sequence.
1. In mus. construction, the more or less exact repetition of a passage at a higher or lower level of pitch. If the repetition is of only the melody it is called a melodic sequence; if it is of a series of chords it is a harmonic sequence. If the intervals between the notes of the melody are to some extent altered (a major interval becoming a minor one and so forth, as is practically inevitable if the key is unchanged) it is called a tonal sequence; if there is no variation in the intervals (usually achieved by altering not merely the pitch of the notes but also the key) it is called a real sequence. If there are several repetitions, some of them tonal and some real, the result is a mixed sequence. A harmonic real sequence is sometimes called rosalia (some authorities, however, require as an additional qualification for this description a rise of one degree of the scale at each repetition).

2. In ecclesiastical use the term sequence is applied to a type of hymn which began as one of the many forms of interpolation in the original liturgy of the Western Christian Church. As the traditional plainsong did not provide for such interpolations, special melodies were composed. In the Church's service sequences follow (whence the name) the gradual and alleluia. The earliest sequences were in prose, not, as later, in rhymed verse, and the term ‘prose’ is still sometimes used instead of ‘sequence’. The following are examples of the sequence: Dies Irae (now a part of the Requiem), Veni Sancte Spiritus, Lauda Sion, and Stabat Mater dolorosa.

se·quence / ˈsēkwəns/ • n. 1. a particular order in which related events, movements, or things follow each other: the content of the program should follow a logical sequence. ∎  Mus. a repetition of a phrase or melody at a higher or lower pitch. ∎  Biochem. the order in which amino acid or nucleotide residues are arranged in a protein, DNA, etc. 2. a set of related events, movements, or things that follow each other in a particular order: a grueling sequence of exercises a sonnet sequence. ∎  a set of three or more playing cards of the same suit next to each other in value, for example 10, 9, 8. ∎  Math. an infinite ordered series of numerical quantities. 3. a part of a film dealing with one particular event or topic: the famous underwater sequence. 4. (in the Eucharist) a hymn said or sung after the Gradual or Alleluia that precedes the Gospel. • v. [tr.] 1. arrange in a particular order: trainee librarians decide how a set of misfiled cards could be sequenced. ∎  Biochem. ascertain the sequence of amino acid or nucleotide residues in (a protein, DNA, etc.). 2. play or record (music) with a sequencer. PHRASES: in sequence in a given order.

sequence in mathematics, ordered set of mathematical quantities called terms. A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the sequence. For example, the sequence 1, 1, 2, 3, 5, 8, 13, … (the Fibonacci sequence) is formed by adding any two consecutive terms to obtain the next term. The sequence - 1/2 , 1, 7/2 , 7, 23/2 , 17, … is formed according to the formula ( n²  - 2)/2 for the n th, or general, term. A sequence may be either finite, e.g., 1, 2, 3, … 50, a sequence of 50 terms, or infinite, e.g., 1, 2, 3, … , which has no final term and thus continues indefinitely. Special types of sequences are commonly called progressions . The terms of a sequence, when written as an indicated sum, form a series ; e.g., the sum of the sequence 1, 2, 3, … 50 is the series 1 + 2 + 3 + … + 50.

Sequence. A chant sung on certain days until 1970 after (now before) the Alleluia of the Mass. Originally the word seems to have denoted a purely melodic extension of the word ‘Alleluia’, sung to its final vowel; in the 9th cent. a syllabic text was provided for the melody; the word was later applied to the resulting musical-textual entity and eventually to the text alone. The first author to make a systematic collection of such texts was Notker Balbulus (d. 912); later authors include Hildegard of Bingen and Adam of St-Victor. In medieval times numerous sequences were in use; now only five remain: ‘Victimae paschali’, ‘Veni, Sancte Spiritus’, ‘Lauda Sion’ (at Corpus Christi), ‘Dies Irae’, and ‘Stabat Mater’, of which only the first two need be used.

sequence
1. A function whose domain is the set of positive integers (or sometimes the set of nonnegative integers). The image set can thus be listed s₁,s₂,… where s_i is the value of the function given argument i. A finite sequence (or list) is a function whose domain is {1,2,…,n} for n ≥ 1

and hence whose image set can be listed s₁,s₂,…,s_n

2. The listing of the image set of a sequence. Hence it is another name for string.

Sequence. A hymn, usually in couplets, sung in the mass on certain days after the epistle. In medieval times a large number of sequences (c.150 melodies and 400 texts, with at least 5,000 having been written) were in regular use, but in the missal only five are now printed.

