[Note by Virginia Benade: This paper is one of a series titled "Acoustique, Musique, Espaces" presented in Paris during the 1983/84 season by various acoustical researchers from the international community.  In preparing the talk for publication (planned by the sponsors but probably never done), Benade made a few revisions and added a Summary and some more references.  He also added a comment in the fall of 1986.  The whereabouts of the recorded examples mentioned in the talk is unknown.]
 

SUMMARY

    In this presentation, the musical signal is traced from a) its extremely stable source in a wind instrument through b) its chaotic path in the concert hall to c) the highly evolved perceptions of the listener.  The multimode nonlinear self-sustained oscillation processes of wind instruments are also outlined.  A good wind instrument is defined here in terms of the many well-defined attributes of the signals it produces.  Any or all of these attributes can be used by the ears to keep track of the progress of an instrument's sounds in the midst of a musical passage that involves several instruments.  The path followed by a signal in a room is random, but the ear can collect information on its source from a group of early reflections, attributing the total information gathered to the time and position of the first arrival of the signal.  A good concert hall is defined as one that provides multiple reflections among the players and offers the listeners sufficient early reflections to transmit the music well to them.  However, a successful hall's design must also minimize the disruptive reflections arriving in the 100- to 200-millisecond range.
 

INTRODUCTION

    It is a pleasure for me to be part of the series "Acoustique, Musique, Espaces." My anticipation of this event has been growing ever since the news came to me that Michel Portal had agreed to preside over this evening's séance. It was my privilege to meet with M. Portal and to spend an afternoon discussing clarinets with him at IRCAM during my most recent visit to Paris, and my admiration for his versatile talents grew even greater last winter when I had the pleasure of hearing Portal's superb score for the film "The Return of Martin Guere." Having expressed my pleasure at being given this opportunity to participate in the series, I must also confess a certain regret that it has not been possible for me to hear the presentations of the other contributors, three of whom I am pleased to count among my friends--Johan Sundberg, Lothar Cremer, and Jürgen Meyer.

    We have a complex task before us, or perhaps it would be better to describe it as an elaborate guided tour. We will visit the domain of the musician, the homeland of the physicist, the kingdom of the craftsman, and the country of the psychologist--and all of this in the service of the architect! As is the case for every kind of international travel, we will have to be somewhat thoughtful about the ways in which we communicate with the natives of each nation. It is not a question of their friendliness, but rather one of precision in our mutual exchange of ideas. In many cases, the words used by the citizens of one part of the world (as they speak their own language) sound familiar to the visitor, but they in fact have an entirely different connotation. Misunderstanding is the most dangerous type of mal-communication! For this reason, I shall inform you explicitly whenever we need to change our mode of discussion from that of one "country" to that of another.

    The structure of my presentation this evening is as follows. Each of the principal ideas will be introduced in outline form, complete with rhetorical questions, numbered assertions, and exclamatory remarks. To borrow a metaphor from our musical friends, each idea will set a theme, and my discussion of it will offer some variations along with a certain amount of explanatory counterpoint. The chief conclusions or major consequences of each section of the discussion will then be given prominence by means of numbered summarizing statements.

    The purpose of this presentation is to outline the general properties of musical wind instruments and to use these as a means for introducing a discussion of the way the auditory system of a musical listener exploits the properties of a concert hall. Clearly it would be impossible to present a microscopically detailed account of the functioning of every individual type of wind instrument. All of the wind instruments, however, whether trumpet, saxophone, flute, oboe, or clarinet, function acoustically in almost exactly the same way, and their musical virtues are almost identical. Since the clarinet proves to be not only a fine musical instrument but also (for many reasons connected with its physical structure) an ideal subject for scientific research, it will be my primary source of examples. One needs only to change a few words to adapt discussions based on the clarinet to the needs of an explanation of the other instruments, so that I will (most of the time) simply omit reference to the other instruments.

    Let us begin the formal part of our discussion by calling attention to the very peculiar looking Fig. 1, which illustrates three things whose relationship seems paradoxical. First, from the point of view of the physicist, the sounds produced by any musical source are extremely stable--the musician can replicate the physical characteristics of the sounds he produces with extreme precision, even after the lapse of several hours, or even, in certain cases, after several months!¹

    We learn next from this diagram that the transmission of sound from the player's position in the room to that of the listener is extremely variable: the various physical features of the sound produced by the player arrive at the listener's ear in a violently modified form.

    The final assertion made in Fig. 1 is that, despite the apparently garbled form of the sound received by the listener, the operations of his auditory system permit him to perceive the subtle consistencies of the player's sound in a very dependable manner. He can not only recognize the instrument, but also can appreciate the nuances of its sound that are essential for any musical performance.

    Pause a moment to assimilate this shocking sequence of assertions and to recognize that at least the first and the last are (in the world of our ordinary musical experience) perfectly familiar. Indeed these two are so familiar that it is only the acoustician who is aware of the chaotic path traversed by the musical signal.

    We should invoke another item of musically familiar information to provoke a yet more vivid sense of wonderment over the operations of the musical source, the signal path, and the listening audience: musicians absolutely despise playing outdoors or in the reflection-free rooms of an acoustics laboratory. In other words, they object to playing in environments where the signal paths are simple and direct. They complain that they cannot hear one another and are plagued by difficulties of coordination in tuning, rhythm, and dynamic level. Similarly, in such reflection-free environments the listener should expect very little in the way of musical subtlety in what comes to his ears. The physicist says that the signal path in a music room is the cause of great confusion, whereas the musician and his audience find that without the room, only music of the most elementary sort is possible! Clearly we have a paradox to resolve as we look for the features of the musical sound that give it sufficient robustness to survive its strenuous voyage to its listeners and as we seek the features of the transmission process itself that permit a cleverly designed auditory system to deduce the nature of the source that produced the original sound.
 

THE VIRTUES OF AN EXCELLENT INSTRUMENT

    From the point of view of the musician, it is not difficult to give a succinct description of the virtues required of any instrument that presumes to call itself "excellent." Let us present a list of musical virtues in a form that is adapted to introduce our consideration of the wind instruments.

    According to the musician, an excellent instrument must

1. "sing" with a full, centered, voice

2. permit a variety of good, clean, articulations

3. possess a readily controllable range of dynamics

4. display stability of pitch under all conditions

5. permit flexible note-by-note variation of pitch

6. respond with good "resistance"--that is, large muscular efforts are required for small musical effects, in order to achieve easy control of nuances.

    When the psychoacoustician looks at this musician's "wish list" he recognizes that an excellent instrument must possess a large number of well-defined sensory attributes.  We may say that a good instrument has a well-developed personality, whose features provide a variety of identification clues that can simultaneously serve many modalities of auditory perception. The auditory system may then utilize whatever fraction of this information that survives the complexities of the transmission path in the room. To repeat: a good instrument gives the listener numerous modes of recognition at every instant during a performance, and he can utilize any reasonable combination of these to deduce what it is that the player intends for him to hear. [Recorded Example 1.]
 

SOUND TRANSMISSION IN A ROOM

    The fact that all of these recognition cues are dependent on a limited number of parameters in the oscillation physics of the instrument is what ultimately makes possible the perceptual stability of a musical instrument and greatly simplifies the problems of the instrument maker.

    Having glanced briefly at some of the musical features that are required of a good musical instrument and having recognized their initial sensory implications, let us turn our attention next to the nature of the sound path in a room. To put it more precisely, let us see what happens from the point of view of a physicist when a sound signal is transmitted from one place to another in a room.

    Figure 2 shows the experimental arrangement. An electrical oscillator is used to excite the acoustical output of a small loudspeaker located at some arbitrarily chosen place in the room. At some other point in the room is placed a microphone provided with an apparatus that can measure the strength of the received signal. The excitation signal that is fed to the loudspeaker is of the simplest possible type, a so-called "pure tone" or "sinusoid." The smooth hum of a tuning fork, the cooing of a dove, or the sound of a man whistling are all familiar examples of this kind of sound. This type of signal has been selected because suitably chosen collections of sinusoids can serve as building blocks from which the physicist can construct all other sounds. Suppose now that the oscillator is charged with the task of providing a signal whose frequency is slowly rising, beginning from some low- pitched value, and that the microphone's recording apparatus is provided with a means for tracing out on a moving strip of paper a record of the strength of the received signal, to show the variation of the received signal strength during the time the excitation frequency is steadily varied.

