Explanatory Notes for Charles Warren, "Brunelleschi's Dome and Dufay's Motet"

p.92: "cantus firmus, isorhythmic and isomelic symmetries" These are musical terms. Cantus firmus is a fragment of often borrowed melody that is used as the basis for polyphonic elaboration. Isorhythm is a way of organizing a cantus firmus and thereby a composition. It entails repeating a rhythmic pattern and pitch pattern throughout a composition. Isomelic refers to similarity in the melodies of the upper voices of the work.

p.93: On harmonic proportions: Warren is suggesting that cathedrals in the Trecento (the 14th century) were built based on harmonic proportions: the a due quadri (2:1) and a uno quadro e mezzo (3:2), both correspond to the Pythagorean consonance ratios.

p.96: "Mensuration" - Mensuration is the name for the speed of a section of music as well as the symbols used to designate those speeds. Thus, in the Dunstable motet we could speak of the ratios of duration of sections (3:2:1) as a proportional relationship of mensurations. In the Dufay motet, this ratio is 6:4:2:3. Substitute the word "Speed" throughout. Thus "smaller mensuaration" can be interpreted as "quicker speed."

p.96: "Tactus" - Tactus is simply a fancy way of saying "pulse" or "beat."

p.96: "Breve" - Breve is the term used to represent a note that has 8 beats, what may be called a "Double whole note." It doesn't necessarily represent a note that is held for a long time.

p.96 (bottom): Performance practice differs on whether or not tempus perfectum diminutum would be performed slightly slower or faster. Warren is positing that his calculations are based not on a slightly slower or faster beat, but instead on a steady beat.

p.97: "Semibreve" - Semibreve is the British term to represent a note that has 4 beats, what Americans call a "whole note."

p.98: "braccia" - Braccia is a measurement unit in Renaissance Italy. It corresponds to approximately 2 feet.

p.98: "two tenors" - This is in reference to the voice part of a tenor; from the Latin tenere: to hold. It does not necessarily equate with modern usage, that is, the higher of the male vocal range. In our recording the double tenor is played by two instruments.

p. 101: "five points of imitation" - Points of imitation are short phrases that are repeated within a musical work.

p.102: "strophe" = "stanza"

p.104: "Missa Caput" and "Missa Se la face ay pale" - Two of Dufay's most celebrated compositions: polyphonic settings of sections of the Mass.

All text © Todd Tarantino 2002-2012.
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