Περὶ τῆς ἐν Τιμαίῳ ψυχογονίας

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İngilizce Yunanca

19 Others, placing the two extremes of the diatessaron, the acute part in 288, and the lower sound in 216, in all the rest observe the same proportions, only that they take the remainder between the two middle intervals. For the base, being forced up a whole tone, makes 243; and the upper note, screwed downward a full tone, begets 256. Moreover 243 carries a sesquioctave proportion to 216, and 288 to 256; so that each of the intervals contains a full tone, and the residue is that which remains between 243 and 256, which is not a semitone, but something less. For 288 exceeds 256 by 32, and 243 exceeds 216 by 27; but 256 exceeds 243 by 13. Now this excess is less than half of the former. So it is plain that the diatessaron consists of two tones and the residue, not of two tones and a half. Let this suffice for the demonstration of these things. Nor is it a difficult thing to believe, by what has been already said, wherefore Plato, after he had asserted that the intervals of sesquialter, sesquiterce, and sesquioctave had arisen, when he comes to fill up the intervals of sesquiterces with sesquioctaves, makes not the least mention of sesquialters; for that the sesquialter is soon filled up, by adding the sesquiterce to the sesquioctave, or the sesquioctave to the sesquiterce.