De institutione musica V.14: Descriptio octachordi, qua ostenditur diapason minorem esse sex tonis.
Ptolemy teaches, by the division of a certain octachord, that the diapason falls within six tones, in this way. Let eight strings be stretched, namely A, B, C, D, E, F, G, H, and let there be made the sesquioctave of AK, which is BL, and of BL, which is CM, and of CM, which is DN, and of DN, which is EX, and of EX, which is FO, and of FO, which is GP. There will then be six tones. Again, let the string H be divided in the middle at R. AK will then be double of HR. Struck together, AK and HR will sound the equisonance of the diapason. But if someone strikes GP, it will always be a little higher than HR, and therefore six tones exceed the diapason consonance. For if AK and GP, struck, sounded the diapason, the diapason consonance would be of six tones. But if, when these do not sound together, AK and HR sound the diapason, and HR is higher than GP, the diapason consonance would exceed six tones. Now since, when AK and HR are consonant, the same HR is found to be lower than GP, it cannot be but that six tones exceed the diapason consonance. And so it can also be gathered by sense that the diapason consonance falls within six tones. In this way, therefore, the error of Aristoxenus is convicted beyond doubt.