The systematic study of musical acoustics existed as early as the first century B.C., as documented by Vitruvius in his ten books on architecture. Great strides in understanding were achieved in the nineteenth century, especially with the work of Hermann Helmholtz. The twentieth century has spawned a near explosion in the field, as witnessed by the great number of recent publications on all types of acoustics.

Research in physical acoustics has produced theories leading to improvements in the design of musical instruments and has greatly influenced the design of concert halls built in the last 100 years. Research in psychoacoustics has likewise influenced instrument design and auditorium acoustics.

One might expect that all this activity would have produced better instruments, better music, and happier musicians. This article attempts to show that this has not always happened. Some observations on the reason for this are presented, along with some suggestions for further research. The areas considered are (1) auditorium acoustics, (2) psychoacoustics, and (3) musical instrument design.



Probably the first truly scientific architectural acoustician was Wallace Clement Sabine of Harvard University. He is credited with the acoustical design of Symphony Hall, built in Boston in 1900. Sabine investigated the measurement of reverberation time and devised the first formula to predict reverberation time from the dimensions of a room and the amount of sound absorption in it. He invented the concepts of acoustical absorption coefficients and absorption units, now called Sabins. (One Sabin is defined as one square foot of total sound absorption. The absorption of a given area of a material may be predicted by multiplying its absorption coefficient by its area in square feet.) Sabine also did much work on the measurement of absorption coefficients of many materials. He was probably the first to suggest that materials be manufactured for the express purpose of sound absorption—in effect making him the father of acoustical tile.

Over the past 80 years Symphony Hall has been universally claimed by musicians and audiences to possess superlative acoustics. Some would agree with the 1950 opinion of Rudolf Elie, music critic of the Boston Herald: "It is very clear to me now that Symphony Hall is the most acoustically beautiful hall in the United States. It is to the orchestra what a Stradivarius is to the great violinist in providing a sound box of the utmost brilliance and sensitivity."

While Sabine deserves credit for many of the hall's acoustic features, he was also very lucky in that a good many of the hall's design features were not planned specifically for acoustic reasons, yet they contributed positively to the hall's qualities. Examples are the basic shape of the space, the large amount of sound-diffusing surfaces which are relatively broad-based in action, and the well-placed resonant frequencies of the wall and ceiling surfaces.

Later in the century, as a sequel to Sabine's work, the measurement of reverberation time in halls became fashionable, and along with this came the ability to control the reverberation time by the use of special sound-absorbing materials. The "control" of reverberation rapidly attained the status of an architectural fad. Existing auditoriums and all types of public buildings were "corrected" by liberal applications of acoustical tile, or acoustical plaster. Many architects, acousticians, and especially acoustic tile salesmen were convinced that all manner of acoustical defects could be cured simply by the liberal application of sound absorbing material. Books on architecture and musical acoustics began to appear, nearly all citing reverberation time as the most significant aspect of the acoustics of a room, in spite of such an authority as Vern Knudsen writing in 1963, "A felicitous shape is a requirement of the highest priority. Unfortunately, many architects believe that faulty shapes can be corrected by covering the offending surfaces with highly absorptive materials and by adjusting the reverberation time. Thus deluded, they adopt a fashionable construction method, such as a concrete shell, and produce a building that is an acoustical perversion. A bad shape is a permanent liability."

It became apparent very early that reverberation time could be made to have different values at different frequencies. It was noted that many existing buildings had much longer reverberation at low frequencies than at high frequencies. The reaction to this observation was to introduce selective absorption so that the reverberation would be nearly constant with frequency, the rationale being that the overall tonal quality would be more uniform over the musical pitch range. It was thought that longer low-frequency reverberation caused the music to sound "muddy" and ill defined, and that uniform reverberation vs. frequency would improve musical clarity and definition.

The result of this thinking was the construction of many new music auditoriums with very hard, crisp or "tinny" sound with very little warmth and solidity. In a few cases the trend was carried to such an extreme that the high-frequency reverberation time actually exceeded that of low frequencies. Of course the musicians knew better all the time, and acousticians and architects began to be held in contempt.