    Figure 3 shows the resulting record of the transmission of such a sound from a loudspeaker to each of two positions in a laboratory room. The first feature of these two tracings to catch the eye is their extreme irregularity. We notice next that the two traces are entirely different. If, as a matter of fact, we were to produce thirty or forty traces of this type using various randomly chosen positions for the sound source and the detector, the traces would all be different. The mathematical theory underlying this chaotic behavior is very well understood,^2,3,4 being a distant cousin to that which describes the random bombardment of the walls of a cavity by the gas molecules contained within it. As a matter of fact the similarity extends yet further. Just as the average rate and vigor of the molecular bombardment determines what we call the pressure of the gas, so also does the mathematical average of the various microphone signal curves have a well-defined meaning--it serves to inform the physicist of the strength of the loudspeaker signal itself. The sloping dashed lines shown in the two parts of Fig. 3 serve thus to indicate that the loudspeaker in the present experiment produced a steadily increasing excitation of the room as its frequency was progressively raised.

    The experiments just outlined have the function of illustrating just how irregular is the signal transmission path in a room, and also they provide us with a hint of how the scientist might go about measuring the sound output of a musical instrument. The essential features of his method are as follows:

1. He records the sound signal at numerous points in the room (about thirty are required if he desires a precision of about ten percent, and four times as many points are needed to assure an accuracy of five percent).

2. He performs an analysis to determine the strengths of the various constituent sinusoids arriving at each individual point of observation.

3. He averages the results of all of the separate analyses.

Note: To combine all the microphone signals at the input of a single analyzer accomplishes nothing more than a reshuffling of the statistical cards. Contrary to the belief of some recording engineers, the result has no more significance than does the analysis of a single microphone!

How can the musical listener's ears accomplish the task of obtaining meaningful information in an instant, when the acoustician may have to struggle for many hours to achieve the same result?

THE STRUCTURE OF A WOODWIND INSTRUMENT

    Figure 4 will serve to introduce us to the essential features of a musical wind instrument, as it is seen by the physicist.⁵ To begin with, the player is responsible for providing a supply of compressed air to the instrument's reed system, which functions dynamically as a flow controller. On the downstream side of this controller we find an adjustable air column that is normally terminated by some sort of bell.  What all wind instruments have in common, then, are an air supply, a flow controller, and an adjustable air column.

    The acoustical features that serve to distinguish between the various families of wind instruments may be summarized as follows:

1. A woodwind is recognized by the fact that the length of its air column is adjusted by means of a sequence of tone holes that are opened or closed in various combinations to determine the desired notes. The oboe, clarinet, saxophone, flute, and baroque cornetto are all recognizable as being members of this family.

2. A brass instrument is distinguished by the fact that its air column continues uninterrupted from mouthpiece to bell, the necessary length adjustments being provided either via segments of additional tubing that are intercalated into the bore by means of valves (as in the trumpet or horn) or by means of a sliding extension of the sort found on the trombone.

1. First on our list is the "cane reed" found on the clarinet, oboe, bassoon, and saxophone. We do not need (for present purposes) to distinguish between the two types of such reeds; they both share the dynamical property that the valve action is such as to decrease the air flow through them when the pressure is increased within the players mouth.

2. The "lip reed" normally used on brass instruments and on the cornetto belongs to the second major type of flow controller. Here the valve action is such that the transmitted flow is increased by an increment of the pressure in the player's mouth.

3. Flutes, recorders, and most organ pipes are kept in oscillation through the action of a third type of controller that may aptly be described as an "air reed." Here we find an air jet whose path is deflected in and out of the air column through the action of the velocity of the air as it oscillates up and down the length of the governing air column.

    It is difficult for us to visualize the motion of air within the air column of a wind instrument. However, we can gain some insight with the aid of a parallel that can be drawn between this motion and the oscillatory behavior of water in an elongated channel. Look at the top three parts of Fig. 5. Here we see diagrams of three of the modes of oscillation that are possible for water in a uniform channel closed at both ends. The first diagram illustrates the simplest of these motions, which has a periodic (sinusoidal!) alternation of water height at the two ends of the channel. The second diagram shows the next more complicated type of motion, in which the water alternately piles itself up in the middle, and then at the ends. This oscillation takes place at a more rapid rate of sinusoidal alternation than does the first one. However, we must not fall into the trap of assuming that the second mode will oscillate at precisely twice the rate of the first; such a simple ratio will only be true for a particular variation in the depth of the channel. The third diagram shows a yet more elaborate (and still higher frequency) mode of oscillatory motion. We may deduce from these diagrams the fact that the water height at the ends of the channel alternately rises and falls in synchronism with the vertical motion of the water at certain other positions along the channel. We recognize further that a large oscillatory horizontal flow of water back and forth must exist in the regions of small vertical excursion. This horizontal flow is what alternately fills and empties the water from the regions on either side of it, producing the observed changes in depth.

    We are now in a position to connect our picture of water oscillations with corresponding ideas about the motion of air in an instrument's air column. Clearly, the increase and decrease of water depth at any point in the channel is correlated with an increase and decrease in the amount of water that is present at that point. In an exactly similar way we can recognize that the rise and fall of air pressure at some point in a musical air column is associated with the inflow and outflow of air to this region from the neighboring parts of the air column. As in the case of the water channel, an air column possesses of a large number of "modes of oscillation" each having its own complexity of motion and its own characteristic sinusoidal frequency.

    Consider now the lower part of Fig. 5, which is a diagram of what might very well be called a "water trumpet": a channel of varying trumpetlike depth is supplied on the left with a float that can operate a flow-control valve. This valve permits a flow of water into the channel end whenever the water level there is high and shuts it off when the level is low. It does not take a very large stretch of the imagination to show that a mechanism of this type is able to maintain the oscillation of any one of the vibratory modes of the water. However, there is a complication, one that is crucial to the successful operation of real wind instruments as well as to their hydraulic counterparts: each smooth rise and fall of the float gives rise to an abrupt pulse of injected flow. In a manner of speaking, this impulsive excitation of the water column modes acts to start them all going in exactly the same way that striking a bell with an impulsive force excites all of its modes into oscillation. We now come to an essential feature of our dynamical system. If the various modes of the water (or air!) column were to have irregularly related characteristic modal frequencies, the succeeding swings of each mode would then request a different pulse rate from the flow control valve. Chaos would result! The flow controller might say, "I can do nothing until all of you agree on the actions you wish for me to carry out!"

    Suppose, on the other hand, that the air column shape is cleverly chosen in such a way that its characteristic modal frequencies are in a whole-number relation to one another. That is, suppose that the second, third, and fourth modes like to oscillate at two, three, and four times the frequency of the first one. Under these conditions, the behavior is quite straightforward. Mode 1 will call for an opening of the valve once per cycle of its oscillation, mode 2 will call for two such openings (in the same period of time), while modes 3 and 4 will make requests for three and four such openings. Under these conditions the valve will therefore be opened strongly once each cycle of the first mode, and so excite all of the modes in synchronism to produce a steady, well-defined oscillation that is controlled by all the participating modes acting in concert. We now have deduced the essential secret of a successful musical oscillator: the flow controller must be operated cooperatively by a set of characteristic air column modes.

    In order to progress further in our exploration of the wind instruments it is necessary for us to learn how to characterize the nature of their air columns in a compact and easily read form. Figure 6 will introduce our new characterization by showing its relation to the room response curves that we have already met. The top half of the figure simply reviews the nature of the room experiments. The lower half indicates a similar experiment, in which the microphone is placed within the mouthpiece of an instrument, and the source ("loudspeaker") applies its excitation at an immediately adjacent point. The resulting response curve shows peaks located at the frequencies of the air column modes, with the tallness of the peaks giving a quantitative measure of the responsiveness of these modes to a flow excitation applied in the mouthpiece. Response curves of this kind can be obtained for the air columns used in playing the various notes of the instrument's scale, and these may be read like a book to learn the oscillatory virtues and faults of these notes.

