292 



NATURE 



[Fed. I, 1877 



"ratio can exist only between quantities of the same kind." 

 When mathematicians employ the figures of 4 to 3 in the scale 

 of C, the interval they really obtain is from C down to G (not 

 from F down to C, as they have supposed), and when 5 to 3, 

 they have the major Sixth from E down to G, and not the one 

 from A down to C. 



Music is a much more simple science than most men suppose. 

 All that a mathematician requires is a set of harmonic scales* 

 with powers of 2 and 3, before him. The scales include all 

 ratios, and all consonances with their proportions of accompany- 

 ing dissonances. They are scales of aliquot parts, and those 

 aliquot parts are the corresponding multiples of vibrations. 

 Time spent upon calculating temperament is but thrown away, 

 because no mathematician's figures will be adopted in practice. 

 Practical musicians will continue to tune by listening to the 

 beats, as they have ever done, and perhaps all other musicians 

 before them. The recommendation to eschew temperament 

 may be even worthy of consideration in another point of view. 

 Mathematicians have not given sufficient attention to the 

 musical side of the question. Have we not, of late years, 

 heard much of proposals to divide the octave into ' ' twelve 

 equal semitones"? Are we to imagine that this is a mathe- 

 matician's idea of '^ equal temperament"? If music were 

 but geometry, it would be an admirable arrangement : twelve 

 equal semitones, like twelve equal inches in a foot. But, un- 

 fortunately, a musical scale is the very reverse of a geometrical 

 one, and there are no two intervals alike in it. As it rises, the 

 dimensions become less at every step, in ratio and in length. 

 For instance, the ratio of C to C sharp is 16 to 17, that of G to 

 G sharp (G being the half-way in point of vibrations) is 24 to 25, 

 and from B to octave C is 30 to 32, but only because we omit 

 B sharp, otherwise it would be 31 to 32. Fancy two such ex- 

 tremes ' ' tempered " to the middle note ! Only one of the 

 twelve would fit into a musical scale, and there would be eleven 

 discordant semitones out of the twelve. The discord would not 

 be confined to one key only, but would be the same in every key. 

 The so-called " diatonic semitones " are really tones. E is the 

 seventh to F, which requires F as a bass, and B is the seventh 

 to C in the scale of C. Are these to be changed into chromatic 

 semitones ? 



The diminished attraction of music, some persons even dis- 

 liking it, is mainly, if not wholly due to tempered tones. The 

 first point to be considered by mathematicians who temper scales 

 is the meaning of the two words, "consonance" and "dis- 

 sonance." The charm of music depends upon "coincident," 

 and " non-coincident " vibration. 



In justice to Col. A. R. Clarke, let me add that I find only 

 the first error to be his own, and am still disposed to attribute it 

 to oversight in referring to a wrong scale. All the others are after 

 precedent, and every source might be pointed out, although he 

 is disposed chivalrously enough to defend those upon whom he 

 relied. My excuse for writing at all is that Nature is a purely 

 scientific journal, and that I share with others an earnest wish to 

 uphold it as a fair representative of English thought. Articles 

 such as those of Col. Clarke and my own would be distasteful to 

 any but scientific readers. As to the "comma of Pythagoras," 

 it is not worth discussing. In spite of his chivalry. Col. Clarke 

 knows as well as I do, that such an array of figures, represent- 

 ing vibrations, as 524, 288, cannot arise in less than nineteen 

 octaves. Wm. Chappell 



Strafford Lodge, Oatlands Park, Surrey 



The Nebula of Orion 



In Nature, vol. xv. p. 201, in an account of the American 

 Cambridge Observatory, it is stated that the nebula of Orion had 

 not shown the slightest trace of resolvability under Lord Rosse's 

 3-feet reflector. 



The authority for this statement is, I suppose, Nichol's 

 " Thoughts on the System of the World," where, p. 52, it is 

 said that in 1844-5, the 3-feet did not contain the vestige of a 

 star in the nebula. 



On the occasion there referred to the speculum must have been 

 in bad order, for the resolution of parts of the nebula is quite 

 within the reach of the instrument in its normal condition. In 

 proof of this I may refer to Lord Oxmantown's paper on the 

 Nebula of Orion, Phil. Trans., 1861, and to an extract from my 

 own note-books of an earlier date, February, 1848 : — " With the 

 3-feet saw the nebula of Orion resolved as far up as the little bay 

 and C I Orionis— powers 351 and 320 — best with the latter 

 which is a single lens." 



