine the theme under an interdisciplinary perspective, including musical, acoustical, perceptual and physiological aspects. It is concentrated on the mechanical-reed woodwinds, henceforth reed woodwinds, which comprise the oboe, clarinet, saxophone and bassoon. This interdisciplinary approach is justified by the assumption that it is not possible to fully understand the process of playing a wind instrument if any of these aspects is overlooked in the analysis. Figure 1 shows a schematic representation of the breathing behaviour in wind instrument playing.
Figure 1. Illustration, in the form of a trefoil diagram, of the phenomenon of breathing behaviour in wind instrument playing. As shown, breathing needs to accommodate demands originating from three main systems: performer, instrument and musical work.
As schematically illustrated in Figure 1, breathing behaviour in wind instrument playing is influenced by a great number of different factors, each raising demands on the player's performance. The structural organisation of the music imposes certain requirements regarding tempo, phrase length, dynamic variation, and the musical role in the ensemble. The performing artist has to accommodate these demands within the constraints and potentials of his own physiological system, including respiratory, perceptual, and proprioceptual capabilities. The instrument consumes air, provided by the player’s metabolic system. It consumes air to an extent that depends on many factors, such as the desired acoustical output, the technique of playing, and the responsiveness of the instrument. The task of the musician is to harmonise all these factors so as to reach a satisfactory artistic end result. Many of these factors have been neglected in previous investigation of wind instruments. Conversely, some research in the area of respiration may profit from improved information about breathing characteristics of wind instrumentalists. Likewise, the understanding of the function of wind instruments, as well as of the musical work and its performance, may gain from information about the physiology of the player. In addition, the knowledge gathered and produced in this thesis may have applications in the development of new playing techniques, the designing and improving of instruments, in compositional work, as well as in the development of computer algorithms for artificial instruments. From a wider perspective, the thesis can be regarded as a meeting point of several disciplines, such as musical acoustics, instrument making, music theory, physiology, ergonomics, and instrumental practice.
©1998 by Leonardo Fuks
4. Previous work
4a Physiological Aspects of Music Performance
Early interest in how players behave in order to operate wind instruments dates at least from the last century (Stone, 1874; Barton & Laws, 1902). Most of those studies were produced by physiologists who were mainly interested in the supposedly extreme levels of effort required, their physiological effects on circulation and respiration and on possible association to respiratory diseases (Frucht, 1937; Roos, 1936, 1938, 1940; Faulkner & Sharpey-Schafer, 1959; Singer, 1960; Akgun & Ozgonul, 1967; Watson, 1972; Gibson, 1979; Schorr-Lesnick et al., 1985; Gilbert, 1998). Part of this literature refers to pulmonary emphysema, a chronic pulmonary disease (Becker, 1911; Hävermark & Lundgren, 1957; Rejsek et al.; 1961). In this disease, there is an abnormal enlargement of the air spaces distal to the terminal bronchioles, accompanied by destruction of their walls (Snider, 1994). Yet, the claim that the playing of wind instrument might predispose to the development of pulmonary emphysema has never been confirmed (Bouhuys, 1964; Lucia, 1994). Rather, emphysema has been proved to be connected to smoking habits, to chronical respiratory disease and to genetically-related disposition (Snider, 1994). On the other hand, patients with respiratory problems who have music as an occupation are more likely to experience symptoms triggered by the demands imposed by performance. Similarly, wind players will tend to notice more clearly the physiological modifications associated with aging.
Arend Bouhuys probably contributed most importantly to the present knowledge on physiology of wind instrument playing. He studied pressure, airflow, sound power, efficiency, CO2 variations, heart rates, and other aspects (Bouhuys, 1964, 1965, 1968). Using a pneumograph he assessed qualitatively lung volume variations and also discussed some respiratory techniques, such as circular breathing (Bouhuys, 1964).
