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sequence

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.

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sequence

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.

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sequence

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 nth, 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.

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sequence

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 si 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,…,sn

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

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Sequence

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.

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Sequence

Sequence

a continuous or connected series, 1575.

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

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sequence

sequenceabeyance, 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

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Sequence

SEQUENCE

In the Roman rite, a musical setting of rhymed poetry with paired lines, occurring after the Alleluia verse and before the Gospel in the Mass for certain solemnities and important feasts. The revision of the Lectionary that was promulgated by Paul VI in 1969 brought about some changes in the use of the Sequence. Prior to the revision, five sequences were used: Easter, Victimae paschali laudes (obligatory for the feast and its octave); Pentecost, Veni, Sancte Spiritus (obligatory for the feast and its octave); Corpus Christi, Lauda Sion (obligatory on the feast, optional during the octave, suppressed since 1960); Requiem Masses, Dies irae ; Friday after Passion Sunday and September 15, Feast of Our Lady of Sorrows, Stabat Mater (obligatory on both days). The Council of Trent had suppressed thousands of sequences in its reform of the liturgy, salvaging only the first four for liturgical use. The fifth, Stabat Mater was reinstated by Benedict XIII in 1727.

The General Instruction of the Roman Missal says quite simply: "Except on Easter Sunday and Pentecost the sequences are optional" (GIRM 40). This means, in practice, that the Easter Sequence is optional during its octave; the calendar has eliminated the Pentecost octave, leaving the Sequence for the feast alone; the Lauda Sion is optional for the feast of Corpus Christi; the calendar revision has eliminated duplicate feasts, leaving the feast of Our Lady of Sorrows to be celebrated only on September 15, with its Sequence also optional; the Dies irae has been dropped completely from Masses for the Dead. In the 1969 revision, the Sequence is now placed before the Alleluia, since this acclamation properly belongs to the Gospel proclamation.

Musical structure. Musically the Sequence does resemble the hymn in its monophonic, syllabic structure, but it differs from it in structure and liturgical function. Whereas all the strophes of the hymn are constructed according to the same poetic plan and are sung to the same music in all verses, the Sequence displays progressive repetitions consisting of successive paired lines (double versicles), both of which have the same melody, and often includes a single line at the beginning and end. The conventional diagram is: The x and y represent the optional unpaired introduction and postlude.

The Sequence process consists essentially in underlaying a limited number of well-known tunes with new texts. These texts are freshly created verse lines consisting of words whose succession contains the same or nearly the same number of syllables as there are individual tones in the collective neumes or melismas of the pre-existent melody. In the process the shape of the original tune is literally preserved, but its musical identity is transformed. The striking parallel between this process and the cantus firmus procedure of medieval polyphony should not be overlooked. Unlike the tradition of classical plainchant, moreover, the lyricism of the new text results from the meaning and the representation of individual syllables, and the syntax and shape of the new text are derived from the slower-moving succession of heightened pitches borrowed from a neumatic or melismatic melody. The new text, derived from a transformed melody, has abdicated its own poetic canons and obeys a new kind of syllabic organization.

Emergence of the sequence. The term "Sequence" appeared first in the ninth century, when it signified an extended series of tones. Scholars are uncertain whether the precise etymology of the word is to be viewed as essentially musical (i.e., to describe the quality of a melody as an indifferent succession of tones) or liturgical (to describe the function of a melody to follow a liturgical text). Usage of the term was much less clearly defined then than in later writings; yet in all these ninth-century sources, the series of tones it designated was in some way related to the Alleluia and its verse, as is indicated in an Antiphonale Missarum from Mount Blandin, a text from the De ecclesiasticiis officiis of amalarius, and a famous dedicatory preface by notker balbulus of the Abbey of St. Gall (Sankt Gallen). The Antiphonale contains the phrase cum sequentia at the end of the text for several Alleluia

verses. Amalarius describes the Alleluia verse as a jubilation that the singers called Sequence (haec jubilatio quam cantores sequentian vocant ). These early references seem to suggest that at the end of chants whose texts already conveyed a mood of enthusiasm and exaltation, melodies were at times added to extend in temporal quantity the joyful mood of the liturgy. This extension was accomplished by a sonorous repetition of the word alleluia by the entire choir. The volume, pace, and character of the responsorial chant were, however, modified by this choral repetition of the Alleluia, as was demanded by the rubrics. This repetition, being collective rather than individual, could not be improvised; yet there was an improvisatory spirit to these added Alleluiasno doubt psychologically engendered by the difference between spontaneous textless jubilations and the set, controlled texts of the other chants.