    At first thought, one might think that blowing on an instrument would produce a cacophony of sounds, one belonging to each of its air column response peaks as it "instructs" the reed flow controller to maintain sinusoidal oscillation at its own frequency.  As a matter of fact, nothing of this sort occurs.  No oscillation can be set up from the multiple peaks of the response curve shown in Fig. 3 because the flow controller is nonlinear (that is, the flow is not strictly proportional to the controlling pressure).  As a consequence, a large number of heterodyne frequency components would be generated from the components belonging to the resonances.  (The frequencies of these heterodynes are calculated as sums and differences between the original modal frequencies plus a rather complex set of other heterodynes.)  These frequencies would not lie at the resonances of the air column and so would not be able to maintain an oscillation.  It is only when the air column shape is carefully adjusted to make its response peak frequencies lie in a whole-number harmonic series that the heterodynes themselves remain a part of the original set and thus can facilitate the oscillation.  Thus, musical instrument tones are generated by the cooperative action of a set of harmonically aligned response peaks.⁶  The accuracy of the alignment plays a dominant role in determining the overall goodness of the instrument.

    It is musically very important for us to notice that not only is the harmonic alignment of the air column resonances absolutely essential for the production of the tone, but also the resulting harmonic sound is perceived with particular skill by the auditory system.  It is the only complex sound that is perceived as a single entity.  For example, the sound of a clarinet, flute, or trumpet is always heard as a single entity having definite tone color, rather than as a collection of sinusoids.  For this reason these sounds are particularly useful in music: they are readily recognizable.

    Since the reed itself shows maximum effectiveness as a flow controller when stimulated near its own natural frequency, we find that adjustment of the reed's natural frequency to agree with some harmonic of the playing frequency is essential to the playing of brass instruments and is worthwhile in improving the stability of a woodwind's oscillatory regime.⁷  This adjustment of the woodwind reed's own response peak is normally obtainable via a simple variation of the pressure of the player's lips upon the reed, with no need for alteration of the point of application of this force.  Each note requires its own particular amount of reed-controlling tension, but the range and the necessary precision of adjustment in woodwinds is far less than that required for the crudest and most elementary playing of a brass instrument.

    Let us turn our attention now to Fig. 7, which shows us some of the ways an instrument's book may be read. The heavy dash-dot line marked ppp in this figure shows the sort of response curve one might measure for a wind-instrument air column that has (somehow) been arranged to possess only a single mode of oscillatory motion. The horizontal line marked "break-even" indicates schematically that if the response peak is taller than this, oscillation is possible. The pressure instructions given by the air column to operate the reed valve are strong enough that it then can provide an excitatory flow to the air column sufficient to maintain the oscillation. From the diagram we learn that under conditions of gentle blowing (pianissimo playing), a single air column mode can indeed maintain an oscillation in collaboration with the reed. When we attempt to play a crescendo, however, a number of things begin to take place:

1. Small complexities of flow and the beginnings of turbulence in the air column begin to reduce the height of the response peak. At what might be called a forte level of blowing pressure, we see from the lighter dash-dot line that the response peak has become less tall, making it less able to sustain an oscillation. In other words, blowing harder makes only a very small increase in the loudness of the resulting tone. We should remark here that whatever tone is produced at the ppp and mf blowing levels is very nearly a sinusoid. The resulting sound in the room is therefore very reminiscent of the simple and dull tone of a tuning fork to which a small amount of hissing air noise has been added [Recorded Example 2].

2. As one blows harder, the increasingly impulsive nature of the air flow through the reed leads to the production of oscillatory excitation at double and eventually triple the frequency of the basic oscillation. The arrows pointing downward from the horizontal line at the top of the diagram show where the excitations are found. We have already learned that the flow excitation at the modal frequency is able to produce oscillatory energy because the response curve lies above the break-even line. The other two arrows show the possibility of an energy deficit at double and triple the playing frequency, as is indicated by the fact that the response curve lies far below the break-even line at both of these harmonically related frequencies. Experiment shows that these deficits are so serious that if, in fact, one attempts to play a crescendo on an instrument constructed to have only a single response peak, there is at first almost no increase in loudness, and then the reed abruptly blows shut and chokes off what little sound is originally produced as the system goes into oscillatory bankruptcy [Recorded Example 3].

    We can learn yet more from the diagrams of Fig. 7. Suppose that our original air column is modified to provide it with a second response peak similar to the dotted line that has been drawn so that it rises above the break-even line, with its maximum near to but not coincident with the position of double frequency. If we play softly on this modified instrument, it will behave exactly as before: the tall first peak will dominate the situation and set the frequency of oscillation. However, if we attempt to play a crescendo, the double frequency "messages" sent by the reed to the air column have now a willing "listener," and the second response peak will be able to respond somewhat. As a matter of fact, a very interesting type of mathematical-physical negotiation takes place. We may imagine that the second peak sends an emissary to the first peak, and this emissary says, "If you will consent to supporting the oscillation to run slightly faster than your own favorite frequency (and with only a very slight reduction in your ability to generate energy), then I will be in a position to produce considerably more energy than is possible for me to do if we must run at exactly twice our present frequency." Normally the first mode will respond favorably to such a proposal, and the two peaks set up what is technically called a regime of oscillation, in which the operating frequency has a compromise value chosen in such a way that the total generation of energy is maximized.

    Since the reed itself shows maximum effectiveness as a flow controller when stimulated near its own natural frequency, we find that adjustment of the reed's natural frequency to agree with some harmonic of the playing frequency is essential to the playing of brass instruments and is worthwhile in improving the stability of a woodwind's oscillatory regime. This adjustment of the woodwind reed's own response peak is normally obtainable via a simple variation of the pressure of the players lips upon the reed, with no need for alteration of the point of application of this force. Each note requires its own particular amount of reed-controlling tension, but the range and the necessary precision of adjustment in woodwinds is far less than that required for the crudest and most elementary playing of a brass instrument.

    One of the musical tragedies of the past forty years has been the growing habit of clarinet makers to proportion their air columns in such a way as to frustrate any attempt by the player to exploit the wonderful resource of reed resonance. They have done this in a well-intentioned but misguided attempt to lighten the player's burden, with the result not only of spoiling the tone in several ways but also of depriving the player of the ability to make adjustments of the pitch of his notes in the course of playing them.

    Readers who are musicians will have recognized that the shift of operating frequency that results from negotiations between misaligned response peaks are at the root of the pitch-drifting tendencies of many instruments in the orchestra. A really fine instrument then is one whose response curves are accurately aligned not only to assure a wide dynamic range but also to assure that the pitch does not drift around. Little by little we are learning the physical bases for excellence in wind instruments.

    In a manner that will consolidate the newer ideas with the earlier ones, let us summarize what we have learned so far about wind instruments and what is required for their musical success:

1. Harmonically aligned air column response peaks are required in order to assure the collaboration of the air column and the reed [Recorded Example 4].

2. An additional stabilizing influence is provided by alignment of the reed's natural frequency to agree with some harmonic of the playing frequency.

3. In woodwinds, alignment of the reed resonance is a useful resource. For the brasses it is essential, since the player uses it to select which of the possible notes belonging to a given fingering will sound.

    Once a physicist recognizes the possibility of influencing the operations of a reed by means of the PWW, he is likely to draw for himself schematic diagrams of the sort shown in the lower part of Fig. 8. Here is indicated the valve action of a reed in terms of the motion of a pistonlike mass  m  which slides back and forth over an aperture through which air can be admitted from the upstream to the downstream side of the valve. The mass  m  represents the inertia of the reed itself, while the spring  s  symbolizes its elasticity. For our present purposes it will suffice to take note that the oscillatory forces that can move the reed back and forth are exerted on its front face by the acoustical signals within the instrument (as we have already discussed), while any acoustical disturbances that exist in the PWW are able to act upon the reed's rear face. It is essential to notice that from the point of view of the reed itself, both types of force have equal "rights" in their efforts to control the air flow.

    Just as we have learned to understand the influence of the IAC on the reed in terms of its response curve, so also must we take into account the influence of the PWW. Figure 9 shows in its upper part a typical response curve measured for some air column configuration of a clarinet (this includes a moveable peak that suggests schematically the oscillatory contribution of the adjustable reed resonance). The lower part shows in similar fashion a set of superposed response curves measured for various configurations of a PWW. Notice that for each arrangement of the player's tongue, etc., the response curve shows one strong response peak (which is as tall and, therefore, as influential as any to be found in the IAC curve) along with several weaker, and thereby less important, subsidiary peaks. We find that the player can readily move the frequency of the major peak to any position between about 450 Hz and 2000 Hz. In short, the player has at his disposal a response peak associated with the reed resonance, and he also has one that belongs to his own windway. These then can be located in any way he chooses to participate in the oscillatory regimes of the notes he plays.

