τετρακτύς

Ancient Greek

Etymology

τετράς (tetrás) +‎ -τύς (-tús)

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 • (tetraktū́s) 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

Inflection

Third declension of ἡ τετρᾰκτῡ́ς; τῆς τετρᾰκτῠ́ος (Attic)

Case / #	Singular	Dual	Plural
Nominative	ἡ τετρᾰκτῡ́ς hē tetraktū́s	τὼ τετρᾰκτῠ́ε tṑ tetraktúe	αἱ τετρᾰκτῠ́ες hai tetraktúes
Genitive	τῆς τετρᾰκτῠ́ος tês tetraktúos	τοῖν τετρᾰκτῠ́οιν toîn tetraktúoin	τῶν τετρᾰκτῠ́ων tôn tetraktúōn
Dative	τῇ τετρᾰκτῠ́ῐ̈ têi tetraktúï	τοῖν τετρᾰκτῠ́οιν toîn tetraktúoin	ταῖς τετρᾰκτῠ́σῐ / τετρᾰκτῠ́σῐν taîs tetraktúsi(n)
Accusative	τὴν τετρᾰκτῡ́ν tḕn tetraktū́n	τὼ τετρᾰκτῠ́ε tṑ tetraktúe	τᾱ̀ς τετρᾰκτῦς / τετρᾰκτῠ́ᾰς tā̀s tetraktûs / tetraktúas
Vocative	τετρᾰκτῡ́ tetraktū́	τετρᾰκτῠ́ε tetraktúe	τετρᾰκτῠ́ες tetraktúes
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)

Further reading

“τετρακτύς”, in Liddell & Scott (1940) A Greek–English Lexicon, Oxford: Clarendon Press
“τετρακτύς”, in ΛΟΓΕΙΟΝ [Logeion] (in English, French, Spanish, German, Dutch and Chinese), University of Chicago, 2011

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