The dedicatory letter of Notker accompanied a group of these elongated melodies underlaid with texts, which he sent to Bishop Lieutward of Vercelli c. 885. In this letter, in which he referred to the melodies as Sequences, he confessed that his creative imagination had been stirred when he first beheld compositions of this type in a Norman antiphonary brought to St. Gall by a refugee from the recently devastated Abbey of jumiÈges. Some verses for the long melodies in this antiphonary were written out; and Notker, who explained that as a young man he had had difficulty remembering the very long additions (melodiae longissimae ) to the Alleluia verses, decided to imitate this practice as a memory aid, reducing groups of wordless melismas to syllabic units he could remember. His first efforts, however, must not have been entirely syllabic melodies, for, as he states, it was his master, Yso, who suggested that he adopt a completely syllabic style and praised the results when he did so. It was a collection of these praiseworthy pieces that Notker wished to share with his episcopal friend. The prevailing tone of his document is more psychological than musical, for in reducing larger rhythmical groups (neumes and melismas) to smaller units (syllables and notes) he recognized a solution to his memory problem.

Notker claimed that he had improved upon an existing technique of text adaptation and also suggested that he was a creator and not a mere imitator. Accordingly, certain historians have mistakenly attributed the invention of the Sequence form to him. The title of his collection, Liber hymnorum, does indeed indicate his belief that a new musical as well as liturgical style had been invented, for although the Church's hynm tradition was very old, the hymn as a form was assigned to the Divine Office, not to the Mass. Perhaps Notker was conscious of having contrived a musical form with both popular appeal and liturgical precedent, besides being usable in the Mass, and was intimating to Bishop Lieutward that there was need for just such a form. Whatever artistic refinements Notker and his St. Gall confreres added to the sequence as a liturgical form, most scholars now agree that he did not innovate it. Besides Jumièges, which Norter himself mentions, Saint-Benoît sur Loire, Toul, and Lâon have been cited as possible sources. Southern France, despite the rich resources of the library at Saint-Martial Abbey at Limoges, contributes most to the literature of the Sequence only after the rise of Aquitainian notation (c. 1000).

Development. Between Notker's memory aids and the five present-day Sequences with their parallel structure, their regularity in textual strophic construction, and their use of textual rhyme, there intervened a long and complicated development. Musicologists distinguish between early Sequences and later Sequences and also divide the Sequence repertory into two independent but not separate traditionsan Anglo-French and an Italo-German. These same traditions are observed in the trope, which emerged in the same centers at about the same moment, though its life span was much shorter than that of the Sequence. Stylistically the creative periods of Sequence composition have been designated as the early period

(8501050), transitional period (10501100), and later period (11001300). For the early period, there are three extant manuscript sources from the second half of the ninth century: Munich, Bayerische Staatsbibliothek, Clm. 14823; Verona, Biblioteca Capitolare XC; and Paris, Bibliothèque Nationale, fonds Lat. 1154. These contain texts, mostly without neumes, that are scattered among other paraliturgical forms. In the second half of the tenth century appeared the first cycle of Sequences and texts arranged according to the Church year, the Congregatio prosarum; and this earliest sequentiarythat is, the section of the manuscript containing this cycleis bound with a troper as Paris, Bibliothèque Nationale, fonds Lat. 1240. With the exception of these specific items, the sources for early Sequences and tropes are identical.

As for the two traditions posited by scholars, Anglo-French sources consistently apply the word "Sequence" for a melismatic extension of an Alleluia melody without text; prosa for the text to be underlaid to an extended Alleluia melody, printed with or without the syllabic melody; sequentia cum prosa for an extended Alleluia melody whose neumes have been dissolved by syllables or words; and prosula for a text set to an extended, similarly dissolved melody of some chant other than the Alleluia. The Gradual, the Alleluia verse, or the Offertory verse of the Proper, or the Kyrie, Sanctus, or Benedicamus Domino of the Ordinary contained such extended melodies sometimes underlaid with prosula texts. Italo-German sources, however, consistently apply the word "Sequence" for both text and melody, written together on a single page. The melismatic extension of an Alleluia melody is written in the margin around the text. In this tradition, the term implies the total picture of words and music as they appear on a manuscript page. The practice of referring to both text and tune by the collective term apparently began in the Italo-German tradition shortly after the time of Notker, who, as noted above, called his compositions hymns. English scholars often use the term sequelae to describe the extended and wordless melismas of the Alleluia at the end of the Alleluia verse. As a pedagogic device, this usage is sometimes convenient, since it obviates the double meaning for the word "sequence." There