    Analysis of the physics of reeds sandwiched between two air columns shows that we may simply add their response curves together to obtain an accurate picture of what controls the various oscillatory regimes that are possible for the system. Furthermore, physics allows us to predict (correctly) the very strange way in which the two air columns influence the actual sound recipes produced on the two sides of the reed:

1. On either side of the reed, placement of a response peak at some harmonic of the playing frequency has the effect of greatly strengthening the corresponding component of the tone as observed on same side. This by itself is a fairly straightforward matter to understand.

2. Surprisingly enough, one does not normally detect very much change in the sound observed on the opposite side of the reed! This is true despite the fact that the flow that is controlled by the reed passes through both the upstream and the downstream air columns.

3. All this is true despite the fact that the mutual alignment of the response peaks on the two sides of the reed can greatly stabilize the oscillation and make it a more docile subject for the musician's control.

    The lower part of Fig. 10 shows in a similar way the changes observed in the component amplitudes on the upstream side of the reed, which is where the peak alignment took place. Here we find that the strength of component 4 is enhanced by 40 decibels, which translates to a hundredfold growth in the amplitude. There are also large changes in the amplitudes of certain of the other sound components.

    In the first part of Recorded Example 5, a small microphone is being used to eavesdrop on the sound in the clarinet player's mouth as he plays an outwardly steady note, but with the response peak of his PWW being moved slowly back and forth over the frequency region inhabited by the second and higher components of the tone. We can clearly hear the momentary increase in the strength of the various components as the PWW peak passes across them. Let us now transfer our attention (via Part 2 of this tape segment) to what can heard via a microphone implanted in the clarinet's own mouthpiece. In other words we are listening to the sound on the downstream side of the reed as changes are made on the upstream side. Despite the fact that this downstream version of the clarinet's sound was recorded on one channel of the tape at the same time the other channel was recording the upstream version, we find almost no auditory evidence in the mouthpiece sound of the drastic changes that are taking place only a few millimeters away on the other side of the reed.

    What does this say then to the musician? In the first place, he is well advised to use PWW alignments as a means to steadier and more controllable sounds. He will be aided in his search for the optimum configurations of the PWW by the fact that sounds from within his mouth are transmitted to some degree to his ears via the pathways of bone conduction, etc., within his head. In other words, he is able to hear effects such as those that have just been demonstrated on the tape, and so to learn the acoustical status of his physiological adjustments.

    The situation is less obvious from the point of view of the listener. Adjustments of the PWW do not make very extensive changes in the sound detected within the instrumental mouthpiece, which after all are the ones that are ultimately emitted in modified form into the room from the tone holes and the bell. Despite the fact that the listener receives relatively little direct information about the player's exploitation of his PWW, he is perfectly well able to enjoy the sounds produced by a happy and well-adjusted instrument

    Two more questions will come to the mind of anyone considering the ideas set forth here about the performer's physiological resources. First: if the player can stabilize an oscillation by making proper use of the PWW, then one may justly inquire whether he can also disrupt a regime of oscillation and so generate some strange sound that can be heard in the concert hall. The answer to this question is yes. Once the player has gained conscious control of the PWW he can play disruptive games with nearly every note of his normal repertoire and thereby produce peculiar sounds.

    Recorded Example 6 provides several examples of the sounds that can be produced in this way. Two features of these sounds are worth commenting on at this juncture. They are clearly under the player's control as they come and go and as one of them metamorphoses into another. In addition we notice an auditory feature of these sounds that is not shared by the musical tones that are the usual product of a wind instrument. Every one of the "normal" sounds of a wind instrument is perceived as a single entity having a well-defined pitch and tone color despite the fact that it is made up of a large number of harmonically related sinusoidal components. The new sounds, on the other hand, are heard as (what musicians quite properly call) a multiphonic. That is, we become aware of several coexisting (though perhaps rough or ill-defined) tones, each with its own pitch. In other words, the irregular, nonharmonic collections of sinusoids that make up these new sounds are operated upon by the auditory system in such a way that several subsets of approximately harmonic components are selected from the overall collection, and each one of these is heard as a separate entity. Every one of these subentities is endowed with an approximation to our normal concept of pitch and tone color, and we are aware of them as individuals despite the fact that they all emanate from the same instrument

    The second question that might be asked is whether the reed of a wind instrument can be persuaded to oscillate under the governance of the PWW response peak, so that the player can produce some rough approximation to music by his deliberate manipulation of the PWW itself. Recorded Example 7 shows conclusively that this is indeed possible!

    We now conclude our examination of the wind instruments with a set of summarizing remarks that not only suggest why they are well adapted for survival in the concert hall but that also lead us naturally back to a consideration of the hall itself.

1. Good wind instruments gain their best stability, controllability, and responsiveness as the result of the alignment of many response peaks.

2.  Some of these alignments are produced in the instrument itself to an extent depending on the skill of its maker, while some of them are products of the player's own ability to adapt his physiological operations to the needs of the successive notes that he plays.

3. The sounds produced by a reed interacting with a set of accurately aligned response peaks (regardless of their upstream or downstream position) are of a well-defined type having many stable features (only a few of which we have mentioned). We have already learned that a multiplicity of well-defined features is one of the requirements for survival during the complicated voyage from instrument to listener in a room. Wind instrument sounds may therefore be said to be perceptually robust.
 

    So far in this presentation we have learned that the transmission process of sounds in a room is (from the point of view of the physicist) very complex. We have also learned how it is that the production of instrumental sounds can be extremely stable because of the multiplicity of cues available to the player to guide his exploitation of his instrument. In addition, we have become acquainted with the fact that in the practical world of music, the room somehow serves as a necessary adjunct to the listening process, rather than as a source of confusion. It is time therefore to inquire about the methods of signal-processing that are used by the auditory system that permit it to make "measurements" of the arriving sound at a rate that far exceeds the abilities of a scientist using his best equipment.^9,10

    Let us begin by considering the signals received by the listener's ear during the commencement of a musical sound in a room. Figure 11 illustrates the essential features of this initial epoch. The listener is provided with a series of early reflections. The first to arrive is the direct sound from the instrument, and then come in quick succession the first reflections from the walls, the floor, and the ceiling of the room.

    If we were using our eyes in a mirrored room instead of our ears, we could say that these initial reflections provide us with a front viewand left- and right-hand views, plus information about what would be seen from above and from below. In both the acoustical and the optical versions we find a further sequence of reflections of reflections, these being weaker and less well defined as the various complexities of the reflection and transmission process take their toll. At this stage in our considerations we have recognized that the sequence of early reflections presents the listener/observer with a great deal of physical information about all the aspects of the signal source.

    The observer in a mirrored concert hall can, so-to-speak, see a player from all sides. To do this however, he must assemble many pieces of information by literally shifting his attention from one reflection to another, after which he must intellectually construct his total impression. This visual information-gathering and interpretation process normally takes several seconds to carry out. However, when this same person plays his role as a musical listener in a room with reflecting walls, the acoustical situation is quite different.

    The auditory system (among its many other abilities) can "instantly" collect, store, compare, and interpret the properties of the early reflections arriving at the listener's ears. The successful collection, storage, comparison, and interpretation of this information depends on two things:

1. The various arrivals must not be excessively different from one another.

2. The early reflections must arrive within a time interval of about 35 milliseconds of one another.

    There is one more feature of the signal processing behavior of the musical ear to which we must give our serious attention:

3. Reflections that have traveled distances of 30 to 60 meters farther than the direct sounds are actively disruptive of the musical recognition process.

    We should take a moment here to examine in a preliminary way the manner in which the auditory system makes use of the information that it gains from these early signals or, better, the way in which the listener's conscious mind receives their compiled form. We begin by emphasizing that while the ear can collect data over a considerable period of time, all these early reflections are fused into a single percept.   This percept is formed very quickly, so that one is never aware of the time required to form it, even in the course of rapid music having sounds from many different instruments. If we are aware of the sound of a particular note, we may be sure that our perception of it has all or nearly all of the following features:

1. Its time of occurrence is taken to be the instant at which the earliest contribution arrives, which is normally the arrival time of the direct sound from the instrument.

