Eta (uppercase , lowercase ; grc, ἦτα ''ē̂ta'' or ell, ήτα ''ita'' ) is the seventh letter of the

Greek alphabet The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...

, representing the

close front unrounded vowel The close front unrounded vowel, or high front unrounded vowel, is a type of vowel sound that occurs in most spoken languages, represented in the International Phonetic Alphabet by the symbol i. It is similar to the vowel sound in the English ...

. Originally denoting the

voiceless glottal fricative The voiceless glottal fricative, sometimes called voiceless glottal transition, and sometimes called the aspirate, is a type of sound used in some spoken languages that patterns like a fricative or approximant consonant '' phonologically'', bu ...

in most dialects, its sound value in the classical

Attic dialect Attic Greek is the Greek dialect of the ancient region of Attica, including the ''polis'' of Athens. Often called classical Greek, it was the prestige dialect of the Greek world for centuries and remains the standard form of the language that ...

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic p ...

was a long

open-mid front unrounded vowel The open-mid front unrounded vowel, or low-mid front unrounded vowel, is a type of vowel sound used in some Speech communication, spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is a Latinised varia ...

, raised to in hellenistic Greek, a process known as

iotacism Iotacism ( el, ιωτακισμός, ''iotakismos'') or itacism is the process of vowel shift by which a number of vowels and diphthongs converged towards the pronunciation in post-classical Greek and Modern Greek. The term "iotacism" refers to ...

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 Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those ...

eta represents 8. Eta was derived from the Phoenician letter

heth Heth, sometimes written Chet, but more accurately Ḥet, is the eighth letter of the Semitic abjads, including Phoenician Ḥēt 𐤇 , Hebrew Ḥēth , Aramaic Ḥēth , Syriac Ḥēṯ ܚ, Arabic Ḥā' , and Maltese Ħ, ħ. Heth origina ...

. Letters that arose from eta include the Latin H and the Cyrillic letter И and Й.

History

Consonant h

The letter shape 'H' was originally used in most Greek dialects to represent the

. 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 Many local variants of the Greek alphabet were employed in ancient Greece during the archaic and early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms ...

), 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 In the polytonic orthography of Ancient Greek, the rough breathing ( grc, δασὺ πνεῦμα, dasỳ pneûma or ''daseîa''; la, spīritus asper) character is a diacritical mark used to indicate the presence of an sound before a vowel, ...

or ''spiritus asper'', which brought back the marking of the sound into the standardized post-classical (

polytonic Greek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography ( el, πολυτονικό σύστημα γραφής, translit=polytonikó sýstīma grafī́s), which includes fiv ...

) orthography.Nick Nicholas (2003), "Greek "

Dionysius Thrax Dionysius Thrax ( grc-gre, Διονύσιος ὁ Θρᾷξ ''Dionýsios ho Thrâix'', 170–90 BC) was a Greek grammarian and a pupil of Aristarchus of Samothrace. He was long considered to be the author of the earliest grammatical text on the Gre ...

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 Ionic Greek ( grc, Ἑλληνικὴ Ἰωνική, Hellēnikē Iōnikē) was a subdialect of the Attic–Ionic or Eastern dialect group of Ancient Greek. History The Ionic dialect appears to have originally spread from the Greek mainland acro ...

, 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 The open front unrounded vowel, or low front unrounded vowel, is a type of vowel sound used in some spoken languages. It is one of the eight primary cardinal vowels, not directly intended to correspond to a vowel sound of a specific language b ...

, which later merged in East Ionic with the long

instead. In 403 BC,

Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital city, capital and List of cities and towns in Greece, largest city of Greece. With a population close to four million, it is also the seventh List ...

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 Koine Greek (; Koine el, ἡ κοινὴ διάλεκτος, hē koinè diálektos, the common dialect; ), also known as Hellenistic Greek, common Attic, the Alexandrian dialect, Biblical Greek or New Testament Greek, was the common supra-reg ...

, the sound represented by eta was raised and merged with several other formerly distinct vowels, a phenomenon called ''iotacism'' or ''

itacism Iotacism ( el, ιωτακισμός, ''iotakismos'') or itacism is the process of vowel shift by which a number of vowels and diphthongs converged towards the pronunciation in post-classical Greek and Modern Greek. The term "iotacism" refers to ...

'', after the new pronunciation of the letter name as ''ita'' instead of ''eta''. Itacism is continued into

Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek (, ), refers collectively to the dialects of the Greek language spoken in the modern era, including the official standardized form of the ...