Based on the fact that blowing pressure in the observed brass instruments presented wider ranges than in woodwinds, Bouhuys hypothesised that mouth pressure control would be more important for those instruments than in any other type of winds. It must be borne in mind, however, that in brass instruments, where the lips serve as the oscillating reeds, the lip tension control is as important as the expiratory pressure. In woodwind, the embouchure, i. e. the link between the player’s mouth and the instrument (see below), is also very relevant, although it does not affect the pitch to the same critical extent as in brass instruments.
Other contributions to the physiology of wind instrument playing were given by Navrátil & Rejsek (1968), Vivona (1968), Benade (1986), among others.
4b Music Acoustics
Wind instruments have been intensely investigated in the domain of music acoustics. From the pioneering contributions of Weber (ca. 1830, as quoted by Bouasse, 1929) and Helmholtz (1863), followed by the important work of Bouasse (1929), the physics of wind instruments has attracted the attention of several generations of investigators.
With regard to reed woodwinds, particularly significant contributions were offered by Meyer (1961), Backus (1961, 1963a, 1963b, 1977), Benade (1968, 1976, 1986, 1988), Nederveen (1969), Worman (1971), Bak (1978), Plitnik & Strong (1979), Thompson (1979), Stewart & Strong (1980), Schumacher (1981), McIntyre et al. (1983), Pawlosky & Zoltowsky (1985, 1987), Gilbert (1986, 1989, 1991), Meynial (1987), Sommerfeldt & Strong (1988), Gibiat (1990), Hirschberg et al. (1990), Keefe (1990), Idogawa et al. (1993), and others.
A majority of the studies of reed instruments concern the acoustics of the clarinet, a quasi-cylindrical tube resonator excited by a simple-reed oscillator. The large concentration of studies on this instrument is probably due to the fact that the instrument possesses characteristics that are favourable from the point of view of experimental research. For example, the amplitude of vibration may be relatively small and the reed does not necessarily beat against the mouthpiece. This and the quasi-constant cross-sectional area of the tube resonator reduce complexity, particularly as compared to double reeds attached to conical tubes. In addition, the clarinet is a widespread and reasonably low-priced instrument, homogeneous in terms of design and used in many types of ensembles and styles.
The combined theoretical and experimental knowledge provided by the above-mentioned and other studies, permits simulation and prediction of instrument behaviour, at least under specific circumstances. However, many problems need still to be solved before the full system can be exhaustively described. The instruments are geometrically complex with a multitude of tonehole configurations, the reeds are neither standard, nor homogeneous, and the player’s behaviour cannot be assumed to be constant and absolutely reproducible. In addition, music requires quite fast and complex changes of the output sound. All this causes difficulties in defining parameters and initial conditions of a system of equations intended to describe, at least hypothetically, the phenomena involved. Fletcher & Rossing (1998) point out that an accurate prediction of the airflow through a wind instrument, that takes into account the effect of viscosity, necessarily requires the solution of the Navier-Stokes equations (e.g. see Yih, 1969). These are non-linear and would demand numerical methods for their solution, once the system is suitably defined.
4c Musical Pedagogy
Many pedagogical text-books for wind instruments, sometimes called "methods", often considers techniques for respiration and breathing for sound production (Quantz, 1752; Rockstro, 1890; Palmer, 1952; Rothwell, 1953, 1976; Thurston, 1956; Spencer, 1958; Stein, 1958; Sprenkle & Ledet, 1961; Bonade, 1962; Teal, 1963; Timm, 1964; Putnik, 1970; Goossens, 1977; Weait, 1979; Mazzeo, 1981; Mauk, 1986; Rehfeldt, 1994). In some cases, these sections review some basic anatomy of the respiratory apparatus, sometimes complemented by descriptions of the inspiratory and expiratory muscles, recommendations on posture during playing and on optimum inhalation strategy and instructions on how to achieve "support" and "use the diaphragm". Unfortunately, these two latter terms seem vague and used in diverging meanings among different authors. In addition, differing meanings of the same term are often used in different fields. Obviously, this lack of consensus regarding the meaning of terms will cause misunderstandings and confusion among students and colleagues.