2. It is perceived as coming from the point in the room from which the instrument itself transmits the first-arriving signal.

3. Its loudness is perceived as being accumulated from the entire sequence of early arrivals.

4. The individual arrivals are used together to provide a mutually confirmatory basis upon which one can assess such musical features as tone color, stability of production, and the type of articulation chosen by the performer for the note under consideration.

    Feature 2 permits us to keep account of the various orchestral voices as they perform in parallel or in contrast. While this is useful, it proves to be far less important musically than one would guess from the endless discussion of "stereo" by the high fidelity industry. It is worthwhile to recognize that our ability to process the arrival pattern of early reflections allows us to localize a sound source with one ear totally or partially covered. This is something that is nearly impossible in reflection-free surroundings, where one must perform all judgments upon the basis of the direct sound alone. "Stereo" phonograph records often provide the listener with extremely confusing directional impressions because commercial recording processes tend to exclude or disarrange the early reflection information that would come to the listener in a good concert hall.

    Designers of sound reinforcement systems for churches, lecture halls, and outdoor concert shells have exploited Feature 3 for about two-and-a-half decades. The engineer can, for example, supply the listener with a reinforcing signal whose acoustical energy is ten times greater than that of the original source, thus providing the listener with signals of adequate loudness, without making him aware that this has been accomplished by artificial means. In order to do this, the designer must merely ensure that the amplified signal is similar to its prototype and that it is delayed by an amount corresponding to a travel distance of about two to ten meters.

    It is Feature 4 that helps us to understand how a listener can feel so confident about the instrumental sounds he hears. Each note comes to him as a complete view, literally from all sides of the originating instrument. One reason that such an all-round view is important is that every instrument sends a different arrangement of components out in each possible angular direction.¹¹ To hear an instrument in reflection-free surroundings is very much like looking at a person from only a single direction. While one can often recognize a familiar friend from a single view, one learns much more about someone when it is possible to observe in addition the shape of his face, the nature of his profile, the straightness of his back, or whether the top of his head is bald.

    A more important reason for the usefulness of our reflection-collecting machinery has already been referred to a number of times. Through the mechanisms of early reflection processing, the auditory system can supply itself with many of the distinctive features of an instrument. Since it is normally able to perform its recognition and interpretation tasks upon the basis of a relatively restricted subset of these, it would require a rather elaborate set of accidents for all traces of an instrumental note to be lost. It is for these reasons we can claim the perceptual robustness of musical sounds in a properly designed room, and thence we can understand why music is so difficult to produce and to hear in a reflection-free environment.

    We must consider yet another property of the sound in a room and of the way in which the ear responds to it. Physicists have calculated and observed the patterns of arrival of reflections in a room. While the first handful of reflections comes to the listener's ear separated by one or two dozen milliseconds, the later ones arrive at an ever- increasing rate, until they come tumbling into our ears as a decaying cascade of overlapping stimuli.

    We have already learned that the earliest reflections (which are reasonably well spaced from each other in time) are put to very significant use by our auditory systems, even though we are not consciously aware of them. We have also learned that if by chance a few delayed signals arrive, they can disrupt the clarity of our impressions. Beyond this, during the epoch when the various reflections are hopelessly merged into a steadily decaying melange of sound, our ears acquire only a general impression, an aura, or perhaps an aroma of what has gone before. When this aroma is not overpowering, it provides a very pleasant adjunct to the more detailed impressions we have gained from the early reflections. Perhaps we can liken this to the aroma of a fine meal, which enhances our pleasure in the flavors of the elegant dishes that have joined to make their contributions to the whole.

    Clearly, the diffuse reminiscence of earlier sounds in a concert hall is pleasant for, and perhaps even useful to, the concert-goer. There is, however, little rationality in the attempts of some architects to base the entire design on an attempt to provide an optimum value for the "reverberation time," which is a technical measure of the duration of the run-together part of the sound of a room. The implausibility of such attempts becomes apparent to anyone who troubles to read more than one book on concert hall acoustics. Each book suggests its own carefully worked out set of "ideal" reverberation times selected for every size of hall and for every genre of music from the baroque to the avant- garde. One notices that each author comes to his own conclusions, which agree with those of his colleagues only in the most general way: "Yes, there should be about two seconds of reverberation," and "No, five seconds is too long except for a few fanatical admirers of romantic pipe-organ music"!
 

THE ACOUSTICAL REQUIREMENTS FOR A SUCCESSFUL CONCERT HALL

    We are at last in a position to set forth a list of the major requirements that must be met in the design of a successful concert hall. Essentially every one of these requirements has been recognized by a large number of successful designers over a period of many years, although the relative importance given to one or another has been much more variable. Despite the fact that these basic ideas are not essentially new, a significant number of halls have been built during the past two decades in which essential features of these requirements have been ignored or set aside. Every hall that has been the subject of controversy, that has required rebuilding, or that in particular possesses vigorous critics among the musical performers is a hall that lacks one or more of the properties that are about to be enumerated and explained. The acoustical design community has tended to foster a public belief that the design of concert halls is a hazardous undertaking, and one in which numerous post-construction "tunings" and "adjustments" must normally be carried out. There are, to be sure, difficulties and constraints (such as economic ones) that must be surmounted, but there is little more excuse today for an unsuccessful first trial of a hall than there is for the unsuccessful flight of a newly designed airplane or the collapse of a new bridge.

    The present account is based on a) a careful study of the theoretical and experimental properties of the sound transmission process in rooms, b) knowledge of the major mechanisms of auditory processing, c) discussion and joint experimentation with practicing musicians (who have increasingly come to me for advice concerning their own use of stage-placement techniques), d) discussions over a period of thirty years with my late colleague Robert Shankland (who has the correction of many previously unsatisfactory halls to his credit as well as the successful design of many of his own), e) study of the literature of concert hall design (in which I have been greatly helped by the extensive, heavily annotated reprint and book collection that has come to me from Shankland along with his detailed memos of conversations with scientists, architects, conductors, and performers over a span of fifty years, and f) through the results of laboratory experiments I have done which are designed to relate accurately known properties of musical instruments to the facts of music perception in large rooms.

    The concert hall is the meeting place of two groups of people whose interests are interrelated but not identical--performers and listeners. The performers in a concert hall assemble to play some carefully composed music in which the utmost of ensemble accuracy is required, an accuracy that must nevertheless leave room for considerable flexibility in the details of the individual player's actions. If there is a conductor, it is his responsibility to lay down the general outlines of "musical policy" and to organize (in rehearsal) the way it is to be carried out. He does not make the music himself. The actual carrying out of the chosen policy is the joint responsibility of the players, and in meeting this responsibility they must be able to hear one another with clarity and precision. The exact instant at which a given player makes an entry and the articulation he uses or the detailed way in which he modifies his tempo during a musical phrase is controlled by the rhythmic context provided by his fellow players.

    Similarly, the musician must continually modify the pitches of his notes so that they fit correctly into the shifting chords of the music. Textbook discussion of equal temperament has prevented many people (even some musicians) from realizing the extent to which every player needs in the course of performance to move his notes up and down relative to their nominal pitches. Adjustments of this sort are not possible unless the instruments are flexible (as we have seen at the beginning) and unless every player has a clear idea of what his colleagues are doing at all times. We need only to mention tone color and instrumental type to bring to mind the questions of musical balance that must also be continually answered during a performance. Clearly, the musicians must be able to hear one another extremely well if they are to adequately carry out their complicated task.

    It only requires a few sentences to describe what the phrase "to hear one another well" means in a technical sense. Each player's early-reflection processing machinery must be supplied with at least two or three suitable reflections along with the directly transmitted sounds from members of each major division of the orchestra. In general, players find it best to receive these quickly processible messages from the walls on each side, from floor reflections, and from the wall behind them.  (Signals from overhead are not as useful, though on a wide and/or deep stage it is better to have data from overhead than to have nothing.)  In order to further facilitate the communication process on stage, the musicians need to be protected from the actively disruptive signals that are delayed by having traveled 30 to 60 meters farther than has the direct sound to the ear. This is, in the long run, more important for their musical health and well-being than the prevention of the individual, strong, long-delayed signals that are heard as "echo" events that can sometimes stand out from the smoothly decaying reverberant sound.