In the November 5, 1955 New Yorker Joseph Wechsberg wrote, "Most of the people who have set themselves up as consultants on matters of acoustics contend, not unnaturally, that by applying certain laws of physics and using certain testing devices they can determine in advance how hospitable to sound a new auditorium will be. The fact is, however, that several auditoriums built in Europe recently under the guidance of consultants who presumably applied the laws of physics and using the testing devices have turned out to have dreadful acoustics."

The eminent American acoustician Leo Beranek read these words and was forced to admit that most modern auditoriums were not free of criticism. Beranek then undertook a systematic study of 54 concert halls located in various parts of the world. He identified several acoustical characteristics other than reverberation which contribute in large measure to the acoustics of halls. One of these measures is the Initial Time Delay Gap, or ITDG as Beranek called it. The ITDG is defined as the time interval between a listener's hearing of the direct sound from a source and the earliest reflected sound from the walls or ceiling. It is a measure of the subjective "intimacy" of a music hall, a shorter ITDG corresponding to the subjective impression of smaller rooms and vice versa. Beranek reasoned that a large concert hall must have a high ceiling to attain sufficient reverberation, but should have a low ceiling to provide a sufficiently short ITDG for subjective intimacy. The two requirements are mutually exclusive, and this led Beranek to the invention of relatively small sound-reflecting panels (called acoustical clouds) suspended from the true ceiling and forming a second lower but partially acoustically-transparent sound ceiling. The reasoning was that sounds reflecting from the clouds would provide a short ITDG, while sounds passing between the clouds would excite the reverberation of the entire room volume.

Beranek was the acoustician for Philharmonic Hall at Lincoln Center in New York, completed in 1962. His well-written and researched book, Music, Acoustics, and Architecture, was published in 1962; it tells the story of the hall's design in painstaking detail. The book is fascinating, both in regard to its technical completeness and in respect to the complex fate of Philharmonic Hall since its opening. As is well known, the hall was subjected to criticism from all areas of music from its opening, and several expensive attempts to correct it were made, ending in a $750,000 remodeling in 1969. This remodeling purportedly eliminated the clouds but retained the same shape. Even after this, musicians and music lovers were not happy with the acoustics and finally the building was gutted and a completely new concert hall constructed within the four walls at a cost of $17,000,000. The new auditorium was named Avery Fisher Hall in honor of the man who donated most of the needed funds. The new hall, designed by the acoustician Cyril Harris, is similar in shape to Symphony Hall in Boston, the hall the New York Philharmonic Society had asked Beranek to emulate in the first place (letter from George Judd, Jr., to Max Abramovich, dated April 20, 1959, quoted in Beranek, op. cit.). At last the controversy over Philharmonic Hall seems to have ended, but the obvious question is "What went wrong?" Beranek is in every sense a respected and accomplished acoustician and it is obvious from his book that he did his homework. The answer must come from psychoacoustics: the study of our perception of what we hear.

There is an excellent but relatively unknown book by Georg von Bekesy called Sensory Inhibition (Princeton University Press, 1967). In this fascinating work which summarizes much of Bekesy's research spanning many years, there are some strong clues to why the clouds at Lincoln Center did not behave as expected. Bekesy points out that an array of acoustical clouds will reflect high frequencies while permitting low frequencies to pass through and be reflected from the true ceiling above. This means the high frequency portion of complex musical sounds reach the listener earlier than the lower frequency components of those sounds. Bekesy had established earlier that sounds arriving in quick succession at the ear result in complex nervous system processing whereby a part of the response is inhibited, and he called this phenomenon auditory inhibition. He states, "In the concert hall the low frequencies will lose their effectiveness in brief pulses of sound heard by a listener. These tones are physically present but are inhibited because they are delayed in arrival at the listener's ears. This type of distortion may be called 'room acoustics phase distortion' and represents an interesting new field. The construction of auditoriums and the subsequent discovery of these distortions represent very expensive experiments on inhibition." Bekesy then points out that this type of phase distortion is not noticed if it is slight, but when it is increased, a threshold is reached where suddenly the unexpected happens. Such thresholds exist also for other sensory phenomena. "These sensory thresholds present barriers that often prevent technical extensions into what otherwise might be unlimited fields."

