View source for Eta

{{Short description|Seventh letter in the Greek alphabet}}
{{hatnote group|
{{distinguish|text=the Latin letters [[H]], [[Ƞ]], or [[ŋ]], or the Cyrillic letter [[Н]]}}
{{other uses}}
}}
{{Greek Alphabet|letter=eta}}
'''Eta''' ({{IPAc-en|'|iː|t|ə|,_|'|eɪ|t|ə|audio=LL-Q1860 (eng)-Flame, not lame-Eta.wav}} {{respell|EE|tə|,_|AY|tə}};<ref>{{OED|eta}}</ref> uppercase '''{{Script|Grek|Η}}''', lowercase '''{{Script|Grek|η}}'''; {{langx|grc|ἦτα}} ''ē̂ta'' {{IPA|el|ɛ̂ːta|}} or {{langx|el|ήτα}} ''ita'' {{IPA|el|ˈita|}}) is the seventh letter of the [[Greek alphabet]], representing the [[close front unrounded vowel]], {{IPA|el|i|}}. Originally denoting the [[voiceless glottal fricative]], {{IPA|el|h|}}, in most dialects of [[Ancient Greek]], its sound value in the classical [[Attic Greek|Attic dialect]] was a long [[open-mid front unrounded vowel]], {{IPA|el|ɛː|}}, which was later raised to {{IPA|el|i|}} in [[Hellenistic Greek]], a process known as [[iotacism]] or itacism.

In the ancient [[Attic numerals|Attic number system]] (Herodianic or acrophonic numbers), the number 100 was represented by "{{Script|Grek|Η}}", because it was the initial of {{lang|grc|ΗΕΚΑΤΟΝ}}, the ancient spelling of {{lang|el|ἑκατόν}} = "one hundred".  In the later system of (Classical) [[Greek numerals]] eta represents 8. 

Eta was derived from the [[Phoenician alphabet|Phoenician letter]] [[heth]] {{Script/Phoenician|𐤇}}. Letters that arose from eta include the Latin [[H]] and the [[Cyrillic script|Cyrillic]] letters [[I (Cyrillic)|И]] and [[Short I|Й]].

==History==

===Consonant h===
[[File:41 - Stoà of Attalus Museum - Ostracism against Megakles (487 BC) - Photo by Giovanni Dall'Orto, Nov 9 2009.jpg|thumb|right|Eta ([[heta]]) in the function of {{IPA|/h/}} on the [[ostrakon]] of [[Megacles]], son of Hippocrates, 487 BC. Inscription: {{lang|grc|ΜΕΓΑΚLES HIΠΠΟΚRATOS}} equivalent to the later {{lang|grc|Μεγακλῆς Ἱπποκράτους}}. On display in the Ancient Agora Museum in Athens, housed in the [[Stoa of Attalus]].]]
[[File:Hermes e Sarpedon.jpg|thumb|Eta in the function of {{IPA|/h/|cat=no}} on an Attic [[Red-figure pottery|red-figured]] [[calyx-krater]], 515 BC. Amongst the depicted figures are [[Hermes]] and [[Hypnos]]. Inscriptions: {{lang|grc|ΗΕΡΜΕΣ}} – {{lang|grc|ΗΥΠΝΟΣ}}.]]
{{main|Heta (letter)}}
The letter shape 'H' was originally used in most Greek dialects to represent the [[voiceless glottal fricative]], {{IPA|el|h|}}. In this function, it was borrowed in the 8th century BC by the [[Old Italic alphabet|Etruscan and other Old Italic alphabets]], which were based on the [[Cumaean alphabet|Euboean]] form of the Greek alphabet. This also gave rise to the Latin alphabet with its letter [[H]].

