Zeta

Zeta (uppercase Ζ, lowercase ζ; Greek: ζήτα, classical [ˈdzɛːta] or [ˈzdɛːta] zḗta, Greek pronunciation: [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 (UK) and zee (US), the names of the Latin letter Z in English. However, many Romanic languages (such as Italian and Spanish), and Scandinavian languages 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

Letter

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

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

Most handbooks^[who?] 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^[where?].

Arguments for [zd]

PIE *zd becomes ζ in Greek (e.g. *sísdō > ἵζω). Contra: these words are rare and it is therefore 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^[Why?].
Without [sd] there would be an empty space between [sb] and [sɡ] in the Greek sound system (πρεσβύς, 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 is 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).
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 Αζωτος.
Some inscriptions have -ζ- written for a combination -ς + δ- resulting from separate words, e.g. θεοζοτος for θεος δοτος "god-given".
Some Attic inscriptions have -σζ- for -σδ- or -ζ-, which is thought to parallel -σστ- for -στ- and therefore to imply a [zd] pronunciation.
ν disappears before ζ like before σ(σ), στ: e.g. *πλάνζω > πλᾰ́ζω, *σύνζυγος = *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).
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.
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].
The grammarians Dionysius Thrax 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).
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.

Arguments for [dz]

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.)
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], and such use of special letters may be justified by the fact that they are the only double sounds that could appear at a word initial. 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.)
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).
Greek in South Italy has preserved [dz] until modern times. Contra: a) this may be a later development from [zd] or [z]; b) even if it is derived from an ancient [dz], it may be a dialectal pronunciation.
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. 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 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 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).

Meteorology

The name Zeta was a name used in the 2005 Atlantic hurricane season as the record-breaking Tropical Storm Zeta.

Character Encodings

Greek Zeta / Coptic Zata

Character information
Preview	Ζ		ζ		Ⲋ		ⲋ
Unicode name	GREEK CAPITAL LETTER ZETA		GREEK SMALL LETTER ZETA		COPTIC CAPITAL LETTER ZATA		COPTIC SMALL LETTER ZATA
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex
Unicode	918	U+0396	950	U+03B6	11402	U+2C8A	11403	U+2C8B
UTF-8	206 150	CE 96	206 182	CE B6	226 178 138	E2 B2 8A	226 178 139	E2 B2 8B
Numeric character reference	Ζ	Ζ	ζ	ζ	Ⲋ	Ⲋ	ⲋ	ⲋ
Named character reference	Ζ		ζ
DOS Greek	133	85	157	9D
DOS Greek-2	169	A9	223	DF
Windows 1253	198	C6	230	E6
TeX			\zeta

Mathematical Zeta

Character information
Preview	𝚭		𝛇		𝛧		𝜁		𝜡		𝜻
Unicode name	MATHEMATICAL 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
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	120493	U+1D6AD	120519	U+1D6C7	120551	U+1D6E7	120577	U+1D701	120609	U+1D721	120635	U+1D73B
UTF-8	240 157 154 173	F0 9D 9A AD	240 157 155 135	F0 9D 9B 87	240 157 155 167	F0 9D 9B A7	240 157 156 129	F0 9D 9C 81	240 157 156 161	F0 9D 9C A1	240 157 156 187	F0 9D 9C BB
UTF-16	55349 57005	D835 DEAD	55349 57031	D835 DEC7	55349 57063	D835 DEE7	55349 57089	D835 DF01	55349 57121	D835 DF21	55349 57147	D835 DF3B
Numeric character reference	𝚭	𝚭	𝛇	𝛇	𝛧	𝛧	𝜁	𝜁	𝜡	𝜡	𝜻	𝜻

Character information
Preview	𝝛		𝝵		𝞕		𝞯
Unicode name	MATHEMATICAL 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
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex
Unicode	120667	U+1D75B	120693	U+1D775	120725	U+1D795	120751	U+1D7AF
UTF-8	240 157 157 155	F0 9D 9D 9B	240 157 157 181	F0 9D 9D B5	240 157 158 149	F0 9D 9E 95	240 157 158 175	F0 9D 9E AF
UTF-16	55349 57179	D835 DF5B	55349 57205	D835 DF75	55349 57237	D835 DF95	55349 57263	D835 DFAF
Numeric character reference	𝝛	𝝛	𝝵	𝝵	𝞕	𝞕	𝞯	𝞯

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.

References

Allen, William Sidney: Vox Graeca: A guide to the pronunciation of Classical Greek. Cambridge University Press 1987, pp. 56–59.
Hinge, George: "Die Aussprache des griechischen Zeta", in: Die Sprache Alkmans: Textgeschichte und Sprachgeschichte (PhD dissertation), Aarhus 2001, pp. 212–234 = [1]
Méndez Dosuna, Julián: "On <Ζ> for <Δ> in Greek dialectal inscriptions", Die Sprache 35, 1993, pp. 82–114.
Rohlfs, Gerhard: "Die Aussprache des z (ζ) im Altgriechischen", Glotta 8, 1962, pp. 3–8.
Teodorsson, Sven-Tage: "The pronunciation of zeta in different Greek dialects". In: E. Crespo i.a. (ed.): Dialectologia Graeca: Actas del II Coloquio Internacional de Dialectología Griega. Universidad Autónoma de Madrid 1993, pp. 305–321.