Attempt at a New Theory of Music

from the simplest structures up to the most complex, at least such as the sense of hearing can still tolerate. In this enumeration, we soon encounter the generaIn ancient music theory, a 'genus' (plural: genera) refers to the different ways of tuning a tetrachord—a series of four notes. accepted by use in both the most ancient and more recent times. Among these were the very simple genus of Mercury, and the diatonic, chromatic, and enharmonic of the ancients. The first two of these, indeed, agreed exceptionally well with those principles which harmonyoriginal: "harmonia"; here referring to the mathematical laws of musical intervals. has provided to us; however, in the remaining ones—namely the chromatic and enharmonic—only a similarity is perceived. For since the ancients reached their conclusions guided partly by hearing alone and partly by confused reasoning, it is not surprising if they obtained only likenesses of true harmony. In the meantime, however, it is evident that they themselves already recognized the defects of these genera of theirs. They were also occupied for a long time with the diatonic genus before it was rendered consistent with true harmony, because it