is no evidence that it was ever employed in such official books as the gradual and antiphonary containing canonical texts, or such unofficial books as troper and sequentiary containing paraliturgical texts.

Prosa, Prosula, Sequence. Prosula texts, as was indicated above, are intended as an underlay to certain texts of the official repertory, the official texts being set in a musical style that is neumatic, with occasional melismatic extensions. Something of the nature of the new prosula may be discovered by comparing it with its liturgical model. Numerous examples have been published, including the prosula text Non vos homines for the Alleluia verse; Non vos me elegistis, in Analecta hymnica (Leipzig 18861922) 49:252, ed. C. Blume; or the prosula text and melody Mirabilis atque laudabilis for an Alleluia verse, Mirabilis Dominus, cited by P. Evans. The prosula text is asymmetrical; it is free rhythmic prose with irregular accents, and assonance seems to be the only poetic device employed. The structural canons of its poetry come to light when compared with the poetry and music of the original. The prosula is a melody-orientated verse. Its high points are dictated by the canons of melody, not by those of poetry. The number of syllables corresponds generally to the number of notes occurring in a given melisma between melodic high points. The placing of end assonance is occasioned by the position of certain vowel sounds in the melodic pattern of the official text. The number of individual notes in the neumes and melismas of the original liturgical piece being underlaid determines the length of the new verse. While there is indeed craftsmanship displayed here, it is of a different order from that which characterizes the official chant, for the phraseology and tone groupings of the classical chant have been transformed into the sounds and individual notes of a new musical texture. Volumes 7 and 53 of Analecta hymnica contain texts of the earliest Sequences. While these texts display many of the same characteristics as prosula texts, assonance is less prevalent in them. Without an official text with given sounds at given pitch levels to be matched by the same sounds in the new text, the prosa composer was freer in his choice of syllabic succession than the composer of the prosula. Anglo-French texts frequently began with the word "Alleluia." In the subsequent prosa, the assonance "a" was prevalent. An "e" assonance, generated from the same introductory Alleluia, characterizes Spanish texts of the same Anglo-French tradition. Italo-German texts, on the other hand, begin directly without the word "alleluia" and display less assonance.

Melodic extension by phrase repetition is freer in the Sequence than in the prosula melody. Literal repetition of shorter antiphons to prolong the solemnity of a feast is mentioned in John's life of Odo of Cluny (Patrologia Latina, 217 v. [Paris 187890] 133:4368). This may have been the liturgical reason for the repetition by phrase in the longer Sequences. It is usually indicated by letter abbreviations: d (duplex, dupliciter ), t (trahere ), and s (semel ). Musical content of the Sequence extensions permitted greater freedom of invention than corresponding continuations of prosulae. The latter extensions returned to the melodic line of the official melody, while the Sequence melody apparently did not. ekkehard, in the Casus Sancti Galli (Patrologia Latina, 217 v. [Paris 187890] 131:1003), praises some of Tuotillo's tunes invented on the rolla or psalterium. Melodies invented to extend the spirit of a liturgical feast and to be participated in by a community of modest musical ability may have displayed corresponding ties with folk idiom, as this liturgical folk style developed.

Whatever their differences in terminology for the early period of Sequence writing, modern scholars agree on the artistic process involved: It was a procedure of text underlay to an already existing melody. Inventing a new text to a familiar tune is not an uncommon practice in any period and seems to have been fairly common in the liturgy during this period. A collection of new texts, apparently for liturgical use, exists in the earliest sequentiary (Paris, Bibliothèque Nationale, fonds Lat. 1240) under the collective heading Congregatio prosarum. Two forms of a melody for some of these texts are included in different parts of the book: one, a syllabic form written over a prose text; the other, a neumatic or a melismatic form written either with the official text if it is neumatic, or as one of a group of Sequences if it is melismatic. This is the ordinary method of notation for books of the Anglo-French tradition.

