τετρακτύς

English (LSJ)

ύος, ἡ, (τετράς) Pythagorean name for

   A the sum of the first four numbers, i.e. 10 (= 1+2+3+4), ναὶ μὰ τὸν ἁμετέρᾳ ψυχᾷ παραδόντα τετρακτύν, παγὰν ἀενάου φύσεως Carm.Aur.48, cf. S.E.M. 7.94, TheoSm.p.94 H., Hierocl.in CA20p.465M.    II the four terms (6:8:9:10) of the proportion corresponding to the chief musical intervals, Nicom.Exc.7, 10; also their sum +1 (= 36), ibid.; the sum of the first 8 numbers, Plu.2.381f.