Editing Zeta

{{short description|Sixth letter in the Greek alphabet}}
{{Other uses}}
{{more footnotes|date=December 2011}}
{{Greek Alphabet|letter=zeta}}{{Distinguish|text=[[Z]]}}
'''Zeta''' ({{IPAc-en|UK|'|z|iː|t|ə}}, {{IPAc-en|US|'|z|eɪ|t|ə|audio=LL-Q1860 (eng)-Flame, not lame-Zeta.wav}};<ref>{{OED|zeta}}</ref> uppercase '''Ζ''', lowercase '''ζ'''; {{langx|grc|ζῆτα}}, {{langx|el|ζήτα|label=[[Demotic Greek]]}}, classical {{IPA|grc|d͡zɛ̌ːta|}} or {{IPA|grc|zdɛ̌ːta|}} ''zē̂ta''; {{IPA|el|ˈzita|label=[[Modern Greek]]:}} ''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 alphabet|Phoenician letter]] [[zayin]] [[File:phoenician zayin.svg|20px|Zayin]]. Letters that arose from zeta include the Roman [[Z]] and Cyrillic [[Ze (Cyrillic)|З]].

==Name==
Unlike the other [[Greek alphabet|Greek letters]], this letter did not take its name from the [[Phoenician alphabet|Phoenician]] letter from which it was derived; it was given a new name on the pattern of [[Beta (letter)|beta]], [[eta]] and [[theta]].

The word ''zeta'' is the ancestor of ''zed'', the name of the Latin letter [[Z]] in Commonwealth English. [[Swedish language|Swedish]] and many [[Romance language]]s (such as [[Italian language|Italian]] and [[Spanish language|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==
<!-- DO NOT ADD THE USE OF THE LOWERCASE ZETA AS A ZOOPHILE SYMBOL, UNLESS MULTIPLE, HIGH QUALITY SOURCES ARE PROVIDED -->

[[File:NAMA Alphabet grec.jpg|thumb|The Greek alphabet on a [[black figure]] vessel, with the Phoenician {{mono|I}} shape of the zeta]]

===Letter {{anchor|Pronunciation}} ===
The letter ζ represents the [[voiced alveolar fricative]] {{IPA|el|z|IPA}} in [[Modern Greek]].

The sound represented by zeta in Greek before 400&nbsp;BC is disputed. See [[Ancient Greek phonology]] and [[Pronunciation of Ancient Greek in teaching]].

Most handbooks{{who|date=December 2011}} agree on attributing to it the pronunciation {{IPA|/zd/}} (like ''Mazda''), but some scholars believe that it was an affricate {{IPA|/[[voiced alveolar 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 dialect|Attic]]; for example, it could count as one or two consonants metrically in Attic drama.{{where|date=April 2013}}

