Twelve Books on Harmony

...create the given musical harmonies. original: "Consonantias" This is demonstrated in Proposition 12 of the French book on Discords original: "Dissonantiis", and shown in the following figure. The figure uses black dots to mark the positions of weights where these harmonies will be heard.

However, it is uncertain whether heavy falling objects, such as iron globes or stones, produce sounds as they fall. No sound is heard when they drop from the tops of towers. This is perhaps because they have not yet reached the speed required to produce a sound. If someone knew the speed necessary for this, it would be very easy to find the locations from which these heavy objects must fall. The explanation for this figure should be sought in the cited proposition. However, if you understand the seven columns of numbers, you may not need further explanation. These columns contain the times and distances of the falls.

A circular figure is attached to this. Thirteen syllables serving the scale of the octave are written around its circumference. These syllables, such as Ut, X, Mi, and Fa, represent the various harmonies and discords created when compared to others. original: "VT, X, MI, FA". Ut was the original name for the note Do. The X represents the seventh note, which was not yet universally named Si or Ti in this period. You can gain a perfect understanding of these numbers from the Preface of the French book on Harmonies. You will surely praise the genius of the dedicated man who created this figure. Without any teacher and knowing only the French language, he captured the ratios of all musical intervals original: "intervallorum Musicorum" in this figure. You will recognize his name and talent in Proposition 22 of Book 3 on Instruments. Many other things are in the French books, from which you may gather the following.

A complex geometric and mathematical diagram. On the left is a circle with thirteen points marked on its circumference. These points are interconnected by a dense web of lines representing chords. Each is labeled with numbers. To the right of the circle is a vertical chart consisting of seven columns of numbers of varying scales. The text identifies these as representing the times and distances of falling bodies that correspond to musical intervals.

PROPOSITION III.

To determine whether the time it takes for heavy objects to fall vertically toward the center is related to the time of an angled fall, in the same way the angled path is related to the vertical path.

It is established from what was said in Propositions 24 through 27 what the vertical fall of heavy objects toward the center consists of, by which toward the center