The lesson from this is that architectural acousticians must be mindful of psychoacoustics and sensory inhibition, and must be wary of extrapolating known designs into larger scales. Also, perhaps a different point of view should be sought. Levarie and Levy bemoan the fact that architectural acoustics is still thought of in terms of reverberation and absorption of sound. In other words geometrical acoustics, or ray acoustics, has been used because of its ease of theoretical simplification and measurements. When addressed from the standpoint of volume resonance and wave theory, room acoustics measurements seem much better correlated to what a person hears with his complex auditory mechanism. There has been recent work, much of it instigated by Manfred Schroeder of Göttingen, on the importance of strong side wall reflections and diffused ceiling reflections in concert halls; this work appears promising. New auditoriums designed to provide strong reflection from the side walls across the audience have been designed recently by some acousticians, notably Paul Venekloser of Los Angeles; these rooms are praised by musicians and audiences alike. The Japanese acoustician Yoichi Audo, in collaboration with Manfred Schroeder, is doing much work to place a firm theoretical formulation under this concept. In this work the somewhat simplistic ITDG is being replaced by the IACC, or Inter-aural cross correlation function, which is a mathematical measure of the "sameness" of the sounds reaching the two eardrums. Audo has been able to establish a connection between the IACC function and the degree of preference expressed by listeners to different sound fields. Perhaps this will allow innovative concert halls to be designed and still attain acceptance by musicians.



In efforts to determine how our auditory system works, a great many experiments have been performed which effectively isolate various hearing phenomena. One of the best known of these was the measurement of equal loudness contours by Fletcher and Munson in the early 1930s. By presenting pure tones of many frequencies and intensities to various subjects, it was shown that the ear's sensitivity varies with the frequency of the test tone. Most notably, tones of low frequencies must be many times more intense than high frequency tones to be judged equally loud. Also the auditory threshold, or least intensive sounds that can be heard at a given frequency, is drastically higher at low frequencies and at very high frequencies compared to the most sensitive region of about 3000 Hz. To be heard at all, any sound must be above the threshold in intensity at its frequency, and presumably any sounds below threshold will not be heard.

This observation holds true, of course, for single pure tones, but when the ear is subjected to more than one tone at a time, things get complicated quickly. It has been shown that the presence of any tone which is above threshold will raise the auditory threshold for other frequencies. In other words the presence of a single relatively intense tone can cause a less intense tone of another frequency to be inaudible. This phenomenon is called masking; masking contours have been plotted which show under what conditions of frequency and intensity tones can be heard. These masking contours have different shapes for masking tones of different frequencies and intensities, making the situation somewhat complicated.

Examination of this masking data leads one to believe that many instances occur in common experience when sounds cannot be heard even though they are known to exist. This has been the case in the field of electronic reproduction of music, known popularly as "high fidelity." Music reproducing equipment always adds some spurious signals to the music in the form of distortion of various kinds. Distortion has been reduced as equipment has become more sophisticated, especially in the case of amplifiers. Some amplifier manufacturers claim the distortion added by their equipment is inaudible because of its extremely low intensity and its being masked by the music itself. Many people have been skeptical of these claims, believing that they could easily tell differences between various amplifiers all having very low distortion.

An interesting study was performed in Finland and reported in the Audio Engineering Society Journal in 1978 (cf. Petri-Larmi, Otala and Lammasniemi). A special machine was built to introduce controlled amounts of Transient Intermodulation Distortion to recorded musical examples. One surprising result was that the detector threshold was .003% rms distortion for piano recordings. The authors acknowledge that this is "difficult to explain" because the distortion components are so low in intensity as to be below the hearing thresholds of the subjects! In other words, adding certain sounds which are so low in intensity that they are inaudible by themselves to a piano recording will result in a detectable difference in the piano sound. Clearly more work needs to be done in audibility of low intensity sounds, and the Fletcher-Munson curves do not predict the audibility of some complex sounds.

