286 
NAAT AE 
[ Fan. 13, 1870 
1867, is in a great measure due to the disturbing action of 
Venus. ; a 
6. Wolf’s 56-year cycle is determined by the joint 
action of Mercury and the Earth. And, 
Finally, the hypothesis proposed accounts, as we have 
seen, for all the well-defined cycles of spot-vartations. 
NOTE ON THE CORRELATION OF COLOUR 
AND MUSIC 
\ Wye engaged in the preparation of an article on 
‘VY the Analogy of Light and Sound for the current 
number of the Quarterly Fournal of Science, 1 was led 
to examine the grounds of the frequently-assumed rela- 
tionship between the colours of the solar spectrum and 
the notes of the musical scale. It is well known that 
Newton found a connection between the relative spaces 
occupied by each colour and the relative vibrations of the 
notes of the scale. But this, I presume, cannot be more 
than an accidental coincidence. The common basis of 
comparison is obviously the ratio of the wave-lengths in 
the two cases. Although according to the tables given in 
text-books no satisfactory connection can be found, yet 
many considerations appear to justify a stricter comparison 
of these natural scales of colour and sound. 
The ratio of wave-lengths of the two extremes of 
the spectrum is usually taken as 1 : 0.57, or corresponding 
to the interval of a seventh in music. 
But this statement is only true when a glass prism is 
employed; the ultra-violet rays are then suppressed. 
Substituting quartz for glass, light of higher refrangibility 
is seen; the limits of the spectrum can thus be extended 
from the solar line A to the solar line L.* Now, the wave- 
oO 
length of A (according to Angstr6m) is 760 millionths of a 
millimetre, and the wave-length of L (according to Mas- 
cart) is 381 millionths of a millimetre, or as the ratio of 
I : 0’50, exactly corresponding to the interval of an octave 
in music, 
The ratios of the extreme colours of the spectrum and 
the extreme notes of an octave are coincident. 
The next object is to compare the ratio of wave- 
lengths giving rise to the intermediate colours of the 
spectrum with the ratio of wave-lengths giving rise to the 
intermediate notes of the scale. 
The most careful localisation of the colours of the 
spectrum with which I am acquainted is that by Prof. 
Listing.t In his recent memoir on the wave-lengths of 
the spectra of the metals, M. Thalén gives Prof. Listing’s 
estimation of the extreme limits of each colour as follows :+ 
Taste I. Limiting 
Name. Wave lengths in ten-millionths 
of a millimetre. 
il 4 4 5 of ob 6 o f Oo om DRY ey (orp 
Oy 66 4 o o oD -a 4 6472 to 5856 
Wellow. = = : 5856 to 5347 
Green 2 5347 to 4919 
IRE Gp ¢@ So Go ¢ 6 0 2OLO 1OAGR5 
Ibebige? GG 6 o 0 bo Go oc CRG, io Ziaa 
Wile 4 6 6 os zee) | 42d Te toNso07, 
Taking the mean of the two limits to represent the 
average wave-length of each colour, we have the follow- 
ing series :— 
Taste II. 
Name. Mean wave-lengths in ten- Ratio. 
millionths of a millimeter. 
IRS 5 9 6 oo oF ERY so og oo eo 6 Hee 
Orem 5 of a oo COU Bb a oe 6 a hs) 
NOUR G oo 655 o eet 5 55 oa ooo 
(as Bl on og bl Oo IRR Oa o oo O° FB 
WIG 6 poo 6 tye Oo uo o oom a GB) 
luni GS 6 6 o YEE 5 6 o a 6 0) 6A 
Waele 5 Ag MY 5 5 5 5 6 a Oe) 
* Mr. Crookes informs me that on favourable occasions he has even seen 
beyond L. 
+ Poggendorff’s ‘“‘Annalen,” 1868, vol. 131, p. 564. 
t Trans. Roy. Soc. Upsal, third series, vol. vi.: also Annales de Chimie 
et de Physique, October 1869, and Naturr, No. 2, 
Calling the wave-length of the mean red 100, the num- 
bers in the third column express the corresponding ratios 
of the mean wave-lengths of the other colours. 
In the next table is given the similar data as regards 
sound. The frst column contains the names of the 
musical notes ; the secovd their actual wave-lengths start- 
ing from the middle C; the ¢/zvd column gives the rela- 
tive wave-lengths in fractions of C ; and the fourth, the 
ratio without fraction, C being taken as 100, 
Tase III. 
Wave-length 
Name. amanehes Ratio of wave-lengths. 
: peers SUEY 
Cay. 52 og Loe OTe TOO 
Dison 464 3 89 
1B) ¢ 2a - ¢ Bue 110) 
126 39 t 75 
Gi c 35 ay 67 
Ale 5 31 + : 60 
13} 27% 1 53 
(C4 a 26 $ 50 
Placing together the ratio given in the last columns of 
Tables I]. and III., the following remarkable correspon- 
dence comes out :— 
TaBLe IV. 
Colour. Ratio. Notes Ratio. 
Red . SON > a 5 ‘Cae 100 
Orange 89 . 6 1D 9 89 
Yellow 81 ae . 80 
Greenyemroee- canes: er o 75 
Taig a mean, 67 (Crs 67 
Wioletic: + sini G-)Oo)he- eee eer eee Ce reg (9) 
[Ultra-Violet . S3lict ees ie eR eee 
[Obscure . SO] ce rotten s Coupee O. 
Assuming the colour 7e@d to correspond to the note 
C, then we find orange exactly corresponds to D ; yellow 
is almost exactly the same as E; and if we take the wave 
length of E from observation and not from theory, we 
have 52 :42=100:80'8, a still closer approximation to 
yellow. The ratio of green is identical with that of F. 
Blue, however, does not correspond to G, nor /zdigo to 
A; but blue and indigo are practically one colour in the 
spectrum,—the line of demarcation, difficult to fix between 
any other colours, is impossible to be established here. 
I think, therefore, I am justified in putting them together, 
and if we do so we find their mean ratio exactly corre- 
sponds to G. Violet now exactly corresponds to the ratio 
given by A. Here all distinct colour ends. But bevond 
this region Sir John Herschel detected a lavender colour, 
which finally shades away into a dusky grey. The wave- 
length of this ultra-violet region is not given by Prof. 
Listing ; hence the ideal position is calculated and inserted 
in the table within brackets. As the lower C is placed at 
the mean red, the upper C would then correspond to a 
region in the spectrum altogether obscure: viz., at the 
solar line O. But as already stated above, if we place the 
lower C at the extreme red, then its higher octave would 
fall on the line L, or within the range of vision.* The 
great difference of position thus produced at the violet 
extremity by a slight movement at the other end of the 
spectrum, is caused by the crowding together of the 
colours at the red end. This is shown, together with the 
correspondence of the ratios of sound and colour, in the 
accompanying diagram. 
The musical scale is thus literally a rainbow of sound. 
Harmony in colour and music may thus, probably, be 
found to havea common physical basis. ° There are many 
indications that this is the case. For example, the juxta- 
position of two colours nearly alike is bad, and so also 
two adjacent notes of the scale sounded together produce 
discord. The succession of colours in the spectrum 
* A suggestion, made, I believe, by Sir J. Herschel, that the colours of 
the spectrum would probably repeat themselves if we could see beyond the 
lavender, both supports, and gains support from, this analogy. 
