Steady-State Processes in Acoustics ¹)

G. Backhaus

Contents

IV. Some questions of electroacoustics.

1. Methods for investigating nonstationary acoustic processes.
2. Steady-state processes in electroacoustic apparatus.

V. Steady-state processes in speech sounds.

1. Organs of speech. 12. Nonstationary processes. 13. Consonants.

VI. Nonstationary processes in musical instruments.

1. General survey. 15. Bowed instruments. 16. Wind instruments. 17. Organ. 18. Piano. 19. Percussion instruments. 20. Electromusical instruments.

IV. Some Questions of Electroacoustics

9. Methods for Investigating Nonstationary Acoustic Processes

At the present time, in the study of acoustic processes, a method of investigation is used almost exclusively in which the processes occurring in the sound field are converted, by means of a microphone, into electrical oscillations. In most cases, microphones are used that register pressure oscillations. It is not within the scope of the present article to consider the various designs of microphones. Here we shall touch briefly only on the design of the condenser microphone, which is very suitable for such measurements and is therefore widely used. The capacitance of such a condenser microphone changes under the influence of the oscillating pressure, and these changes in capacitance are detected by one or another electrical apparatus. In this connection there exist, in principle, two different methods: according to the circuit of Rieger and F. Trendelenburg¹⁷ the microphone is included in a high-frequency oscillatory circuit, the tuning of which changes depending on the oscillation of the capacitance. As a result of this, the amplitude of the high-frequency oscillations

¹) See Uspekhi fizicheskikh nauk, 19, 236, 1938.

is modulated in step with the changes of pressure near the microphone. Another method consists in connecting the microphone, through a large resistance, to a source of constant voltage, so that changes in capacitance cause discharge and charging currents, producing an alternating voltage drop across the resistance, which is then amplified. This second method, owing to its greater simplicity, and also because with it one need not observe the special precautions required when using high frequency, has found the widest application. With regard to the elimination of nonlinear phenomena, the two methods are approximately equivalent, since amplitudes are transmitted sufficiently correctly over a wide range of frequencies. If, however, one strives for the exact transmission of the correct process curve, it must be taken into account that in the low-frequency circuit phase distortions arise which, at low frequencies (approximately up to 200 Hz, depending on the capacitance of the microphone used), cause distortions of the curves obtained on the oscillogram.

In some cases, especially with a small number of overtones, one can be satisfied with a direct recording of the establishing process. From the resulting curve the duration of establishment, the time constant, and the decrement can easily be calculated. If, however, the process is characterized by numerous and strong overtones, then the question must be raised as to the extent to which decomposition into individual vibrations may prove useful here. The author of this article³ was among the first to record the process, as far as possible, without amplitude and phase distortions. In order to establish which frequency regions are most strongly expressed at definite moments of time in this nonperiodic process, it is necessary to carry out a harmonic analysis with an arbitrarily chosen fundamental period. In doing so, the period of the established sound is taken as the fundamental period. If subsequent time segments of the selected interval are analyzed, then those overtones which are closest to the actually present ones are obtained as the most intensified as a result of the analysis, and the result will be quite unambiguous. The amplitudes of the individual overtones may be represented in the form of step curves consisting of horizontal straight lines (whose length corresponds to their period), between which, of course, there is no continuous transition. If these curves are approximately represented by a continuous curve, the resulting results should not be understood in the sense that they strictly express the decomposition of the process into individual overtones. It is quite impossible to assert that an overtone of a periodic process of the same constant frequency is also present in the establishing process. However, such a method of construction indicates how strongly expressed are those frequency regions which are close to the corresponding overtone at each moment of the nonstationary process.

Transient Processes in Acoustics

The method described above is extremely laborious, since numerous graphical analyses have to be carried out in order to obtain a single overtone of a transient process. Therefore various attempts have been made to simplify the procedure. The known automatic methods of analysis are inapplicable in this case because of the limited speed of the analyzing apparatus. Such an analysis requires, even under especially favorable conditions, at least several seconds. However, this technique may be used in the analysis of nonperiodic processes in cases where it is possible to reproduce the sound process repeatedly with sufficient accuracy. By this method Meyer and Buchmann^28 investigated transient and decaying sound processes and found in musical instruments, in many cases, not only harmonic linear spectra but also a continuous sound spectrum. These results, however, even if they are readily reproducible, must be treated with caution, since more rapidly changing components, under certain circumstances, may prove insufficient to be detected, and their coincidence with the frequency of the analyzer’s “probing” tone may turn out to be largely accidental.

The investigation of rapidly changing acoustic processes for the purpose of determining the variation in time of individual overtones is, strictly speaking, impossible, nor is there any particular need for it. It is sufficient to establish at what instants of time oscillations lying in a certain frequency region are more or less strongly expressed. To achieve this goal a whole series of methods was developed, whose common feature is the use of frequency filters. F. Trendelenburg and Franz^63 used for this purpose an octave filter according to the Tilo and Steudel^71 scheme, in which the transmitted frequency bands, with an interval of one octave, are switched on successively, so that the entire frequency range from 37.5 to 9,600 Hz can be covered. In doing this, several oscillograms must be taken for each octave, as well as, simultaneously, the unfiltered process, so that its reproducibility can be verified. A further development of this idea is represented by the so-called “sound frequency spectrometer” according to Freystedt’s^65 scheme. Here, for each octave, 3 filters in logarithmic succession are already used. These filters are switched on in turn by means of a rotating switch; the oscillations passed by them produce the deflection of a cathode oscillograph, which is connected to the corresponding filters. The entire process is recorded by means of a cinematographic apparatus. Finally, mention must be made of the method of “oscillography by means of octave filters,” which was developed simultaneously and independently by F. Trendelenburg and Franz^88 on the one hand, and by Friling^64 on the other. This method consists in the fact that the sound oscillation, repro-

received by the microphone is simultaneously fed to 6 octave filters in the range from 100 to 6400 Hz through 6 channels, the sounds passed through the filters being simultaneously fed to 6 oscillographs, and, in addition, a 7th oscillograph records the unfiltered process. Trendelenburg[^88] investigated in detail the possibilities of this method. He came to the conclusion that sound processes proceeding with a decrement greater than the intrinsic decrement of the octave filter used are unacceptably distorted. In octave filters for simultaneous application the intrinsic decrements were of the order of 0.21; in the previously used filters[^63] (switched separately) the intrinsic decrement was of the order of 0.7. In studies of speech and the sounds of musical instruments, a decrement of the order of 0.21 is quite sufficient.