Another interesting auditory phenomenon is that of the critical band. A critical band can be defined as a frequency interval within which two pure tones sounding together will be perceived as a single pitch. Critical bands are generally between whole tones and minor thirds in width; this means two pure tones about a whole tone apart will be perceived as a single tone! But Roederer says, "This may come as a surprise to musicians: they will claim that they can hear out very well two component tones when a minor third is playing on musical instruments! The point is this: the results shown apply only to pure tone superpositions, sounding steadily with constant intensity. When a musical interval is played with real instruments, the tones are not simple tones, they do not sound steadily, and a stereo effect is present. All this gives additional cues to the auditory system that are efficiently used for tone discrimination."

In a quick experiment I performed recently, two musicians were presented two simultaneous tones spaced a semitone apart. Both observers consistently identified both pitches with no trouble, even though many researchers report otherwise. The tones were continuous and of constant intensity, and were presented via loudspeakers in an average-sized classroom. No attempt was made to replicate any experiment which had been reported to show the existence of the critical band, and I do not know why my results differ from those generally reported. Perhaps one difference between musicians and nonmusicians is the lack of the critical band in musicians!

Generally, psychoacoustic testing is performed with headphones rather than loudspeakers in order to facilitate exact control of the signals reaching the ears. Audiometric testing is always done with earphones, presumably for the same reason. But earphones present formidable problems in standardizing sound levels at the eardrum and in attaining standardized frequency response with different listeners. The seal between the phone and the head greatly affects the low frequency response and the shape of the listener's pinna greatly affects the middle and high frequency response. Greater than 10 dB frequency response discrepancies between subjects using the same earphones have been reported (Sank, op. cit.). Also the presence of the earphone on the ear increases the audibility of the listener's own physiological processes. This is somewhat akin to hearing the ocean roar when holding a seashell to one's ear. Those extraneous noises can act as masking signals and could, it would seem, invalidate audiometric testing. Is it possible that critical bands and loudness contours are artifacts caused by using earphones? In any case it is obvious that earphone listening is an unnatural condition for our hearing mechanism, and it seems that insofar as possible psychoacoustic testing should be done under free field conditions.

Problems can occur when trying to apply the results of psychoacoustic testing to musical experiences. Most experiments aimed at investigating our hearing ability have used sine waves—pure tones—as independent variables. One phenomenon which was noticed early is that the perceived pitch of a tone varies with intensity, and is not directly correlated with its frequency (Stevens, op. cit.).

Low pitches are made subjectively lower with increasing intensity and high pitches are made subjectively higher with greater intensity. One might expect this to explain out-of-tune playing among orchestra members, but it happens that according to some researchers the effect disappears with complex tones! However, this has not been shown to be true under all conditions and more studies need to be done.

In summary I think it would be desirable if psychoacoustic research could be conducted with sounds which more clearly imitate natural sounds, and the use of earphones should be approached with caution.



It has been known for many years that the overtones present in the sound of the piano are not accurately tuned to the frequencies of the harmonic series, but are in fact higher in frequency. This sharpening of the overtones increases with the order of the overtone. Because the piano is tuned in octaves up and down from a central temperament octave, the piano will be tuned progressively sharp in the treble octaves and progressively flat in the bass. On the surface it would appear that this is a defect in the piano. As long ago as 1949 F. Miller proposed that if small masses were applied to the strings near their ends, the inharmonicity could be cancelled. He proposed that the piano could be improved by this method, but there seemed to be essentially no interest among piano makers to adopt the improvement. Then in 1962 Harvey Fletcher et al. reported that synthesized piano tones which did not contain inharmonicity were not preferred by listeners over synthetic tones which did contain inharmonicity. The nonstretched tones were described as dull, uninteresting, and not piano-like. After a series of similar listening experiments, the Conn Company came to a similar conclusion. Thus it turns out that a "defect" in the piano tone, as discovered by physical measurement of the sound, is actually an important factor in the quality of the instrument.

