For this reason, upon the second day of the Saturnalian festival, the famous Onesicrates invited certain persons, the best skilled in music, to a banquet ; by name Soterichus This is not to be confounded with the reduced octachord of Terpander. This heptachord includes two tetrachords so united that the lowest note of one is identical with the highest note of the other ; wliile the octachord includes two tetrachords entirely separated, with each note distinct. The former connection is called Kara avva^rjv, the latter Kara diul^ev^Lv. Of the eight notes of the octachord, the first four (counting from the lowest), vkuttj, irapvmiTT}, Xtxavug, and fiioT], are the same in the heptachord ; Tvapafiiarj is omitted in the heptachord ; while rpmi, TrapavT/TT]; and vt/tt] in the heptachord are designated as rpiTTj ovvTjfifievuv, napavijTij ovvT]/j,/j.evuv, and v^r?; avvrin^ievuv, to distinguish them from the notes of the same name in the octachord, which sometimes have the designation (ke^evyfiivuv, but generally are written simply Tpiri], &c. These simple scales were enlarged by the addition of higher and lower notes, four at the bottom of the scale (i.e. before vnurri), called irpoaXaixjSavofievo^, vkuttj vTraribv, TTapvnuTi^ viraTuv, h-Xfivoc inraTuv; and three at the top (above i^f/rri), called VT/TTj, napavTjTrj^ TpiTTj, each with the designation vTreplSoXaluv. The lowest three notes of the ordinary octachord are here designated by fieauv, when the simple names are not used. Thus a scale of fifteen notes was made ; and we have one of eighteen by including the two classes of Tpir?}, Trapavrj-rri, and vrirr] designated by avvijfifih-cjv and diEi^evy/jiivuv. The harmonic intervals, discovered by Pythagoras, are the Octave (6lu naatjv), with its ratio of 2 : 1 ; the Fijih {6iu nivTe), with its ratio of 3 : 2 {Tioyog rjfuokio^ or Sesquialter) ; the Fourth {duj. rtaaupuv), with its ratio of 4:3 (Ariyof eniTpiTog or Sesquiterce) ; and the Tone {tovo^), with its ratio of 9 : 8 (kbyog krcoydoog or Sesquioctave). (G.) of Alexandria, and Lysias, one of those to whom he gave a yearly pension. After all had done and the table was cleared, — To dive, said he, most worthy friends, into the nature and reason of the human voice is not an argument proper for this merry meeting, as being a subject that requires a more sober scrutiny. But because our chiefest grammarians define the voice to be a percussion of the air made sensible to the ear, and for that we were yesterday discoursing of Grammar, — which is an art that can give the voice form and shape by means of letters, and store it up in the memory as a magazine, — let us consider what is the next science to this which may be said to relate to the voice. In my opinion, it must be music. For it is one of the chiefest and most religious duties belonging to man, to celebrate the praise of the Gods, who gave to him alone the most excelling advantage of articulate discourse, as Homer has observed in the following verses : — With sacred hymns and songs that sweetly please, The Grecian youth all day the Gods appease ; Their lofty paeans bright Apollo hears, And still the charming sounds delight his ears.* Now then, you that are of the grand musical chorus, tell your friends, who was the first that brought music into use ; what time has added for the advantage of the science ; who have been the most famous of its professors ; and lastly, for what and how far it may be beneficial to mankind.