10. Transient processes in electroacoustic apparatus

The quality of electroacoustic apparatus was formerly judged almost exclusively on the basis of its frequency characteristic, i.e., on the basis of how uniformly different frequencies are transmitted. On the basis of the known theoretical relations between resonance curves and transient processes, such a criterion may in principle be considered entirely sufficient. But these relations can be used, as the author has shown1, only for very simple forms of resonance curve and cannot be transferred directly to the more complex curves encountered chiefly in loudspeakers and sometimes also in microphones. For this reason experimental investigations of transient processes in loudspeakers and microphones appear to be absolutely necessary. In other electrical transmission apparatus, such as amplifiers and transformers, distortions caused solely by the reasons just mentioned can be eliminated by methods developed in electrical engineering. The corresponding description is given by Bjork, Kotovsky, and Lichte[^83] (p. 10). The question that must be answered on the basis of experiment may be formulated as follows: do the parasitic frequencies produced in the corresponding apparatus during the transmission of nonstationary sound processes, owing to the occurrence of damped oscillations of its natural frequency with sufficiently large amplitude, interfere with the transmission? Or, in other words, does the apparatus transmit the given nonstationary process without noticeable distortions?

Investigating hornless loudspeakers with a large surface, the author1, by recording the build-up processes and decay processes in the sound field, and also by recording the motion of the membrane excited by an impulse, showed that in this case weakly damped natural oscillations with a frequency of about 50 Hz occur,

The settling time for better loudspeakers was approximately 40 msec; for poorer ones it reached 1 sec. The reason for this lies in the fact that, in loudspeakers of this design, owing to the soft fastening of the membrane, strongly pronounced oscillations with a natural frequency of about 50 Hz are observed. The peculiar muffled timbre observed in loudspeakers of the design under investigation is evidently due to these low natural oscillations, which arise constantly during the reproduction of non-steady processes. The design can be considerably improved by means of a softer fastening of the membrane, so that the natural frequency would be shifted to the lower boundary of the region of auditory perception, and also by means of stronger damping. An increase of damping in electrodynamic loudspeakers, as Neumann indicated^30, similarly to what takes place in moving-coil galvanometers, can be achieved by strengthening the magnetic field. Neumann showed experimentally that this measure has a very favorable effect both on the form of the frequency curve and on the course of non-stationary processes. In horn loudspeakers with a relatively small membrane, the natural frequency, owing to the influence of the elasticity of the transition chamber, is shifted toward higher frequencies; at the same time a rather considerable increase in damping is also observed. MacLachlan and MacKay^52 showed this theoretically. Experimental results relating to this case were obtained by Schafstein^62. Transmitting apparatus and chiefly loudspeakers, with respect to distortions in settling processes, were also investigated by Buerck, Kotowski, and Lichte^53 with the aid of the methodology described above (see III, 7). It was found that near the natural resonance in small loudspeakers considerable time constants are observed. At high frequencies, in the minimum between two resonance curves, “negative” time constants (i.e., excitation of impulses) are observed, which can be explained by the detector action of the loudspeaker. The named investigators came to the conclusion that, although noticeable distortions are observed in loudspeakers during settling processes, they interfere with perception much less than distortions caused by other reasons, among which subharmonic oscillations of the membrane (the so-called “gong song”)^49 are the most significant.

Settling processes in microphones, which have a comparatively small surface, are of considerably less importance than in loudspeakers. A highly tuned microphone, possessing a sufficiently flat horizontal frequency characteristic within the limits of the region of auditory perception, does not give, as is easy to understand, noticeable non-stationary processes. On the other hand, experimental investigation of a microphone with respect to

of transient processes is not as simple as that of a loudspeaker, since it is difficult to apply to a microphone a tone without a transient process. With a telephone or loudspeaker this cannot be done. Therefore Barth\({}^{50}\), in his detailed investigation of this question, excited the microphone either by means of a thermophone or by means of an electrostatic “tweezers.” He showed that a highly tuned condenser microphone of suitable design indeed gives no noticeable transient process. In the further investigation of other microphones, the condenser microphone was used for comparison simultaneously with the microphones under study, excited by a loudspeaker. By means of this method the following were investigated: 1) a condenser microphone of Ritter’s design, 2) a ribbon microphone, 3) a high-quality carbon microphone of Reis’s design, 4) an ordinary microphone capsule of a microtelephone handset, 5) an electromagnetic microphone (telephone). The result of the investigation may be formulated as follows: in order to transmit correctly all the transient processes occurring in speech and in music, the microphone must practically settle within approximately \(3\) msec. This requirement corresponds to a certain limiting damping

\[ D_{\lim}=\frac{\vartheta_{\lim}}{\pi}, \]

where \(\vartheta\) denotes the logarithmic decrement. Experiments showed that in microphones 1 and 3 this limiting damping had already been exceeded, in 2 it had just been reached, and in 4 and 5 it had not yet been reached. This corresponds to a certain form of resonance curve, from which the damping can likewise be determined.

V. Transient Processes in Speech Sounds

11. Speech Organs

The mechanism of formation of speech sounds has been elucidated in detail in the recent works of W. Trendelenburg and his collaborators\({}^{59,60,77,78}\). They established\({}^{59}\) (in complete agreement with the views of Helmholtz\({}^{6}\)) that during phonation the vocal cords in the larynx pass short impulses of air, caused by the increased pressure in the lungs, and then close completely. In this case the closing phase continues (especially at low tones) sometimes longer than the opening phase; at high tones this may not be observed. The process occurring during one period may be represented as follows: the cavities of the pharynx, nose, and mouth adjacent to the larynx are set into their own oscillations as a result of this short impulse of air. In doing so, damped oscillations arise, which can be distinctly observed on oscillograms of certain speech sounds. W. Trendelenburg\({}^{78}\) established that all vowels recorded on oscillograms taken with the aid of a microphone begin—

are a group of strongly expressed oscillations, which occupy approximately \(1/3\)—\(1/5\) of the period. This “initial group” coincides very precisely in time with the opening of the glottis, as was established by simultaneous recording of the sounds of the voice and of the movements of the glottis on a larynx apparatus.

From the obtained vowel curves it was established, on the basis of their shape at the beginning of each period, that the oscillatory process begins precisely with this initial group, arising as a result of the abrupt opening of the glottis (Fig. 17). At the same time it was confirmed that this initial group really arises as a result of the opening of the glottis. For sounds of a higher register, in which the opening phase occupies a significantly larger share of the period, the initial group is obtained less distinctly expressed.