Stringed instruments such as the violin, viola, cello and bass viol have been built for so many years that one would expect their design to have been optimized by now. Many people have studied most aspects of stringed instruments and the consensus has been that the violin has been optimized insofar as its size and shape in relation to its pitch are concerned. Acoustically the violin has its resonances properly placed to ensure a uniform tonal output, and its size allows relative ease of playing. The cello is also close to an ideal size for its pitch range. The viola and string bass, however, are too small physically to radiate optimally in their pitch range. Carleen Hutchins of the Catgut Acoustical Society has studied this situation and has proposed new designs for the viola and bass which nearly optimize their size and shape to their respective ranges. Because of its larger size the Hutchins viola must be played vertically in the manner of the cello. According to one violinist who has mastered the instrument, this is not an important advantage. The so-called Great Bass is significantly larger than its double bass cousin, making it somewhat awkward to play, at least by persons of normal size. These instruments are characterized by a greater production of the fundamental frequencies, especially in the lower register. The difference is quite striking.

Hutchins envisioned the use of the new instruments in orchestras, where their greater strength in the low register would be welcome. Perhaps at last the viola section could compete on a more equal basis with the violins, and perhaps the Great Basses would finally provide the rich, strong support in the low frequencies which has been lacking in symphony orchestras. However, sufficient time has passed that these instruments should have made definite inroads in orchestra make-up if they are going to do so. The Great Bass in particular was praised by Leopold Stokowski; this alone should have encouraged its introduction and use, but no such revolution has occurred. The initial interest and excitement has seemingly dissipated.

Can this fact be attributed to a simple inertia and unwillingness on the part of musicians to try something new? Is it simply a matter of time before we see vertical violas and Great Basses in all our symphony orchestras? I think not. I believe that even though the new instruments may be optimized from the standpoint of their acoustical performance in some sort of absolute sense, they are not necessarily well suited to performance of the existing body of symphonic music. It must be remembered that composers have had to work around the so-called inadequacy of existing instrument design, and the structure of the music has been designed to exploit the tonal characteristics of existing instruments. The introduction of a relatively new and different sound to the performance of this music must be expected to meet with significant resistance. Innovations in instrument design probably should not exhibit great differences in tone quality if they are to be accepted by the musical community. An example is the transverse flute designed by Boehm in the nineteenth century. Boehm's work resulted in greater ease of playing and improved tuning in both the flute and clarinet, and musicians readily accepted the changes. The basic sound of the instruments was changed very little. Perhaps our research efforts should be aimed at greater ease of performance and tuning stability of instruments rather than at the creation of new sounding instruments which "correct" the deficiencies of existing instruments as measured by scientific instrumentation and techniques.



Beranek, Leo. Music, Acoustics, and Architecture (New York: John Wiley & Sons, 1962).

Fletcher, Harvey et al. "Quality of Piano Tones," Journal of the Acoustical Society of America Vol. 34, No. 6 (June 1962).

Hutchins, Carleen. "Founding a Family of Fiddles," Physics Today Vol. 20 (February 1967).

Knudsen, Vern O. "Architectural Acoustics," Scientific American Vol. 209, No. 5 (November 1963).

Levarie and Levy. Tone: A Study in Musical Acoustics (Kent State University Press, 1968).

Miller, F., Jr. "Proposed Loading of Piano Strings for Improved Tone," Journal of the Acoustical Society of America Vol. 21, No. 4 (July 1949).

Petri-Larmi, Otala, and Lammasniemi. "Psychoacoustic Detection Threshold of Transient Intermodulation Distortion," Journal of the Audio Engineering Society Vol. 28, No. 3 (March 1980).

Roederer, Juan. Introduction to the Physics and Psychophysics of Music (Heidelberg Science Library, 1975).

Sank, J.R. "Improved Real-Ear Tests for Stereophones," Journal of the Audio Engineering Society Vol. 28, No. 4 (April 1980).

Stevens, S.S. "The Relation of Pitch to Intensity," Journal of the Acoustical Society of America Vol. 6, No. 3 (January 1935).

Terhardt, E. "Influence of Intensity of the Pitch of Complex Tones," Acustica Vol. 33 (1975).

1871 Last modified on October 24, 2018