Transitional period. With the emergence of the cathedral as a parochial entity, the character of the liturgy was modified; this change in liturgical structure occasioned concomitant changes in the forms that were expressions of this structure, the Sequence among them. While retaining an organic relation with the past, the Sequence became a different kind of artistic form.

The Victimae Paschali laudes, attributed to Wipo, a diocesan priest of Burgundy, is an example of a Sequence from the transitional period. The text, while retaining elements of the unrhymed and irregular earlier Sequences, presages the regular form of the Sequences of adam of saint-victor and the later composers. In its terseness and brevity, it employs at times regular alternation of accented and unaccented syllables, as well as rhyme. The melody, while borrowing its Incipit from an Alleluia currently assigned to the fourth Sunday after Easter, continues freely as a melody. It has been called the perfect musical expression of Easter. The clarion melody of the Sequence has a character different from the continuation of the Alleluia melody. Moreover, the dialog form characterizing the second part of the Sequence was a purposeful artistic nuance, not the result of a process of text underlay, and was achieved by a play of motives in different ranges.

Later Sequences. The final period in the development of the Sequence was reached with the Victorine poets, particularly Adam. With them the form as it is known today was defined and fixed, and the musical style became relatively consistent. The musical style in general is logogenic, that is, the tunes follow the words and are musically comparable to those of a popular folk style of the period. In the late period, an irregular folk style discovered in an existing liturgical practice had become a regular folk style with fixed criteria for both its poetry and its music. Some of these later Sequence melodies were at times eminently suited to the musical expression of sentiments already contained in the words of the Sequence texts. As musical expressions in themselves or as expressions of the period of which they were a part, however, they were by no means sophisticated or progressive. Like similar examples in earlier or perhaps even ancient musical tradition, the better examples of this repertory were often merely good renderings in song of a collective sentiment. Hence they were destined by their very nature to be modest and conservative. Their symmetry was predictable, their range limited, and their stress on the individual word. This primitive style was suitable for active participationappealing to an audience of modest competence and to a performer or group of performers without virtuoso skills.

In the literary purview, even in the refined texts of Adam there are features reminiscent of more primitive early processes. His terraced rhymes, which gain in weight and frequency as the climax approaches, elicit a musical response to the mounting tension. His word play and word coinage are sometimes at the level of the common pun. Limerick-style prosody, as well as poetic effects derived from the canons of music, were features of the Sequence of the early period. Adam's verse was in a metrical mold already popular in the hymn. It consists of a group of rhymed trochaic lines of eight syllables with a caesura after the fourth syllable at the end of a word closing with a seven-syllable line. Each of these three-line stanzas is set to identical music, thus preserving the rhyming and parallel structure.

Bibliography: p. aubry and e. misset, eds., Les Proses d'Adam de Saint-Victor (Paris 1900). c. blume et al., eds., Analecta Hymnica v. 49. (Leipzig). w. h. frere, ed., The Winchester Troper (London 1894). h. m. bannister, Anglo-French Sequelae, ed. a. hughes (London 1934). a. schubiger, Die Sängerschule St. Gallens (Einsiedeln 1858). p. evans, "Some Reflections on the Origin of the Trope." Journal of the American Musicological Society 14 (1961) 119130. h. husmann, "Alleluia, Vers und Sequenz," Annales musicologiques 4 (1956) 1953; "Sequenz und Prosa," ibid. 2 (1954) 6191; "Die Alleluia und Sequenz der Mater-Gruppe," International Musicological Society: Report of the Congress 5 (1956) 276284; "Die älteste erreichbare Gestalt des St. Galler Tropariums." Archiv für Musikwissenschaft 13 (1956) 2541; "Die St. Galler Sequenz-tradition bei Notker und Ekkehard," Acta musicologica 26 (1954) 618. p. dronke, "The Beginnings of the Sequence," Beiträge zur Geschichte der deutschen Sprache und Literatur 87 (1965) 4373. r. crocker, "Some Ninth-Century Sequences," Journal of the American Musicological Society 20 (1967) 367402; The Early Medieval Sequence (Berkeley 1977).

[e. leahy/

l. durst,eds.]

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