Other regional variants of the Greek alphabet ([[epichoric alphabets]]), in dialects that still preserved the sound {{IPA|el|h|}}, employed various glyph shapes for consonantal ''heta'' side by side with the new vocalic ''eta'' for some time. In the southern Italian colonies of [[Heraclea Lucania|Heraclea]] and [[Taranto|Tarentum]], the letter shape was reduced to a "half-heta" lacking the right vertical stem (Ͱ). From this sign later developed the sign for [[rough breathing]] or ''spiritus asper'', which brought back the marking of the  {{IPA|el|h|}} sound into the standardized post-classical ([[Greek diacritics|polytonic]]) orthography.<ref name="Nicholas">[http://www.tlg.uci.edu/~opoudjis/unicode/unicode_aitch.html Nick Nicholas (2003), "Greek /h/"] {{webarchive|url=https://archive.today/20130901210905/http://www.tlg.uci.edu/~opoudjis//unicode/unicode_aitch.html|date=2013-09-01}}.</ref> [[Dionysius Thrax]] in the second century BC records that the letter name was still pronounced ''heta'' (ἥτα), correctly explaining this irregularity by stating "in the old days the letter Η served to stand for the rough breathing, as it still does with the Romans."<ref>{{lang|grc|παρὰ τοῖς ἀρχαίοις ὁ τύπος τοῦ Η ἐν τύπῳ δασείας ἔκειτο, ὥσπερ καὶ νῦν <παρὰ> τοῖς Ῥωμαίοις}}. Alfredus Hilgard (ed), "In artis Dionysianae §6" in ''Grammatici Graeci. Scholia in Dionysii Thracis Artem Grammaticam'' (1901), p. 486.</ref>

===Long e===
In the East [[Ionic dialect]], however, the sound {{IPA|el|h|}} disappeared by the sixth century BC, and the letter was re-used initially to represent a development of a long [[open front unrounded vowel]], {{IPA|el|aː|}}, which later merged in East Ionic with the long [[open-mid front unrounded vowel]], {{IPA|el|ɛː|}} instead.<ref>
{{cite book
|title=New Comparative Grammar of Greek and Latin
|first=Andrew L.
|last=Sihler
|edition=illustrated
|publisher=Oxford University Press
|year=1995
|location=New York
|ISBN=0-19-508345-8
|url=https://books.google.com/books?id=IeHmqKY2BqoC
|pages=10–20
}}
</ref> In 403 BC, [[Athens]] took over the Ionian spelling system and with it the vocalic use of H (even though it still also had the {{IPA|el|h|}} sound itself at that time). This later became the standard orthography in all of Greece.

===Itacism===
During the time of post-classical [[Koine Greek]], the {{IPA|el|ɛː|}} sound represented by eta was [[Vowel height|raised]] and merged with several other formerly distinct vowels, a phenomenon called ''iotacism'' or ''[[itacism]]'', after the new pronunciation of the letter name as ''ita'' instead of ''eta''.

Itacism is continued into [[Modern Greek]], where the letter name is pronounced {{IPA|[ˈita]}} and represents the [[close front unrounded vowel]], {{IPA|el|i|}}. It shares this function with several other letters ([[Iota|ι]], [[Upsilon|υ]]) and [[Digraph (orthography)|digraphs]] (ει, οι, υι), which are all pronounced alike.

===Cyrillic script===
Eta was also borrowed with the sound value of {{IPA|[i]}} into the [[Cyrillic script]], where it gave rise to the Cyrillic letter [[I (Cyrillic)|И]].

==Uses==

===Letter===
In [[Modern Greek]], due to [[iotacism]], the letter (pronounced {{IPA|el|ˈita|}}) represents a [[close front unrounded vowel]], {{IPA|el|i|}}. In [[Ancient Greek language|Classical Greek]], it represented the long [[open-mid front unrounded vowel]], {{IPA|el|ɛː|}}.

===Symbol===

====Upper case====
The uppercase letter Η is used as a symbol in [[textual criticism]] for the [[Alexandrian text-type]] (from [[Hesychius of Alexandria|Hesychius]], its once-supposed editor).

In [[chemistry]], the letter H as symbol of [[enthalpy]] sometimes is said to be a Greek eta, but since enthalpy comes from ἐνθάλπος, which begins in a smooth breathing and epsilon, it is more likely a Latin [[H]] for 'heat'.

In information theory the uppercase Greek letter Η is used to represent the concept of [[Entropy_(information_theory)#Definition|entropy]] of a discrete random variable.