==== Arguments for {{IPA|[zd]}}  {{anchor|Arguments in favor of [zd]}} ====
# PIE *''zd'' becomes ζ in Greek (e.g. *''sísdō'' > {{lang|grc|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{{citation needed|date=July 2016}}<!-- they can go both ways, e.g. kitchen>cistin, college>colláiste, Alexandria>Al-Iskandariya, perhaps exeo~>esco, but also C(es)aragusta>Zaragoza, musta3rab>mozárabe; the question is, how can we count the probability from a never complete set of data? Or was it judged more likely on the basis of some physiological experiments, think Ohala? --> than the other way around (which would violate the [[sonority hierarchy]]).
# Without {{IPA|[sd]}} there would be an empty space between {{IPA|[sb]}} and {{IPA|[sɡ]}} in the Greek sound system ({{lang|grc|πρέσβυς, σβέννυμι, φάσγανον}}), and a voiced affricate {{IPA|[dz]}} would not have a voiceless correspondent. '''Contra:''' a) words with {{IPA|[sb]}} and {{IPA|[sɡ]}} are rare, and exceptions in phonological and (even more so) phonotactic patterns are in no way uncommon; b) there was {{IPA|[sd]}} in {{lang|grc|ὅσδε, εἰσδέχται}} etc.; and c) there was in fact a voiceless correspondent in Archaic Greek ({{IPA|[ts]}} > Attic, [[Boeotian Greek|Boeotian]] {{lang|grc|ττ}}, [[Ionic Greek|Ionic]], [[Doric Greek|Doric]] {{lang|grc|σσ}}).
# [[Old Persian|Persian]] names with ''zd'' and ''z'' are transcribed with ζ and σ respectively in Classical Greek (e.g. ''Artavazda'' = {{lang|grc|Ἀρτάβαζος/Ἀρτάοζος}} ~ ''Zara(n)ka-'' = {{lang|grc|Σαράγγαι}}.  Similarly, the [[Philistine]] city [[Ashdod]] was transcribed as {{lang|grc|Ἄζωτος}}.
# Some inscriptions have -ζ- written for a combination -ς + δ- resulting from separate words, e.g. θεοζοτος for θεος δοτος "god-given".
# Some [[Attic Greek|Attic]] inscriptions have -σζ- for -σδ- or -ζ-, which is thought to parallel -σστ- for -στ- and  therefore to imply a {{IPA|[zd]}} pronunciation.
# ν disappears before ζ like before σ(σ), στ: e.g. *{{lang|grc|πλάνζω}} > {{lang|grc|πλᾰ́ζω}}, *{{lang|grc|σύνζυγος}} > {{lang|grc|σύζυγος}}, *{{lang|grc|συνστέλλω}} > {{lang|grc|σῠστέλλω}}. '''Contra:''' ν may have disappeared before /dz/ if one accepts that it had the allophone {{IPA|[z]}} in that position like /ts/ had the allophone {{IPA|[s]}}: cf. [[Cretan Greek|Cretan]] {{lang|grc|ἴαττα}} ~ {{lang|grc|ἀποδίδονσα}} (Hinge).
# Verbs beginning with ζ have {{lang|grc|ἐ-}} in the perfect reduplication like the verbs beginning with στ (e.g. {{lang|grc|ἔζηκα}} = {{lang|grc|ἔσταλται}}). '''Contra:''' a) The most prominent example of a verb beginning with στ has in fact {{lang|grc|ἑ-}} < *''se-'' in the perfect reduplication ({{lang|grc|ἕστηκα}}); b) the words with /ts/ > σ(σ) also have {{lang|grc|ἐ-}}: [[Homer]] {{lang|grc|ἔσσυμαι, -ται}}, Ion. {{lang|grc|ἐσσημένῳ}}.
# [[Alcman]], [[Sappho]], [[Alcaeus of Mytilene|Alcaeus]] and [[Theocritus]] have σδ for [[Attic-Ionic]] ζ. '''Contra:''' The tradition would not have invented this special digraph for these poets if {{IPA|[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 [[Alexandria|Alexandrine]] rather than historical. Thus, {{lang|grc|σδ}} indicates only a different pronunciation from Hellenistic Greek {{IPA|[z(ː)]}}, i.e. either {{IPA|[zd]}} or {{IPA|[dz]}}.
# The grammarians [[Dionysius Thrax]]<ref>{{quote|text=
{{lang|grc|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.
|multiline=yes
|author=[[Dionysius Thrax]]
|title=Περὶ στοιχείου
|source=''[https://el.wikisource.org/wiki/%CE%A4%CE%AD%CF%87%CE%BD%CE%B7_%CE%93%CF%81%CE%B1%CE%BC%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AE Τέχνη Γραμματική]'' (~100&nbsp;BCE).
}}.</ref> and [[Dionysius of Halicarnassus]] class ζ with the "double" ({{lang|grc|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 {{IPA|[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 I|Xerxes]]).
# Some Attic transcriptions of Asia Minor toponyms (βυζζαντειον, αζζειον, etc.) show a -ζζ- for ζ; assuming that [[Attic Greek|Attic]] value was {{IPA|[zd]}}, it may be an attempt to transcribe a dialectal {{IPA|[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]  {{anchor|Arguments in favour of [dz]}} ====
# The Greek inscriptions almost never write ζ in words like {{lang|grc|ὅσδε, τούσδε}} or {{lang|grc|εἰσδέχται}}, so there must have been a difference between this sound and the sound of {{lang|grc|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 {{IPA|[zd]}}, which could be represented by σδ without any problems. {{IPA|/ds/}}, on the other hand, would have the same sequence of plosive and sibilant as the double letters of the Ionic alphabet ψ {{IPA|/ps/}} and ξ {{IPA|/ks/}}, thereby avoiding a written plosive at the end of a syllable. '''Contra:''' the use of a special symbol for {{IPA|[zd]}} is no more or no less improbable than the use of ψ for {{IPA|[ps]}}  and ξ for {{IPA|[ks]}}, or, for that matter, the later invention ϛ ([[stigma (letter)|stigma]]) for {{IPA|[st]}}, which happens to be the voiceless counterpart of {{IPA|[zd]}}.  Furthermore, it is not clear that ζ was pronounced {{IPA|[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 {{IPA|[zd]}}. (For a parallel development, note that original palatal [[Proto-Slavic language|Proto-Slavic]] {{IPA|/tʲ/}} developed into {{IPA|/ʃt/}} in [[Old Church Slavonic]], with similar developments having led to combinations such as зд and жд being quite common in [[Russian language|Russian]].)
# [[Boeotia]]n, [[ancient Elis|Elean]], [[Laconia]]n and [[Creta]]n ''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 {{lang|grc|πλαδδιῆν}} (Aristoph., ''Lys''. 171, 990) and Boeotian {{lang|grc|σαλπίδδω}} (Sch. Lond. in Dion. Thrax 493), which suggests that these dialects have had a phase of [[metathesis (linguistics)|metathesis]] (Teodorsson).
# Greek in South Italy has preserved {{IPA|[dz]}} until modern times. '''Contra:''' a) this may be a later development from {{IPA|[zd]}} or {{IPA|[z]}} under the influence of Italian; b) even if it is derived from an ancient {{IPA|[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 {{lang|grc|-ίζω}} > Italian. ''-eggiare'', French ''-oyer''. Italian, similarly, has consistently used Z for {{IPA|[dz]}} and {{IPA|[ts]}} (Lat. ''prandium'' > It. ''pranzo'', "lunch"). '''Contra:''' whether the pronunciation of {{lang|grc|ζ}} was {{IPA|[dz]}}, {{IPA|[zd]}} or {{IPA|[zː]}}, ''di'' would probably still have been the closest native Latin sound; furthermore, the inscriptions are centuries later than the time for which {{IPA|[zd]}} is assumed.