This investigation of the processes occurring during a single period considerably clarifies the mechanism of action of the speech organs. For a complete explanation of the formation of the sound of speech, however, this investigation is insufficient. For this it is also necessary to take into account that the above-mentioned openings of the glottis occur periodically after definite intervals of time, and consequently it is necessary to keep in mind this strictly periodic, or at least almost periodic, process. It is very expedient to carry out the expansion of this periodic process into a Fourier series, and not only on the basis of purely mathematical considerations, but chiefly on the basis of physical considerations, taking into account the property of our ear as a frequency analyzer (“according to Fourier”). Air impulses are passed by the glottis in time with the fundamental frequency and contain a considerable number of harmonic overtones of rather considerable amplitude. The resulting acoustic process, which we call the sound of speech, acquires its characteristic coloring, its timbre, as a consequence of the fact that the corresponding overtones are strengthened owing to resonance in the cavities of the nose, pharynx, and mouth. This conception of the mechanism of the formation of speech sounds is in all respects equivalent to the previously presented conception of the processes occurring during a single period. With a strict and logical development of these two theories, evidently, completely identical results must be obtained. Therefore it is wholly unfounded to develop different theories of the formation of vowel sounds, proceeding from these two mutually equivalent basic premises. V. Trendelenburg \(^{59}\) noted many features of similarity in the mechanism of action of the speech organs and bowed instruments. The two interconnected systems—namely, the string and the body of the instrument—correspond to the vocal cords and the resonating cavities. Damping in the first case is reduced owing to the action of the bow, in the second owing to the current of blown air. The corresponding electrical analogy, as the author has shown \(^{81}\), is represented by a tube generator with an intermediate circuit. V. Trendelenburg

it was further possible, on the basis of our experiments with preparations by changing the resonant cavities adjoining the larynx, to show that the vibrations of the vocal cords are not noticeably altered thereby. On the basis of these experiments one must conclude that there is a very weak coupling between these two oscillatory systems.

12. Non-stationary processes in the formation of vowels

In the phonation of isolated vowels, the initial phase of the growth of oscillations is not observed. The author \(^{33}\) established that, in the ordinary pronunciation of a vowel, the form of oscillations characterizing this sound is fully established already after the passage of a few milliseconds. V. Trendelenburg \(^{78}\) likewise established that, with sharp pronunciation of a vowel, stationary oscillations begin immediately (Fig. 17). On this basis it may be considered that vowels completely lack that distinctive feature which, in other sounds—especially in the sounds of musical instruments—serves to characterize the sound itself. In vowels the initial phase has no significance, since they can be recognized with complete certainty on the basis of their stationary timbre, on the basis of their formants. In the case of the sounds of musical instruments the situation is quite different. The author of the present article \(^{33}\) was able to substantiate this fact by the consideration that the regions of resonance to which, in pronouncing vowels, the cavities of the mouth and nose are tuned are very broad. As a result, the formants characterizing a given vowel region reinforce not some single definite overtone, but an entire region of overtones. This blurred resonance is due to the strong damping resulting from friction against the soft walls of the resonant cavities. This large damping must, moreover, cause the rapid cessation of the process of growth of the oscillations, as was indeed established in the investigation of vowels. This theory was confirmed by the investigations of V. Trendelenburg \(^{77}\), who recorded the sound oscillations arising in the cavity of the mouth, tuned for the pronunciation of the corresponding vowel and excited by means of a short impulse. From the curves obtained in this way, the natural frequencies and the decrement of the oral cavity were determined. The impulses causing oscillations of the oral cavity were produced either by a sharp separation of the lips when the mouth was opened quickly, or by a sharp blow with a finger, or, finally, by the rupture of a saliva film, which can easily be formed between the lips. With proper tuning of the oral cavity, extremely large damping decrements of the order of \(0.2—0.37\) were established, and, in addition, the formant regions were determined. These figures agree very well with the values of the decrement previously obtained by F. Trendelenburg and Franz \(^{63}\) with the aid of an oscillo-

To the article by G. Backhaus

Fig. 17. Oscillograms of sharply pronounced vowels “e” and “a” (after V. Trendelenburg)

Fig. 18. Oscillograms of the syllables Di and Do, taken with octave filters (after F. Trendelenburg and E. Franz)

grams, obtained by means of octave filters, namely: for the vowel “a”—0.13–0.29, and for the vowel “i”—0.2.

It must be firmly emphasized that vowels in principle constitute a strictly periodic process, since from time to time incorrect statements appear on this score[^76]. The decomposition of the oscillations of a linear oscillatory system, which we must take to be both the organ of hearing and the organ of speech, by its own functions inevitably leads to a Fourier series. A vowel sound, sung for a sufficiently long time at constant pitch and amplitude and considered as a whole, in its entire sequence and not only within the limits of a single period, consists of stationary, strictly harmonic overtones. It is precisely such a process that must be regarded as conditioning the perception of vowels. In conversation, changes in the fundamental frequency, amplitude, and timbre are often observed; however, the character of the vowel is not thereby changed in the least. The author1 established that when pronouncing “ba” and “da” the formant of the vowel “a” after 10 msec is observed only in the low range at 660 Hz, and after 20 msec increases to 1155 Hz. W. Trendelenburg[^78] explains this by the fact that, when the mouth opens after the consonant, the lips settle with a certain speed for the pronunciation of the vowel sound “a,” and in this transition they must pass through positions characteristic for the pronunciation of “u” and “o.” In conversational speech, such transitions between pure and distinct vowels and less distinct forms often occur, as was established by Gemelli and Pastori[^51],[^70]. These investigators divide the various forms of curves for the sound of vowels into “typical” and “atypical.” For establishing a vowel sound, two “typical” periods prove quite sufficient. Steinberg[^53] carried out more detailed investigations of changes in amplitudes and in the formant region in conversational speech. Firling and Sengeiser[^96] investigated both short and long vowels by means of oscillography with octave filters, the range investigated extending to 11,200 Hz. They found that the difference between short and long vowels consists not only in the duration of the sound, but that at the same time a considerable difference is observed in spectral character. Short vowels are characterized above all by a significantly larger number of high overtones than long vowels, which until now had mainly served as the subject of investigation. With the vowel “a” all formants shift toward higher frequencies, while with the vowel “e” only the lower formant does so; at the same time a new formant arises in the region 700–1400 Hz.

