Theon of Smyrna gives an incomplete account of Thrasyllus of Mendes' formulation of the greater perfect system, from which the diatonic and enharmonic genera can be deduced. For the chromatic genus, however, all that is given is a 32:27 proportion of "mese" to "lichanos". This leaves 9:8 for the "pyknon", but there is no information at all about the position of the chromatic "parhypate" and therefore of the division of the "pyknon" into two semitones, though it may have been the "limma" of 256:243, as Boethius does later . Someone has referred to this speculative reconstructions as the traditional Pythagorean tuning of the chromatic genus: