Zeta

Zeta (UK: /ˈztə/,[1] US: /ˈztə/; uppercase Ζ, lowercase ζ; Ancient Greek: ζῆτα, Demotic Greek: ζήτα, classical [d͡zɛ̌:ta] or [zdɛ̌:ta] zē̂ta; Modern Greek: [ˈzita] zíta) is the sixth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 7. It was derived from the Phoenician letter zayin . Letters that arose from zeta include the Roman Z and Cyrillic З.

Name

Unlike the other Greek letters, this letter did not take its name from the Phoenician letter from which it was derived; it was given a new name on the pattern of beta, eta and theta.

The word zeta is the ancestor of zed, the name of the Latin letter Z in Commonwealth English. Swedish and many Romanic languages (such as Italian and Spanish) do not distinguish between the Greek and Roman forms of the letter; "zeta" is used to refer to the Roman letter Z as well as the Greek letter.

Uses

The Greek alphabet on a black figure vessel, with the Phoenician I shape of the zeta

Letter

The letter ζ represents the voiced alveolar fricative /z/ in Modern Greek.

The sound represented by zeta in Greek before 400 BCE is disputed. See Ancient Greek phonology and Pronunciation of Ancient Greek in teaching.

Most handbooks agree on attributing to it the pronunciation /zd/ (like Mazda), but some scholars believe that it was an affricate /dz/ (like adze). The modern pronunciation was, in all likelihood, established in the Hellenistic age and may have already been a common practice in Classical Attic; for example, it could count as one or two consonants metrically in Attic drama.

Arguments for [zd]

  1. PIE *zd becomes ζ in Greek (e.g. *sísdō > ἵζω). Contra: these words are rare and it is therefore more probable that *zd was absorbed by *dz (< *dj, *gj, *j); further, a change from the cluster /zd/ to the affricate /dz/ is typologically more likely than the other way around (which would violate the sonority hierarchy).
  2. Without [sd] there would be an empty space between [sb] and [sɡ] in the Greek sound system (πρέσβυς, σβέννυμι, φάσγανον), and a voiced affricate [dz] would not have a voiceless correspondent. Contra: a) words with [sb] and [sɡ] are rare, and exceptions in phonological and (even more so) phonotactic patterns are in no way uncommon; b) there was [sd] in ὅσδε, εἰσδέχται etc.; and c) there was in fact a voiceless correspondent in Archaic Greek ([ts] > Attic, Boeotian ττ, Ionic, Doric σσ).
  3. Persian names with zd and z are transcribed with ζ and σ respectively in Classical Greek (e.g. Artavazda = Ἀρτάβαζος/Ἀρτάοζος ~ Zara(n)ka- = Σαράγγαι. Similarly, the Philistine city Ashdod was transcribed as Ἄζωτος.
  4. Some inscriptions have -ζ- written for a combination -ς + δ- resulting from separate words, e.g. θεοζοτος for θεος δοτος "god-given".
  5. Some Attic inscriptions have -σζ- for -σδ- or -ζ-, which is thought to parallel -σστ- for -στ- and therefore to imply a [zd] pronunciation.
  6. ν disappears before ζ like before σ(σ), στ: e.g. *πλάνζω > πλᾰ́ζω, *σύνζυγος > σύζυγος, *συνστέλλω > σῠστέλλω. Contra: ν may have disappeared before /dz/ if one accepts that it had the allophone [z] in that position like /ts/ had the allophone [s]: cf. Cretan ἴαττα ~ ἀποδίδονσα (Hinge).
  7. Verbs beginning with ζ have ἐ- in the perfect reduplication like the verbs beginning with στ (e.g. ἔζηκα = ἔσταλται). Contra: a) The most prominent example of a verb beginning with στ has in fact ἑ- < *se- in the perfect reduplication (ἕστηκα); b) the words with /ts/ > σ(σ) also have ἐ-: Homer ἔσσυμαι, -ται, Ion. ἐσσημένῳ.
  8. Alcman, Sappho, Alcaeus and Theocritus have σδ for Attic-Ionic ζ. Contra: The tradition would not have invented this special digraph for these poets if [zd] was the normal pronunciation in all Greek. Furthermore, this convention is not found in contemporary inscriptions, and the orthography of the manuscripts and papyri is Alexandrine rather than historical. Thus, σδ indicates only a different pronunciation from Hellenistic Greek [z(ː)], i.e. either [zd] or [dz].
  9. The grammarians Dionysius Thrax[2] and Dionysius of Halicarnassus class ζ with the "double" (διπλᾶ) letters ψ, ξ and analyse it as σ + δ. Contra: The Roman grammarian Verrius Flaccus believed in the opposite sequence, δ + σ (in Velius Longus, De orthogr. 51), and Aristotle says that it was a matter of dispute (Metaph. 993a) (though Aristotle might as well be referring to a [zː] pronunciation). It is even possible that the letter sometimes and for some speakers varied in pronunciation depending upon word position, i.e., like the letter X in English, which is (usually) pronounced [z] initially but [gz] or [ks] elsewhere (cf. Xerxes).
  10. Some Attic transcriptions of Asia Minor toponyms (βυζζαντειον, αζζειον, etc.) show a -ζζ- for ζ; assuming that Attic value was [zd], it may be an attempt to transcribe a dialectal [dz] pronunciation; the reverse cannot be ruled completely, but a -σδ- transcription would have been more likely in this case. This suggests that different dialects had different pronunciations. (For a similar example in the Slavic languages, cf. Serbo-Croatian (iz)među, Russian между, Polish między, and Czech mezi, "between".)