13. Consonants

Vowels constitute the basis of speech. Consonants, however, are typical examples of nonstationary processes, for which it is difficult

to indicate definite properties characterizing them in acoustic terms. Their participation in the formation of speech sounds consists in the fact that they influence both the process of establishing the vowel following them and the process by which the preceding vowel ceases to sound. An intermediate position is occupied by the voiced semivowels “m,” “n,” “l,” “r.” Comparatively long ago F. Trendelenburg ^18 established that these sounds are a mixture of various sounds, consisting of strongly expressed harmonic and non-harmonic overtones, chiefly of the high range. This was shown especially convincingly by oscillography with the aid of octave filters ^58. In this case, the vibration of the vocal cords is not the sole source of sound. Not all the kinetic energy of the air stream is converted in the larynx into sound energy; some part of the steady stream, superimposed on the oscillatory motion of the air, produces noises at the constricted places in the pharyngeal cavities, arising mainly as a result of the formation of vortices. F. Trendelenburg determined the frequencies characterizing the sounds “l,” “m,” “n,” in full agreement with Stumpf’s earlier observations ^20; however, we shall not examine this work in detail here, since it falls outside the scope of our article. Gemelli and Pastori ^61 established that, when the sounds “l,” “m,” “n” are pronounced, the accompanying vowels influence the character of the consonants’ sounding, precisely in the sense that they give them the formants characterizing the corresponding vowel. Thus, for example, the sound “l” in the word “kabala” is accompanied by the formant of the vowel “a,” while in the word “mokkolo” it is accompanied by the formant “o.”

The sound “r” has certain special features. When the alveolar “r” (linguale) is pronounced by means of vibration of the tongue, or when the uvular “r” (uvulare) is pronounced by means of vibration of the uvula, interruptions of the air stream are observed, occurring with a frequency of 20–40 Hz. As a result, an amplitude modulation of the sound arises. F. Trendelenburg ^18 showed that this process should be regarded as the superposition of two close sinusoidal oscillations, which in general are not in harmonic relation to one another. Consequently, “r” must be regarded as a mixture of different sounds.

To the mixture of different sounds one must further assign the voiced sibilants. F. Trendelenburg and Franz ^63 showed by means of oscillography with octave filters that in the low range, up to 600 Hz, there lie strictly harmonic overtones arising as a result of the vibration of the vocal cords, while in the high-frequency region there lie non-harmonic overtones, which arise as a result of the formation of vortices when the air stream passes around the teeth. In voiceless sibilants only these noises are observed, which, according to the observations of Grotzmacher ^6, with very sharp pronunciation extend up to 13,000 Hz.

Of particular importance for the question under consideration are the so-called

explosive sounds (Explosivlaute), which are conveniently divided into two groups: the first, consisting of “b”, “d”, “g” (Mediae), and the second, consisting of “p”, “t”, “k” (Tenues). Helmholtz\(^6\) made some very valuable subjective observations concerning these sounds. A more detailed investigation was carried out by the author of the present article\(^ {33}\) and by F. Trendelenburg and Franz\(^ {63,88}\), with the aid of oscillography through octave filters. In pronouncing the sounds of the second group (“p”, “t”, “k”) the glottis remains open, whereas in pronouncing the sounds of the first group (“b”, “d”, “g”) it is at first closed, and then, during pronunciation, begins to vibrate. Consequently the sounds of the first group should be regarded as voiced sounds. Depending on the position of the place at which closure occurs so that, in pronouncing the sound, a release takes place that determines the corresponding sound, the sounds are divided into labials—“b” and “p”, dentals—“d” and “t”, and gutturals—“g” and “k”. The objective distinction between the various sounds consists above all in the duration of the noise accompanying the given sound. F. Trendelenburg\(^ {88}\) found on average the following durations of sounding, in milliseconds, in good agreement with the results obtained by the author of the present article\(^ {33}\), namely:

“pe” — 65, “te” — 57, “ke” — 79, “be” — 13, “de” — 19, “ge” — 22.

The same durations are also observed when the corresponding consonant sounds between two vowels. Obata and Tesima\(^ {57}\) give data on the duration of the sounding of consonants in the Chinese and Mongolian languages that partly coincide with those cited above. In pronouncing the sounds of the second group (Tenues) the noise characterizing the consonant is expressed chiefly; in pronouncing the sounds of the first group (Mediae), voiced components are also observed simultaneously with a considerable weakening of the noise components. F. Trendelenburg\(^ {88}\), in complete agreement with Helmholtz’s\(^6\) subjective observations, established that the voiced components arise earlier than the noise components characteristic of the given sound. When Mediae sounds are pronounced between two vowels, the voiced components remain, whereas when Tenues sounds are pronounced they disappear completely. The guttural sounds “g” and “k” are characterized by the fact that the noises specific to these sounds arise like impulses. In pronouncing Tenues sounds, the author\(^ {33}\) established that after the first onset there follows a certain intermediate phase characterized by aspiration. This process is observed especially strongly in the pronunciation of the sound “p”, as was found by F. Trendelenburg\(^ {88}\) and Lichte\(^ {67}\). In pronouncing this sound there is observed a distinct and strong impulse created by the air current. On the basis of earlier observations it was established that the formation of the formants of the vowel following Mediae

in general occurs more quickly than in the pronunciation of Tenues. F. Trendelenburg^88 showed in this connection that the time required for the establishment of the formant depends to a very large degree on how far the position of the tongue and the tuning of the oral cavity corresponding to the given consonant differ from those needed for the tuning required for pronouncing the vowel. Thus, for example, when pronouncing “d” the tongue is located near the upper teeth, and for pronouncing “i” it need be moved back only slightly, whereas for pronouncing “o” the tongue must be moved considerably farther away from the teeth and a constriction must form between the back part of the tongue and the uvula. Observation fully confirms these considerations. In Fig. 18 are presented curves obtained by Trendelenburg^88 with the aid of octave filters, while Fig. 19 presents the maximum values observed in separate octave intervals when pronouncing “di” and “do,” as a function of time.

Fig. 19a and b. Peak values in separate octave intervals when pronouncing the syllables Di and Do (after F. Trendelenburg and E. Franz)

VI. Nonstationary processes in musical instruments

14. General survey

In the sounds of musical instruments, nonstationary processes play an extremely important role, especially the processes occurring during the build-up of oscillations. On the basis of Schumpf’s^20 investigations it became known that assigning a given sound to one or another musical instrument, and likewise distinguishing from one another sounds produced by different musical instruments, cannot be performed even by an experienced musician if only a purely stationary sound is heard, without the accompanying nonstationary processes, i.e., the processes occurring during the growth and decay of the sound. Hence^83 it follows that the distinctive features of the differences between the sounds of various instruments are conditioned not by their “musi-

cal timbre (spectrum), but chiefly by the processes of growth, which differ very greatly among individual musical instruments. Meyer28 was the first to show that formants, i.e., those regions of frequencies whose amplification is characteristic of a given sound, are hardly of any great importance in this question. In this matter one observes relations exactly opposite to those in vowel sounds: the resonating systems in musical instruments are, in most cases, very weakly damped; as a result, their resonance curves often consist of sharp peaks, as was first shown by the author of this article81 in the investigation of violin sounds. Therefore the question of a regular formation of formants cannot arise here, since the corresponding overtones of the exciting system often fall in the region of a trough of the resonance curve. On the other hand, nonstationary processes, owing to the small damping, must be very clearly expressed and relatively prolonged. It is precisely in them, chiefly in the processes that occur during the growth of oscillations, that the principal distinctive features characterizing the sound of one or another musical instrument lie.