Occasionally there is a marked discrepancy between the contents found in musical text-books and the current knowledge in respiratory physiology and mechanics; sometimes totally neglected are the great advances, achieved particularly after the end of WWII (see e.g., Rahn, 1946; Agostoni 1964, 1965, 1967; Wade, 1954; Konno and Mead, 1967, 1968; for a broad and detailed account of respiration, see Roussos, 1995). This obviously hampers interdisciplinary communication.
A professional brass instrument player and teacher, Arnold Jacobs (1915-1998), in particular, has paid major attention to respiratory aspects. Jacobs was probably the most influential wind instrument teacher in the USA and other countries, particularly among brass players. His pedagogical activities were exclusively oral, through private lessons and workshops (Stewart, 1987; Frederiksen, 1996). In his lessons, Jacobs used an ensemble of devices, developed for respiratory clinical purposes, providing visual feedback to the students regarding pulmonary pressure, air flow and lung volume. Also, he designed or adapted some equipment aiming at stimulating respiratory function in players and at increasing the degree of consciousness and training regarding muscular control. Interestingly, Jacobs used a terminology that was more pedagogically-oriented than based on physical facts. For instance, he emphasises "flow" as a keyword for playing control, as opposed to "pressure", which he deemed a negative term. This seems to be due to the psychological effect of these words. Different terms may tend to trigger different behaviours in players. Probably he did not overlook the fact that reed wind instruments and brass instruments are generally regarded as pressure-controlled systems (Benade & Gans, 1968; Elliot & Bowsher, 1982). There is also another reason for emphasising "flow". In brass instruments there is a wide range of combinations of mouth pressure and lip resistance that produce the same output level. If the player is able to use configurations requiring lower pressures, i.e., lower embouchure resistance and/or stiffness, the airflow should be maximised and the playing effort reduced (Nederveen, 1969). These general principles are likely to apply also to woodwind instruments, at least to some extent.
Music acoustics research would have the potential of contributing importantly to music pedagogy and performance. Definitions of terms based on scientific data should be easier to accept than definitions derived from experts’ introspection. Likewise, realistic ideas of anatomy and physiology have a great potential to gain wide acceptance, thus promoting interdisciplinary exchange.
©1998 by Leonardo Fuks
5. Instruments analysed
This investigation was focused on reed woodwind instruments and on voice, the latter with respect to a particular effect of vocal-ventricular phonation. Limiting the instrumental study to four types of instruments was due to practical and methodological considerations. A practical consideration was the huge amount of experiments and data processing required to achieve some degree of depth in the analysis of a given instrument. A methodological consideration was the vast differences in the principles that regulate the sound generation in different types of wind instruments, e.g., the above-mentioned mechanical reed, free reed (harmonica, accordion), air-reed (flutes, recorders, etc.) and lip-reed (brass) instruments. These differences lead to separate playing techniques, necessitating the use of different theoretical approaches for each instrument type. Nevertheless, most of the studies and procedures in this work might be useful in future investigations of other types of wind instruments.
The idea to include the human voice in this work originated from the observation of some apparent similarities between the mechanical system of reed instruments and certain properties of the specific phonation mode studied. These similarities will be explained in greater detail below.
5a Reed woodwinds
Figure 2. Bassoon plant. Despite standard and accurate manufacturing procedures adopted by the maker, the different parts of an instrument must be mutually adjusted, so that equivalent parts are not usually interchangeable. The instruments shown incorporate the German Heckel system (Blei & Baumann, 1987).
Mechanical reed woodwinds constitute an important group of wind instruments, which in western classical tradition includes oboes, clarinets, saxophones and bassoons. In these instruments, the function of the reed is to modulate the airstream that enters the air-column of the instrument, exciting and maintaining the vibrations in the bore.
