178 A. M. Mayer— Researches in Acoustics. 
Fig. 3 is the curve of a musical note, being the resultant of 
the simple ar oe of its first six harmonics. The first six 
harmonics having been drawn on a common axis, I erected 500 
equidistant oedinatess and extended these ordinates some dis- 
tance below the axis on which I desired to construct the result- 
ant. The algebraic sum of the ordinates, passing through the 
harmonic curves, were transferred to the corresponding ordinates 
of the lower axis, and by drawing a continuous line through 
these points, I formed the resultant curve. The first six har- 
monies are alone — in the combinations which I have given, 
because the 7th, 9th, 11th harmonics, and the major number of 
those above the pr form dissonant combinations with the lower 
and more powerful harmonics. Indeed, the harmonics above 
the 6th are purposely eliminated from the notes of the piano by 
striking the string in the neighborhood of its 7th nodal point. 
The amplitudes of the harmonics of fig. 3 are made to vary as 
the wave-length ; not that this variation represents the general 
relative intensities in such a composite sound, but they were so 
m ring out strongly the characteristic flexures of the 
resultant. To simplify the consideration of the curves, they 
are all represented with the same phase of initial vibration. 
Of course the resultants have an infinite variety of form, depend- 
ing on the difference in the initial phase, and on the amplitudes 
of the harmonic elements. 
Resultant curve of a musical note combined with tts octave. 4: 37:: 1: 4- 