    The effect of reverberant sound (i.e., sound that belongs to the later epochs of the development of each new contribution to the overall sound) is relatively small for the players on stage provided that they get their "minimum daily requirement" of early reflections!  The musician and the conductor are, to be sure, interested in the general flavor imposed on their music by the reverberant sound field, and they have their preferences about it (which can change with the type of music being played), but such matters are not of direct concern to the act of performance.

    Let us turn our attention now to the problem of assuring satisfactory acoustical conditions for the listening audience. It has been traditional to take a "consumerist" view of concert hall design, with primary attention being paid to means for getting the musicians' sounds to the audience and with only secondary attention being paid to the auditory processes that take place on stage. This order of priorities is a major contributor to the problems of many recently built halls. It should seem obvious that if the performers cannot adequately carry out their tasks, then the audience is provided only with a ringside seat at a performance that may be little more than the avoidance of collapse. Groups such as the Guarneri Quartet and the Cleveland Orchestra are able to perform reasonably well in halls with poor stage acoustics, but their performances can be sublime in a hall where the on- stage communication is good. Lesser ensembles, for example groups of conservatory students, are extremely vulnerable to the adverse effects of halls that offer only poor on-stage communication.

    The acoustical properties that serve the needs of the audience are almost identical with (though perhaps less demanding than) those that are needed for the players. In brief, the listeners need to be provided with a reasonable supply of direct sound, which may be said to provide the scaffolding upon which their complete perception will be built using materials supplied by the set of early reflections from the stage area. They also need to be protected from an oversupply of the actively disruptive middle-delay reflections, and from the long-delayed individual arrivals that are heard as simple echoes. We should call attention at this point to the importance of providing the audience with a smoothly decaying uncolored supply of reverberant sound. These decaying reminiscences provide us with a constant aura of what has gone before, and sometimes serve to accent and to make more vivid the dramatic silences with which a composer may punctuate his music.

    However, these smoothly decaying reverberant sounds are less important than those aspects of the listening process that provide the musical details, which are important for the musical enjoyment of any listener other than the one who wishes to merely sit and allow the music to wash over him. Much of the discussion that one hears to the effect that different parts of the same hall have a different balance of loudness between sections of the orchestra, or different overall tone color, arise from inequalities of distribution of early reflections. In those parts of the hall where the listener is not provided with adequate musical detail, he must perforce fall back on noticing only those tonal generalities that do come to his ears.
 

POSSIBILITIES FOR ELECTROACOUSTIC ADJUSTMENT

    In this era of easily constructed electroacoustic elaboration we must face in a serious way the following question: Is it not possible to improve the acoustical functioning of a concert hall by means of cleverly placed microphones and loudspeakers? The briefest possible answer is "Probably yes, in pathological cases." However, a closer look at the question shows that one might expect the electronic solution to be complex, and fraught (at least at our present stage of understanding) with more hazards than those that accompany the design of a "nonelectronic" hall. Let us glance briefly at some of the implications of electronic supplementation of the normal signal paths within a room.

    Over a period of at least fifty years there has been talk of augmenting the reverberation time of excessively absorptive rooms by use of microphones and loudspeakers placed far from the orchestra and from each other. Sometimes the system includes "long-wire" or "metal-plate" reverberation devices that are intended to electronically imitate the behavior or room reverberations, and sometimes there is a small auxiliary "reverberation room" in the signal path. The electrical amplification provided in the system is then to be adjusted at a level somewhat below that which would produce the crescendo howl familiar to all who have been present when the gain of a public-address system is raised excessively.

    Since the 1940s a number of such systems have been built and they are indeed helpful in solving the problem set for them. However, we need only to recall the secondary usefulness of reverberant sound for the musical listener to understand one of the reasons for the limited usefulness of such techniques. There is another (and perhaps more fundamental) limitation on the worth of such systems of "assisted reverberation": in a real room, the early reflections come at a relatively slow rate, while the later ones arrive at a constantly increasing rate so that they tend to melt into a homogeneous auditory soup. In the case of the long-wire type of reverberator, the reflections arrive at a uniform average rate, and the "shapes" of the individual arrivals are rapidly degraded by what is called the dispersive nature of wave propagation on a wire. The situation is only slightly different in the case of the plate-type reverberator. In any case, the sounds produced through the action of such systems are recognizably different from those heard in a large room, as are (to a lesser extent) the sounds resulting from an auxiliary reverberation room. We may close this part of the discussion by noting that various forms of electronic reverberation are employed much more frequently in the production of disc and tape recordings than they are in the amelioration of concert hall defects. In both cases we will do well to be aware that such systems are not normally based on a clear appreciation of the ways in which the human auditory system uses the signals that come to it.

    We have already learned that reinforcement of the loudness of a single source may be achieved by providing a suitably delayed replica of the original sound. Under these circumstances, the listener perceptually fuses the later reinforcement with the original signal and is unaware that any tricks have been played upon him. For the simple task of speech reinforcement in a lecture hall or a church, this technique has proved its worth over a period of thirty years. Over the past dozen years there have been numerous attempts to apply the same principles in the concert hall to convey detailed information about each section of the orchestra to each listener in the audience. At first thought, such a system would seem to be ideal. Carefully placed microphones would pick up the signals from the various sections of stringed instruments, the woodwinds, the brasses, and the percussion. An additional microphone would capture the musical contribution of the soloist. Sets of these signals would then be suitably delayed and amplified and combined for the benefit of listeners in each region of the hall. The designer of such a system normally thinks of possible confusions that might arise if sounds from one part of the orchestra are inadvertently picked up and transmitted to the listeners via the microphone channel intended for a neighboring part. To obviate this difficulty, he tends to specify the use of directional microphones, each of which is aimed at its own part of the ensemble.

    On first hearing, a concert in a hall provided with such a system can very well prove exciting. The listener reports that he can hear every instrument in microscopic detail. He can even hear the clicking of the clarinet's keys, the breathing of the players, the scrape of violin bows, the rustle of turning pages, and the creaking of the chairs- -he feels himself transported magically into the very midst of the orchestra! All this is true, and it is perhaps a thrilling experience to be present on the stage with a distinguished orchestra. However, there are many objections to arrangements of this kind:

1. The conductor will at once object to the system because it deprives him of the ultimate decision about instrumental balance. He is at the mercy of an elaborate system that may well be operated by someone of very little musical training and experience. Certainly the conductor will find it difficult to acknowledge the supremacy of an electronic technician in an area as central as this to the performance of concerted music!

2. To give the listener a single, dominating version of the sound of each instrument deprives him of contextual information that helps him relate the arrival patterns of the various instruments. The listener needs rapid sequences of early reflections from various parts of the entire orchestra so that he can deduce the relations between the various instruments. Electronic delays can only be chosen to serve the individual signal paths, and cannot at the same time provide a suitable relationship between them.

3. Each instrument has its own directional pattern for the emission of its sounds. To place a single microphone at some position over an orchestral section then provides the listener with only a single "view" of the sound of the instruments in that section. While there has always been much talk in the audio engineering world about the special properties of this or that directional microphone, there is an almost total disregard of the fact that instruments themselves show very complex directional behavior. Furthermore, even if there were to be some magic position for a microphone for recording the "true sound" of an instrument, to use one microphone per orchestral section is certain to cause distortion of at least some of the sounds. We have learned that one of the functions of a concert hall is to supply the listener a collection of rapidly arriving data from each instrument, which data are integrated into a complete and well-rounded perception of the instrumental voice. Usage of a single, dominant microphone is inadequate, as can be illustrated by thinking about its visual counterpart. Suppose that the directional microphone is replaced by an equally carefully aimed television camera. The viewer is then asked to benefit aesthetically from a microscopically precise, close-up view of the violinist's shaggy beard, or of the complex motions of a clarinetist's left hand. We may exploit this visual analogy yet further by pointing out that an inherent property of all directional microphones is that they strongly modify the patterns received from off-axis sound sources. The visual counterpart of this might be to arrange for the colors of images at the periphery of the camera's field of view to be totally changed and also for the shapes of objects portrayed from this region to suffer a severe distortion.
 

    Let us summarize the acoustical requirements for a successful concert hall, and then glance at some good and bad examples.

Priority 1: Provide sufficient early reflections to supplement the direct sound transmission between different parts of the stage. The purpose of these is to assure good communication among the performers.

