De institutione musica IV.18: Quemadmodum indubitanter musicae consonantiae aure diiudicari possint.
But so that the reasoning of the consonances may be gathered beyond doubt, it can be done with a very short and simple instrument. Let there be a carefully stretched rule AD. On it let two half-spheres, which the Greeks call magades, be placed in such a way that a line drawn from the curvature E to the point B makes right angles about itself. Likewise let a line drawn from the curvature F to the point C make right angles about itself. Let these be placed equally on every side, and for the same uses let other equal ones be prepared. Over these let a string, equal throughout, be stretched, namely AEFD. If, then, I wish to find what the diatessaron consonance is like, I shall proceed thus. From the point E, where the string touches the half-sphere, to the point F, where on the other side the string again meets the half-sphere, I divide the space EF into seven parts, and at four sevenths I set the point K. EK is therefore to KF in the sesquitertian ratio. If, then, I set the half-sphere equally to K beneath the upper ones, and EK and KF are struck in turn with the plectrum, the distance of the diatessaron will sound; but if I strike both at once, I recognize the diatessaron consonance. And if we wish to produce the diapente, I divide the whole into five parts, and give three to one portion and two to the other, and having placed the half-sphere thus, in the manner said above, I weigh the consonances and dissonances. Likewise, if I wish to try the diapason consonance, I cut the whole into three parts and, distributing them into one and two, I strike both together or either, and learn what each sounds in concord or discord. The triple, which arises from mixed consonances, is produced thus: if we divide the whole by divisions of four parts, and the whole length of the string is divided into three and one, then the half-sphere placed at the three yields the dissonance and consonance of the triple proportion.