Each of the instruments are available in two or more "voices", according to pitch range: soprano oboe, oboe d’amore, English horn; soprano clarinet (in Bb and in A), Eb clarinet, basset horn, bass clarinet; soprano, alto, tenor, bass saxophones; bassoon and contra-bassoon. There are still more variants. Usually, different voices of an instrument use almost identical fingerings. There are, however, instruments designed with different key systems and tonehole configurations, particularly for the oboe and the bassoon, which may also differ in sound quality and in playability, see Figure 2.
Among the four instrument types, we selected the four most commonly used, shown in Figures 3-6. The reeds for the alto soprano and the clarinet are very similar, the first being larger in all dimensions, see Figure 7. The reeds for all four instruments are generally made of a species of bamboo, Arundo donax. Other, mainly synthetic, materials are also available. However, the bamboo is by large the most common among professional classical users. Since oboe and bassoon reeds are autonomous pieces, directly attached to the instrument bore, they will be referred to as reeds or mouthpieces. Figures 3 to 7 from Nederveen (1969).
Figure 4. Soprano clarinet
Figure 5. Bassoon
Figure 6. Alto-saxophone
Figure 7. A clarinet/saxophone mouthpiece. The reed is rigidly clamped by the ligature in one extreme. The blade is free to oscillate along the curved profile of the mouthpiece. The airflow slit is the varying opening area between the reed margins and the mouthpiece lay. Embouchure sets a different contact region between the parts, moved towards the tip, characterised by a less rigid and more damped attachment (see Figures 10a and b).
Reed woodwind instruments produce tones at pitches which are dependent on many factors: the length of the acoustical air-column inside the instrument, the shape of the instrument bore, the sound speed of the air inside the instrument, the natural vibrating frequencies of the reeds and, to some extent, the blowing pressure. Also, the so-called embouchure is highly influential. The term embouchure is somewhat vague (Porter, 1967; 1973). In this thesis it is assumed to be the constellation of forces and positions in the lips, mouth region and face that act on the instrument. A more detailed account for the effects of the embouchure is given in the end of this section.
The length of the air-column is mainly determined by the fingering applied to the instrument mechanism, which permits a large combination of open and closed tone-holes. This length can be modified by the longitudinal position of the mouthpiece, which allows fine tuning adjustment of the instrument with respect to an intonation reference. The tuning is also affected by the acoustical length of the reed, which depends on the physical reed length and shape.
The shape of the instruments' bore may be roughly approximated to a cylinder in the clarinet and to a truncated cone in the oboe, saxophone and bassoon. In simplified terms, the sound waves travelling in a cylindrical tube closed at one end, such as in an idealised clarinet, may be considered as quasi plane. The frequencies of the resonance modes approach a harmonic series containing the odd multiples of the lowest resonance. For a conical tube, the waves produced are quasi spherical, thus a series comprising all multiples of the lowest resonance frequency. In reality, those resonance modes present inharmonicities, i.e. they are not exact integer multiples of the lowest resonance (Bouasse, 1929; Benade, 1968; Gilbert, 1991).
The speed of sound propagation in the instrument is of great importance. The reason is that the reed oscillations are controlled by a vibratory regime in the bore; acoustic pulses, created by the reed’s modulation of the airstream from the mouth, travel along the bore, are reflected at the effective end point of the air-column and return back to the reed chamber. The travel time depends on the length of the bore and of the sound speed. This speed depends on the temperature, humidity and the composition of the gas inside the instrument, which thus affect the fundamental frequency of the tones, see Figure 8. The magnitude of these effects is investigated in detail in Papers IIIa and IIIb.
Figure 8. Players must adapt themselves to perform under various conditions. At low temperatures, the normal fundamental pitch of a wind instrument should decrease considerably, for example, almost a semitone at -10°C. However, as the instruments are warmed up, this deviation should be greatly reduced. Photo by Blei & Baumann (1987).
