reverberation, he added that he found it difficult to avoid pitching his voice to that note which the auditorium most prolongs notwithstanding the fact that he found this the worst pitch on which to speak. This brings out, perhaps more impressively because from practical experience instead of from theoretical considerations, the two truths that auditoriums have very different reverberation for different pitches, and that excessive reverberation is a great hindrance to clearness of enunciation. Another incident may also serve, that of a church near Boston in regard to which the writer has just been consulted. The present pastor, in describing the nature of its acoustical defects, stated that different speakers had different degrees of difficulty in making themselves heard; that he had no difficulty, having a rather high pitched voice; but that the candidate before him, with a louder but much lower voice, failed of the appointment because unable to make himself heard. Practical experience of the difference in reverberation with variation of pitch is not unusual, but the above cases are rather striking examples. Corresponding effects are not infrequently observed in halls devoted to music. Its observation here, however, is marked in the rather complicated general effect. The full discussion of this belongs to another series of papers, in which will be taken up the subject of the acoustical effects or conditions that are desirable for music and for speech. While this phase of the subject will not be discussed here at length, a little consideration of the data to be presented will show how pronounced these effects may be and how important in the general subject of architectural acoustics.

In order to show the full significance of this extension of the investigation in regard to reverberation, it is necessary to point out some features which in earlier papers were not especially emphasized. Primarily the investigation is concerned with the subject of reverberation, that is to say, with the subject of the continuation of a sound in a room after the source has ceased. The immediate effect of reverberation is that each note, if it be music, each syllable or part of a syllable, if it be speech, continues its sound for some time, and by its prolongation overlaps the succeeding notes or syllables, harmoniously or inharmoniously in music, and in speech always towards confusion. In the case of speech it is inconceivable that this prolongation of the sound, this reverberation, should have any other effect than that of confusion and injury to the clearness of the enunciation. In music, on the other hand, reverberation, unless in excess, has a distinct and positive advantage.

Perhaps this will be made more clear, or at least more easily realized and appreciated, if we take a concrete example. Given a room com

paratively empty, with hard wall surfaces, for example plaster or tile, and having in it comparatively little furniture, the amount of reverberation for the sounds of about the middle register of the doublebass viol and for the sounds of the middle register of the violin will be very nearly though not exactly equal. If, however, we bring into the room a quantity of elastic felt cushions, sufficient, let us say, to accommodate a normal audience, the effect of these cushions, the audience being supposed absent, will be to diminish very much the reverberation both for the double-bass viol and for the violin, but will diminish them in very unequal amounts. The reverberation will now be twice as great for the double-bass as for the violin. If an audience comes into the room, filling up the seats, the reverberation will be reduced still further and in a still greater disproportion, so that with an audience entirely filling the room the reverberation for the violin will be less than one third that for the double-bass. When one considers that a difference of five per cent in reverberation is a matter for approval or disapproval on the part of musicians of critical taste, the importance of considering these facts is obvious.

This investigation, nominally in regard to reverberation, is in reality laying the foundation for other phases of the problem. It has as one of its necessary and immediate results a determination of the coefficient of absorption of sound of various materials. These coefficients of absorption, when once known, enable one not merely to calculate the prolongation of the sound, but also to calculate the average loudness of sustained tones. Thus it was shown in one of the earlier papers, though at that time no very great stress was laid on it, that the average loudness of a sound in a room is proportional inversely to the absorbing power of the material in the room. Therefore the data which are being presented, covering the whole range of the musical scale, enable one to calculate the loudness of different notes over that range, and make it possible to show what effect the room has on the piano or the orchestra in different parts of the register.

To illustrate this by the example above cited, if the double-bass and the violin produce the same loudness in the open air, in the bare room with hard walls both would be re-enforced about equally. The elastic felt brought into the room would decidedly diminish this reenforcement for both instruments. It would, however, exert a much more pronounced effect in the way of diminishing the re-enforcement for the violin than for the double-bass. In fact, the balance will be so affected that it will require two violins to produce the same volume of sound as does one double-bass. The audience coming into the room will make it necessary to use three violins to a double-bass to secure the same balance as before.

