April 1, 1875] 



NA TURE 



425 



Hence ( 



■ W a 



1/_"1_" in radians per second. 



Hence number of revolutions per second = -^tvtts- 



ir W k- 



Substiluting tlie numbers given in the question, we Lave for 

 the ansvfer — 



2 X 981 '4 X 2250 X 6 



University, Glasgow 



3-1416 X iSoo X 16 

 293 revolutions per second. 



D. M'Farlane 



The Sounds of the String Organ 



Mk. Baillie Hamilton's invention of a conjoined string 

 and reed which is now being carried out in a musical instrument 

 to be called the string organ, has caused a marked interest both 

 in its musical and in its scientific aspects. My attention was at- 

 tracted to it strongly, for one reason, that it promised to add a new 

 member to the family cf keyboard instruments, and for another 

 reason, that the study of its possibilities and practical working 

 showed conditions so close in analogy to those of the organ- 

 pipe as viewed under the theory advanced by me in Nature, 

 that the corroborative evidence thus furnished might with truth 

 be called palpable. By the last word I refer to the visible dis- 

 placement and travelling of the node, which can be affected at 

 will in obedience to changes in the relative conditions of reed 

 and string. I find that "tension " on the string is equivalent to 

 " scale " m organ-pipes. To give high tension to a string is in 

 effect the same as to use a narrow scale of pipe ; thus, keeping 

 the reed-force constant, we may respectively, by giving higher 

 tension to the string, or by using a narrower pipe, drive the 

 node higher, and conversely, slackening tension or using a wider 

 scale of pipe, we may displace the node to a lower position. In 

 the conjoined reed and string we can see this change taking 

 place, order how it shall take place, and may clip the nodal 

 point with our fingers without disturbance of the continuity of 

 vibrations. The process is visible, the result tangible. 



The estimate Lord Rayleigh * has given of the instrument as 

 "modified reed" is undoubtedly right, yet it can scarcely be 

 said that the opposition estimate is undoubtedly wrong. An 

 orthodox organ is a pipe-instrument, and also is a wind-instru- 

 ment, yet in acoustical relations the pipe is out of theoretical 

 conformity, is a modified pipe ; the air- reed likewise, according 

 to the kind of pipe it is allied with, is a modified reed, and simi- 

 larly in this novel organ the string and reed modify each other ; 

 sever the union, and the manifestations of the two independent 

 forces will be wholly different. Specifically it is a wind-instru- 

 ment, and I cannot but think we should admit it to be both 

 " modified reed " and "modified string;" they work together 

 as a system, each contributing its own character, and each in 

 degree determining, through compromise and affinity, the issue 

 of the union. Strongly impressed with this behef, my explana- 

 tions will consequently differ from those generally current con- 

 cerning this ingenious combination. 



Lord Rayleigh, in explanation of his estimate, says, "the 

 intermittent stream of air, which does not take its motion from 

 the reed, gives rise to a highly compound musical note." Either 

 I do not understand this affirmation, or I misunderstand it ; I 

 have always considered the intermittence of the stream to be the 

 result of the reed's motion. And further on, another sentence to 

 strengthen his distinction: "The fact that the pilch of the 

 system is mainly dependent upon the string seems to have dis- 

 tracted attention from the important part played by the stream 

 of air, and yet it is obvious that wind cannot be forced through 

 such a passage as the reed affords without the production of 

 sound." Speaking, not without experience in varieties of free 

 leeds, I cannot recall a single instance of the wind forced through 

 the passage afforded by the reed producing anything like a 

 musical sound. Our views probably differ in expression and in 

 interpretation more than in perception. 



With some temerity I think 1 may say that the working of the 

 free reed is not fairly estimated by scientific observers. It is 

 generally supposed that the pressure of the wind originates the 

 vibration of the reed in instruments, whereas the fact is that 

 the free reed may be so set that although perfectly free to pass, as 

 may be seen on holding it up to the light, perfectly free to 

 sound, as may be proved by percussion, yet, placed within the 

 instrument, it w^iU be dumb to all pressure of the wind. The 

 essential condition for speech is for the reed to be so set that a 

 * See Nature, vol xi. p. 308. 



