Etymology
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a (1)

indefinite article, form of an used before consonants, mid-12c., a weakened form of Old English an "one" (see an). The disappearance of the -n- before consonants was mostly complete by mid-14c. After c. 1600 the -n- also began to vanish before words beginning with a sounded -h-; it still is retained by many writers before unaccented syllables in h- or (e)u- but is now no longer normally spoken as such. The -n- also lingered (especially in southern England dialect) before -w- and -y- through 15c.

It also is used before nouns of singular number and a few plural nouns when few or great many is interposed.

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a (2)
as in twice a day, etc., a reduced form of Old English an "on" (see on (prep.)), in this case "on each." The sense was extended from time to measure, price, place, etc. The habit of tacking a onto a gerund (as in a-hunting we will go) was archaic after 18c.
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A 

first letter of the Roman alphabet, based on Greek alpha (see alpha). In music from c. 1600 as the name of the sixth note of the natural scale; it is the note given by a fixed-tone instrument (usually oboe or organ) to which all the instruments of an orchestra are tuned. As a blood type, 1926, denoting A agglutinogens. The A side of a two-sided record (by 1962, see side (n.)) held the material chosen for promotion. A-bomb, short for atom bomb, was in newspaper headlines by Aug. 8, 1945.

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a- (1)

prefix or inseparable particle, a relic of various Germanic and Latin elements.

In words derived from Old English, it commonly represents Old English an "on, in, into" (see on (prep.)), as in alive, above, asleep, aback, abroad, afoot, ashore, ahead, abed, aside, obsolete arank "in rank and file," etc., forming adjectives and adverbs from nouns, with the notion "in, at; engaged in." In this use it is identical to a (2).

It also can represent Middle English of (prep.) "off, from," as in anew, afresh, akin, abreast. Or it can be a reduced form of the Old English past participle prefix ge-, as in aware.

Or it can be the Old English intensive a-, originally ar- (cognate with German er- and probably implying originally "motion away from"), as in abide, arise, awake, ashamed, marking a verb as momentary, a single event. Such words sometimes were refashioned in early modern English as though the prefix were Latin (accursed, allay, affright are examples).

In words from Romanic languages, often it represents reduced forms of Latin ad "to, toward; for" (see ad-), or ab "from, away, off" (see ab-); both of which by about 7c. had been reduced to a in the ancestor of Old French. In a few cases it represents Latin ex.

[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]
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-a (1)
word-forming element which in English is characteristic of fem. nouns and adjectives of Latin or Greek origin (such as idea, coma, mania, basilica, arena, formula, nebula). From Latin -a (plural -ae) and Greek -a, (plural -ai, Latinized as -ae). The Latin suffix also became Italian -a (plural -e), Spanish -a (plural -as). It is represented in Old English by -u, -e, but even then the suffix was fading and by the time of modern English was totally lost or swallowed into silent final -e-.

It also appears in Romanic words from Latin that have been borrowed into English, such as opera, plaza, armada. It figures in scientific names coined in Modern Latin (amoeba, soda, magnolia, etc.) and is common in geographical names formed according to Latin or Greek models (Asia, Africa, America, Arabia, Florida, etc.)

In English it marks sex only in personal names (Julia, Maria, Alberta) and in a few words from Italian or Spanish where a corresponding male form also is in use (donna, senora).
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-a (2)
nominative neuter plural ending of certain nouns and adjectives in Latin and Greek that have been adopted into English (phenomena, data, media, criteria, etc.). It also is common in biology in Modern Latin formations of class names (Mammalia, Reptilia, Crustacea).
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a- (2)
word-forming element meaning "away," from Latin a "off, of, away from," the usual form of Latin ab before consonants (see ab-). As in avert, avocation. It is also the a in a priori and the à in Thomas à Kempis, Thomas à Becket.
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a- (3)
prefix meaning "not, without," from Greek a-, an- "not" (the "alpha privative"), from PIE root *ne- "not" (source also of English un-).

In words from Greek, such as abysmal, adamant, amethyst; also partly nativized as a prefix of negation (asexual, amoral, agnostic). The ancient alpha privatum, denoting want or absence.

Greek also had an alpha copulativum, a- or ha-, expressing union or likeness, which is the a- expressing "together" in acolyte, acoustic, Adelphi, etc. It is from PIE root *sem- (1) "one; as one, together with."
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a cappella 

1868, earlier alla capella (1824), from Italian, "in the style of Church music, in the manner of the chapel," literally "according to the chapel," from cappella "chapel" (see chapel). Originally in reference to older church music (pre-1600) which was written for unaccompanied voices; applied 20c. to unaccompanied vocal music generally. Italian a is from Latin ad "to, toward; for; according to" (see ad-); alla is a la "to the." Sometimes in the Latin form a capella.

Also denoting "that instruments are to play in unison with the voices, or that one part is to be played by a number instruments." ["Chambers's' Encyclopaedia," 1868]

You are not the first person puzzled by the expression "A Capella," or, at any rate, unable to understand it should signify the exact reverse of what it literally does signify. The chorales in oratorios were invariably accompanied, either by double-bass or the whole band. Hence they were, with perfect correctness, said to be performed "a capella." But, as other chorales, sung as part of the church service, were written in the same and simple style the expression "a capella" came in time to be applied to them also, despite their being sung without any instrumental accompaniment whatever. [The Music World, Sept. 11, 1875]
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a deux 
French, à deux, literally "for two," from à, from Latin ad "to, toward; for" (see ad-) + deux (see deuce). By 1876 as a French term in English.
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