Eta

Eta /ˈiːtə, ˈeɪtə/ EE-tə, AY-tə^[1] (uppercase Η, lowercase η; Ancient Greek: ἦτα ē̂ta [ɛ̂ːta] or Greek: ήτα ita [ˈita]) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel IPA: [i]. Originally denoting the voiceless glottal fricative IPA: [h] in most dialects, its sound value in the classical Attic dialect of Ancient Greek was a long open-mid front unrounded vowel IPA: [ɛː], raised to IPA: [i] 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 "Η", because it was the initial of ΗΕΚΑΤΟΝ, the ancient spelling of ἑκατόν = "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 letters И and Й.

History

Consonant h

The letter shape 'H' was originally used in most Greek dialects to represent the voiceless glottal fricative IPA: [h]. 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 IPA: [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 Heracleia and 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: [h] sound into the standardized post-classical (polytonic) orthography.^[2] 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."^[3]

Long e

In the East Ionic dialect, however, the sound IPA: [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: [aː], which later merged in East Ionic with the long open-mid front unrounded vowel IPA: [ɛː] instead.^[4] 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: [h] 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 IPA: [ɛː] 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 [ˈita] and represents the close front unrounded vowel IPA: [i]. 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 [i] into the Cyrillic script, where it gave rise to the Cyrillic letter И.

Uses

Letter

In Modern Greek, due to iotacism, the letter (pronounced [ˈita]) represents a close front unrounded vowel, IPA: [i]. In Classical Greek, it represented the long open-mid front unrounded vowel IPA: [ɛː].

Symbol

Upper case

The uppercase letter Η is used as a symbol in textual criticism for the Alexandrian text-type (from 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 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, 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 mesons.
Experimental particle physics, η stands for pseudorapidity.
Cosmology, η represents conformal time; dt = adη.
Cosmology, baryon–photon ratio.
Relativity and Quantum field theory (physics), η (with two subscripts) represents the metric tensor of Minkowski space (flat spacetime).
Statistics, η² 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.
Astronomy, the seventh-brightest (usually) star in a constellation. See Bayer designation.
Mathematics, η-reduction in lambda calculus.
Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass eta function.
In category theory, the unit of an adjunction or monad is usually denoted η.
Biology, a DNA polymerase found in higher eukaryotes and implicated in Translesion Synthesis.
Neural network backpropagation, and stochastic gradient descent 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, η represents absolute atmospheric vorticity.
Rheology, η represents viscosity.
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

Character information
Preview	Η		η		Ͱ		ͱ		Ⲏ		ⲏ
Unicode name	GREEK CAPITAL LETTER ETA		GREEK SMALL LETTER ETA		GREEK CAPITAL LETTER HETA		GREEK SMALL LETTER HETA		COPTIC CAPITAL LETTER AYTA		COPTIC SMALL LETTER AYTA
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	919	U+0397	951	U+03B7	880	U+0370	881	U+0371	11406	U+2C8E	11407	U+2C8F
UTF-8	206 151	CE 97	206 183	CE B7	205 176	CD B0	205 177	CD B1	226 178 142	E2 B2 8E	226 178 143	E2 B2 8F
Numeric character reference	Η	Η	η	η	Ͱ	Ͱ	ͱ	ͱ	Ⲏ	Ⲏ	ⲏ	ⲏ
Named character reference	Η		η
DOS Greek	134	86	158	9E
DOS Greek-2	170	AA	225	E1
Windows 1253	199	C7	231	E7
TeX			\eta

Mathematical Eta

Character information
Preview	𝚮		𝛈		𝛨		𝜂		𝜢		𝜼
Unicode name	MATHEMATICAL BOLD CAPITAL ETA		MATHEMATICAL BOLD SMALL ETA		MATHEMATICAL ITALIC CAPITAL ETA		MATHEMATICAL ITALIC SMALL ETA		MATHEMATICAL BOLD ITALIC CAPITAL ETA		MATHEMATICAL BOLD ITALIC SMALL ETA
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex	dec	hex	dec	hex
Unicode	120494	U+1D6AE	120520	U+1D6C8	120552	U+1D6E8	120578	U+1D702	120610	U+1D722	120636	U+1D73C
UTF-8	240 157 154 174	F0 9D 9A AE	240 157 155 136	F0 9D 9B 88	240 157 155 168	F0 9D 9B A8	240 157 156 130	F0 9D 9C 82	240 157 156 162	F0 9D 9C A2	240 157 156 188	F0 9D 9C BC
UTF-16	55349 57006	D835 DEAE	55349 57032	D835 DEC8	55349 57064	D835 DEE8	55349 57090	D835 DF02	55349 57122	D835 DF22	55349 57148	D835 DF3C
Numeric character reference	𝚮	𝚮	𝛈	𝛈	𝛨	𝛨	𝜂	𝜂	𝜢	𝜢	𝜼	𝜼

Character information
Preview	𝝜		𝝶		𝞖		𝞰
Unicode name	MATHEMATICAL SANS-SERIF BOLD CAPITAL ETA		MATHEMATICAL SANS-SERIF BOLD SMALL ETA		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL ETA		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL ETA
Encodings	decimal	hex	dec	hex	dec	hex	dec	hex
Unicode	120668	U+1D75C	120694	U+1D776	120726	U+1D796	120752	U+1D7B0
UTF-8	240 157 157 156	F0 9D 9D 9C	240 157 157 182	F0 9D 9D B6	240 157 158 150	F0 9D 9E 96	240 157 158 176	F0 9D 9E B0
UTF-16	55349 57180	D835 DF5C	55349 57206	D835 DF76	55349 57238	D835 DF96	55349 57264	D835 DFB0
Numeric character reference	𝝜	𝝜	𝝶	𝝶	𝞖	𝞖	𝞰	𝞰

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

^ "eta". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
^ Nick Nicholas (2003), "Greek /h/" Archived 2013-09-01 at archive.today
^ 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.
^ Sihler, Andrew L. (1995). New Comparative Grammar of Greek and Latin (illustrated ed.). New York: Oxford University Press. pp. 10–20. ISBN 0-19-508345-8.

[1] "eta". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)

[Nicholas-2] Nick Nicholas (2003), "Greek /h/" Archived 2013-09-01 at archive.today

[3] 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.

[4] Sihler, Andrew L. (1995). New Comparative Grammar of Greek and Latin (illustrated ed.). New York: Oxford University Press. pp. 10–20. ISBN 0-19-508345-8.

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