sufficient amount of air shall with velocity pass the sides and 

 through the mortice of the reed equal to causing a suction on the 

 under side of the reed ; then only will the reed proceed on its 

 course, and the check given to the stream when the reed reaches 

 the level of the block intensifies the suction, the development 

 whereof progresses until the back-lash or return of the reed creates 

 a stronger partial vacuum with a promptness of power effectual 

 for establishing the condition of vibration. There are pecu- 

 liarities, too, in the process of the suction, not lightly to be 

 passed over by the scientific observer. The true test of action is 

 the degree of quickness in speech. The mrst prompt articulation 

 is that in which the process of suction is most gradual ; this is 

 not paradoxical, though it may seem so. If a large amount of 

 nnnd is allowed to pass, the action will be sudden, yet, notwith- 

 standing, the speech, comparatively estimated, will be slow. The 

 suction should first attack the tip of the reed and gradually draw 

 upon the stem. If you allow passage to the wind near the root 

 of the reed, or if you hollow or arch the stem, permitting wind 

 more freely to pass the middle of the reed, it is inevi'-ably at the 

 sacrifice of quickness of speech, and nothing is more fatal than 

 allowing extra opening for a rush of air between the tip of the 

 reed and the frame, for you thereby impair the perfectness of the 

 suction at its most vital point. 



In the case of a reed and string conjoined, the string is a 

 weight to be moved ; the force of wind will effect the displace- 

 ment if the string has held the reed in position to allow passage 

 of wind; and when the equilibrium of the string has been in the 

 least degree distuibed, the return motion becomes a source of 

 additional impetus, inducing the reed to follow by recriprocation ; 

 yet even here we do not escape the demand for suction ; the 

 value for this purpose of a tube or a channel beyond the reed is 

 as evident as in the harmonium. The difference between the 

 modem harmonium and the old seraphine is, that the former has 

 pipes or channels to every reed, the latter had its reeds placed 

 over apertures in plain boards ; the reed conjoined to a string 

 when so placed over a simple aperture will sound as would the 

 reed in the old seraphine, but generally with the exhibition of 

 the same defect, slowness of speech. Select an instance of such 

 a string and reed so sluggish that the attainment of speech to the 

 semblance of a musical note is a trial of patience ; then add a 

 tube of suitable character, and, in comparison of condition, the 

 promptitude of response and power of tone will give certain 

 evidence of its value, for here, as in all musical instruments, the 

 function of the tube is to aid and to develop more strongly the 

 force of suction. The suction I mean is that which is caused by 

 the issue of a current of compressed or condensed air into the 

 atmosphere. 



A very curious problem is afforded in the peculiar quality of 

 tone given by the new mechanical action of " reed-and- string" 

 working linked together, and I have not heard, from any of the 

 numerous thinkers and ob3er\'ers who have commented upon it, 

 a satisfactory solution. Lord Rayleigh truly states, " it is cer- 

 tain that the note actually heard is compound," and also that 

 " the peculiar character of the string, that its notes form a har- 

 monic scale, does not come into play." 



What is it, then, that we hear, and how comes this highly 

 compound musical note into being ? Let me > ffer this solution, 

 if only as a suggestion. It is generally agreed that " there is a 

 great deal of octave in the tone," sometimes the fifth, and fre- 

 quently and most strikingly a beautiful major tenth, so clear that 

 it seems to sing away by itself as if in independent existence ; this, 

 whilst it is certain that the string is not vibrating in forms either 

 of the octave, fifth, or tenth or of any other of the accessory tones 

 so often present to the ear. Rightly to apprehend the action of 

 strings in musical instruments, it is, I think, desirable to regard 

 every string as a tuning-fork acting upon the soimd-board through 

 the bridge, which, thus considered, is its stem for the communi- 

 cation ol its vibrations. The intensity of sound from a tuning- 

 fork or from a string depends not alone on amplitude of move- 

 ment, but on pressure, the amount of such pressure being mainly 

 determined in the case of the string by the angle the string 

 makes in its strain upon the bridge under the particular tension 

 to which it is subjected. A tuning-fork sounds loudly or softly, 

 according as its stem is pressed strongly or lightly by the hand 

 upon the soimd-board. A string deflected right and left delivers 

 each way its pulse through the bridge to the sound-board ; a free 

 reed, moving forward and backward, gives an effective impulse 

 as musical vibration one way only — in the back-lash, or return ; 

 consequently, in this matter of conjoined reed and string, it 

 appears to me we have always hvo fundamentals — two tones 



