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sound example 0.1: Igor Stravinsky, Le sacre du printemps (1913), the end of the "Cortège du Sage," ending at rehearsal number 71 with a "general pause" (G. P.) Performed by the New England Conservatory Philharmonia, Hugh Wolff, conductor.
sound example 0.2: Igor Stravinsky, Le sacre du printemps (1913), the beginning of the introduction. Performed by the New England Conservatory Philharmonia, Hugh Wolff, conductor.
sound example 1.1: "Adila," a Gurian trio song (first half) from western Georgia, transcribed by Nino Tsitsishvili from a recording made during the 1930s or 1940s; the bass part is sung by the well-known Georgian traditional singer/musician Varlam Simonishvili. Text: "A rose was asked: Why are you so pretty, your face and body? I am surprised that you are so thorny and so hard to find."
sound example 1.2: "Ndrodje balendoro," a Banda-Linda orchestral piece from the Central African Pygmy people, performed by the Ongo Ensemble and transcribed by Simha Arom.
sound example 1.3: The Seikilos skolion. Text: "While you live, shine. Don't suffer at all; life is short and in the end time will have its way." Performed by Consuelo Sanudo.
sound example 1.4: Euripides, Orestes, lines 338–344, a modern transcription of a fragmentary score copied about 200 BCE with an aulos accompaniment. Performed by Ensemble De Organographia. Text [Chorus of women of Argos]: "I grieve, I grieve—your mother's blood that drives you wild. Great prosperity among mortals is not lasting: upsetting it like the sail of a swift sloop some higher power swamps it in the rough doom-waves of fearful toils, as of the sea."
sound example 2.1: The first verse of the Gregorian chant "Kyrie cunctipotens genitor," performed by the Hilliard Ensemble. Text: "Lord, have mercy."
sound example 2.2: A Gregorian chant for Christmas Day, "Viderunt omnes," performed by Tonus Peregrinus. Text: "All the ends of the earth have seen the salvation of our God: rejoice in God, all the earth."
sound example 2.3a: Parallel organum at the fourth from the Musica enchiriadis. Text: "You are the eternal son of the Father." Performed by Consuelo Sanudo.
sound example 2.3b: Free organum from the Musica enchiriadis, in which the voices may move obliquely, rather than in strict parallel. Text: "King of heaven, lord of the sounding sea, of the shining Titan sun, and the gloomy Earth." Performed by Consuelo Sanudo.
sound example 3.1: An example of St. Martial organum, performed by the Hilliard Ensemble. Text: "Benedicamus [domino]" ("Let us bless [the Lord]"). The long notes of the lower voice sound the Gregorian chant for this text.
sound example 3.2: Leonin, Viderunt omnes, based on the Gregorian Gradual for Christmas Day (sound example 2.2), performed by Tonus Peregrinus. Text: "All [the ends of the Earth] shall see [the salvation of our God: all the Earth shall rejoice in God]."
sound example 3.3: Perotin, Viderunt omnes, measures 1–40, performed by Tonus Peregrinus. Based on the Gregorian chant in sound example 2.2, the text is the same as for sound example 3.2.
sound example 3.4: The round (rota) "Sumer Is Icumen In," performed by Lumina Vocal Ensemble. Text: "Spring has arrived, sing loudly, cuckoo. The seed is growing and the meadow is blooming and the wood is coming into leaf now. Sing, cuckoo!"
sound example 3.5: Motet: O Mitissima (Quant voi)—Virgo—Hec dies, performed by Lumina Vocal Ensemble. Texts: Triplum (upper line in the Bamberg Codex): "O sweetest Virgin Mary, beg Thy Son to give us aid and relief against the deceiving wiles of the demons and their wickedness." Triplum (upper line in the Montpellier Codex, here included as a subsidiary line): "When I see the summer season returning and all the little birds make the woods resound, then I weep and sigh for the great desire which I have for fair Marion, who holds my heart imprisoned." Motetus (middle line): "Virgin of virgins, Light of lights, restorer of men who bore the Lord: through Thee, O Mary, let grace be given as the angel announced: Thou art Virgin before and after." Tenor (lowest line): "This is the day [which the Lord hath made]."
