March 29, 1877] 



NATURE 



477 



forming thirty-five perfect Fifths, which, by the contriv- 

 ance of using the eighth Fifth down as the major Third, 

 into the place of which its finger-key is placed, gives very 

 free play for modulation in all directions with perfect 

 uniformity, although of course slightly imperfect in- 

 tonation.i 



To this system of perfect Fifths and major Thirds 

 identified with eight Fifths down, we must attach all the 

 other contrivances for reducing the number of notes 

 necessary to tertian harmony, without seriously offending 

 the ear. The practicability of arranging any number of 

 dozens of such notes in the Octave, up to at least seven 

 dozen, so that they should be entirely under the command 

 of the performer, be fingered precisely in the same way 

 in all keys, and have a style of fingering which is of about 

 the same difficulty as that for three sharps or three flats 

 on the piano, has been proved to demonstration by the 

 "generalised keyboard" of Mr. Bosanquet, exhibited at 

 the Loan Collection, for his enharmonic harmonium, and, 

 up to four dozen finger keys to the Octave, to the Musical 

 Association upon his enharmonic Organ.2 This key- 

 board is quite a triumph of ingenious construction, 

 founded on rigorously scientific principles, for the prac- 

 tical solution of an apparently insoluble problem. 



The modifications of the perfect Fifth system (to which 

 Mr. Bosanquet seems much inclined, op. cit.^ p. 57) depend 

 on the discovery that fifty-three perfect Fifths exceed 

 thirty-one Octaves by only about jjig^ of an equal semi- 

 tone, or very nearly ^^ of a comma. Helmholtz proposed 

 to reduce every Fifth by ^V of a comma. This would make 

 fifty-three of the flattened Fifths to be about ^^ of a semi- 

 tone less than thirty-one octaves, too large an interval for 

 good ears not to perceive, being nearly half a comma, 

 but then all his Fifths would be audibly perfect, and all 

 his major Thirds absolutely perfect. Mr. Bosanquet 

 endeavoured to tune a stop on his enharmonic organ in 

 that way, but the effect with stopped pipes did not repay 

 the immense trouble of tuning {ibid), which cannot be 

 truly effected without much mechanical assistance, and is 

 therefore generally impracticable. 



The great difficulty of tuning is also an objection which 

 applies to Mr. Bosanquet's own proposal to divide the 

 Octave absolutely into fifty-three parts (see op. cit.,^. 56). 

 This would flatten the Fifth still less, but of course would 

 also make the major Thirds nearly as flat as those in the 

 system of perfect Fifths, from which his differ only by 

 about 4V of a comma. It is not likely that Mr. Bosanquet 

 has been able to tune to such a degree of accuracy. And 

 as the object of the division of fifty-three is only to 

 modulate ad injinitum, such accuracy is needless for 

 general purposes, for which forty-eight perfect Fifths (or, 

 as I believe, six sets of eight perfect Fifths, differing by 

 perfect major Thirds from each other, and hence com- 

 paratively easy to tune by Fifths and check by Thirds), 

 would fully suffice.^ 



' The notes may be considered to be those in Gen. Thompson's second 

 column continued up to Ask. and down to Kf/f/1. (or A quadruple flat), the 

 names being altered to those of the finger-keys corresponding to those on 

 the ordinary piano, so that no more sharps and flats are used than in ordinary 

 notation Unfortunately the bellows and some parts of the mechanism 

 were injured in the carriage, and hence the full effect could not be appre- 

 ciated. There were two extra rows of keys to bring out Herr Appunn's 

 favourite minor Third, i5 : iq, which is slightly closer than that on the 

 piano, and very effective in certain cases, but the fingering for these was 

 new and difficult, and could not be considered practical. 



^ The first, with eighty-four notes to the Octave, is figured in Mr. Bosan- 

 quet's book {fip. cii.y p. 23). where it is fully described, and is al.so explained 

 at length in my Helmholtz, pp. 692-696. In both books the builder's name 

 and address are given, with his prices for compasses of two to seven dozen 

 keys per Octave. Such instruments are indispensable for the scientific culti- 

 vation of music. It is also suited for mean-tone intonation. 



