Regarding the tonality of these scales there is not very much to be said. In the case of the Hypo-dorian and Dorian octaves it will be generally thought probable that the key-note is _a_ (the [Greek: mesê kata dynamin]). If so, the difference between the two species is not one of 'mode,'--in the modern sense,--but consists in the fact that in the Hypo-dorian the compass of the melody is from the key-note upwards, while in the Dorian it extends a Fourth below the key-note. It is possible, however, that the lowest note (_e_) of the Dorian octave was sometimes the key-note: in which case the _mode_ was properly Dorian. In the Phrygian octave of Ptolemy's description the key-note cannot be the Fourth or Mesê [Greek: kata thesin] (_g_), since the interval _g-c_ is not consonant (9/8 × 9/8 × 28/27 being less than 4/3). Possibly the lowest note (_d_) is the key-note; if so the scale is of the Phrygian mode (in the modern sense). In the Hypo-phrygian octave there is a similar objection to regarding the Mesê [Greek: kata thesin] (_c_) as the key-note, and some probability in favour of the lowest note (_g_). If the Pythagorean division of the tetrachord _g-c_ were replaced by the natural temperament, which the language used by Ptolemy[1] leads us to regard as the true division, the scale would exhibit the intervals-- _g_ 5/4 _b_ 6/5 _d_ 7/6 _f_ 8/7 _g_ which give the natural chord of the Seventh. This however is no more than a hypothesis. It evidently follows from all this that Ptolemy's octaves do not constitute a system of _modes_. They are merely the groups of notes, of the compass of an octave, which are most likely to be used in the several keys, and which Ptolemy or some earlier theorist chose to call by the names of those keys. [Footnote 1: _Harm._ i. 16 [Greek: plên kathoson adousi men akolouthôs tô dedeigmenô syntonô diatonikô, kathaper exestai skopein apo tês tôn oikeiôn autou logôn parabolês, harmozontai de heteron ti genos] (sc. the Pythagorean), [Greek: xynengizon men ekeinô, k.t.l.]] § 32. _Remains of Greek Music._