PART II. (pp. 152–233).

ON THE INTERRUPTIONS OF HARMONY.

CHAPTER VII. COMBINATIONAL TONES, pp. 152–159.

Combinational tones arise when vibrations which are not of infinitesimal magnitude are combined, 152
Description of combinational tones, 153
Law determining their pitch numbers, 154
Combinational tones of different orders, 155
Difference of the strength of combinational tones on different instruments, 157
Occasional generation of combinational tones in the ear itself, 158

CHAPTER VIII. ON THE BEATS OF SIMPLE TONES, pp. 159–173.

Interference of two simple tones of the same pitch, 160
Description of the polyphonic siren, for experiments on interference, 161
Reinforcement or enfeeblement of sound, due to difference of phase, 163
Interference gives rise to beats when the pitch of the two tones is slightly different, 164
Law for the number of beats, 165
Visible beats on bodies vibrating sympathetically, 166
Limits of rapidity of audible beats, 167

CHAPTER IX. DEEP AND DEEPEST TONES, pp. 174–179.

Former investigations were insufficient, because there was a possibility of the ear being deceived by upper partial tones, as is shown by the number of beats on the siren, 174
Tones of less than thirty vibrations in a second fall into a drone, of which it is nearly or quite impossible to determine the pitch, 175
Beats of the higher upper partials of one and the same deep compound tone, 178

CHAPTER X. BEATS OF THE UPPER PARTIAL TONES, pp. 179–197.

Any two partial tones of any two compound tones may beat if they are sufficiently near in pitch, but if they are of the same pitch there will be consonance, 179
Series of the different consonances, in order of the distinctness of their delimitation, 183
Number of beats which arise from mistuning consonances, and their effect in producing roughness, 184
Disturbance of any consonance by the adjacent consonances, 186
Order of consonances in respect to harmoniousness, 188

CHAPTER XI. BEATS DUE TO COMBINATIONAL TONES, pp. 197–211.

The differential tones of the first order generated by two partial tones are capable of producing very distinct beats, 197
Differential tones of higher orders produce weaker beats, even in the case of simple generating tones, 199
Influence of quality of tone on the harshness of dissonances and the harmoniousness of consonances, 205

CHAPTER XII. CHORDS, pp. 211–233.

Consonant triads, 211
Major and minor triads distinguished by their combinational tones, 214
Relative harmoniousness of chords in different inversions and positions, 218
Retrospect on preceding investigations, 226