3 See the full explanations in my Helmholtz, pp. 656, 657, 783. Tuning 

 by perfect intervals is the only system practicable without mechanical 

 assistance. But even to tune the thirty-five Fifths of Appuiin is impossible 

 by car alone. I find tuners have a difficulty with only eight notes, forming 

 seven successive Fifths. But when the next eight notes are taken as major 

 Thirds to these, all verihed by forming Fifths with each other and producing 

 correct differential tones with the original set, we may hope for some cor- 

 rectness. The only really satisfactory way of tuning is by calculating the 

 pitch of each note, and taen causing a set of forks, or Appunn reeds, to be 

 constructed, each too flat by four vibrations, which can be done exactly by 



The instruments exhibited in the Loan Exhibition and 

 the others indicated in the preceding lines may, there- 

 fore, be said to have practically solved the difficulty of 

 tertian harmony on instruments with fixed tones, and 

 they have even approached to a solution for septimal 

 harmony (which uses the harmonic Seventh ; see Bosan- 

 quet, op. cit., p. 41). Voices in part music, when unac- 

 companied, must sing in just tertian or even septimal 

 harmony, but when accompanied they will inevitably 

 follow the instrument. Violinists can do what they like, 

 but are too much inclined to Greek intonation, which is 

 all very well by itself, but which the performer should 

 learn to modify by something better than a rule of finger, 

 in double-stopped passages and part music. With the 

 bass the comma stop may be made effective to a great 

 extent, and Dr. Stone is trying what he can do with the 

 oboe and clarinet {pp. cit., p. 35), so that there are some 

 hopes of improving even the orchestra. Enough, at least, 

 has been done on the instruments mentioned and in the 

 practice and system of study of the Tonic Solfaists 

 (Helmholtz, p. 640) to show that it is practically possible 

 greatly to improve musical intonation. 



Alexander J. Ellis 



ON PHOTO.CHEMICAL PROCESSES IN THE 

 RETINA 



T N an article which lately appeared in Nature (vol. 

 ■L XV., p. 308), I gave an account of certain very remark- 

 able discoveries made by Prof. Kiihne, of Heidelberg, 

 which added additional interest to the startling announce- 

 ment contained in a recent communication made by Prof. 

 Boll, of Rome, to the Berlin Academy, to wit, that the 

 external layer of the retina is, during life, of a purple 

 colour, which disappears at death, but which is, during 

 life, continually being bleached by the action of light. 

 In my first communication I stated that the account of 

 Boll's researches which I was able to give, was only 

 quoted at second-hand from Kiihne's paper, as the num- 

 ber of the Proceedings of the Berlin Academy containing 

 Boll's communication^ had not yet reached Manchester. 

 Having now had the opportunity of reading that com- 

 munication, I am able to state that the summary of it 

 contained in my first article was correct in every par- 

 ticular. As the paper is, however, one -of peculiar im- 

 portance I propose, with the concurrence of the Editor 

 of Nature, to insert a verbatim but annotated translation 

 of it in next week's number of Nature. 



It is with great surprise that I have heard that the 

 prominence given to Prof. Kiihne's researches on the 

 " Vision-purple" in my article in Nature has given some 

 pain to Prof. Boll, who probably feels some disappoint- 

 ment in not having been allowed to remain in sole pos- 

 session of the promising field of research upon which he 

 had entered. It is with still greater surprise, however, that 

 I have read the remarks which D . Warlomont, editor of 

 the Annales d'Oculistigue, has added to the literal trans- 

 lation of my article which he has published in that jour- 

 nal,-' and which follows a brief abstract>f Boll's paper. 



" Nous appelons toutc I'attention de nos lecteurs sur 

 les deux articles qu'ils viennent de lire, et qui signalent 

 une ddcouverte propre a rdvolutionner la physiologie de 

 la recine, a renverser quelques unes des idces revues, h. en 

 affirmer beaucoup d'autres. Toict le nicrite de la decou- 

 verte de la coloration propre de la retine appartient d, M. le 

 prqfesseur Boll, avec toiitcs ses consequences, dont M. 

 Kiihne nous parait s'etre prcmaturdment empard. M. 



Appunn's tonometer. After tuning a note roughly to one of these, sharpen 

 it till it beats four times in a second with the standard. Any temp-rament, 

 even Helmholtz's, the best in existence, can thus be easily and perfectly 

 realised note by note. 



' jVIonatsbericht der kOniglichen preussischen Akademie der Wissenschaften 

 zu Berlin, November, 1S76. Gesammtsitzung vom 23 November, 1876, 

 S. 783-787- . , . 



2 Annales a'Oculistique, tome Ixxvu., Jaiivier-Fevner 1877, pp. 78-81* 



