Attempt at a New Theory of Music

...possesses within itself, or what amounts to the same thing, how much mental faculty is required to perceive it. From this, it can be understood how much more easily some ratios can be noticed than others, wherever they may be present. Furthermore, it will be clear that this distinction between ratios is not based on the names that the ancients Referring to classical Greek theorists like Aristoxenus or Ptolemy assigned to them. Nor is it as it seemed to the Pythagoreans Followers of Pythagoras who believed that the beauty of music was governed by simple mathematical proportions, who held that multiple ratios multiple ratio: a ratio where the larger number is a clean multiple of the smaller, like 2:1 or 3:1 are more easily perceived than superparticular ratios superparticular ratio: a ratio where the larger number is the smaller plus one, like 3:2 or 4:3, and that these in turn are easier than superpartient ratios superpartient ratio: a ratio where the larger number contains the smaller plus more than one part, like 5:3.

Instead, the criterion must be sought from a far different source, from which a much more solid understanding and judgment of consonances Musical intervals that sound stable and pleasant to the ear—one most consistent with experience—may arise. And upon these two principles, one physical and the other metaphysical, we have built the entire theory of music.

As for the actual execution of the work, it must be noted above all else that music is comprised of two primary parts