Both cases cited above are only broadly illustrative. As a matter of fact the effect of the room and the effect of the audience in the room is perceptibly different at the two ends of the register of the violin and of the double-bass viol.

There is still a third effect, which must be considered to appreciate fully the practical significance of the results that are being presented. This is the effect on the quality of a sustained tone. Every musical tone is composed of a great number of partial tones, the predominating one being taken as the fundamental, and its pitch as the pitch of the sound. The other partial tones are regarded as giving quality or color to the fundamental. The musical quality of a tone depends on the relative intensities of the overtones. It has been customary, at least on the part of physicists, to regard the relative intensities of the overtones, which define the quality of the sound, as depending simply on the source from which the sound originates. Of course, primarily, this is true. Nevertheless, while the source defines the relative intensities of the issuing sounds, their actual intensities in the room depend not merely on that, but also, and to a surprising degree, on the room itself. Thus, for example, given an eight-foot organ pipe, if blown in an empty room, such as that described above, the overtones would be pronounced. If exactly the same pipe be blown with the same wind pressure in a room in which the seats have been covered with the elastic felt, the first upper partial will bear to the fundamental a ratio of intensity diminished over 40 per cent, the second upper partial a ratio to the fundamental diminished in the same per cent, the third upper partial a ratio diminished over 50 per cent, while the fourth upper partial will bear a ratio of intensity to the fundamental diminished about 60 per cent. Quality expressed numerically in this way probably does not convey a very vivid impression as to its real effect. It may signify more to say merely that the change in quality is very pronounced and noticeable, even to comparatively untrained ears. On the other hand, if one were to try the experiment with a six-inch instead of with an eight-foot organ pipe, the effect of bringing the elastic felt cushions into the room would be to increase the relative intensities of the overtones, and thus to diminish the purity of the tone.

All tones below that of a six-inch organ pipe will be purified by bringing into the room elastic felt. All tones above and including that pitch will be rendered less pure. The effect of an audience coming into a room is still different. Assuming that the audience has filled the room and so covered all the elastic felt cushions, the effect of the audience is to purify all tones up to violin C, 512, and to have very

little effect on all tones from that pitch upward. On very low tones the effect of the audience in the room is more pronounced. For example, again take C1 64, the effect of the audience will be to diminish its first overtone about sixty per cent relative to the fundamental and its second overtone over seventy-five per cent.

The effect of the material used in the construction of a room, and the contained furniture, in altering the relative intensities of the fundamental and the overtones, is to improve or injure its quality according to circumstances. It may be, of course, that the tone desired is a very pure one, or it may be that what is wanted is a tone with pronounced upper partials. Take, for example, the "night horn" stop in a pipe organ. This is intended to have a very pure tone. The room in contributing to its purity would improve its quality. On the other hand, the mixture stop in a pipe organ is intended to have very pronounced overtones. In fact to this end not one but several pipes are sounded at once. The effect of the above room to emphasize the fundamental and to wipe out the overtones would be in opposition to the original design of the stop. To determine what balance is desirable must lie of course with the musicians. The only object of the present series of papers is to point out the fundamental facts, and that our conditions may be varied in order to attain any desired end. One great thing needed is that the judgment of the musical authorities should be gathered in an available form; but that is another problem, and the above bare outline is intended only to indicate the importance of extending the work to the whole range of the musical scale, the work undertaken in the present paper.

The method pursued in these experiments is not very unlike that followed in the previous experiments with C, 512. It differs in minor detail, but to explain these details would involve a great deal of repetition which the modifications in the method are not of sufficient importance to justify.

Broadly, the procedure consists first in the determination of the rate of emission of the sound of an organ pipe for each note to be investigated. This consists in determining the durations of audibility after the cessation of two sounds, one having four or more, but a known multiple, times the intensity of the other. From these results it is possible to determine the rate of emission by the pipes, each in terms of the minimum audibility for that particular tone. The apparatus used in this part of the experiment is shown in Figure 1. Four small organs were fixed at a minimum distance of five meters apart. It was necessary to place them at this great distance apart because, as already pointed out, if placed near each other the four sounded to