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Eta (uppercase , lowercase ; grc, ἦτα ''ē̂ta'' or ell, ήτα ''ita'' ) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel . Originally denoting the voiceless glottal fricative in most dialects, its sound value in the classical Attic dialect of Ancient Greek was a long open-mid front unrounded vowel , raised to in hellenistic Greek, a process known as iotacism or itacism. In the ancient Attic number system (Herodianic or acrophonic numbers), the number 100 was represented by "", because it was the initial of , the ancient spelling of = "one hundred". In the later system of (Classical) Greek numerals eta represents 8. Eta was derived from the Phoenician letter heth . Letters that arose from eta include the Latin H and the
Cyrillic , bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця , fam1 = Egyptian hieroglyphs , fam2 = Proto-Sinaitic , fam3 = Phoenician , fam4 = G ...
letter И and Й.


History


Consonant h

The letter shape 'H' was originally used in most Greek dialects to represent the voiceless glottal fricative . In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic alphabets, which were based on the 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 , employed various glyph shapes for consonantal ''heta'' side by side with the new vocalic ''eta'' for some time. In the southern Italian colonies of Heracleia and
Tarentum Tarentum may refer to: * Taranto, Apulia, Italy, on the site of the ancient Roman city of Tarentum (formerly the Greek colony of Taras) **See also History of Taranto * Tarentum (Campus Martius), also Terentum, an area in or on the edge of the Cam ...
, 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 sound into the standardized post-classical ( polytonic) orthography.Nick Nicholas (2003), "Greek "
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."


Long e

In the East Ionic dialect, however, the sound disappeared by the sixth century BC, and the letter was re-used initially to represent a development of a long open front unrounded vowel , which later merged in East Ionic with the long open-mid front unrounded vowel instead. 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 sound itself at that time). This later became the standard orthography in all of Greece.


Itacism

During the time of post-classical Koiné Greek, the sound represented by eta was 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 and represents the close front unrounded vowel . It shares this function with several other letters ( ι, υ) and digraphs (ει, οι), which are all pronounced alike.


Cyrillic script

Eta was also borrowed with the sound value of into the Cyrillic script, where it gave rise to the Cyrillic letter И.


Uses


Letter

In Modern Greek, due to iotacism, the letter (pronounced ) represents a close front unrounded vowel, . In Classical Greek, it represented the long open-mid front unrounded vowel .


Symbol


Upper case

The uppercase letter Η is used as a symbol in textual criticism for the
Alexandrian text-type In textual criticism of the New Testament, the Alexandrian text-type is one of the main text types. It is the text type favored by the majority of modern textual critics and it is the basis for most modern (after 1900) Bible translations. Over 5,8 ...
(from Hesychius, its once-supposed editor). In
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, 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 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, or packing fraction. *
Aeronautics Aeronautics is the science or art involved with the study, design, and manufacturing of air flight–capable machines, and the techniques of operating aircraft and rockets within the atmosphere. The British Royal Aeronautical Society identifies ...
, the propulsive efficiency, or percentage of chemical energy converted to kinetic energy. *
Chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, the hapticity, or the number of atoms of a ligand attached to one coordination site of the metal in a
coordination compound A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...
. For example, an
allyl group In organic chemistry, an allyl group is a substituent with the structural formula , where R is the rest of the molecule. It consists of a methylene bridge () attached to a vinyl group (). The name is derived from the scientific name for garlic, ...
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 The term quantum efficiency (QE) may apply to incident photon to converted electron (IPCE) ratio of a photosensitive device, or it may refer to the TMR effect of a Magnetic Tunnel Junction. This article deals with the term as a measurement of ...
of detectors. * Particle physics, to represent the
η meson The eta () and eta prime meson () are isosinglet mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson () and bottom eta meson () are similar forms of quarkonium; they have the same spin and parity ...
s. * Experimental particle physics, η stands for pseudorapidity. * Cosmology, η represents
conformal time The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the univers ...
; dt = adη. * Cosmology, baryon–photon ratio. * Relativity and
Quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
(physics), η (with two subscripts) represents the
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
of Minkowski space (flat spacetime). *
Statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, ''η''2 is the "partial regression coefficient". ''η'' is the symbol for the linear predictor of a
generalized linear model In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and b ...
, 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 Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...
. * Astronomy, the seventh-brightest (usually) star in a
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the e ...
. ''See''
Bayer designation A Bayer designation is a stellar designation in which a specific star is identified by a Greek or Latin letter followed by the genitive form of its parent constellation's Latin name. The original list of Bayer designations contained 1,564 stars. ...
. *Mathematics, η-reduction in lambda calculus. *Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass eta function. *In
category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
, the unit of an
adjunction In mathematics, the term ''adjoint'' applies in several situations. Several of these share a similar formalism: if ''A'' is adjoint to ''B'', then there is typically some formula of the type :(''Ax'', ''y'') = (''x'', ''By''). Specifically, adjoin ...
or monad is usually denoted ''η''. * Biology, a DNA polymerase found in higher
eukaryotes Eukaryotes () are organisms whose cells have a nucleus. All animals, plants, fungi, and many unicellular organisms, are Eukaryotes. They belong to the group of organisms Eukaryota or Eukarya, which is one of the three domains of life. Bacte ...
and implicated in Translesion Synthesis. *
Neural network A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...
backpropagation, and
stochastic gradient descent Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of ...
more generally, η stands for the learning rate. * 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. * Power electronics, η stands for the efficiency of a power supply, defined as the output power divided by the input power. *
Atmospheric science Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climat ...
, η represents absolute atmospheric vorticity. * Rheology, η represents viscosity. *
Oceanography Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynamic ...
, η is the measurement (usually in metres) of sea-level height above or below the mean sea-level at that same location.


Character encodings


Greek Eta, Coptic Ayta


Mathematical Eta

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

* Hurricane Eta


References

{{Reflist Greek letters Vowel letters