τετρακτύς

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Ancient Greek

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Etymology

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τετράς (tetrás) +‎ -τύς (-tús)

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

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Noun

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τετρᾰκτῡ́ς (tetraktū́sf (genitive τετρᾰκτῠ́ος); third declension

  1. 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’.)

Inflection

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Descendants

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Further reading

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