456 



NATURE 



[August 8, 191 8 



Dr. Laurent, of Marseilles, contributes descriptions 

 of a few Angiosperms from Neocomian rocks. The 

 account of the Jurassic f^ora of Waikawa, Southland, 

 includes an interesting description of a remarkable 

 petrified forest composed chiefly of trees of an Arau- 

 carian type associated with petrified Osmundaceous 

 stems. Forty-eight species are figured ; of these at 

 least fourteen are regarded as new, the remainder 

 being widely distributed Mesozoic tjpes. The admir- 

 able drawings and photographs are well reproduced, 

 and there is an excellent bibliography. 



This latest contribution by a paleeobotanist . whose 

 untimely death is a serious loss to science is of great 

 value from the point of view of phytogeographical 

 problems ; the author has cleared up several difficulties 

 and corrected erroneous statements frequently quoted 

 from the meagre literature on New Zealand plants. 

 It is to be hoped that this thorough piece of work 

 will stimulate New Zealand students to do their best 

 to obtain additional material from the various locali- 

 ties in the islands, and thus provide data for the con- 

 tinuation of Dr. Arber's memorable work. 



A. C. S. 



VIBRATIONS: MECHANICAL, MUSICAL, 



AND ELECTRICAL.^ 



V. — Brass Instruments and the Low " F." 



LEAVING the pendulums which have only two vibra- 

 tions at a time, the case of brass instruments with 

 a number of simultaneous vibrations was next con- 

 sidered. It is well known that the vibrations from 

 most musical instruments are what is called compound. 

 They consist of a series of tones of commensurate 

 frequencies sounded together. Thus if the pitch of 

 the note is said to be loo per second, there is not only 

 a prime tone of this frequency, but also a second tone 

 of 200 per second, a third of 300 per second, and so 

 forth. This law applies to strings, to open parallel 

 pipes, and to a complete cone with its base open. It 

 also applies as a close approximation to the brass 

 instruments in general use. This approximation is 

 traceable to the departure from the strictly conical 

 forms as regards the mouthpiece, the bell, and the 

 special shape of the intermediate portion. 



In these brass instruments the possibility of this 

 compound tone, or multiple resonance, is utilised for 

 the production of distinct notes. Thus out of the 

 tones possible to the instrument the player may elicit 

 the set 200, 400, 600, 800, etc. ; or the set 300, 600, 

 900, 1200, etc. These would be said to have the 

 pitches of their primes or lowest components, 200 or 

 300 respectively. Or, to put it musically, they would 

 be the octave or the twelfth of the fundamental (or 

 pedal) possible on the instrument. The pedal of the 

 instrument is not usually employed for musical pur- 

 poses, but can be sounded if specially wished. Now 

 there is a tradition among players of brass instru- 

 ments that a note called by them a low "F" can be 

 sometimes obtained This note would have on the 

 foregoing scheme the frequency 1333. At first the 

 possibility of this " F " seems scarcely credible to the 

 theoretician. But after hearing and producing the 

 note the necessity of accounting for its possibility was 

 forced home. 



Really the explanation proves very simple. It 

 usually depends upon two points : — (a) The spread or 

 diffused resonance of the pedal, and (b) its intentional 

 mistiming with respect to the other notes of the instru- 

 ment. These are taken in order. 



(a) For theory shows that, other things being equal, 



1 Abstract of a discourse delivered at the Royal Institution on Friday, 

 March 8, by Prof. Edwin H. Barton, F.R.S. Continued from p. 439. 



the lower the note of such an instrument, the easier 

 it is to force its vibrations out of tune, sharper or 

 flatter. Thus with the pedal the range of resonance 

 is such that the note may be sounded at any pitch 

 whatever over a range of five or six semitones. 



(b) Since the law of frequencies loo, 200, 300, 400, 

 etc., is only approximately true for these instruments, 

 in order to secure good relative tuning of the higher 

 notes which are in constant use the pedal (which is 

 not used musically) is purposely mistyned. On some 

 instruments it may be, say, D or Ep instead of C. 



Hence, if the central pitch of the pedal is sharpened 

 two or three semitones — and it is possible to force 

 this note both up and down two or three semitones — 

 it becomes possible to sound the pedal of true pitch 

 C, to sound the low " F," and to sound notes of every 

 pitch between. (This was demonstrated by Mr. White 

 on a euphonium, kindly lent by Messrs. Boosey arid 

 Co.) The low "F" is also possible on the bombardon. 

 Both these instruments are characterised by large 

 conical tubing, and the low "F" is obtained by the 

 spread resonance of the sharpened pedal. 



In the case of the trumpet, cornet, and French horn 

 with much narrow tubing the pedals are flattened, so 

 that a pedal of true pitch can be obtained only by. the 

 spread resonance, and the " F " is impossible. On 

 the trombone, which has much small parallel tubing, 

 the low " F " may be obtained occasionally by the 

 downward-spread resonance of the second partial (or 

 note number two), which is an octave abot'e the 

 pedal. (Demonstration.) The pitches of the notes 

 which have been obtained on six types of instruments 

 by four experimenters are shown in Table II. 



VI. — Monochord Vibrations. 



Consideration was next given to the vibrations of 

 stringed instruments, beginning with the monochord 

 because of its striking simplicity 



From the work of mathematicians (with a- little help 

 ft-om experimen:) the various possible vibrations of 

 strings, whether plucked, struck, or bowed, have long 

 been well known. But a little reflection will show 

 that many other problems are still left confronting the 

 physicist. For identical strings, excited in the same 

 way, but mounted on different instruments, will pro- 

 duce very different effects on the ear. In other words, 

 the worth of a violin does not lie in its strings, but 

 in its sound-box. 



This leads to the inquiry as to what happens to 

 modify the vibrations as, passing from the strings, 

 they reach in turn the bridge, the belly (or sound- 

 board), and the adjacent air. 



It is easy to see that this problem is somewhat com- 

 plicated, since it presents so large a number of vari- 

 ables. Thus there lie at the experimenter's disposal 

 the pitch of the string, its material and dimensions, 

 the place and manner of excitation, the material and 

 disposition of the associated parts of the instrument, 

 the place of observing the belly, the portion of the 

 bridge observed and the directions of its motions, and, 

 lastly, the spot at which the motion of the air is 

 observed. In this way a scheme for more than a 

 thousand observations could be sketched, even for an 

 instrument with but one string. 



Hence, no exhaustive treatment of the problem can 

 be quickly obtained. But a beginning has been made, 

 and by very simple means. 



In a series of experiments simultaneous records 

 have been photographically obtained of the vibrations 

 of the string and of some other part of the instru- 

 ment. The monochord was placed on a table and 

 light from a vertical slit was focussed upon the string 

 near its centre. The real image of this slit, crossed 

 bv the shadow of the string, was then focussed by a 



NO. 2545, VOL.- lOl] 