The reeds generally oscillate at frequencies that are far below their inherent frequencies, i.e. frequencies at which they would vibrate should they not be coupled to an air-column (Helmholtz, 1863; Bouasse, 1929; Benade, 1976). For instance, when the player increases the load forces in the embouchure, thus increasing the reed stiffness, the inherent frequency of the reed is raised. This increases to some extent the sounding pitch. Players continuously use this principle for fine adjustments of intonation. Also, in clarinets and saxophones the single reed is bent against the curved lay of the mouthpiece, see Figure 7. This implies an increase in load force and a shortening in the vibrating length of the reed, which raises the fundamental frequency to some degree. This affects the equivalent length of the instrument (Gilbert, 1991, and see below). "Squeak" sounds, high-pitched sounds that accidentally occur mainly in the clarinet, are explained as a consequence of an insufficient coupling of the reed to the air-column modes. In this case, the reed vibrates closer to its natural frequency, occasionally reinforced and assisted by a resonant peak of the mouth cavity and/or the instrument bore. "Squeak" sounds are sometimes used in contemporary music, often controlled by the direct contact of the teeth on the reed (Rehfeldt, 1994) and/or by skilful shaping of the vocal tract.
Apart from the embouchure’s effect on reed stiffness, it probably also adds to its effective mass. The surface of the lips that touches the reed should form a layer of tissue that participates in the oscillations. This should reduce the natural frequency of the reed, implying that the fundamental frequency should decrease somewhat. This seems to be a neglected factor in previous investigations. In a pilot experiment, we applied a thin film of plastic gum of 0.1 g on both sides of a bagpipe reed, connected to its air-column (a conical chanter), blowing at constant pressure. This caused the fundamental frequency to decrease by more than 15 cents. The bagpipe reed is located inside a cap, isolating it from the lips. This result suggests that the mass added to the reed by the lips is significant.
Blowing pressure is intimately related to airflow in reed woodwinds. Analysis of the static airflow, void of oscillation, across a reed-like device has shown characteristic relations between the two, see Figure 9 (from Fletcher and Rossing, 1998, after Wijnands & Hischberg, 1995 and Worman, 1971). They reveal that, for a given embouchure, airflow varies with pressure according to a bell shaped curve. Acoustical and aerodynamical considerations show that self sustained oscillations will only be possible on the descending side of the curve and that these oscillations can be started at a threshold pressure, i.e., approximately one third of the pressure that completely closes the reed. The pressure-flow curves are different for double reeds, such as oboes and bassoons, although similar principles apply. The differences consist of the fact that in curve III there is hysteresis, implying that an increase of the upstream pressure to a maximum will suddenly interrupt the flow, while a different behaviour occurs when going the reverse direction.
In practical terms, the static flow curves show that for a fixed embouchure the airflow and the sound power radiated by the instrument should decrease with increasing blowing pressure. Papers I and II investigate the pressure and airflow in naturally played instruments.
Figure 9. Pressure-flow curves through a static reed, i.e. without oscillations. With a blowing pressure of p0 and an internal pressure of p, flow increases from O until it reaches a maximum at A and decreases until the closure point C. For the two curves on the left, the instruments can only operate in the descending part of the bell-shaped curves. Filled line represents the typical case of the clarinet (Worman, 1971). Double reeds may behave according to one of the three curves, because of internal flow resistance. From Fletcher & Rossing (1998), after Wijnads & Hirschberg (1995).
Another important phenomenon occurring in instruments is overblowing. In reed woodwinds it refers to the situation that the reed vibration frequency is controlled by a higher oscillation mode of the air column. Overblowing is caused by a particular combination of embouchure and input parameters, sometimes assisted by a special fingering. As mentioned above, conical bores have modes at approximately integer multiples of the frequency of the lowest mode. Thus, overblowing will make the reed oscillate at higher resonance modes in the air-column. Similarly, in conical bores overblowing establish reed vibrations at frequencies which are about 3, 5, 7 etc. times the lowest mode. The overblowing phenomenon delimits the different registers of the instrument. Generally, the reed instruments use no more than three registers but under special circumstances, additional registers may occur.