Priority 2: Arrange suitable early reflections as a part of the signal path between each part of the stage and each region in the audience area.

Priority 3: Ensure that 100- to 200-millisecond delays (corresponding to travel distances of about 30 to 60 meters) are not appreciable in either the on-stage or the stage-to- audience signal paths.

Priority 4: Arrange that the reverberation time is in the range of 2 to 3 seconds, that it is reasonably uniform as measured in all parts of the hall, and that it varies little when measured at high and low frequencies.

    While it is relatively easy to assure success in a hall that seats less than about 1500 persons, there are many excellent halls in the world having much larger capacity. Comparison of the Troy hall with these other halls shows clearly their similarity: Symphony Hall in Boston and the Musikvereinsaal in Vienna are examples of such halls, along with Carnegie Hall in New York City. Shankland has shown that the quality of communication on stage dominates the aesthetic judgment of the hall.¹²  A good hall is a place where music is well played, and after this it is a place where the listener can clearly hear the performance.^13,14 Halls as good as these can hardly be the result of accident, whether or not they were designed before the founding of the formal science of architectural acoustics in 1900 by Clement Sabine. Carnegie Hall was inaugurated in 1891, before this scientifically important date. Its designer, Burnett Tuthill, later wrote a booklet describing his work in detail. Drawings in it illustrate his explicit words on the importance of assuring a plenitude of early reflections and of reducing the number of disruptive middle-delay reflections. The proportions of the hall and its recognized musical success shows clearly Tuthill's ability to achieve his design goals and the correctness of his principles. While he did not possess a formal scientific basis for his efforts, Tuthill makes it clear that he was perfectly aware of the important phenomena that influence the practical design of a concert hall.

    [Note added by Benade in the fall of 1986:  I recently made a survey of first-chair players in a large number of major North American orchestras.  Among other things, each was asked to rate halls in terms of the communication among the members of the player's own section and also the ability to hear what was going on in other sections of the orchestra.  The response to these questions was vigorous and immediate and very nearly unanimous: the halls with good overall reputation all provide good communication on stage, and the troublemaking ones, with almost no exception, are poor in this regard. The exceptions have mostly to do with other failures of communication, such as poor communication from stage to audience.  The responses covered many well-known halls, satisfactory and unsatisfactory, new and old.]

    The lower part of Fig. 12 shows in slightly generalized form a type of concert hall design that has become quite common all over the world in the past fifteen or twenty years. It should be a matter for everyone's regret that the construction of such halls continues, since they are (to quote a player in one of the worlds most distinguished orchestras) "a purgatory for the musician." Many years ago George Szell gave Robert Shankland a very detailed criticism of one such that exists here in Europe, a criticism that is particularly informative because it came from a man whose reputation rested on his meticulous attention to detail. He did not simply shout at his orchestra members until they produced what he desired, he gave them explicit instructions, often with enough detail on instrumental technique as to leave the players astonished (if occasionally resentful!). It was also well known to musicians that he did not demand the impossible. One of his major criticisms of halls of the sort we are discussing was that even the finest orchestras could not hear themselves well enough in them to provide the precision of ensemble for which he was famous.

    Let us examine the lower part of Fig. 12 in the light of what we have learned. To begin, we notice there are no reflecting surfaces (other than the floor) anywhere near the players. Each player is left to struggle, encouraged only by whatever sound reaches him from his immediate neighbors. He is provided with only the smallest hint of the musical efforts of his colleagues in other sections of the orchestra. When the musical score requires him to play a phrase joining seamlessly with a similar one from another part of the orchestra, he has no way to know the precise pitch of the notes he is intended to match; he cannot know the instant at which he should begin, nor the exact rhythmic shape of his colleagues' notes that he is supposed to echo. Furthermore, he has only the slightest idea of the dynamic level to which he should adapt his own playing.

    In the same figure, we should next focus our attention on the reflectors that are hung high over the heads of the orchestra. If by chance a few of these are aimed directly back down toward the orchestra, they certainly supply some form of communication between parts of the ensemble. However, the fact that these reflectors are placed very high means that signals coming from them to the orchestra arrive so late that they actually work to disrupt what little information transfer is taking place on stage.

    In some halls we find that many reflectors are in fact placed low enough to be of some direct use to the players. After playing in such a hall the player will report that he can hear his colleagues and himself reasonably well, but he also tends to make remarks of the following sort (these are actual quotes): "It seems as though someone just like me is dogging my footsteps," or "Somehow I feel as though I hear a confused version of everything we do along with the sounds of our actual notes." The explanation is simple: the sounds that pass around the useful reflectors travel upward to the ceiling or to any higher-up reflectors and are returned in delayed form. The player then is in the same position as the person making the transatlantic call referred to earlier. The clear (direct and early-reflection) version of what he hears serves as a well-defined reference against which he can compare the delayed reflections, and his confused response is a result of the excessive delay more than it is of any lack of fidelity of the second version.

    The situation of the audience in the hall that serves as our bad example is little different from that of the orchestra. Once again we notice the paucity of early reflections in the communication path between each part of the orchestra and each region of the seating area. The combination of the extreme width and depth of the hall means that reflections arriving at the listener's ears from the sides and rear have a long delay. Whatever contribution they make to the orchestral sound is at best only a warm, indefinite blur, but they are counterproductive in their influence on the perception of musical detail.

    The function of the reflecting objects hung from the ceiling is our next concern. I have heard amusing (apocryphal?) stories about how these reflectors are sometimes "adjusted" with the aid of searchlight beams that are intended to mimic the reflection behavior of beams of sound. It seems that, after careful planning, a light is placed at each one (in turn) of several positions on the stage, and aimed at one or another of the reflectors. The angles of these reflectors are then laboriously modified until each one of the reflected beams of light has been arranged to illuminate its own meticulously chosen part of the audience area. By such means does the engineer expect to assure that a uniformly distributed, multicolored rain of musical sound descends upon each listener, with each musical color being properly transported from its own originating part of the performing ensemble! To be sure, from the point of view of physics it is possible to arrange a uniform distribution of sound by such means and to verify its correctness by means of measurements using microphones and electronic instrumentation. However, we are not in a concert hall to enjoy the electrical interpretations of a sound-level meter, we are there to process the acoustical signals by means of our own auditory mechanisms, which deal with their signals in a way that distinguishes clearly between the early and the late parts of the stimulus. In short, the sounds reaching the listener's ears from the reflectors will have arrived late enough to derange his sense of musical coherency, leaving him with little more than a perception of loudness and perhaps of the massed tone color of the orchestral line.
 

RECAPITULATION

    As we approach the end of our travels in the adjoining worlds of music, perception, and physics, we should collect our impressions and reminiscences into a reasonably coherent whole. At the beginning we were reminded that musicians are enormously skilled at producing well-defined sounds from their instruments. We learned also that despite the familiar fact that musical listening is more easily carried on in a room than it is outdoors, the physicist finds that sound transmission in a room is literally chaotic, and that he can make measurements only by means of elaborate averaging procedures. Because of this we came to suspect that the auditory processes of the human ear are carried out by means quite different from those familiar to the physicist. We also learned that all good musical instruments possess a common set of well-defined features, features of a sort that can aid us in recognizing them in a complex physical or musical environment.

    We then paid an extended visit to the nation of the wind instruments, where we studied the ways they can produce the controllable yet stable sounds that are required for their musical uses. In particular we learned that in all cases the natural frequencies of an instrument's own air column (and preferably those of the players windway) must be given a harmonic alignment. Only under these conditions of alignment can air columns successfully negotiate with the flow-controlling reed to produce physically stable sounds. We came also to understand how the successful alignment of response peaks can by itself assure a very large fraction of the musical virtues required of a fine instrument.

    The next part of our tour took us into the province of psychoacoustics, or at any rate into that part of this wonderful and complex subject that deals with the auditory processing of sounds transmitted in rooms. Here we learned of the absolutely essential role played by the earliest-arriving reflections from the walls, floor, and ceiling. It is these early arrivals that are fused perceptually with the direct sound to give the listener a very complete auditory "picture" of the tone color, pitch, and dynamics of each note as it is played by each instrument in the ensemble. We also learned that somewhat delayed sounds have a strong tendency to confuse the clarity of this already-formed picture, and that the rapidly arriving, very much delayed (reverberant) sounds associated with the old age of each played note are boiled down into a soup along with the remnants of all the other notes to provide a sort of general background against which the actual performance is heard.