====Lower case====
The lowercase letter η is used as a symbol in:
*[[Thermodynamics]], the efficiency of a [[Carnot heat engine]],<ref>{{Cite book |title=Carnot Cycle and Heat Engine Fundamentals and Applications |date=2020 |publisher=MDPI - Multidisciplinary Digital Publishing Institute |isbn=978-3-03928-845-8 |editor-last=Feidt |editor-first=Michel |location=Basel, Switzerland |pages=3 |quote=Without any doubt, the main result was the so-called CA-efficiency ''η'' =…}}</ref> or [[packing density|packing fraction]].<ref>{{Cite book |last=Hansen |first=Jean-Pierre |title=Theory of simple liquids: with applications to soft matter |last2=McDonald |first2=Ian Ranald |date=2013 |publisher=Elsevier/AP |isbn=978-0-12-387032-2 |edition=4th |location=Amstersdam |pages=102 |quote=… and the system reduces to that of two, identical, pure fluids confined to the same volume at a packing fraction ''η''.}}</ref>
*[[Aeronautics]], the [[propulsive efficiency]], or percentage of chemical energy converted to kinetic energy. 
*[[Chemistry]], the [[hapticity]], or the number of atoms of a ligand attached to one coordination site of the metal in a [[coordination compound]]. For example, an [[allyl group]] can coordinate to [[palladium]] in the η¹ mode (only one atom of an allyl group attached to palladium) or the η³ mode (3 atoms attached to palladium).
*[[Optics]], the [[electromagnetic impedance]] of a medium, or the [[quantum efficiency]] of detectors.
*[[Particle physics]], to represent the [[η meson]]s.
*[[Particle physics|Experimental particle physics]], η stands for [[pseudorapidity]].<ref>{{Cite book |last=Larkoski |first=Andrew J. |title=Elementary particle physics: an intuitive introduction |date=2019 |publisher=Cambridge university press |isbn=978-1-108-49698-8 |location=Cambridge New York |pages=118 |quote=Pseudorapidity ''η'' is zero for central collisions, directly perpendicular to the beam at the interaction point.}}</ref>
*[[Cosmology]], η represents [[conformal time]]; dt = adη.<ref>{{Cite book |last=Huterer |first=Dragan |title=A course in cosmology: from theory to practice |date=2023 |publisher=Cambridge university press |isbn=978-1-316-51359-0 |location=Cambridge |pages=28 |quote=A very closely related quantity is '''conformal time''' ''η'' (sometimes labeled as ''τ'', and sometimes called coordinate time),...}}</ref>
*[[Cosmology]], [[Big_Bang_nucleosynthesis#Baryon–photon ratio|baryon–photon ratio]].<ref>{{Cite book |last=Grupen |first=Claus |title=Astroparticle physics |date=2020 |publisher=Springer |others=Tilo Stroh |isbn=978-3-030-27341-5 |edition=Second |series=Undergraduate texts in physics |location=Cham |pages=209 |quote=Further, the baryon-number-to-photon ratio can be defined: η =...}}</ref>
*[[Theory of relativity|Relativity]] and [[Quantum field theory]] (physics), η (with two subscripts) represents the [[metric tensor (general relativity)|metric tensor]] of [[Minkowski space]] (flat spacetime).<ref>{{Cite book |last=Rybicki |first=George B. |title=Radiative processes in astrophysics |last2=Lightman |first2=Alan P. |date=1979 |publisher=Wiley |isbn=978-0-471-04815-2 |series=A Wiley-Interscience publication |location=New York |pages=123}}</ref>
*[[Statistics]], ''η''<sup>2</sup> is the "partial regression coefficient". ''η'' is the symbol for the linear predictor of a [[generalized linear model]], and can also be used to denote the median of a population, or thresholding parameter in Sparse Partial Least Squares regression.
*[[Economics]], ''η'' is the [[Elasticity (economics)|elasticity]].
*[[Astronomy]], the seventh-brightest (usually) star in a [[constellation]]. ''See'' [[Bayer designation]].
*Mathematics, [[lambda calculus#η-reduction|η-reduction]] in lambda calculus.
*Mathematics, the [[Dirichlet eta function]], [[Dedekind eta function]], and [[Weierstrass eta function]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Dirichlet Eta Function |url=https://mathworld.wolfram.com/DirichletEtaFunction.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en}}</ref><ref>{{Cite web |last=Weisstein |first=Eric W. |title=Dedekind Eta Function |url=https://mathworld.wolfram.com/DedekindEtaFunction.html |access-date=2025-01-22 |website=mathworld.wolfram.com |language=en}}</ref><ref>{{Cite book |last=Bronshtein |first=I. |title=Handbook of Mathematics |last2=Bronshtein |first2=I. N. |date=2015 |publisher=Springer Berlin Heidelberg |isbn=978-3-662-46220-1 |location=Berlin |pages=589 |quote=Weierstrass eta-function}}</ref>
