τετρακτύς · tetraktys — LSJ
the sum of the first four numbers
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 CA 20p.465M.
II the four terms, of the proportion corresponding to the chief musical intervals, their sum +1 (= 36), the sum of the first 8 numbers
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. Isid. 2.381f.