NATURE 
[ Feb. 24, 1870 
LETTERS TO THE EDITOR 
[Zhe Editor does not hold himself responsible for opinions expressed 
by his Correspondents. No notice is taken of anonymous 
communications. | 
Red-Necked Grebe 
A FINE specimen of the Red-necked Grebe, picked up alive, 
but wounded, near Bedford, on the 11th of February, has been 
sent to me clad, and is being stuffed. It is a female, in winter 
plumage. 
Taunton, Feb. 16 W. TuCKWELL 
Professor Listing’s Amplifier 
In reference to your report of the Boston Natural History 
Society in NATURE of 27th January, nothing more is requisite 
to amplify the power of a microscope than to cut off the rims of 
two or three eye-pieces and insert them in pairs into the ends of 
a draw tube. Any degree of amplification can be obtained 
whilst the achromatism is preserved. The Huyghenian eye-piece 
has generally been preferred because the dust accumulating on the 
inverted eye lens of a positive eye-piece is inconyeniently magni- 
fied, and obscures the field of view. To those who are desirous 
of trying Professor Listing’s plan, described in your last number, 
this simple method of mounting may be acceptable. 
Lansdowne Crescent, W. Royston Picorr 
Analogy of Colour and Music 
It appears to me that in the discussion raised by Mr. Barrett’s 
letter in your columns, too little attention has been paid to diffe- 
rences between harmony in music and harmony in colour, which 
are sufficiently great to show that the coincidences pointed out 
cannot be regarded as more than xzmerical. Your correspon- 
dents have hitherto regarded the subject rather from an optical 
than a musical point of view. I propose, with your permission, 
to make a few remarks from the latter stand-point. It is well 
known that to get a good concord, exact tuning is requisite— 
z.e., that a slight deviation from the right pitch is sufficient to 
make a concord into a discord. Moreover, the better the con- 
cord, the more intolerable is any appreciable variation of its 
pitch. Thus unisons, fifths, and octaves are the most sensitive 
to defective tuning, while the intervals adjacent to them, such as 
minor seconds, sharp fourths, and sevenths are the harshest 
discords in the scale. The degree to which this holds will be 
seen at once by the following diz roughly copied from 
Helmholtz’s ‘‘ Ton-empfindungen.”’ ‘The ordinates of the curve 
represent the amount of ‘‘roughness”—7.e., discordancy cor- 
responding to the intervals marked on the line of abscissze. 
The guality of tone selected is that of the violin. 
A glance at the figure will show that the sounds which pro- 
duce the most discordant effects with the key-note lie in the 
immediate neighbourhood of the unison, the octave and the 
fifth ; and further, that a very slight departure from accurate 
pitch in any concord will provoke a harsh dissonance. 
If we now turn to the spectrum, the state of things is widely 
different. The various colours shade off insensibly one into the 
other, and in any one colour there is very little, if any, change of 
tint, except close to its extremities. Thus, then, as far as mere 
colour goes, any part of any one colour-division produces an 
equally harmonious effect on the eye, and has an equal claim to 
be compared to a concord of the gamut. 
Mr. Barrett, by taking the central point of each band of the 
spectrum as the basis of his comparison, has left this important 
circumstance out of sight. If we take it into consideration, the 
result will, I think, be to deprive Mr. Barrett’s comparison of 
any serious importance. 
In order to fix our ideas, let’us assume that the mean red of 
the spectrum corresponds to middle C of the pianoforte with 
264 vibrations per second. Taking the limiting and mean 
wave-lengths as quoted from Prof. Listing by Mr. Barrett, and 
calculating the number of corresponding sound-yibrations per 
second, we get the following table :— 
Corresponding 
positions on gamut, 
with number of 
vibrations. 
247°5 B 
Number of 
sound vibrations 
‘per second. 
250 
Wave-lengths 
in 10 millionths 
of a millimetre. 
( 7234 6 50) eae 
Red . GEISY 9 0 oO 5 } 204 . . « 264. (ee 
(UP 6 Ono 280-. 282 —- Ch 
Orange 4 6164 4 293°5. 
5856 (aaa 5 297 om 
Yellow 456015. . . . |53-. 3175, OF 
5347 | 338+. . 330° ME 
Green pee pees 352 F 
4919 368 — 376 FR 
Blue / 473 382 - c 
( 4555 (3974 39 A 
Indigo 1 4398 Re j 
4241 0 0 6 427i ie - 422 GZ 
Violet {4104 ' 4 441 - 
3967 456+ se 
2) ; ; 469 + Ag 
(+ or — means that the number of vibrations given is a fraction 
less than 4 above or below the actual amount. In the last 
column are given the vibration-numbers of the sounds of the 
chromatic scale. ) 
3y comparing the last two columns it will be seen that Red 
covers very nearly the portion of the scale between B natural 
and C sharp: Orange that from CE to half-way between D and 
Dg, and soon. ‘The whole relation is exhibited in the follow- 
ing figure :— 
ae 
eRe a rt =e 
=a: 
Blue Indigo Violet 
a to 
Red Orange Yellow Green 
It will be seen that each colour, on the whole, corresponds to 
very discordant intervals in the scale of pitch, and that only at 
one point in each (and that by no means always the middle 
point of each band) can it answer to a concord. 
What has been said is probably enough to show how little real 
‘*correlation” Mr. Barrett’s letter has succeeded in establishing. 
I will now notice the observations on Newton’s rings contained 
in that signed “ W. S.Okely.” The diameters of these rings vary 
in lights of different refrangibility, as the sguware root of the wave- 
lengths, * and therefore they give a spectrum unfit for the purpose 
to which Mr. Okely applies them. Indeed this is otherwise 
obvious from the lengths of these diameters given in his letter 
from a work by Prof. Zannotti. They are as 1, 24/3, 94/2, 34/4, 
34/2, 3a/8 3%, °s/4, and therefore, of course, the intervals 
) BA/y o 
between them are not as Mr. Okely makes them, $2, +4, 4, 3, 
19,46, 2, but the cude roots of these fractions. The interval 
from red to red *4/4, comes out rather less than 1°26, which lies 
between a major third anda fourth. Mr. Okely’s view, which 
requires the interval from red to red to correspond to an octave, 
must therefore fall to the ground at once. 
Mr. Deas’ conception of ‘‘ millions” of violinists performing 
“every conceivable sound within” the octave, with a view to 
the production of the ‘‘ purest and most ethereal of sounds,” 
seems to me the wildest delusion. Let us suppose the compara- 
tively modest number of thirty-three at work on the interval from 
middle C to D, so that the first produces 264 vibrations per 
second, the second 265, the third 266, and so on up to the last, 
with 297 vibrations. We should obtain a charming variety of 
beats, one a second, two a second, three a second, &c., up to 
thirty-three a second, those near the higher limit adapted to pro- 
duce the very worst barking dissonance attainable. Mr. Deas’ 
million-fiddler-power sound, so far from being ‘‘ pure” or 
** ethereal,” would not be a musical sound at all, but a mere 
bewildering chaos of noises, likely to drive the inventor himself, 
* See Airy's Tracts or Lloyd’s Wave Theory of Light. 