However, the special importance of the nonstationary processes occurring in musical instruments is due not only to the reasons mentioned above. A strictly stationary sound produces a monotonous impression and is not very pleasant. The auditory impression becomes considerably more interesting if a certain amount of sounds nonharmonic with it is admixed to the stationary sound; this is achieved, for example, by introducing percussion instruments into the orchestra. Those musical instruments, for example bowed instruments, whose sound can easily be modulated, are the most widely used. Conversely, the absence of any possibility of modulation in the organ causes great regret. As a result, the sound acquires a kind of frozen character, and the organ can be used only for the performance of quite definite pieces, for which the effect it creates is appropriate.

15. Bowed instruments

The process of growth in violin sounds is very strongly expressed and lasts approximately 100 msec. In Fig. 20 the gradual development of the individual partial tones is presented. During the first 30 msec, predominantly high overtones in the region from 3000 to 5200 Hz prevail. They are caused by the well-known noise during the motion of the bow. These same overtones are also well expressed in the steady-state sound. The development of the lower overtones apparently occurs as a result of the fact that the pressure of the bow in the first phases of the attack is still insufficient

to create oscillations with a predominance of the fundamental tone. With time the pressure of the bow increases; as a result, the order of the predominant overtone becomes lower and lower until, finally, the fundamental tone begins to predominate; this occurs approximately after 100 msec. Further, it was established, by determining the amplitudes of the individual overtones over a sufficiently long time, that even in the case when the performer strives to maintain as constant and even a sound as possible, relatively pronounced changes in the amplitudes of the individual overtones are nevertheless observed, inevitably arising as a consequence of the specific features of the motion of the bow by the hand1.

Fig. 20. Changes over time of individual components of the sound of the violin (according to H. Backhaus).

In order to eliminate the irregularities caused by the motion of the bow by the hand, the author of this article2 recorded the establishing processes observed in violin sounds when the sound was excited by means of a special automatic device. In investigating a string rigidly fixed at both ends, the presence of a certain optimal degree of bow pressure was established, at which, on the one hand, the processes of increase of the sounds proceed more rapidly and, on the other hand, the fundamental tone is expressed most strongly. The decrement of a single string proved to be extremely small, approximately

\[ \vartheta = 0.004. \]

As a consequence of the work necessary for deforming the bridge, the decrement of the string increases considerably and becomes, on the average, approximately

\[ \vartheta = 0.04, \]

a value which is also observed for the decrement of the resonating body, so that both parts of the system—the string and the body—are damped practically equally strongly. The duration of the increasing process of the individual strings proved to be as follows: string \(g\)—0.4 sec., string \(d\)—0.24, string \(a\)—0.16 sec., string \(e\) (metal)—0.16. These values were determined for individual strings stretched on the instrument. The attenuations calculated from this,

\[ \frac{\vartheta}{\pi}, \]

turn out for the free string all to be of one and the same order—0.01.

For shortened strings values approximately 2 times larger are observed. The attenuations calculated on the basis of records of nonstationary oscillations prove to be of the same order

0.01; in this case a distinct maximum is observed in the region of the violin’s main resonance—about 500 Hz. In addition, the damping increases with increasing string thickness. With appropriate treatment of the violin body, which results in a smaller thickness of the wooden walls, an increase in damping is observed, evidently as a consequence of increased radiation. In transient processes in the region of the main resonance, especially simple relations are observed for the filtered fundamental tone, which theoretically should occur in a system with two degrees of freedom, the separate parts of which have the same natural frequency and the same damping. Using the theoretically obtained relations, one can, on the basis of the recorded curves, calculate the magnitude of the coupling coefficient and of the damping. Both of these quantities decrease as the string thickness decreases, as was established on all the instruments investigated. With regard to the coupling coefficient, this conclusion can readily be understood if one takes into account that the transmission of vibrations to the violin soundboard is effected chiefly by means of the left foot of the bridge. To improve the quality of a violin, it is evidently advisable to recommend the closest possible coupling between the string and the body.

Firling^64 made recordings of transient processes in violin sounds by means of a logarithmic amplifier. He did not obtain a rectilinear decrease and concluded from this that, as the amplitude of the vibrations decreases, an ever smaller number of individual parts of the instrument take part in the vibration, and as a result the damping decreases. In violins the observed effect is, to a considerable degree, further masked by the circumstance that, as is known from the theory of free vibrations of a system with several degrees of freedom, one cannot here expect a strictly exponential decay, especially in the presence of strong coupling.

In bowed instruments, especially in the cello, unstable phenomena are sometimes observed, known under the name “wolftone” (Wolfton). This question is the subject of Vollmer’s work^90 (see also^81). Investigations with octave filters showed that strong beats of the fundamental tone arise in this case, occurring with a frequency of approximately 10–15 Hz. Raman^8 gave an explanation of this phenomenon based on energy considerations. For a clearer understanding of this process, it should be recalled that the mechanism of action of a bowed instrument has a great analogy with the action of a tube generator with an intermediate circuit or with the action of a reed pipe. In both cases there are so-called entrainment phenomena, observed by Wien and Vogel in organ pipes. An explanation of the cause of the occurrence of the wolftone can be obtained from Rogowski’s theory, concerning the tube generator with an intermediate circuit^15. It turns out that, with properly selected feedback

it is possible, when the two systems are tuned to one another, to de-damp them. In this case free, weakly damped vibrations of the coupled system arise, which produce beating with one another. The coupling coefficients calculated on this basis agree very well with the values obtained on the basis of other considerations. The formation of a wolf tone should be regarded as a defect of the instrument. It does not follow from this, however, that the poor quality of an instrument can be inferred from the mere presence of a wolf tone alone. Wolf tones are often found in some famous violin instruments. The prerequisite for their formation is a strongly pronounced main resonance. On this basis we may regard the wolf tone as an undesirable side effect accompanying the good quality of an instrument. Elimination of the wolf tone can be achieved either by increasing the damping of the main resonance, or by placing rubber between the body and the fingerboard, or by means of an appropriate excitation of the second string.