, where the letter name is pronounced and represents the

. 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 The Cyrillic script ( ), Slavonic script or the Slavic script, is a writing system used for various languages across Eurasia. It is the designated national script in various Slavic, Turkic, Mongolic, Uralic, Caucasian and Iranic-speaking cou ...

, where it gave rise to the Cyrillic letter И.

Uses

Letter

, due to

, the letter (pronounced ) represents a

, . In

Classical Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

, it represented the long

Symbol

Upper case

The uppercase letter Η is used as a symbol in

textual criticism Textual criticism is a branch of textual scholarship, philology, and of literary criticism that is concerned with the identification of textual variants, or different versions, of either manuscripts or of printed books. Such texts may range in ...

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 ...

(from Hesychius, its once-supposed editor). In chemistry, the letter H as symbol of

enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...

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 Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

of a discrete random variable.

Lower case

The lowercase letter η is used as a symbol in: *

Thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...

, the efficiency of a

Carnot heat engine A Carnot heat engine is a heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1 ...

, 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 identif ...

, the

propulsive efficiency In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency \eta is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accel ...

, or percentage of chemical energy converted to kinetic energy. * Chemistry, the

hapticity In coordination chemistry, hapticity is the coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms. The hapticity of a ligand is described with the Greek letter η ('eta'). For example, η2 describes a l ...

, 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 Palladium is a chemical element with the symbol Pd and atomic number 46. It is a rare and lustrous silvery-white metal discovered in 1803 by the English chemist William Hyde Wollaston. He named it after the asteroid Pallas, which was itself nam ...

in the η¹ mode (only one atom of an allyl group attached to palladium) or the η³ mode (3 atoms attached to palladium). *

Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultra ...

, the

electromagnetic impedance The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic ...

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 Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and ...

, 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 Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and b ...

, η stands for

pseudorapidity In experimental particle physics, pseudorapidity, \eta, is a commonly used spatial coordinate describing the angle of a particle relative to the beam axis. It is defined as :\eta \equiv -\ln\left tan\left(\frac\right)\right where \theta is the a ...

. *

Cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosophe ...

, 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 Elementary particle, particles could have traveled to the observation, ...

; dt = adη. *

, baryon–photon ratio. *

Relativity Relativity may refer to: Physics * Galilean relativity, Galileo's conception of relativity * Numerical relativity, a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativit ...

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 a ...

(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 allo ...

Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the ...

(flat spacetime). * Statistics, ''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 by ...

, and can also be used to denote the median of a population, or thresholding parameter in Sparse Partial Least Squares regression. *

Economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...

, ''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 Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, the seventh-brightest (usually) star in a constellation. ''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. T ...

. *Mathematics, η-reduction in lambda calculus. *Mathematics, the

Dirichlet eta function In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0: \eta(s) = \sum_^ = \frac - \frac + \frac - \frac + \c ...

Dedekind eta function In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string ...

, and

Weierstrass eta function In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and \wp functions is analogo ...

. *In category theory, 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 ...

monad Monad may refer to: Philosophy * Monad (philosophy), a term meaning "unit" **Monism, the concept of "one essence" in the metaphysical and theological theory ** Monad (Gnosticism), the most primal aspect of God in Gnosticism * ''Great Monad'', an ...

is usually denoted ''η''. *

Biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditar ...

, a

DNA polymerase A DNA polymerase is a member of a family of enzymes that catalyze the synthesis of DNA molecules from nucleoside triphosphates, the molecular precursors of DNA. These enzymes are essential for DNA replication and usually work in groups to create ...

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. Bact ...

and implicated in Translesion Synthesis. *

Neural network A neural network is a network or neural circuit, 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 ...

backpropagation In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions gener ...

, 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 In machine learning and statistics, the learning rate is a Hyperparameter (machine learning), tuning parameter in an Mathematical optimization, optimization algorithm that determines the step size at each iteration while moving toward a minimum of ...

. *

Telecommunications Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than tha ...

, η stands for efficiency *

Electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...

, η stands for the ideality factor of a

bipolar transistor A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipola ...

, 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 Power electronics is the application of electronics to the control and conversion of electric power. The first high-power electronic devices were made using mercury-arc valves. In modern systems, the conversion is performed with semiconducto ...

, η stands for the efficiency of a

power supply A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a ...

, defined as the output power divided by the input power. * Atmospheric science, η represents absolute atmospheric vorticity. *

Rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appli ...

, η represents

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

. * Oceanography, 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.

References

{{Reflist Greek letters Vowel letters