Arguments for [dz]

  1. The Greek inscriptions almost never write ζ in words like ὅσδε, τούσδε or εἰσδέχται, so there must have been a difference between this sound and the sound of ἵζω, Ἀθήναζε. Contra: a few inscriptions do seem to suggest that ζ was pronounced like σδ; furthermore, all words with written σδ are morphologically transparent, and written σδ may simply be echoing the morphology. (Note, for example, that we write "ads" where the morphology is transparent, and "adze" where it is not, even though the pronunciation is the same.)
  2. It seems improbable that Greek would invent a special symbol for the bisegmental combination [zd], which could be represented by σδ without any problems. /ds/, on the other hand, would have the same sequence of plosive and sibilant as the double letters of the Ionic alphabet ψ /ps/ and ξ /ks/, thereby avoiding a written plosive at the end of a syllable. Contra: the use of a special symbol for [zd] is no more or no less improbable than the use of ψ for [ps] and ξ for [ks], or, for that matter, the later invention ϛ (stigma) for [st], which happens to be the voiceless counterpart of [zd]. Furthermore, it is not clear that ζ was pronounced [zd] when it was originally invented. Mycenean Greek had a special symbol to denote some sort of affricate or palatal consonant; ζ may have been invented for this sound, which later developed into [zd]. (For a parallel development, note that original palatal Proto-Slavic /tʲ/ developed into /ʃt/ in Old Church Slavonic, with similar developments having led to combinations such as зд and жд being quite common in Russian.)
  3. Boeotian, Elean, Laconian and Cretan δδ are more easily explained as a direct development from *dz than through an intermediary *zd. Contra: a) the sound development dz > dd is improbable (Mendez Dosuna); b) ν has disappeared before ζ > δδ in Laconian πλαδδιῆν (Aristoph., Lys. 171, 990) and Boeotian σαλπίδδω (Sch. Lond. in Dion. Thrax 493), which suggests that these dialects have had a phase of metathesis (Teodorsson).
  4. Greek in South Italy has preserved [dz] until modern times. Contra: a) this may be a later development from [zd] or [z] under the influence of Italian; b) even if it is derived from an ancient [dz], it may be a dialectal pronunciation.
  5. Vulgar Latin inscriptions use the Greek letter Z for indigenous affricates (e.g. zeta = diaeta), and the Greek ζ is continued by a Romance affricate in the ending -ίζω > Italian. -eggiare, French -oyer. Italian, similarly, has consistently used Z for [dz] and [ts] (Lat. prandium > It. pranzo, "lunch"). Contra: whether the pronunciation of ζ was [dz], [zd] or [zː], di would probably still have been the closest native Latin sound; furthermore, the inscriptions are centuries later than the time for which [zd] is assumed.

Summary

  • σδ is attested only in the lyric poetry of the Greek isle of Lesbos and the city-state of Sparta during the Archaic Age and in Bucolic poetry from the Hellenistic Age. Most scholars would take this as an indication that the [zd]-pronunciation existed in the dialects of these authors.
  • The transcriptions from Persian by Xenophon and testimony by grammarians support the pronunciation [zd] in Classical Attic.
  • [z(ː)] is attested from c. 350 BC in Attic inscriptions, and was the probable value in Koine.
  • [dʒ] or [dz] may have existed in some other dialects in parallel.

Numeral

Zeta has the numerical value 7 rather than 6 because the letter digamma (also called 'stigma' as a Greek numeral) was originally in the sixth position in the alphabet.

Mathematics and science

The uppercase zeta is not used, because it is normally identical to Latin Z. The lower case letter can be used to represent:

  • The Riemann zeta function in mathematics
  • The damping ratio of an oscillating system in engineering and physics
  • The rotational quantity of angular jerk in physics
  • The effective nuclear charge on an electron in quantum chemistry
  • The electrokinetic potential in colloidal systems
  • The lag angle in helicopter blade dynamics
  • Relative vorticity in the atmosphere and ocean
  • A number whose discrete values (eigenvalues) are the positive roots of transcendental equations, used in the series solutions for transient one-dimensional conduction equations
  • The heat flux across or through a plane (industrial materials technology)
  • The Weierstrass zeta-function
  • In physical chemistry equilibrium computations (using lower case Zeta (ζ)), the extent of reaction

