Those intervals in which few or no beats occur are called consonances. As the combination or interfering tones, as well as the beats, have importance and interest only in harmonizing several voices, in tuning pianos, as well as in composition in general, and as we have in view in these pages only the culture of single voices, we cannot further enlarge on these discoveries, interesting as they are. According to the purpose of this little work, I introduce only so much of the latest investigations and discoveries as will help to show the prevailing evils of our mode of teaching singing, and, by their practical application to the business of instruction, serve to improve the vocal art. But whoever has an interest in this branch of science will find in the invaluable work of Helmholtz, “Die Lehre von den Tonempfindungen,” an abundance of most interesting observations and of the most thoroughly scientific illustrations of the theory of music, and of those processes in the domain of tone which we have hitherto always felt, but never understood. APPLICATION OF THE NATURAL LAWS LYING AT THE FOUNDATION OF MUSICAL SOUNDS TO THE CULTURE OF THE VOICE IN SINGING The parts of the human voice that generate tones are the membranous vocal ligaments or chords, which are subject to the same natural laws as all sounding bodies; of this we may satisfy ourselves by observing the different registers of the voice by means of the laryngoscope. The lower, stronger tones of both series of the chest register show the ligaments in full vibration, and becoming more strongly stretched with every higher tone. In the second series the glottis appears, by the inaction of the arytenoid cartilages, to be shortened. In the falsetto register the vibrating body is diminished, as only the edges vibrate, while the same processes are repeated as in the chest register by the greater stretching of the ligaments and the shortening of the glottis. The head register, likewise, shows the glottis partly closed, and the vibrating ligaments gradually stretched more and more. The vocal ligaments are made to vibrate by the air coming from the lungs through the trachea, to which they present resistance. These vibrations are communicated to the air in the mouth and outside, and are felt by the ear as sound. As the strength of the tone depends upon the amplitude of the waves of sound, they, in their turn, depend upon the structure of the organ of singing, and of the parts of the mouth serving as a sounding-board or resonant apparatus, but, above all, upon the skilful management of the vibrating air. And although a fine timbre of the tones and due skill in increasing the amplitude of the vibrations may cause the voice to appear fuller and stronger, yet it is not in our power, when once the vocal organs have been fully developed, to make a strong voice out of a weak one.