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

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

===Mathematics and science {{anchor|Symbols}} ===
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]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Riemann Zeta Function |url=https://mathworld.wolfram.com/RiemannZetaFunction.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en}}</ref>
*The [[Hurwitz zeta function|Hurwitz Zeta Function]] in mathematics<ref>{{Cite web |title=DLMF: Chapter 25 Zeta and Related Functions |url=https://dlmf.nist.gov/25 |access-date=2025-01-31 |website=dlmf.nist.gov}}</ref>
*The [[Weierstrass functions#Weierstrass zeta-function|Weierstrass zeta-function]]<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Weierstrass Zeta Function |url=https://mathworld.wolfram.com/WeierstrassZetaFunction.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en}}</ref>
*The [[damping ratio]] of an oscillating system in engineering and physics<ref>{{Cite book |last=Wilkie |first=Jacqueline |title=Control engineering: an introductory course |last2=Johnson |first2=Michael |last3=Katebi |first3=Reza |date=2002 |publisher=Palgrave |isbn=978-0-333-77129-7 |location=Basingstoke |pages=179 |quote=We shall refer to ζ as the damping ratio throughout this text.}}</ref>
*The rotational quantity of angular [[Jerk (physics)|jerk]] in physics<ref>{{Cite book |last=Gallardo-Alvarado |first=Jaime |title=Mechanisms: kinematic analysis and applications in robotics |last2=Gallardo-Razo |first2=José |date=2022 |publisher=Academic Press, an imprint of Elsevier |isbn=978-0-323-95348-1 |series=Emerging methodologies and applications in modelling, identification and control |location=London |pages=328}}</ref>
*The effective nuclear charge on an electron in quantum chemistry
*The [[electrokinetic potential]] in [[colloid|colloidal systems]]<ref>{{Cite book |last=Hunter |first=Robert J. |title=Zeta potential in colloid science: principles and applications |date=1988 |publisher=Academic Press |isbn=978-0-12-361961-7 |edition=New paperback |series=Colloid science |location=London San Diego |pages=6 |quote=It is also possible to correlate the ζ-potential with the sedimentation behaviour of colloidal systems and with the flotation behaviour of mineral ores.}}</ref>
*The lag angle in [[helicopter]] blade dynamics<ref>{{Cite book |last=Padfield |first=Gareth D. |title=Helicopter flight dynamics: the theory and application of flying qualities and simulation modeling |date=2007 |publisher=American Inst. of Aeronautics and Astronautics |isbn=978-1-56347-920-5 |edition=2nd |series=AIAA education series |location=Reston, Va |pages=xxxi}}</ref>
*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)
*In physical chemistry equilibrium computations (using lower case Zeta (ζ)), the extent of reaction
*The [[Boundary layer thickness|height of the surface]] of a fluid layer