16. Wind instruments

In wind instruments, non-stationary processes have considerably less significance than in bowed instruments. In a tone sounding for a long time, its amplitude and timbre change very little. Meyer and Buchmann ^28 found that formants can be detected in the sounds of the oboe and bassoon. The reason for this is apparently the strong damping of the air column owing to the narrow reed opening. Accordingly, the transient processes in these instruments last a very short time. F. Trendelenburg and Franz ^88 carried out some measurements with the oboe. The process of the growth of the sound here proceeds very uniformly and lasts about 10 msec. In the clarinet ^33 this process lasts 50—70 msec. At first low overtones appear here. F. Trendelenburg ^88 found in this case a less uniform course of the process. Ashov ^87 made observations on the basis of which both the mechanism of action of the clarinet and the processes observed in “overblowing” were clarified; when the lips are pressed very strongly, beatings arise, resembling the wolf tone of bowed instruments and arising for analogous reasons. The author of the present article ^33 found the duration of the rising process in the saxophone to be approximately 40 msec; in this case there is a somewhat more considerable strengthening of the high frequencies than in the sounds of the clarinet. The most striking feature in the course of this process proved to be the decrease in the amplitudes of most overtones in the middle of the sounding. Evidently, it is this that accounts for the peculiar howling characteristic of the saxophone. The rising process of the flute sound lasts a very long time, 200—300 msec. Sometimes ^33 a more rapid introductory phase is observed, end-

...lasting for 50 and 60 msec, after which the sound once again diminishes, only later reaching its full strength. Often the sound begins with a somewhat different frequency; this circumstance must be explained by the instability of the very mechanism by which the sound is blown. The entrance of the flute sound therefore creates an insufficiently definite, blurred impression. Firling^64 obtained, with the aid of oscillography and by means of octave filters, similar results. In addition, he showed that, despite such a long process of the sound’s growth, the transition from one tone to another occurs considerably faster, namely in less than half the time required for the sound to grow. During this transition a beat is observed, arising between the rapidly reappearing second tone and the more slowly dying first tone.

For brass wind instruments, the processes of the growth of sound have so far been recorded only for the trumpet. The author^33 found a very rapid increase of all overtones to the maximum value, followed by a gradual decrease to a constant value. F. Trendelenburg and Franz^88 also found, at the beginning of the sounding process, the presence of inharmonic noises formed during blowing.

17. Organ

The sound of an organ arises as a result of air being blown into pipes, while the beginning and end of the air supply are produced by means of special mechanisms. The sound obtained in this case is very even and monotonous. A change in the strength of the tone of a given register is achieved only by means of a very imperfect mechanism, similar to a shutter. A change in timbre generally cannot be obtained unless additional pipes are used. Organ builders, quite unconsciously, sought to eliminate this shortcoming of the organ by creating, in various registers, the most diverse processes of growth of sounds.

Very detailed investigations of the processes occurring during the growth of organ sounds were carried out by F. Trendelenburg and his collaborators^82,^86. They established that, in registers with reed pipes (trumpet, trombone, cornet, oboe, human voice), the sound generally arises quickly and very stably; in registers with pipes without reeds (principal, stopped, flute, string), the stationary state arises slowly, is insufficiently stable, and in most cases is accompanied by a considerable change over time in the composition of the sound. This observation corresponds fully to the results obtained in the investigation of the separate flute. Imitation of musical instruments by means of the various registers of the organ appears insufficiently successful to the ordinary listener.

The reason for this lies to a lesser degree in the difference of musical timbre than in the differences in the processes of the sound’s growth. Imitation is most successful on the registers of the trumpet and trombone, which, like their models, are characterized by a very rapid establishment of the sounding process, as also on the oboe register. On the register of the human voice, the rapidly establishing sound has significant inharmonic low components. The difference between the sound of the register and the imitated sound is explained as follows. There is a great analogy between the process considered here and the processes observed with explosive consonants, when a consonant belonging to the group Mediae is followed by a vowel. In the stationary sound, in this case, a great analogy with the vowels of the human voice is observed chiefly in the region of the high formants. F. Trendelenburg sees the reason for this chiefly in the different construction of the reeds. On the trumpet and trombone registers these reeds are made short, wide, and thick, whereas on the register of the human voice they are longer, narrower, and thinner.

Special attention should be paid to the recordings of the sounds of the “Lieblich Gedackt” register (Fig. 21). The sounding of the fundamental tone is preceded by a tone whose frequency is approximately \(5 \frac{1}{2}\) times greater than the frequency of the stationary tone, i.e. quite inharmonic with the fundamental tone. Trendelenburg \(^{82}\) explains the origin of these “precursors” of the tone by the fact that a quite definite air pressure is required to maintain the sounding of the stationary fundamental tone, owing to the great instability of the process of blowing air in. If the necessary air pressure has not yet been reached, the sound of the pipe jumps to a higher tone. On this register it is possible to produce an extremely peculiar and colorful sonority, namely: when tones follow one another very rapidly, only the “precursor” tones are heard, and only in sustained pieces do stationary sounds arise. On another similar register, F. Trendelenburg established an unusually long and uniform process of sound growth, lasting approximately 400 msec. Subjectively this creates the impression of a gradual increase of sound, which, in general, cannot be achieved in organs, but here is produced owing to the special form of the establishing process. It must be emphasized that these phenomena were established not only on individual organs, but that they are observed in all expensive and, chiefly, old instruments. “In this colorful variety presented chiefly by the processes of growth lies the reason for that profound impression produced by playing on a truly good organ; moreover, this peculiar impression can never be achieved by any timbral changes of a stationary sound.”

Obviously, these questions concerning the processes of the establishment of sounds are of extremely great importance for organ builders.

To the article by G. Backhaus

Fig. 21. Additional sounding for the organ stop “Lieblich Gedackt”; pitch \(c^1\) (after F. Trendelenburg and E. Franz).

Gausman[^43] investigated the influence of organ bellows and the shape of valves on the processes by which oscillations become established in organ pipes. In those cases where it is necessary that the fundamental tone begin to stand out from the sound of the organ especially quickly, such an arrangement of the console and valves is needed in which the pipe supplying the air would be as short as possible and as straight as possible.

However, F. Trendelenburg’s investigations by no means lead to the conclusion that in all cases such a sound, in which the fundamental tone would stand out, is desirable.

