Eta (letter)
Encyclopedia
Eta ) is the seventh letter of the Greek alphabet
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

. Originally denoting a consonant
Heta (letter)
Heta is a conventional name for the historical Greek alphabet letter Eta and several of its variants when used in their original function of denoting the consonant /h/. The letter Η had been adopted by Greek from the Phoenician letter Heth originally with this consonantal sound value, and Hēta...

 /h/, its sound value in the classical Attic dialect
Attic Greek
Attic Greek is the prestige dialect of Ancient Greek that was spoken in Attica, which includes Athens. Of the ancient dialects, it is the most similar to later Greek, and is the standard form of the language studied in courses of "Ancient Greek". It is sometimes included in Ionic.- Origin and range...

 of Ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

 was a long vowel [ɛː], raised to i in medieval Greek
Medieval Greek
Medieval Greek, also known as Byzantine Greek, is the stage of the Greek language between the beginning of the Middle Ages around 600 and the Ottoman conquest of the city of Constantinople in 1453. The latter date marked the end of the Middle Ages in Southeast Europe...

, a process known as itacism.

In the system of Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

 it has a value of 8. Letters that arose from Eta include the Latin H
H
H .) is the eighth letter in the basic modern Latin alphabet.-History:The Semitic letter ⟨ח⟩ most likely represented the voiceless pharyngeal fricative . The form of the letter probably stood for a fence or posts....

 and the Cyrillic
Cyrillic alphabet
The Cyrillic script or azbuka is an alphabetic writing system developed in the First Bulgarian Empire during the 10th century AD at the Preslav Literary School...

 letter И
I (Cyrillic)
I is a letter used in almost all ancient and modern Cyrillic alphabets.It commonly represents the close front unrounded vowel , like the pronunciation of ⟨i⟩ in "machine", or the near-close near-front unrounded vowel , like the pronunciation of ⟨i⟩ in "bin".-History:The Cyrillic letter I was...

.

Consonant h

The letter shape H was originally used in most Greek dialects to represent the sound /h/, a voiceless glottal fricative
Voiceless glottal fricative
The voiceless glottal transition, commonly called a "fricative", is a type of sound used in some spoken languages which patterns like a fricative or approximant consonant phonologically, but often lacks the usual phonetic characteristics of a consonant...

. In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic alphabets
Old Italic alphabet
Old Italic refers to several now extinct alphabet systems used on the Italian Peninsula in ancient times for various Indo-European languages and non-Indo-European languages...

, which were based on the Euboean form of the Greek alphabet. This ultimately gave rise to the Latin alphabet with its letter H
H
H .) is the eighth letter in the basic modern Latin alphabet.-History:The Semitic letter ⟨ח⟩ most likely represented the voiceless pharyngeal fricative . The form of the letter probably stood for a fence or posts....

.

Long e

In the East Ionic dialect, however, the sound /h/ disappeared by the sixth century BC, and the letter was re-used initially to represent a development of a long vowel /aː/, which later merged in East Ionic with /ɛː/ instead. In 403 BC, Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...

 took over the Ionian spelling system and with it the vocalic use of H (even though it still also had the /h/ sound itself at that time). This later became the standard orthography in all of Greece.

Other regional variants of the Greek alphabet (epichoric alphabets), in dialects that still preserved the sound /h/, employed various glyph shapes for consonantal Heta side by side with the new vocalic Eta for some time. One of them was a tack-like shape, looking like the left half of an H. This system was first used in the southern Italian colonies of Heracleia and Tarentum. When Greek orthography was codified by grammarians in the Hellenistic era, they used a diacritic
Diacritic
A diacritic is a glyph added to a letter, or basic glyph. The term derives from the Greek διακριτικός . Diacritic is both an adjective and a noun, whereas diacritical is only an adjective. Some diacritical marks, such as the acute and grave are often called accents...

 symbol derived from this half-H shape to signal the presence of /h/, and added as its counterpart a reverse-shaped diacritic to denote absence of /h/. These symbols were the origin of the rough breathing and smooth breathing diacritics that became part of classical Greek orthography. The tack symbol has been reintroduced into modern scholarly representation of archaic Greek writing under the name of Heta
Heta (letter)
Heta is a conventional name for the historical Greek alphabet letter Eta and several of its variants when used in their original function of denoting the consonant /h/. The letter Η had been adopted by Greek from the Phoenician letter Heth originally with this consonantal sound value, and Hēta...