The oboe, Figure 3, has a length of approximately 644 mm, including the reed, and its usual range is Bb3-G6. The first register is limited by the note C5. The second runs up to C6, and has fingerings very similar to those in the first register. The fingerings in the third register are less systematic for reasons of tuning. The double reed, consisting of two opposed, curved blades tied to a metal staple, is shown in more detail in the same figure. Of paramount importance is the design and finishing of the reed scrape, as it affects the playing properties of the reed. Usually, oboe and bassoon players make and adjust their reeds according to the instruments, the material properties, and to personal preference.
The Bb clarinet, Figure 4, has a bore measuring about 664mm and is approximately cylindrical. The instrument typically ranges between D3 and B6. Ab4 limits the first register. Because its air-column modes are odd multiples of the fundamental mode, the second register gives three times the fundamental frequency, in musical terms a duodecim or a twelfth. This register is available from A4, which uses the fingering of D3 plus the register hole. This register continues up to Bb5 (position corresponding to Eb4). From this point on, the third register follows until B6, with non-sequential fingerings as in the former registers. Only Boehm system clarinets, the most widespread, were used in our experiments.
The bassoon, Figure 5, like the oboe, consists of a conical tube with a double reed, measuring approximately 2560 mm and ranges typically between Bb1 and D5. The first register spans from Bb1 to F3. This is considerably larger than the other instruments. From F#3 up to D4, the fingerings are similar to the previous octave, with the assistance of some keys. Then, the last octave comprises fingerings that vary greatly. In our experiments, all bassoons belonged to the German (Heckel) system, see Figures 2 and 5.
The alto saxophone, Figure 6, consists of a quasi-conical bore of 1062 mm and a typical playing range between Db3 to A5. The first register reaches E4, the second register covers the range F4 to A5, and uses fingerings similar to those used in the first register. For saxophones, mostly one single system is used.
From the above, it is evident that the embouchure serves many different purposes, all controlled by the player. Figure 10b presents a tentative schematic model for how the mechanical parameters of the embouchure are distributed along the reed. The lips are pressed against the reed with a load force distributed on the surface (dFm). The tissue has a stiffness (dKm) and a mass distribution (dMm), and also attenuates the oscillations with a damping coefficient (dRm).
Figures 10a and 10b. Simplified representation of the embouchure (a) and a detail with its mechanical parameters (b) on a single reed instrument. For double reeds, obviously both blades will be in contact with the lips and the factor of the reed bending along the mouthpiece lay is not present.
The purposes of the embouchure are as follows:
- Providing an airtight seal between mouth and mouthpiece. To meet this demand, the embouchure may sometimes be adapted to the blowing pressure. For instance, a pressure increase might require increase of the lip contraction so as to prevent air leakage. This may potentially affect the reed behaviour. In the oboe and bassoon, both lips are folded over the teeth, while in the clarinet and the saxophone only the lower lip usually folds over the teeth while the upper teeth are in direct contact with the mouthpiece. In addition, the upper lip is pressing anteriorly against the upper surface of the mouthpiece and laterally against its sides. Some clarinet players fold the upper lip around the teeth too, like oboe and bassoon players. This technique, called "double-lip", is argued to ensure a more relaxed, steady and balanced embouchure.
- Controlling the degree of damping of the reed vibrations (Nederveen, 1969; Wilson & Beavers, 1974). This damping can be applied in different regions along the reed surface, enabling a wide variation of the timbral output tone and vibration modes. Also, it is used to inhibit undesired modes of reed vibrations ("squeaks" e.g., in clarinet and saxophone).
- Regulating the stiffness of the reed by means of load force. This force, applied normal to the reed surface, affects the reed deflections and, in the cases of clarinet and the saxophone, also the bending of the reed along the curved mouthpiece profile, as mentioned (Nederveen, 1969; Gilbert, 1991; Stewart & Strong, 1980; Meynal, 1987). Both factors increase fundamental frequency. Gilbert (1991) measured an increase of more than 30 cents, at a constant blowing pressure, between a relaxed and a tense embouchure in a high-pitched alto-saxophone note (E5, real note).