Sequence

a continuous or connected series, 1575.

Examples : sequence of causes, 1829; of chambers, 1668; of reflections, 1823; of saints, 1589.

sequence •abeyance, conveyance, purveyance •creance • ambience •irradiance, radiance •expedience, obedience •audience •dalliance, mésalliance •salience •consilience, resilience •emollience • ebullience •convenience, lenience, provenience •impercipience, incipience, percipience •variance • experience •luxuriance, prurience •nescience • omniscience •insouciance • deviance •subservience • transience •alliance, appliance, compliance, defiance, misalliance, neuroscience, reliance, science •allowance •annoyance, clairvoyance, flamboyance •fluence, pursuance •perpetuance • affluence • effluence •mellifluence • confluence •congruence • issuance • continuance •disturbance •attendance, dependence, interdependence, resplendence, superintendence, tendance, transcendence •cadence •antecedence, credence, impedance •riddance • diffidence • confidence •accidence • precedence • dissidence •coincidence, incidence •evidence •improvidence, providence •residence •abidance, guidance, misguidance, subsidence •correspondence, despondence •accordance, concordance, discordance •avoidance, voidance •imprudence, jurisprudence, prudence •impudence • abundance • elegance •arrogance • extravagance •allegiance • indigence •counter-intelligence, intelligence •negligence • diligence • intransigence •exigence •divulgence, effulgence, indulgence, refulgence •convergence, divergence, emergence, insurgence, resurgence, submergence •significance •balance, counterbalance, imbalance, outbalance, valance •parlance • repellence • semblance •bivalence, covalence, surveillance, valence •sibilance • jubilance • vigilance •pestilence • silence • condolence •virulence • ambulance • crapulence •flatulence • feculence • petulance •opulence • fraudulence • corpulence •succulence, truculence •turbulence • violence • redolence •indolence • somnolence • excellence •insolence • nonchalance •benevolence, malevolence •ambivalence, equivalence •Clemence • vehemence •conformance, outperformance, performance •adamance • penance • ordinance •eminence • imminence •dominance, prominence •abstinence • maintenance •continence • countenance •sustenance •appurtenance, impertinence, pertinence •provenance • ordnance • repugnance •ordonnance • immanence •impermanence, permanence •assonance • dissonance • consonance •governance • resonance • threepence •halfpence • sixpence •comeuppance, tuppence, twopence •clarence, transparence •aberrance, deterrence, inherence, Terence •remembrance • entrance •Behrens, forbearance •fragrance • hindrance • recalcitrance •abhorrence, Florence, Lawrence, Lorentz •monstrance •concurrence, co-occurrence, occurrence, recurrence •encumbrance •adherence, appearance, clearance, coherence, interference, perseverance •assurance, durance, endurance, insurance •exuberance, protuberance •preponderance • transference •deference, preference, reference •difference • inference • conference •sufferance • circumference •belligerence • tolerance • ignorance •temperance • utterance • furtherance •irreverence, reverence, severance •deliverance • renascence • absence •acquiescence, adolescence, arborescence, coalescence, convalescence, deliquescence, effervescence, essence, evanescence, excrescence, florescence, fluorescence, incandescence, iridescence, juvenescence, luminescence, obsolescence, opalescence, phosphorescence, pubescence, putrescence, quiescence, quintessence, tumescence •obeisance, Renaissance •puissance •impuissance, reminiscence •beneficence, maleficence •magnificence, munificence •reconnaissance • concupiscence •reticence •licence, license •nonsense •nuisance, translucence •innocence • conversance • sentience •impatience, patience •conscience •repentance, sentence •acceptance • acquaintance •acquittance, admittance, intermittence, pittance, quittance, remittance •assistance, coexistence, consistence, distance, existence, insistence, outdistance, persistence, resistance, subsistence •instance • exorbitance •concomitance •impenitence, penitence •appetence •competence, omnicompetence •inheritance • capacitance • hesitance •Constance • importance • potence •conductance, inductance, reluctance •substance • circumstance •omnipotence • impotence •inadvertence • grievance •irrelevance, relevance •connivance, contrivance •observance • sequence • consequence •subsequence • eloquence •grandiloquence, magniloquence •brilliance • poignance •omnipresence, pleasance, presence •complaisance • malfeasance •incognizance, recognizance •usance • recusance