    The final segment of our musical-acoustical tour was devoted to a visit to the concert hall itself, where we could see how the needs of the player and of the listener could be met to their mutual satisfaction. It was here that we came to understand the primacy of the stage acoustics and to recognize that much of the confusion associated with judgments of concert halls arises when such judgments are based on questions of the ability of a hall to "blend" and to "balance" the orchestral voices. We were reminded that it is the task of the conductor and his colleagues to provide the unification, and it is the task of the hall to transmit the results of their efforts to the audience.

    It has always been a truism in the musical world that clarity is an important requirement in the performance of baroque and of classical music. All too often this requirement has been interpreted by the engineer to mean that the reverberation time must be short in a hall suited to such music. In fact, one can readily verify that if the short- time communication paths are adequate, perfectly wonderful performances of such music are possible in rooms having a very long reverberation time.

    Another truism of the musical world is that blend is very important for the playing of romantic music. There is no doubt that this is true, and there are no doubt certain romantic composers (or performers!) of limited ability who benefit from a certain amount of vagueness and confusion in the received sound. It is these members of the musical world who might therefore benefit from hall acoustics that provide long reverberation times without providing the precise early signal that would otherwise betray their weaknesses.

    On the other hand, we can never forget the rich complexities of Richard Strauss, or those of the arch-romantic Gustav Mahler, who was obsessed with clarity. He strove unceasingly as a conductor and as a composer to provide his listeners with the most accurate messages to convey his musical purposes. When he desired a full but featureless blend of sound, he took the responsibility of writing the music to produce it and notated his score to call attention to the fact. It is not an accident that he lived in Vienna, and that his symphonies were first played in the Musikvereinsaal!
 

CONCLUSION

    I would like to end this arduous navigation of difficult waters with a summary of how one may gain a quick but reasonably precise judgment of the quality of a concert hall. Following this, I wish to provide a few comments on how we might usefully strive toward the construction of better halls in the future.

    A quick look around a hall before the concert begins will show whether there are nearby reflectors for the musicians on the stage (often one finds that some but not all of the players are provided with these essential tools for their trade). One can usually gain a similar, but less detailed, ideal of the reflection facilities provided for the audience. Next one can look for sets of distant (and therefore counterproductive) reflecting surfaces that may contribute loudness and fullness to the sound, but destroy the clarity of auditory impressions.

    The ultimate test comes as the music begins. Watch the players: Are their entrances slightly tentative? Do they play more crisply for a few moments after a trumpet blast or tympani boom provides a temporary synchronizing signal? Do they look a little tense at places where the musical line is passed from one section to another? Are there lapses or irregularities in the tuning between parts of the orchestra? All these imperfections are symptoms of inadequate communication on stage, and even the finest of groups will display them to some extent under difficult conditions.

    In today's world the designer of halls often finds it difficult to gain information from the players about their problems with a hall. There are several reasons for this.

a) Players are brought up with a "you pay, I play" psychology. It is not wise for a musician to complain about a hall, or he may not be asked to play there again. He also has a certain professional pride in being able to do an acceptable job regardless of the difficulties of his environment.

b) Players tend to be intimidated by technical people, and they will often (sometimes resentfully) defer to the presumed superiority of so-called "objective" measurements over their own judgments. They may well say, "I don't know any acoustics," forgetting that their own profession is a manifestation of the highest possible skill in practical acoustics.

c) The engineer and the musician do not have a well-defined vocabulary for mutual discourse. Musicians normally can tell each other what they think about the properties of a hall, although even here they lack precise ways of expressing themselves. The engineer has, on the other hand, a highly developed language by means of which he can discuss those features of a hall that belong properly to physics. However, he is often ignorant of the fact that there is anything more to be said about the room. As a result he may show traces of arrogance as he discounts the opinions of the musicians.

ACKNOWLEDGEMENT

    Much of the work reported here was supported by grants from the National Science Foundation.
 

REFERENCES

1.  Benade, A. H., and C. O. Larson, Requirements and techniques for measuring the musical spectrum of a clarinet, J. Acoust. Soc. Am. 78:1475-1497, 1985.  See Sections I and II.

2.  Kuttruff, H., Room Acoustics, Applied Science Publishers, London, 1973.

3.  Op. cit., Benade and Larson, 1985.  See Section IV, which includes a detailed summary of the statistical behavior found in rooms and an extensive bibliography.

4.  Benade, A. H., Fundamentals of Musical Acoustics, Oxford University Press, New York, 1976. See Chapter 11.

5.  Op. cit., Benade, 1976.  See Chapters 20, 21, 22, and 25.

6.  McIntyre, M. E., R. T. Schumacher, and J. Woodhouse, On the oscillations of musical instruments, J. Acoust. Soc. Amer. 74:1325-1345, 1983.

7.  Thompson, S. C., The effect of reed resonance on woodwind tone production, J. Acoust. Soc. Amer. 66:1299-1307, 1979.

8.  Benade, A. H., Air column, reed, and player's windway interaction in musical instruments, Proceedings of the Conference on Physiology and Biophysics of Voice, University of Iowa, May 1983, Ingo Titze, ed., The Denver Center for the Performing Arts, Denver, 1984.

9.  Op. cit., Benade, 1976.  See Chapters 12, 13, and 15.

10.  Op. cit., Kuttruff, 1973.  See Chapter VII.

11.  Benade, A. H., From instrument to ear in a room: Direct, or via recording, J. Audio Eng. Soc., 33:218-233, 1985.

12.  Shankland, R. S., Acoustical designing for performers, J. Acoust. Soc. Am. 65:140-150, 1979.

13.  Marshall, A. H., Acoustical design and evaluation of Christchurch Town Hall, New Zealand, J. Acoust. Soc. Amer. 65:951-956, 1979.

14.  Barron, M., and A. H. Marshall, Spatial impression due to early lateral reflections in concert halls: The derivation of a physical measure, J. Sound and Vibr. 77:211-232, 1981.
 
 

Figure Captions

Figures in PDF format [470 KB, PDF]

Fig. 1.  The musical signal path.  The definiteness of transmission over a random path raises crucial questions for concert hall design.

Fig. 2.  Transmission of sound from a fixed loudspeaker to each of two microphones in a room.  The transmission varies randomly from one path to another but has a well-defined average that is shown by the slanting dashed line in the figure.

Fig. 3.  Transmission of a sound in a room to two different positions.

Fig. 4.  Generic wind instrument and its major parts.

Fig. 5.  Above:  The oscillation of water in a channel.  Below:  The "water trumpet."

Fig. 6.  Above:  Measuring the pressure response in the mouthpiece to a flow stimulus injected there.  Below:  Sample response curve.  The air column shape is such that the response peaks are irregularly spaced along the frequency axis.

Fig. 7.  The effect of increasing the dynamics on an instrument that has only a single mode of oscillation.

Fig. 8.  Above:  The three interacting parts of a wind instrument's playing system--the instrument's own air column (IAC), the reed, and the player's windway (PWW).  The PWW extends past the larynx into the lungs.  Below:  The flow-controlling mechanism (the reed).  The reed mass  m  is moved to increase or decrease the flow  u  under the influence of the pressure difference between the upstream and downstream pressures (P_u - p_c) across the reed.

Fig. 9.  Above:  Measured response curve of a clarinet air column (IAC).  Also shown is a peak of adjustable frequency associated with the reed resonance.  Below:  Examples of measured resonance peaks belonging to the player's windway (PWW).  The largest peak may be moved over a wide frequency range.

Fig. 10.  The effect of peak alignment.  Above, solid line:  No alignment;  dashed line:  The addition of a single PWW peak.  Below:  What happens when the amplitude on the upstream side of the reed is changed.

Fig. 11.  Early signals traveling between source and listener in a room.  Each carries its own supply of information about the source.

Fig. 12.  Above:  Stage area of the much-admired concert hall at Troy, New York.  Early reflections are in good supply.  Below:  A type of concert-hall design that causes great difficulty for the musicians and poor communication to the audience.  Early reflections are almost absent.  [Drawings by Eleanor (Mrs. Robert S.) Shankland.  Used with permission.]