The human eye beholding the interior of a Gothic cathedral perceives a deep harmony between a bewildering complexity of elements. Horizontal bands of architecture proceed upwards, each with their own internal rhythms: the ponderous steps of the great columns marching down the aisle, surmounted by a tripling of speed in the smaller rank of triforium gallery arches, in turn crowned by the radiance of the clerestory windows and often yet another celestial rank in the upper rose windows. Each builds upon its foundation in an architectural style that appears literally to strive upwards toward the transcendent Godhead. In much the same way, the music of the Notre Dame School of polyphony harmonizes a complex musical architecture to strive toward perfection in the act of divine worship.

Very little is known about the two leading composers of the Notre Dame School. An unnamed English student at the University of Paris (known to posterity only as Anonymous IV) wrote long after their deaths of the great masters Leoninus (Léonin) and Perotinus Magnus (Pérotin). Léonin apparently composed an entire book around the middle of the twelfth century, the Magnus Liber Organi, of polyphonic elaborations upon the Parisian liturgy, to which Pérotin later made revisions and additions. Two pieces of Pérotin's music Anonymous IV specifically mentions are Viderunt omnes and Sederunt, which may be identified in manuscript collections of Notre Dame polyphony as the first compositions for four voices anywhere in Europe. The foundation of Viderunt omnes is a plainchant that likely served the Parisian liturgy for Christmas Day. The text comes from verses of Psalm 98 in the Vulgate's Latin (Ps. 98:3b-4a, 2), jubilantly singing of the moment when God's salvation is made known to all the Earth. (Incidentally, the text naturally seems to call for such a concord of many voices!) Following the responsory form of plainchant, Viderunt omnes consists of a solo incipit, a chanted conclusion, a short verset (also perhaps for solo), and a repeat of the opening section. Pérotin's setting preserves the form and retains the liturgically correct chant melody, but embellishes it by two "discant clausulae," sections of composed polyphony that substitute for the solo chants. For each clausula, the choir sings the notes of the chant melody, but each note is greatly extended. Above this abstracted chant is woven a web of three solo voices dancing about one another in long, metrical melismas on the chant syllables. The most astounding innovation of Notre Dame polyphony was the addition of rhythm to such ornamental voices: the upper voices sing dozens of notes above each step of the chant, regulated by the six modal rhythms. The rhythmic patterns possible (which may shift in each voice phrase to phrase) are each related to a poetic foot: long/short (trochaic), short/long (iambic), long/short/short (dactylic), short/short/long (anapestic), long/long (spondeic), and short/short (pyrrhic). Within the limitations of these rhythms, the voices move freely as if by elaborate improvisation. Often sequential melodic motifs are expounded, and in this piece Pérotin even uses canonic relationships between voices. But the power of the piece doesn't come from this intricacy, but rather from the deep sense of harmony. Each phrase begins with a "perfect" harmony of fifths and octaves; the music then progresses in a compelling filigree upon the chant tone, a lengthy marginal gloss. But each phrase returns irrevocably from dissonance to perfection of harmony. And the final moments of the music are given to the liturgically perfect plainchant alone, in unison singing as if to represent the unity of the Church itself.

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