I may add that Nichol also states, p. 55, that he had received 

 from Lord Rosse, March 19, 1846 intelligence "that all 

 about the trapezium is a mass- of stars (in the six feet) ; the rest 

 of the nebula also abounding with stars, and exhibiting the 

 characteristics of resolvability strongly marked." 



Observatory, Armagh, January 19 T. R. RoBlNSON 



Basking Shark 



My notice of Prof. Steenstrup's paper was written in the 

 autumn of 1875, to accompany an electrotype of the woodcut in 

 that paper of the baleen-like fringes of the basking shark, sent 

 to me for Nature from Copenhagen. 



At the time I was quite ignorant that my friend and former 

 master, Dr. Allman, had written on the subject, nor could the 

 keenest bibliographer have known much of the contents of his 

 memoir, as the only reference to it in the Fourth Annual Report 

 of the Dublin Natural History Society for 1841-42, is "Two 

 [papers] have been read on Icthyology ; that on the basking 

 shark {Selachus maximus) by Mr. Allman, caused him to notice 

 the value of the fisheries of our southern coasts, abounding in 

 large fishes and cetacea, whose capture would prove highly pro- 

 fitable to our fishermen from the quantity of oil they would 

 yield." In June, 1876, on the arrival of the specimen in Dublin 

 from Bofin, I had a woodcut made of a branchial arch with the 

 fringe attached, and added a brief account of the specimen now 

 in the Dublin Museum. About that time Dr. Allman told me 

 that notes of his paper had been published in the Saunders's 

 News Letter, but that he had forgotten the date. Guided by the 

 notice in the Dublin Natural History Society's Report, I 

 searched the files of that paper for the years 1841 and 1842 with- 

 out success, but I fully purposed to mention what Dr. Allman 

 had told me, ffom memory, of his researches, when I should get 

 a proof of my manuscript. Unfortunately, from press of matter, my 

 notes were not published until many weeks after they were sent, 

 and the proof reached me during long vacation, when I com- 

 pletely forgot to do as I had intended. I regret this exceedingly, 

 and hope Dr. Allman will accept my apology. I cannot, how- 

 ever regret, that it has induced Dr. Allman to publish an abstract 

 of his paper (Nature, vol. xiv. p. 368), and perhaps he may 

 still further furnish us with the date of its original publication. 



In answer to the note of Prof. Enrico Giglioli, which has 

 called my attention again to this subject, I have simply to state 

 that finding no notice in the Zoological Records for 1873 or for 

 1874 (this latter published May, 1876) of any papers on Selache, 

 I concluded, as it now appears wrongly, that nothing had been 

 written during these years on the subject. This was my misfortune, 

 perhaps my fault ; but regarding Italy as the mother country of all 

 the sciences, being well aware of the advances she has made in 

 biological researches during the last twenty years, and having gone 

 each year, while one of the zoological recorders, to Florence to 

 work out the Italian literature of the preceding year, I cannot 

 accuse myself of any intentional neglect of the labours of Italian 

 biologists. It is to be hoped that Prof. Giglioli will favour us 

 with an abstract of Prof. Pavesi's memoir, especially of the 

 reasons that induce Prof. Pavesi to assert that our Bofin shark 

 is S. rosirata and not S. maxima, for to me it appears that our 

 seas may possess both these species. 



It may also be mentioned that no reference to Prof. Pavesi's 

 memoir will be found in the account of the Pelerin appended 

 to Prof. Liitken's "Fishes of Greenland," prepared for the use 

 of the British North Polar Expedition, 1875. 



E. Percival Wright 



Sense of Hearing in Insects and Birds. "Towering" of 

 Birds 



I AM glad to learn from Mr. M'Lachlan that stridulation is 

 known to occur in several species of Lepidoptera ; for this shows 

 that the sense of hearing in these insects is probably of general 

 occurrence. With regard to the sense of hearing in birds, I did 

 not say in my previous letter that thrushes, &c., were guided to 

 their food exclusively by this sense ; indeed it would be a very 

 anomalous thing if animals which possess so keen a sense of 

 sight are not in the habit of using it, as Mr. McLachlan sug- 

 gests, in any profitable way they can. But that thrushes trust 

 very largely to their sense of hearing in their search for food— 

 especially in certain conditions of the ground — no one, I think, 

 who has observed the process can doubt. The bird runs rapidly 

 some twelve to twenty feet in a straight line; it then stops 



