774 Transactions of the American Institute. 



11, 6. In a modulation by flats, five is added; thus we have 12, 5, 

 10, 3, 8, 1, 6, as the regular order of tonics. Both series begin 

 and end with the same figures. The seven sounds used in each 

 modulation are determined by this simple rule, viz: If the tonic is 

 an odd number, the next two notes are odd, and the remaining 

 four, even; vice versa, if the tonic is an even number, the next two 

 notes are even, and the remaining notes odd. 



A synopsis of chords expressed by the solfeggio syllables is 

 adapted, by means of the revolving disk, to the twelve difierent 

 modulations made by keyed instruments. 



The relations of sound and color are shown by applying the 

 colors of the solar spectrum to the seven intervals of the septavo. 

 Eed, made by the lowest number of undulations, represents the 

 tonic; yellow, the mediant; and blue, the dominant. I have else- 

 where pointed to the very curious coincidence arising from this 

 arrangement of colors; the darkest color, indigo, falls on the rela- 

 tive minor tonic; and the brightest, yellow, on the brilliant medi- 

 ant; from which the deduction is made that light, heat, and actinism 

 result from the undulations of the same attenuated medium; that 

 the two forces last named vary inversely as the length of undula- 

 tions, while the perception of light and color results from the ratio 

 of undulations embraced in a single octave. 



The intervals of the three major and three minor common chords 

 are respectively measured by 4, 3, and 5 grades and 3, 4, and 5 

 grades. Discovering that, in each case, the sum of the squai'es of 

 the first two numbers was equal to the square of the third number, 

 I was led to represent these triads by right-angled triangles. In 

 comma terms the equation is W-{.l^^=2'2--\.l. The same terms 

 show that twelve consecutive fifths overlap seven consecutive 

 octaves, that is, 31 X 12=53 x 7+1. 



Further deductions have been made which are, however, foreign 

 to the purpose of this paper, but this singular relation of lines and 

 angles to the harmony of color, as well as sound, does suggest that 

 there are certain connecting links between form and motion, the 

 discovery of which may reveal, partially, at least, those processes 

 of nature, producing both permanency and growth; and that, 

 eventually, man may comprehend the operation of those wave- 

 forces which, by harmonious blending, shape cell and crystal and 

 define the forms of leaf and flower. 



In conclusion, I would advocate a change in the solfeggio sylla- 

 bles which gives each a vowel termmation, and, at the same time, 



