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. . . The school of Aristoxenes in the fourth century divided the tone into four "rigorously equal" quarter tones, but in reality this division was not considered as exact because Aristoxenes did admit in practice a certain "freedom of variation of the intervals," a certain "latitude" for each note. (d'Erlanger, Baron Rodolphe, La musique arabe. 3 vols. Paris: Paul Geuthner, 1930) in [Daniélou, Alain, Music and The Power of Sound, Inner Traditions, Rochester, Vermont, 1995, p81

. . . The . . . Fourth . . . its apparent value . . . consists of two and a half tones. [Aristoxenus, The Harmonics of Aristoxenus, translated by Henry S. Macran, M.A., Oxford At The Clarendon Press, Henry Frowde, M.A., Publisher to the University of Oxford, New York, 1902, p182]

. . . there is a problem about what exactly is meant by a 'tone'. The Greek writers define it as the interval by which a fifth is greater than a fourth. Strictly speaking, that is the interval given by the ratio 9 : 8, or 204 cents. But Aristoxenus regards it as being at the same time a unit of which a fourth (properly 498 cents) contains exactly two and a half. In effect he is operating with a tempered tone of 200 cents and a tempered fourth of 500 cents. . . . [West, M.L., Ancient Greek Music, Clarendon Press, Oxford, 1994, p167]