18. Piano

The sounds emitted by the piano are, for the most part, nonstationary. Meyer and Buchmann[^28] established that, besides a harmonic linear spectrum, there is also a continuous spectrum. The source of the noise represented by this continuous spectrum is the string itself at low and middle tones, owing to the detuning caused by the hammer blow. In the region of higher tones the noise of the hammer itself becomes noticeable; moreover, the components of this noise may reach the fundamental tone of the string brought into sounding. This can be explained by the fact that the string must be sufficiently stiff in order to excite the sound of the hammer. And this is possible only at frequencies lower than the string’s own frequency. Similar results were obtained by F. Trendelenburg and Franz[^88] by means of the method of oscillography with octave filters. In addition, they established the natural oscillations of the resonating parts of the piano, arising as a result of individual blows and inharmonic with the fundamental tone; this was observed especially distinctly in the sounding of high tones. Meyer and Buchmann recorded the processes of growth and decay of the oscillations of individual overtones by means of an analyzer with a sounding tone. In so doing, it was found that, in the processes of decay of the oscillations, there were distinct beats, as, indeed, was to be expected in such a coupled system with many degrees of freedom. Similar results were obtained by Wolf and Sette[^73]. Lange[^61] carried out a detailed investigation of the motion of the string and hammer, as well as of the radiated sound. It was thereby established that the velocity of motion of the hammer at the moment of impact is a function only of the velocity of motion of the key. It follows from this that the performer has only a single possibility for changing the character of the sound, namely by changing the velocity of motion of the key. This, incidentally, was to be expected, despite the opposite views of many musicians, since the hammer at the moment of impact moves completely freely and is not connected with the key; therefore the only quantity that can change is its velocity. Gart, Fuller

and Lesby^55 obtained similar results, carrying out simultaneous photography both of the motion of the hammer and of the sound produced. Ghosh^74 established that the form of the vibrations of piano strings does not depend on the velocity of motion of the hammer. However, on the other hand, it is known that the timbre changes depending on the force of the blow. According to the observations of Meijer and Buchmann^38, the number of overtones increases as the force of the blow increases. Firlijn^64,72 established that a tone which arises as a result of a strong blow at first dies away very rapidly, whereas a tone which arises as a result of a weak blow at first dies away considerably less strongly. The damping is due chiefly to losses of energy in the instrument itself, and only an insignificant part is due to radiation; this was established by removing strongly vibrating parts of the resonating soundboard. This dependence on frictional forces may be explained, as Firlijn believes, by the fact that with a stronger blow a significantly larger part of the instrument is set into vibration than with a weaker one. However, this conception was not confirmed by the investigations of Griitzmacher and Lettermoser^85, who measured the vibrational motion of individual parts of the instrument. These scholars investigated in great detail the damping curves of piano sounds with the aid of a self-recording sound-intensity meter (Pegelschreiber). They established, as did Savart^39, on the basis of the process of decay of the vibrations, that there are strongly expressed coupled vibrations between the string and the resonating soundboard. Near the region of the natural frequency of the resonating soundboard, strong beats are observed. This recalls the wolf tone observed in bowed instruments. Under certain circumstances an extremely rapid decrease of the amplitude is observed at the beginning of the process, as a result of which the sounding tone seems dry and lacking in color. The piano tuner eliminates this defect by slightly mistuning, relative to one another, the strings corresponding to the given tone. Firlijn^95 obtained a similar result on the basis of recording the sound with the aid of octave filters. The damping of different instruments in general increases from low tones to high ones.

Firlijn^64 established that in piano sounds the higher components die away more slowly than the lower ones. Subsequently^95 he explained this question in detail by means of experiments on models. With the aid of electrostatic excitation of string vibrations and the recording of the vibrations by means of octave filters, it was established that increased damping of the low components is observed only in the case when the string acts on the resonating soundboard, which responds especially strongly precisely to low frequencies and, as a result, borrows much energy from the corresponding components.

Lange^61, by observing the vibrations of piano strings excited by a special capacitor, both in the direction of motion of the hammer, i.e. in the vertical direction, and in the per-

pendicular, i.e., in the horizontal direction, established that motion in the vertical direction occurs in accordance with the sound, whereas the horizontal motion has an entirely different character. From this he concluded that the action of the horizontal component may be neglected. However, Firling^95, in contrast to this, found that if one confines oneself only to the vertical motion of the string or of the bridge (Steg), then a correct piano tone is not obtained in transmission. In order to obtain the strong decay of the sound immediately after the blow, which is extremely characteristic of the piano tone, it is necessary to include the horizontal motion of the bridge. He explains the origin of this motion by the occurrence of torsional vibrations of the bridge, which, especially at the first large amplitudes, are transmitted to the resonating soundboard. From this point of view it becomes understandable that proper transmission of the sound cannot occur at places of considerable curvature of the bridge, since at these places the bridge presents a significant obstacle to torsional vibrations. In contrast to this, a piano with a straight bridge has a very uniform tone throughout the entire range.

In conclusion, mention should also be made of the investigations of Urbach and Schlesinger^91, who carried out a study of the sound of pianos and grand pianos, using a mechanism regulating the force of the blow on the string. They established that the duration of the decay of the sound generally decreases with increasing pitch.

In the piano the duration of decay for low tones is considerably shorter, and for high tones longer, than in concert grand pianos. If the intensity of the tone is plotted as a function of the force of the blow, then the considerable steepness of such curves proves to be very characteristic for different designs of instruments. In the piano range the average steepness is greatest in salon grand pianos, while in the fortissimo range the greatest steepness is observed in concert grand pianos for low and middle tones.

19. Percussion instruments

Analyses of the sound of percussion instruments were carried out by Meyer and Buchmann^28. These sounds decompose, as was to be expected, into an almost exclusively continuous spectrum with more or less clearly expressed separate harmonic regions. Exceptions are the sounds of the triangle and of the bell, which give distinct, though in most cases inharmonic, overtones. The construction of certain Indian drums (as reported by Raman) is such that the thickness of the membrane increases toward the edges by means of appropriate layers. As a result, the overtones become almost harmonic with the fundamental tone, and po-

a considerably greater euphony is obtained. A similar acoustic effect is achieved in the Japanese instrument “tsudumi,” whose acoustic properties were investigated by Obata and Ozawa[^32]. This instrument consists of a wooden body, hollow inside, thinnest in its middle part and widening bell-like toward the edges. Membranes stretched over wooden frames are fastened to these two open ends, so that they project considerably relative to the body. The tension of the membranes could be varied by means of a cord connecting the two wooden frames and capable of being tightened by another cord in the direction of the axis. This instrument gives very few and almost harmonic overtones, as could be verified on the basis of a sound recording.

The most interesting problem in the sound of bells is presented by the so-called “strike tone” (Schlagton). The results of the old works of Rayleigh[^2], Bille[^10], and Jones[^23] lead to the conclusion that the overtones of a bell are practically inharmonic. Further, on the basis of a large number of investigations it was established that the sound of a bell is the more pleasing the closer its components are in the ratio \(1 : 2 : 2, 4 : 3 : 4\) (minor tuning) or in the ratio \(1 : 2 : 2, 5 : 3 : 4\) (major tuning). Immediately after the blow the 5th overtone stands out especially, and after several seconds the 3rd overtone begins to predominate. In subjective listening, the sound of the bell is assigned a frequency which, according to Jones, is an octave lower than the 5th overtone, i.e. lies in the region close to the 2nd overtone. This tone, the so-called “strike tone,” however, cannot be objectively established in sound analysis and also cannot be amplified by resonators.