- Regulating the dimensions of the slit through which the air passes into the instrument (Nederveen, 1969; Wilson & Beavers, 1974; Bak, 1978). This function is also carried out by means of the application of the load force, as in c. The slit, or gap, is obviously variable due to the reed oscillations. An initial static (without pressure difference across the reed) and an average dynamic gap may be determined by optical or other methods. It can be expected that the dynamic gap will be smaller than the static, since the blowing pressure would add an aerodynamic component to the loading force by the lips (Nederveen, 1969; Bak, 1978; Gilbert, 1991).
- Adding mass to the reed. Because of the direct contact in the embouchure, the lips participate in the reed vibrations, thus increasing its inertia. This effect alone would decrease the natural frequency of the reed to some extent, thus producing a decrease in fundamental frequency, as mentioned.
- Positioning and holding the instrument relative to the player. This refers to the degree of angular freedom provided by the embouchure, affecting the posture including the positioning of the arms and, to some extent, also the fingers. It has consequences for the internal configuration of the mouth and the tongue relative to the reed. The conformation of the players' teeth and jaws are also significant to the embouchure (Porter, 1967, 1973). Also, particularly for fingerings that require the right hand just to hold the instrument (with the thumb) and the left hand to apply unbalanced forces on the instrument, the embouchure may serve to support and stabilise the instrument. One example is the fingering for Bb5 in the clarinet, which tends to force the mouthpiece against the upper lip. This might be called an ergonomical function of the embouchure.
By modulating the embouchure, usually accompanied by a modulation of the blowing pressure, it is possible to produce a gamut of sound effects and gestures, including the so-called "lip vibrato", briefly discussed in Paper II.
It must be stressed that the above descriptions refer to embouchure in reed woodwinds. In the case of brass instruments, where the lips serve as the main oscillator, such function must be added and the purposes represented by items b, c and d do not apply. Also, the embouchure in air-reed instruments, such as flute and recorder, require a different description.
In defining the embouchure, it is possible also to include factors that determine the intraoral configuration, such as the position of the jaw and tongue. The shape of the mouth cavity is frequently assumed to be relevant to the sound production (Benade, 1986; Thomas et al., 1988; Backus, 1963b).
5b Human voice: Ventricular fold phonation
Human voice might be regarded as a special case of wind instrument. The source oscillations are mainly defined by the inertial and viscoelastic properties of the vocal folds and the aerodynamic parameters of the airflow passing them, while the feedback from the air column upon the vocal fold oscillator is generally of minor significance. Yet, a particular type of voicing seems interesting from the point of view of wind instrument acoustics, viz. the one produced by some Tibetan monks and ethnic groups of Central Asia. This type of voicing is characterised by a very low fundamental frequency and a loud tone, rich in harmonics as compared to corresponding tones produced by Western bass singers (Smith et al., 1967; Barnett, 1977; Dmitriev et al., 1983; Campbell & Greated, 1987; Zemp, 1996). The underlying mechanism has not been clearly explained. This raises the question whether structures other than the vocal folds could play the role of an oscillator.
It seemed reasonable to assume that the ventricular (or false) vocal folds vibrate in such voice production. The geometrical configuration of these structures differs considerably from that of the vocal folds. As can be seen in Figure 1, Paper VI, the ventricular folds have a downward angulation. Thus, they can serve as a closing valve, preventing exhalation at high intrathoracic pressures, such as during the initiation of coughing. The vocal folds have the opposite angulation, so that they can serve the purpose of closing the airways during inhalation, such as in hiccup. According to Helmholtz (1863), the valve systems represented by the reeds in musical instruments may be classified into inwards striking "tongues", or valves (e.g. reed woodwinds), and outwards striking valves (brass instruments and voice). An interesting possibility studied in Paper VI was if they then function as an inward closing valve, i.e., similar to a woodwind reed.
©1998 by Leonardo Fuks