170 



DR. J. D. MACDONALD, T. H.E.N., F.K.S., ON 



Table II. 



8-25 



-The Symmetrical Scale of Sound. 

 {Tlie Contra Octave.) 

 -33- 



8-23^ 



D^EiF4CiA?BiBiC 



_ t> 1/5 Lft W 



• W ^, T ^ 



8v 



'^ S^ 'f w w ^ 



xfi '^ m '^ ifi '^ 



*" r»- I> 



N.B. — Tlie note numbers here express the frequency per 

 second, but in both tables the intervening and arc numbers 

 are increments, which demonstrate the symmetry more pal- 

 pably than if the frequency numbers alone were supplied. 



On comparing the two foregoing tables it will be seen 

 that the 1st, 3rd, and 5th C, K, and G in the musical gamut 

 correspond with red, yellow, and blue in the scale of colour, 

 and that the colour (blue) and the note G hold the central 

 position in their respective scales. Moreover, it is all- 

 important to notice that the " intervening increments " are 

 disposed in the most perfect symmetry on either side of the 

 ceiitre in both cases. 



It is rather a good thing that the musician and the painter 

 have not so much to deal with thunder and liglitning or 

 acoustic and optical experiment as with the well-tempered 

 musical and colorific scales. Two important laws or tenets 

 have been brought to bear in the construction of the fore- 

 going tables, namely, 1st, that the nndnlatori/ theory is appli- 

 cable to both light and sound, and 2ndh', tliat the musical ratios 

 ap)pertain, also to colour, though comparatively low numbers 

 in one case have to be compared with billions in the other. 



Angstrom's tables of the wave lengths and frequencies of 

 the undulations of colour, which are now taken as the 

 standard, were consulted and applied in 'J^'able I with no 

 difficulty Avhatever. Herschel's calculations gave some 

 little hope of success, but they were found to be a little too 

 narrow. Thus, the chief difficulty in founding the analogy 

 of sound and colour on a truly scientific basis Avould appear 

 to be swept away ; so that we have now only to apply the 