Especially important for explaining this striking phenomenon are the investigations of Meyer and Klaes[^42]. They carried out, by the probing-tone method, analyses of the sound of a bell set into vibration by blows following one another at regular intervals. In the bell they studied, the second overtone was equal to 495 Hz, and the strike tone was equal to 530 Hz. The analyses confirmed that the strike tone cannot be established by physical methods. The 5th and 7th overtones were respectively equal to 1072 and 1605 Hz. On this basis one could think that the strike tone is nothing other than a subjective first-order difference tone between these two overtones. To test this hypothesis, a carbon microphone possessing a nonlinearity similar to that of the ear was used as the receiving microphone. In this case it was indeed possible to obtain the strike tone objectively in the analysis. Other combination tones also arise in this case; however, the strike tone, possibly as a consequence of its coincidence with objectively existing overtones, is especially strongly expressed. With the aid of this method it was possible to measure, using appropriate filters, the time of its de-

damping. The damping time determined in this way proved to coincide with that observed subjectively. To resolve the question of whether the “strike tone” is the suboctave of the 5th overtone and, consequently, is the result of subjective perception, the sound of the bell was listened to when fed, by means of a carefully designed transmitting device, to a loudspeaker. In this procedure, with the aid of filters, at first only the first two overtones were passed. The strike tone was at first not heard and continued to remain inaudible up to and including the addition of the 5th overtone. Only when the 7th overtone was added did the perception of the strike tone arise. This theory, which regards the strike tone as a difference tone, is based (as the authors themselves emphasize) on observations made on only a single bell. Jones^37 objects to this conclusion, since the bell investigated by Meyer and Klaes had a suboctave of the 5th overtone very closely coinciding with the difference tone between the 5th and 7th overtones. Having investigated bells in which such a close coincidence did not occur, Jones considers it possible to conclude that the coincidence of the observed strike tone with the suboctave of the 5th overtone is considerably better than with the difference tone. He concludes, moreover, that the occurrence of this difference tone strengthens the effect of the suboctave.

20. Electromusical Instruments

The broad possibilities afforded by cathode tubes for the generation of oscillations and for their amplification gave rise to numerous attempts to build electromusical instruments. The literature relating to this question has been collected by Firling^34, ^35 and Yanovskii^41. Here two fundamentally different methods may be distinguished. The most consistent method consists in both perceiving and creating oscillations entirely by electrical means; the other method consists in oscillations being excited by mechanical means, while electrical apparatus receives, amplifies, and reproduces them. The author of this article^44 has already had occasion to point out that, in the construction of these instruments, the question is not only that of imitating the musical timbre of known instruments or creating new musical timbres. Such an electromusical instrument can stand comparison with a good mechanical musical instrument only if it is capable of providing the possibility of fine modulation both in frequency and in amplitude during the sounding of sustained tones, and also possesses the ability to create the same rising and decaying processes as those which, in the sounds of mechanical instruments, appear so beautiful.

Among instruments generating electrical oscillations, the most widespread has been the so-called Trauto-

nium, constructed according to Trautwein’s idea^27,47. In this instrument a special tube generates relaxation oscillations, the frequency of which varies depending on the grid voltage, regulated by means of a corresponding keyboard. These oscillations excite special circuits (formant circuits), which can be switched in to change the timbre. The mechanism for exciting the intermediate circuits is analogous to the mechanism that takes place both in the human voice and in certain musical instruments. Ashov^93 indicated how the form of the sound can easily be changed, and even processes analogous to those occurring in the sounds of instruments with a struck string can be imitated, by introducing a special tube whose grid voltage changes in time with the aid of a capacitor discharge.

With a purely electrical instrument it is easiest and simplest to imitate the organ and the harmonium. A practically feasible solution was proposed by Firling^48. The generator of electrical oscillations was a glow-discharge tube connected to a discharge circuit and stabilized by self-induction (Cock’s idea^45). By changing the voltage applied to the tube, it was possible to obtain a wide change in timbre. “Vibrato” could be realized by means of a switchable device for modulating the voltage with a modulation frequency of 8 Hz. Such instruments make it possible to carry out a continuous change in tone strength and in this respect surpass ordinary organs and harmoniums. It remains unclear for the time being whether, by sufficiently simple means, it will be possible through electric organs to obtain that peculiar beauty which distinguishes the sound of old organs, owing to the extraordinarily great variety of processes occurring during the build-up of oscillations.

Another method, in which oscillations arise by mechanical means, was applied above all by Nernst and Firling, who built two keyboard instruments that had the advantage that they did without a resonating soundboard. Firling^72 came to the conclusion that mechanical generators of oscillations offer greater possibilities than electrical ones, and that with the aid of mechanical methods it is considerably easier to reproduce various processes of the build-up and decay of oscillations. The conversion of mechanical oscillations into electrical ones can be accomplished either by electromagnetic or by electrostatic pickups. For magnetic pickup of oscillations, the impact of an ordinary piano hammer is unsuitable; because of the excessively large amplitude and because of the nonlinearity of the receiving device, an inadmissible noise arises at the moment of impact. Sawade^39 investigated the possibility of striking the string by means of a “micro-hammer” actuated pneumatically; with this method of striking, the above-mentioned noise no longer occurred. Firling^72 pointed to another possibility for eliminating the distortions introduced inadmissibly

with a large increase of the first amplitude. For this purpose he used the fact that, when struck with a hammer, oscillations also arise that are perpendicular to the direction of the blow and that gradually increase. If, in this case, the adapters receiving the sound are shifted somewhat sideways (the shift depends on the pitch), a very satisfactory technique is obtained, in which the sound becomes extremely reminiscent of that of a real piano. Firling found impermissible distortions in magnetic pickups owing to nonlinearity and, as a result, began to use electroacoustic pickups. At the same time it appears possible to modify the timbre considerably by an appropriate choice of the location of the pickup along the string.

The damping of strings in a piano without resonating soundboards is extremely small. To obtain tones resembling piano tones, it is evidently necessary to introduce additional damping. Nernst^39 applied delayed damping for this purpose, which consists in the fact that the first blow occurs without damping and only afterward is damping switched on. To excite sustained tones, very small amplitudes are used. The damping that depends on amplitude is then not very great. This method makes it possible to obtain sounds resembling those of wooden wind instruments. To change the character of the processes by which the oscillations build up, Firling used two strings, which were set into vibration simultaneously by a blow. In this arrangement one of the strings was not damped, while the other, on the contrary, was strongly damped. In the electrical receiving circuit the two sound pickups are connected in series and in such a way that the two strings give equal and opposite potentials, which compensate each other. Owing to this, the first pulses cancel each other, and an oscillatory process arises which subsequently decays more or less slowly depending on the magnitude of the damping of the individual strings.

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