.

Iotacism

During the time of post-classical Koiné Greek
Koine Greek
Koine Greek is the universal dialect of the Greek language spoken throughout post-Classical antiquity , developing from the Attic dialect, with admixture of elements especially from Ionic....

, the /ɛː/ sound represented by eta was raised and merged with several other formerly distinct vowels (iotacism
Iotacism
Iotacism is the process by which a number of vowels and diphthongs in Ancient Greek converged in pronunciation so that they all sound like iota in Modern Greek....

). Thus in Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

, Eta is pronounced [ˈita] and represents the sound /i/ (a close front unrounded vowel
Close front unrounded vowel
The close front unrounded vowel, or high front unrounded vowel, is a type of vowel sound, used in many spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is ....

). It shares this function with several other letters (ι
Iota
Iota is the ninth letter of the Greek alphabet. In the system of Greek numerals it has a value of 10. It was derived from the Phoenician letter Yodh . Letters that arose from this letter include the Roman I and J and the Cyrillic І , Yi , Je , and iotified letters .Iota represents...

, υ
Upsilon
Upsilon is the 20th letter of the Greek alphabet.  In the system of Greek numerals it has a value of 400. It is derived from the Phoenician waw. The name of the letter is pronounced in Modern Greek, and in English , , or...

) and digraphs
Digraph (orthography)
A digraph or digram is a pair of characters used to write one phoneme or a sequence of phonemes that does not correspond to the normal values of the two characters combined...

 (ει, οι), which are all pronounced alike (see iotacism
Iotacism
Iotacism is the process by which a number of vowels and diphthongs in Ancient Greek converged in pronunciation so that they all sound like iota in Modern Greek....

).

Cyrillic alphabet

Eta was also borrowed with the sound value of [i] into the Cyrillic alphabet
Cyrillic alphabet
The Cyrillic script or azbuka is an alphabetic writing system developed in the First Bulgarian Empire during the 10th century AD at the Preslav Literary School...

, where it gave rise to the Cyrillic letter И
I (Cyrillic)
I is a letter used in almost all ancient and modern Cyrillic alphabets.It commonly represents the close front unrounded vowel , like the pronunciation of ⟨i⟩ in "machine", or the near-close near-front unrounded vowel , like the pronunciation of ⟨i⟩ in "bin".-History:The Cyrillic letter I was...

.

Letter

In Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

 the letter, pronounced ˈita, represents a close front unrounded vowel
Close front unrounded vowel
The close front unrounded vowel, or high front unrounded vowel, is a type of vowel sound, used in many spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is ....

, /i/. In Classical Greek, it represented a long open-mid front unrounded vowel, /ɛː/.

Upper case

The upper-case letter Η is used as a symbol in textual criticism
Textual criticism
Textual criticism is a branch of literary criticism that is concerned with the identification and removal of transcription errors in the texts of manuscripts...

 for the Alexandrian text-type
Alexandrian text-type
The Alexandrian text-type , associated with Alexandria, is one of several text-types used in New Testament textual criticism to describe and group the textual character of biblical manuscripts...

 (from Hesychius
Hesychius of Alexandria
Hesychius of Alexandria , a grammarian who flourished probably in the 5th century CE, compiled the richest lexicon of unusual and obscure Greek words that has survived...

, its once-supposed editor).

In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, the letter H as symbol of enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

 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
H
H .) is the eighth letter in the basic modern Latin alphabet.-History:The Semitic letter ⟨ח⟩ most likely represented the voiceless pharyngeal fricative . The form of the letter probably stood for a fence or posts....

 for 'heat'.

Lower case

The lower-case letter η is used as a symbol in:
  • Thermodynamics
    Thermodynamics
    Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

    , the efficiency of a Carnot heat engine
    Carnot heat engine
    A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

    .
  • Chemistry
    Chemistry
    Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

    , the hapticity
    Hapticity
    The term hapticity is used to describe how a group of contiguous atoms of a ligand are coordinated to a central atom. Hapticity of a ligand is indicated by the Greek character 'eta', η. A superscripted number following the η denotes the number of contiguous atoms of the ligand that are bound to...

