cantor

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Related to cantorial: Hazzanut, Chazanim

cantor

[Lat.,=singer], a singer or chanter, especially one who performs the solo chants of a church service. The office of cantor, at first an honorary one, originated in the Jewish synagogues, in which from early times it was the custom to appoint a lay member to represent the congregation in prayer. The notation of the chants was forbidden. In the 6th cent. poetic prayer forms were developed, and with them more complicated modes, or music, thus necessitating professional cantors. In the early Christian church, cantors known as precentors had charge of the musical part of the service. In modern Roman Catholic and Anglican services cantors sing the opening words of hymns and psalms.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Cantor

in the Catholic Church, a singer; in Protestant churches, a singing teacher, choir conductor, and organist, whose duties also often included the composition of music for the church (for example, J. S. Bach at St. Thomas in Leipzig). In a Jewish synagogue, the main singer, or hazan.

cantor

1. Judaism a man employed to lead synagogue services, esp to traditional modes and melodies
2. Christianity the leader of the singing in a church choir
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

Cantor

(person, mathematics)
A mathematician.

Cantor devised the diagonal proof of the uncountability of the real numbers:

Given a function, f, from the natural numbers to the real numbers, consider the real number r whose binary expansion is given as follows: for each natural number i, r's i-th digit is the complement of the i-th digit of f(i).

Thus, since r and f(i) differ in their i-th digits, r differs from any value taken by f. Therefore, f is not surjective (there are values of its result type which it cannot return).

Consequently, no function from the natural numbers to the reals is surjective. A further theorem dependent on the axiom of choice turns this result into the statement that the reals are uncountable.

This is just a special case of a diagonal proof that a function from a set to its power set cannot be surjective:

Let f be a function from a set S to its power set, P(S) and let U = { x in S: x not in f(x) }. Now, observe that any x in U is not in f(x), so U != f(x); and any x not in U is in f(x), so U != f(x): whence U is not in { f(x) : x in S }. But U is in P(S). Therefore, no function from a set to its power-set can be surjective.

Cantor

(language)
An object-oriented language with fine-grained concurrency.

[Athas, Caltech 1987. "Multicomputers: Message Passing Concurrent Computers", W. Athas et al, Computer 21(8):9-24 (Aug 1988)].
References in periodicals archive ?
After the opening, in which he does a perfect imitation of Al Jolson imitating a black singer, he lets loose with some remarkable cantorial passages in flawless mock-Hebrew, which eventually turns into scat-singing.
Music books range from Yiddish songbooks to cantorial anthologies to scores of musicals.
And, "partially to amuse myself and my dad but also to use in services," she said, she had started to write her own cantorial pieces.
"We are starting to see the phenomenon of artists beginning to tap into Jewish tradition and melding it with reggae, cantorial music, Sephardic and klezmer music," Loeffler says.
A related practice can be found in the performance of cantorial music in secular spaces normally reserved for aesthetic performances.
He dismissed synagogue liturgical music and the vocal styles of its cantorial singers as a travesty of song in divine service.
Goldfaden, lacking any musical training but, by his own assertion, possessing a wide knowledge of Jewish and classical music, borrowed heavily from cantorial and folk sources and from European opera for the songs that he included in his operettas.
At the same time, the rapidly expanding Reform summer-camp movement offered a forum for young Jewish musicians with a taste for socially conscious folksong to experiment with material that owed more to Joan Baez and Bob Dylan than it did to traditional hazzanut, or cantorial performance.
(2) The modern Yiddish stage, on the other hand, has been infused since its inception with religious rituals, and an objection to the staging of ceremonies such as the lighting of the Sabbath candles or the performance of cantorial music, and especially of the ever-popular wedding scene, would be incomprehensible to its practitioners and spectators.
In fact, as Israeli musicologists Motti Regev and Edwin Seroussi point out in Popular Music and National Culture in Israel, by 1952, the entire catalog of Hed Arzi, the largest Israeli record label at the time, consisted of a total of 22 songs, "a mixture of Shirei Eretz Yisrael, original songs in trendy pop styles (rhumba, swing, tango, and so on) and translations of foreign songs in the same vein," in addition to a few cantorial numbers.
Robeson had speculated on black-Jewish musicological connections as early as 1927, when an interviewer for the Jewish Tribune, Sulamith Ish-Kishor, claimed to notice a similarity between his rendition of "Rock Me, Rock Me" and "Jewish synagogue music." (37) While diplomatically sidestepping Ish-Kishor's fanciful speculation that Negroes had learned to sing spirituals by overhearing the Jewish cantorial music of antebellum New Orleans, Robeson seized the opportunity to dilate upon the influence exerted on blacks by the Hebrew Bible.
Also of interest to the uninitiated are the four chapters in "Bible, Liturgy, and Cantorial Art," which offer general introductory information on biblical cantillation, liturgical music performance through the nineteenth century, cantorial art, and the Jewish liturgical calendar, respectively.

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