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Finally, the credit must be given to Ptolemy Claudius Ptolemy, the 2nd-century Alexandrian polymath whose work "Harmonics" defined musical theory for centuries. Ultimately, our eighteenth genus corresponds wonderfully with that which is now most in use and is commonly called the diatonic-chromatic original: "diatonico-chromaticum"; a hybrid scale combining whole steps and half steps. For it contains within one octave original: "octaua" twelve sounds separated from one another by almost equal intervals—namely, by semitones original: "hemitoniis" and limmas original: "limmatis"; a small musical interval or "leftover" in Pythagorean tuning, whether major or minor.

Although this genus has already been accepted in practice for a long time, musicians have nevertheless continually introduced new improvements by which it might be made more pleasing to the ear. This labor has turned out so successfully for them that the arrangement of sounds which is now most approved by musicians differs from true harmony by only a single sound marked B. Such a high degree of agreement could scarcely have been hoped for by the sense of hearing alone.