*In [[category theory]], the unit of an [[Adjoint functors#Counit-unit adjunction|adjunction]] or [[Monad (category theory)#Formal definition|monad]] is usually denoted ''η''.<ref>{{Cite book |last=Böhm |first=Gabriella |title=Hopf algebras and their generalizations from a category theoretical point of view |date=2019 |publisher=Springer |isbn=978-3-319-98136-9 |edition=Corrected publication |series=Lecture notes in mathematics |location=Cham, Switzerland |pages=18 |quote=Consider a monad ''t'' on a category '''A''' with unit ''η'' and multiplication ''μ''.}}</ref>
*[[Biology]], a [[DNA polymerase]] found in higher [[eukaryotes]] and implicated in Translesion Synthesis.
*[[Artificial neural network|Neural network]] [[backpropagation]], and [[stochastic gradient descent]] more generally, η stands for the [[learning rate]].<ref>{{Cite book |title=Data Science – Analytics and Applications: Proceedings of the 4th International Data Science Conference – iDSC2021 |date=2022 |publisher=Springer Fachmedien Wiesbaden |isbn=978-3-658-36294-2 |editor-last=Haber |editor-first=Peter |edition=1st ed. 2022 |series=Springer eBook Collection |location=Wiesbaden |pages=28 |quote=We searched for the learning rate η with fixed fraction of participating clients C,… |editor-last2=Lampoltshammer |editor-first2=Thomas |editor-last3=Leopold |editor-first3=Helmut |editor-last4=Mayr |editor-first4=Manfred}}</ref>
*[[Telecommunications]], η stands for efficiency
*[[Electronics]], η stands for the [[ideality factor]] of a [[bipolar transistor]], and has a value close to 1.000.  It appears in contexts where the transistor is used as a temperature sensing device, e.g. the thermal "diode" transistor that is embedded within a computer's microprocessor.<ref>{{Cite book |title=Compound semiconductor electronics: the age of maturity |date=1996 |publisher=World Scientific Pub. Co |isbn=978-981-02-2325-0 |editor-last=Shur |editor-first=Michael |series=Selected topics in electronics and systems |location=Singapore River Edge, N.J |pages=115 |quote=The ideality factor of the base current, η {{sub|''B''}}, |editor-last2=World Scientific (Firm)}}</ref>
*[[Power electronics]], η stands for the efficiency of a [[power supply]], defined as the output power divided by the input power.<ref>{{Cite book |title=Springer Handbook of Power Systems |date=2021 |publisher=Springer |isbn=978-981-329-937-5 |editor-last=Papaēliu |editor-first=Kōstas |location=Singapore |pages=126}}</ref>
*[[Atmospheric science]], η represents [[Vorticity#Atmospheric sciences|absolute atmospheric vorticity]].<ref>{{Cite book |last=Riegel |first=Christopher A. |title=Fundamentals of atmospheric dynamics and thermodynamics |date=1992 |publisher=World Scientific |isbn=978-9971-978-86-0 |location=Singapore |pages=359 |quote=The vertical component of the absolute curl, which we shall simply call the ''absolute vorticity'', is η =...}}</ref>
*[[Rheology]], η represents [[viscosity]].<ref>{{Citation |last=Elert |first=Glenn |title=Special Symbols |date=2023 |work=The Physics Hypertextbook |quote= η viscosity, dynamic viscosity|url=https://physics.info/symbols/ |access-date=2025-02-01 |publisher=hypertextbook |language=en}}</ref>
*[[Oceanography]], η is the measurement (usually in metres) of sea-level height above or below the mean sea-level at that same location.

==Unicode==

* {{unichar|0370|html=}}
* {{unichar|0371|html=}}
* {{unichar|0397|html=}}
* {{unichar|03B7|html=}} ({{tt|\eta}} in TeX)
* {{unichar|2C8E|html=}}
* {{unichar|2C8F|html=}}

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:

* {{unichar|1D6AE|html=}}
* {{unichar|1D6C8|html=}}
* {{unichar|1D6E8|html=}}
* {{unichar|1D702|html=}}
* {{unichar|1D722|html=}}
* {{unichar|1D73C|html=}}
* {{unichar|1D75C|html=}}
* {{unichar|1D776|html=}}
* {{unichar|1D796|html=}}
* {{unichar|1D7B0|html=}}

==See also==
*[[Hurricane Eta]]

==References==
{{Wiktionary|Η|η}}
{{Reflist}}

[[Category:Greek letters]]
[[Category:Vowel letters]]