[[ZETA (fusion reactor)]] (all uppercase) was an early fusion experiment.

<!-- DO NOT ADD THE USE OF THE LOWERCASE ZETA AS A ZOOPHILE SYMBOL, UNLESS MULTIPLE, HIGH QUALITY SOURCES ARE PROVIDED -->

==Unicode==

* {{unichar|0396|html=}}
* {{unichar|03B6|html=}} ({{tt|\zeta}} in TeX)
* {{unichar|2C8C|html=}}
* {{unichar|2C8D|html=}}
* {{unichar|10357|html=}}
* {{unichar|10378|html=}}
* {{unichar|1D6AD|html=}}{{efn|The {{sc|mathematical}} symbols are only used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.}}
* {{unichar|1D6C7|html=}}
* {{unichar|1D6E7|html=}}
* {{unichar|1D701|html=}}
* {{unichar|1D721|html=}}
* {{unichar|1D73B|html=}}
* {{unichar|1D75B|html=}}
* {{unichar|1D775|html=}}
* {{unichar|1D795|html=}}
* {{unichar|1D7AF|html=}}
{{notelist}}

==See also==
{{Wiktionary|zeta|ζ}}
*[[Z|Z, z - Latin]]
*[[Ze (Cyrillic)|З, з - Ze (Cyrillic)]]

==References==
{{Reflist}}

===General references===
*{{cite book |last1=Allen |first1=W. Sidney |authorlink=W. Sidney Allen |title=Vox Graeca: The Pronunciation of Classical Greek |date=1987 |publisher=Cambridge University Press |isbn=978-0-521-33555-3 |pages=56–59 |url=https://books.google.com/books?id=yws4Zey-ZnYC }}
*Hinge, George. “Die Aussprache des griechischen Zeta”, in ''Die Sprache Alkmans: Textgeschichte und Sprachgeschichte''. PhD dissertation. Aarhus: Aarhus University Press, 2001, pp.&nbsp;212–234 = [http://alkman.georgehinge.com/zeta.html]
*Méndez Dosuna, Julián. “On &lt;Ζ&gt; for &lt;Δ&gt; in Greek dialectal inscriptions”, ''Die Sprache'' 35 (1993): 82–114.
*[[Gerhard Rohlfs|Rohlfs, Gerhard]]. 1962. “Die Aussprache des z (ζ) im Altgriechischen”, ''Das Altertum'' 8 (1962): 3–8.
*Sheets, George A. “[https://continuum.fas.harvard.edu/the-pronunciation-of-classical-greek-zeta/ The Pronunciation of Classical Attic Zeta]” ''Classical Continuum'' 2023.07.25.
*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.&nbsp;305–321.

[[Category:Greek letters]]