Character encodings

Greek Zeta / Coptic Zata

Character information
PreviewΖζ
Unicode nameGREEK CAPITAL LETTER ZETAGREEK SMALL LETTER ZETACOPTIC CAPITAL LETTER ZATACOPTIC SMALL LETTER ZATA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode918U+0396950U+03B611402U+2C8A11403U+2C8B
UTF-8206 150CE 96206 182CE B6226 178 138E2 B2 8A226 178 139E2 B2 8B
Numeric character reference&#918;&#x396;&#950;&#x3B6;&#11402;&#x2C8A;&#11403;&#x2C8B;
Named character reference&Zeta;&zeta;
DOS Greek133851579D
DOS Greek-2169A9223DF
Windows 1253198C6230E6
TeX\zeta

Mathematical Zeta

Character information
Preview𝚭𝛇𝛧𝜁𝜡𝜻
Unicode nameMATHEMATICAL BOLD
CAPITAL ZETA
MATHEMATICAL BOLD
SMALL ZETA
MATHEMATICAL ITALIC
CAPITAL ZETA
MATHEMATICAL ITALIC
SMALL ZETA
MATHEMATICAL BOLD ITALIC
CAPITAL ZETA
MATHEMATICAL BOLD ITALIC
SMALL ZETA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120493U+1D6AD120519U+1D6C7120551U+1D6E7120577U+1D701120609U+1D721120635U+1D73B
UTF-8240 157 154 173F0 9D 9A AD240 157 155 135F0 9D 9B 87240 157 155 167F0 9D 9B A7240 157 156 129F0 9D 9C 81240 157 156 161F0 9D 9C A1240 157 156 187F0 9D 9C BB
UTF-1655349 57005D835 DEAD55349 57031D835 DEC755349 57063D835 DEE755349 57089D835 DF0155349 57121D835 DF2155349 57147D835 DF3B
Numeric character reference&#120493;&#x1D6AD;&#120519;&#x1D6C7;&#120551;&#x1D6E7;&#120577;&#x1D701;&#120609;&#x1D721;&#120635;&#x1D73B;
Character information
Preview𝝛𝝵𝞕𝞯
Unicode nameMATHEMATICAL SANS-SERIF
BOLD CAPITAL ZETA
MATHEMATICAL SANS-SERIF
BOLD SMALL ZETA
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL ZETA
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL ZETA
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120667U+1D75B120693U+1D775120725U+1D795120751U+1D7AF
UTF-8240 157 157 155F0 9D 9D 9B240 157 157 181F0 9D 9D B5240 157 158 149F0 9D 9E 95240 157 158 175F0 9D 9E AF
UTF-1655349 57179D835 DF5B55349 57205D835 DF7555349 57237D835 DF9555349 57263D835 DFAF
Numeric character reference&#120667;&#x1D75B;&#120693;&#x1D775;&#120725;&#x1D795;&#120751;&#x1D7AF;

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

References

  1. "zeta". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  2. Ἔτι δὲ τῶν συμφώνων διπλᾶ μέν ἐστι τρία· ζ ξ ψ. διπλᾶ δὲ εἴρηται, ὅτι ἓν ἕκαστον αὐτῶν ἐκ δύο συμφώνων σύγκειται, τὸ μὲν ζ ἐκ τοῦ σ καὶ δ, τὸ δὲ ξ ἐκ τοῦ κ καὶ σ, τὸ δὲ ψ ἐκ τοῦ π καὶ σ. Of the consonants, three are double: ζ ξ ψ. They are called double because each one of them is composed of two consonants, ζ of σ and δ; ξ of κ and σ, ψ of π and σ.
    Dionysius Thrax, Περὶ στοιχείου, Τέχνη Γραμματική (~100 BCE).
    .
  • Allen, William Sidney. Vox Graeca: A guide to the pronunciation of Classical Greek. Cambridge: Cambridge University Press, 1987, pp. 56–59.
  • Hinge, George. “Die Aussprache des griechischen Zeta”, in Die Sprache Alkmans: Textgeschichte und Sprachgeschichte. PhD dissertation. Aarhus: Aarhus University Press, 2001, pp. 212–234 =
  • Méndez Dosuna, Julián. “On <Ζ> for <Δ> in Greek dialectal inscriptions”, Die Sprache 35 (1993): 82–114.
  • Rohlfs, Gerhard. “Die Aussprache des z (ζ) im Altgriechischen”, Das Altertum 8 (1962): 3–8.
  • Teodorsson, Sven-Tage. “On the pronunciation of ancient greek zeta”, Lingua 47, no. 4 (April 1979): 323–32.
  • Teodorsson, Sven-Tage. “The pronunciation of zeta in different Greek dialects”, in Dialectologia Graeca: Actas del II Coloquio internacional de dialectología griega, eds. E. Crespo et al. Madrid: Universidad Autónoma de Madrid, 1993, pp. 305–321.
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