τετρακτύς

Ancient Greek

Etymology

This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.
Particularly: “where does the kappa come from? also seen in τετράκις (tetrákis)”

Pronunciation

(5^th BCE Attic) IPA^(key): /te.trak.ty̌ːs/
(1^st CE Egyptian) IPA^(key): /te.trakˈtys/
(4^th CE Koine) IPA^(key): /te.trakˈtys/
(10^th CE Byzantine) IPA^(key): /te.trakˈtys/
(15^th CE Constantinopolitan) IPA^(key): /te.trakˈtis/

Noun

τετρᾰκτῡ́ς • (tetrăktū́s) f (genitive τετρᾰκτῠ́ος); third declension

Pythagorean name for:
1. the sum of the first four numbers, i.e. 10 (= 1+2+3+4)
  - Carm., Aur. 48:
    ναὶ μὰ τὸν ἁμετέρᾳ ψυχᾷ παραδόντα τετρακτύν, παγὰν ἀενάου φύσεως
    naì mà tòn hametérāi psukhâi paradónta tetraktún, pagàn aenáou phúseōs
  - 160 CE – 210 CE, Sextus Empiricus, Against the Mathematicians 7.94
  - Theo., Sm. p.94.H.
  - Hierocl., in CA 20p.465.M.
2. The four terms (6:8:9:12) of the proportion corresponding to the chief musical intervals; also their sum +1 (= 36); the sum of the first 8 numbers. (6:12::1:2::diapason, 6:9::2:3::diapente, 6:8::3:4::diatessaron; 1:2, 2:3, 3:4 being the ratios of neighboring terms in the sum of the previous definition. 8:9::tonus as a bonus. A diatonic scale may be derived from this; semitonus can be derived to be 243:256 by fitting tonus as many times as possible into a diatessaron and finding out what ratio remains. Tonus times tonus times semitonus equals diatessaron: do–re–mi–fa (6:8). Fa to sol is tonus (8:9). Sol to do’ is another diatessaron: sol–la–si–do’ = tonus times tonus times semitonus = do–re–mi–fa transposed to sol (9:12). 384:432:486:512:576:648:729:786::do:re:mi:fa:sol:la:si:do’.)
  - 60 CE – 120 CE, Nicomachus, Exc. 7.10
  - 46 CE – 120 CE, Plutarch, Moralia 2.381f
(education, historical) quadrivium.
- c. 1148, Anna Komnene, Alexiad:
  ἀλλὰ καὶ τὸ Ἑλληνίζειν ἐς ἄκρον ἐσπουδακυῖα καὶ ῥητορικῆς οὐκ ἀμελετήτως ἔχουσα καὶ τὰς Ἀριστοτελικὰς τέχνας εὖ ἀναλεξαμένη καὶ τοὺς Πλάτωνος διαλόγους καὶ τὸν νοῦν ἀπὸ τῆς τετρακτύος τῶν μαθημάτων πυκάσασα [...] βούλομαι διὰ τῆσδέ μου τῆς γραφῆς τὰς πράξεις ἀφηγήσασθαι τοὐμοῦ πατρὸς
  allà kaì tò Hellēnízein es ákron espoudakuîa kaì rhētorikês ouk ameletḗtōs ékhousa kaì tàs Aristotelikàs tékhnas eû analexaménē kaì toùs Plátōnos dialógous kaì tòn noûn apò tês tetraktúos tôn mathēmátōn pukásasa [...] boúlomai dià têsdé mou tês graphês tàs práxeis aphēgḗsasthai toumoû patròs
  but having studied Greek thoroughly, possessing no less knowledge of rhetoric, having read through the Aristotelian arts and Plato's dialogues, and having filled my mind with the quadrivium of the arts ... I now wish to narrate the deeds of my father through my writing

Inflection

Third declension of ἡ τετρᾰκτῡ́ς; τῆς τετρᾰκτῠ́ος (Attic)

Case / #	Singular	Dual	Plural
Nominative	ἡ τετρᾰκτῡ́ς hē tetrăktū́s	τὼ τετρᾰκτῠ́ε tṑ tetrăktŭ́e	αἱ τετρᾰκτῠ́ες hai tetrăktŭ́es
Genitive	τῆς τετρᾰκτῠ́ος tês tetrăktŭ́os	τοῖν τετρᾰκτῠ́οιν toîn tetrăktŭ́oin	τῶν τετρᾰκτῠ́ων tôn tetrăktŭ́ōn
Dative	τῇ τετρᾰκτῠ́ῐ̈ têi tetrăktŭ́ĭ̈	τοῖν τετρᾰκτῠ́οιν toîn tetrăktŭ́oin	ταῖς τετρᾰκτῠ́σῐ / τετρᾰκτῠ́σῐν taîs tetrăktŭ́sĭ(n)
Accusative	τὴν τετρᾰκτῡ́ν tḕn tetrăktū́n	τὼ τετρᾰκτῠ́ε tṑ tetrăktŭ́e	τᾱ̀ς τετρᾰκτῦς / τετρᾰκτῠ́ᾰς tā̀s tetrăktûs / tetrăktŭ́ăs
Vocative	τετρᾰκτῡ́ tetrăktū́	τετρᾰκτῠ́ε tetrăktŭ́e	τετρᾰκτῠ́ες tetrăktŭ́es
Notes:	This table gives Attic inflectional endings. For declension in other dialects, see Appendix:Ancient Greek dialectal declension.

Descendants

English: tetractys
Italian: tetrattide
Polish: tetraktys
Russian: тетрактис (tetraktis)