UTAH ACADEMY OF SCIENCES 99 
PHYSICAL RELATIONS OF SUBJECTIVE AND OB- 
JECTIVE COMBINATION TONES. 
By JOSEPH PETERSON. 
(Abstract). 
If one blows simultaneously two whistles one will hear, 
besides the two tones thus produced, one or more others 
more or less prominent. The number that will be heard 
depends upon the separation distance in pitch of the two 
primary tones and upon their relative intensities, as well 
as upon their absolute pitch. In this case these extra tones 
seem to be located in the listener’s ears. They are called 
combination tones, and are of two kinds—summation and 
difference tones. Difference tones play an important part 
in consonance and dissonance, or musical relations of tones. 
Helmholtz explained the origin of combination tones 
in three different ways. The importance of the middle-ear 
origin view has been greatly minimized by modern research; 
and I showed in 1907 that the other two explanations are 
identical in physical principle. 
It was early found that of these combination tones, 
some can be reinforced by physical resonators while others 
cannot. The former are called objective; the latter, sub- 
jective. This, as we shall see, does not mean that the 
latter do not have a physical basis as well as the former, 
for they certainly do have. 
Many authorities, with Koenig, have denied the exis- 
tence of difference tones lying between the primaries; e. g. 
5, of the interval 4:9. Rucker and Edser not only proved 
that such tones exist and can be reinforced by physical 
resonators, but they also proved by the same method, the 
objective physical existence of summation tones. Since 
then Krueger and others have established the existence of 
the corresponding subjective combination tones, tones the 
existence of which had been questioned by Max Meyer, 
K. L. Schaefer, et al. Subjective and objective combination 
tones are therefore now brought to a close correspondence, 
a fact supporting my contention of 1907 that the physical 
