In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.

Hence the ancient architects, following in the footsteps of nature, perfected the ascending rows of seats in theatres from their investigations of the ascending voice, and by means of the canonical theory of the mathematicians and that of the musicians, endeavoured to make every voice uttered on the stage come with greater clearness and sweetness to the ears of the audience. For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn, so the ancients devised methods of increasing the power of the voice in theatres through the application of harmonics.

On this principle of arrangement, the voice, uttered from the stage as from a centre, and spreading and striking against the cavities of the different vessels, as it comes in contact with them, will be increased in clearness of sound, and will wake an harmonious note in unison with itself.

And since the proportions of the human voice and the gesticulations of the human body are regulated by the same modulation as that by which sound and the motion of other bodies are, musical thought is subalternated not only to the harmony of human voice and gesticulation, but also of instruments and of those whose delectation consist in motion or sound and with these the harmony of the celestial and non-celestial. And since the concordance of times and the composition and harmony of the lower world and of all things composed of four elements come from celestial motions, and, moreover, since it is necessary to find the harmony of causes in their effects, the study of music also extends to knowing the proportions of times and the constitution of the elements of the lower world, and even the composition of all the elements.

Music is the space between the notes.

Music expresses the motion of the waters, the play of curves described by changing breezes.

There is geometry in the humming of the strings, there is music in the spacing of the spheres.

There is geometry in the humming of the strings, there is music in the spacing of the spheres.

There is geometry in the humming of the strings. There is music in the spacing of the spheres.

Music's exclusive function is to structure the flow of time and keep order in it.

Music, also, the architect ought to understand so that he may have knowledge of the canonical and mathematical theory, and besides be able to tune ballistae, catapultae, and scorpiones to the proper key. For to the right and left in the beams are the holes in the frames through which the strings of twisted sinew are stretched by means of windlasses and bars, and these strings must not be clamped and made fast until they give the same correct note to the ear of the skilled workman.

Music creates order out of chaos: for rhythm imposes unanimity upon the divergent, melody imposes continuity upon the disjointed, and harmony imposes compatibility upon the incongruous.

It was left by Aristoxenus, who with great ability and labour classified and arranged in it the different modes. In accordance with it, and by giving heed to these theories, one can easily bring a theatre to perfection, from the point of view of the nature of the voice, so as to give pleasure to the audience.

The musical scale is a convention which circumscribes the area of potentiality and permits construction within those limits in its own particular symmetry.