    , 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
    Palladium
    Palladium is a chemical element with the chemical symbol Pd and an atomic number of 46. It is a rare and lustrous silvery-white metal discovered in 1803 by William Hyde Wollaston. He named it after the asteroid Pallas, which was itself named after the epithet of the Greek goddess Athena, acquired...

     in the η¹ mode (only one atom of a allyl group attached to palladium)or the η³ mode (3 atoms attached to palladium).
  • Optics
    Optics
    Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

    , the electromagnetic impedance of a medium, or the quantum efficiency
    Quantum efficiency
    Quantum efficiency is a quantity defined for a photosensitive device such as photographic film or a charge-coupled device as the percentage of photons hitting the photoreactive surface that will produce an electron–hole pair. It is an accurate measurement of the device's electrical sensitivity to...

     of detectors.
  • Particle physics
    Particle physics
    Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

    , to represent the η mesons.
  • Experimental particle physics
    Particle physics
    Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

    , η stands for pseudorapidity.
  • Quantum field theory
    Quantum field theory
    Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

     (physics), to represent the metric tensor
    Metric tensor
    In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...

    .
  • Statistics
    Statistics
    Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

    , η2 is the "partial regression coefficient". η is the symbol for the linear predictor of a generalized linear model
    Generalized linear model
    In statistics, the generalized linear model 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 allowing the magnitude of the variance of each measurement to...

    , and can also be used to denote the median of a population.
  • Economics
    Economics
    Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

    , η is the elasticity
    Elasticity (economics)
    In economics, elasticity is the measurement of how changing one economic variable affects others. For example:* "If I lower the price of my product, how much more will I sell?"* "If I raise the price, how much less will I sell?"...

    .
  • Astronomy
    Astronomy
    Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

    , the seventh brightest (usually) star in a constellation
    Constellation
    In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....

    . See Bayer designation
    Bayer designation
    A Bayer designation is a stellar designation in which a specific star is identified by a Greek letter, followed by the genitive form of its parent constellation's Latin name...

    .
  • Mathematics, η-conversion, see lambda calculus
  • Mathematics, the Dirichlet eta function, Dedekind eta function
    Dedekind eta function
    The Dedekind eta function, named after Richard Dedekind, is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive...

    , and Weierstrass eta function.
  • Biology
    Biology
    Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

    , a DNA polymerase
    DNA polymerase
    A DNA polymerase is an enzyme that helps catalyze in the polymerization of deoxyribonucleotides into a DNA strand. DNA polymerases are best known for their feedback role in DNA replication, in which the polymerase "reads" an intact DNA strand as a template and uses it to synthesize the new strand....

     found in higher eukaryotes and implicated in Translesion Synthesis.
  • Neural network
    Neural network
    The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...

     backpropagation
    Backpropagation
    Backpropagation is a common method of teaching artificial neural networks how to perform a given task. Arthur E. Bryson and Yu-Chi Ho described it as a multi-stage dynamic system optimization method in 1969 . It wasn't until 1974 and later, when applied in the context of neural networks and...

    , η stands for the learning rate.
  • Telecommunications, Eta stands for efficiency
  • Electronics
    Electronics
    Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

    , 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
    Power electronics
    Power electronics is the application of solid-state electronics for the control and conversion of electric power.-Introduction:Power electronic converters can be found wherever there is a need to modify a form of electrical energy...

    , η stands for the efficiency of a power supply
    Power supply
    A power supply is a device that supplies electrical energy to one or more electric loads. The term is most commonly applied to devices that convert one form of electrical energy to another, though it may also refer to devices that convert another form of energy to electrical energy...

    , defined as the output power divided by the input power.
  • Atmospheric science, η represents absolute atmospheric vorticity.
  • Rheology
    Rheology
    Rheology is the study of the flow of matter, primarily in the liquid 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 applied force....

    , η represents viscosity
    Viscosity
    Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

    .
  • Relativity
    Theory of relativity
    The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

    , η (with two subscripts) represents the metric tensor
    Metric tensor (general relativity)
    In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...

     of Minkowski space
    Minkowski space
    In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...

     (flat spacetime).
  • Oceanography
    Oceanography
    Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

    , η is the measurement (usually in metres) of sea-level height above or below the mean sea-level at that same location.
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