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The Order of Mass[1] (Latin Ordo Missae), also called the Ordinary of the Mass, is the set of texts of the Roman Rite Mass that are generally invariable. This contrasts with the proper, which are items of the Mass that change with the feast or following the Liturgical Year. The Order of Mass is printed in the Roman Missal as a distinct section placed in the middle of the book, between the Mass of the Easter Vigil and that of Easter Sunday in pre-1970 editions, and between the Proper of the Seasons and the Proper of the Saints thereafter.
Traditional choral texts [link]
The following texts, if not sung by the whole congregation, are traditionally sung by a choir. The texts are invariable except for the Tridentine Mass Agnus Dei.
- Kyrie eleison ("Lord, have mercy")
- Gloria ("Glory to God in the highest")
- Credo ("I believe in one God"), the Nicene Creed
- Sanctus ("Holy, Holy, Holy"), the second part of which, beginning with the word "Benedictus" ("Blessed is he"), was often sung separately after the consecration, if the setting was long. (See Benedictus for other chants beginning with that word.)
- Agnus Dei ("Lamb of God")
The Kyrie eleison was traditionally sung in Greek, the others in Latin. But the use of other languages, once a rare privilege only given to the Slavs of Dalmatia (in present day Croatia) who used Old Church Slavonic written in Glagolitic characters, is now more common than the use of Latin and Greek.
Prior to the Council of Trent the Kyrie was frequently troped; indeed English renaissance composers seem to have regarded the Sarum rite Kyrie as part of the propers and begin their mass settings with the Gloria.
The Kyrie, Sanctus, and Agnus Dei are part of every Mass. Until the 1970 revision of the Roman Missal, the Agnus Dei was modified for Requiem Masses, and prayed not miserere nobis (have mercy on us) and dona nobis pacem (grant us peace), but dona eis requiem (grant them rest) and dona eis requiem sempiternam (grant them eternal rest).
The Gloria is reserved for Masses of Sundays, solemnities and feasts, with the exception of Sundays within the penitential season of Lent (to which, before 1970, were added the Ember Days occurring four times a year, and the pre-Lenten season that began with Septuagesima), and the season of Advent (when it is held back as preparation for Christmas). It is omitted at weekday Masses (called Ferias) and memorials, and at requiem and votive Masses, but is generally used also at ritual Masses celebrated on occasions such as the administration of another sacrament, a religious profession or the blessing of a church.
The Credo is used on all Sundays and solemnities. Until simplified by Pope Pius XII in 1956, the rules (some 400 words in Section XI of the Rubricae generales Missalis) were much more complicated, listing, among other Masses, those of Doctors of the Church, those celebrated during octaves and certain votive Masses.
During the Middle Ages it was common in certain uses of the Roman Rite (such as the Sarum Use) to add tropes to the Kyrie. The tropes were essentially texts particular to a specific feast day interpolated between the lines of the Kyrie. The 1970 revision of the Roman Missal has extended the availability of this practice to all Masses (though in a different way.)
It was at one time popular to replace at a Solemn Mass the second half of the Sanctus (the Benedictus) with hymns such as the O Salutaris Hostia, or, at requiems, with a musical setting of the final invocation of the Dies Irae: "Pie Jesu Domine, dona eis requiem."
The phrase Ite, missa est "Go, it is the dismissal" (referring to the congregation) is the final part of the Order of Massa in the post-Tridentine Mass, but is omitted if another function follows immediately. In the Tridentine Mass, it was followed by a private prayer that the priest said silently for himself, by the final blessing, and by the reading of the Last Gospel (usually John 1:1-14), and in some Masses it was replaced by Benedicamus Domino or Requiescant in pace. These phrases are sung to music given in the Missal, as is the choir's response, Deo gratias or (after Requiescant in pace) Amen. Because of their brevity, the responses have seldom been set to polyphonic music except in early Masses such as the Messe de Nostre Dame by Machaut). The same holds for other short sung responses, such as Et cum spiritu, Gloria tibi, Domine, Habemus ad Dominum, and Dignum et iustum est.
The texts of the Order of Mass other than the five main choir parts can be grouped as follows:
- The Tridentine-Mass Prayers at the Foot of the Altar or, post-1970, the Penitential Rite.
- The prayers said in connection with the Scripture readings.
- The Offertory prayers.
- The Canon of the Mass, or Eucharistic Prayer, with its opening dialogue and its Preface, the latter of which, in spite of being variable, is included in the Order of Mass.
- The Our Father and the following prayers, leading to the priest's communion, to which since 1970 is added the communion of the people, previously not part of the Order of Mass. (The prescribed rite for the distribution of Communion – which Pope John XXIII shortened slightly by omission of the Confiteor and Absolution – was often printed within or after the Order of Mass in missals for use by the faithful, but not in the Roman Missal of the time.)
- The prayer said at the cleansing of the chalice, and the concluding prayers, which in the Tridentine Mass included the reading of what was called the Last Gospel (usually, the first fourteen verses of Saint John's Gospel) as a farewell blessing.
Within these six groupings, there are short phrases (e.g. "Dominus vobiscum" and "Et cum spiritu tuo") that in Tridentine Solemn Mass were sung by priest or deacon and by the choir. If sung in the post-Tridentine form of Mass, the response is usually given by the whole congregation.
See also [link]
References [link]
- ^ "Order of Mass", rather than "Ordinary of the Mass", is the official term for English-speaking Catholics, in both the 1973 translation of the Roman Missal and in the revised translation that in most English-speaking countries will be brought into use on the First Sunday in Advent in 2011 (see The Order of Mass).
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Big O notation
In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error committed" while replacing the asymptotic size, or asymptotic mean size, of an arithmetical function, by the value, or mean value, it takes at a large finite argument. A famous example is the problem of estimating the remainder term in the prime number theorem.
Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation.