sound example 3.6: The Gregorian chant "In exitu Israel de Aegypto" in tonus peregrinus (the "wandering tone"), which moves from reciting on A to reciting on G. Performed by Consuelo Sanudo.
sound example 4.1: the interval √2:1, closely approximated by a tritone (three whole tones, corresponding to the ratio 93:83 = 729:512).
sound example 5.1: Luca Bettini, lauda on "Ecce quam bonum," performed by the Eastman Capella Antiqua. Bettini was a Dominican monk who became a follower and defender of Savonarola. Text: "Behold how good and pleasant it is for brethren to dwell together in unity."
sound example 5.2: Girolamo Savonarola, "Gièsu sommo conforto," performed by the Eastman Capella Antiqua. Text: "Jesu, highest solace, you are all my love and my blessed refuge and holy redeemer. O great goodness, sweet mercy, happy the one united with you!"
sound example 6.1: Guillaume de Machaut, Kyrie I from Messe de Nostre Dame, performed by the Hilliard Ensemble. Text: "Lord, have mercy." Note the alignments on D–A marked with boxes; the isorhythms are detailed in figure 6.2.
sound example 6.2a: The first verse of the Gregorian chant "Kyrie cunctipotens genitor," performed by the Hilliard Ensemble. Text: "Lord, have mercy."
sound example 6.2b: the tenor voice in Machaut's Kyrie I, performed by Consuelo Sanudo. Compared to the original chant in sound example 6.2a, this contains the same twenty-eight pitches in the same order, but now presented in 3/2 meter. Note the "isorhythmic pattern" or talea repeated every four notes, indicated by brackets in figure 6.2b: the same sequence of rhythms in that voice stated in measures 1–4 is then repeated in measures 5–8, 9–12, and so on.
sound example 6.3: Machaut, Christe eleison from his Messe de Nostre Dame, performed by the Hilliard Ensemble. Text: "Christ, have mercy." Here, the tenor's isorhythmic talea pattern contains eight notes, this most "imperfect" of numbers (2 × 2 × 2) underlining the plea to the Savior of human imperfection, as if extending the four-note talea used by the tenor in Kyrie I.
sound example 6.4: Machaut, Messe de Nostre Dame, Gloria, measure 1–5, performed by the Hilliard Ensemble. Text: "And peace on earth." The "double leading-tone cadence" in measures 4–5 involves three voices moving by semitones to their final notes (from C# to D or G# to A), while the other voice (the contratenor) moves downward by step from E to D.
sound example 6.5: Machaut's setting of the words "Jesu Christe" in the Gloria of his Messe de Nostre Dame (measures 90–97), performed by the Hilliard Ensemble; note the double leading tone cadence in measures 96–97. Text: "You alone are most high, Jesus Christ."
sound example 6.6: The words ex Maria Virgine ("from Mary the Virgin") in the Credo of Machaut's Messe de Nostre Dame (measure 68–74), performed by the Hilliard Ensemble; note the cadence in measures 72–73.
sound example 6.7: Johannes Ockeghem, Kyrie I from Missa prolationum, performed by Ensemble Musica Nova. The top two voices share the same melody; the bottom two share a different melody. Each voice proceeds in a different meter (2/2, 3/2, 6/4, 9/4) while always sharing the same underlying pulse (the half note).
sound example 6.8: The subject of Josquin des Prez's Missa La sol fa re mi, performed by Consuelo Sanudo; a pure descending scale would have ended mi re.
sound example 6.9: Josquin, Kyrie I from Missa La sol fa re mi, performed by The Tallis Singers. Note that the subject appears in its original form in the superius (measures 1–5) and in the bassus (10–13), then transposed a fifth higher (starting on E) in the tenor (5–8).
sound example 6.10: Josquin, opening of the Gloria from Missa La sol fa re mi, performed by The Tallis Singers. The subject (transposed to begin on E) runs through the tenor. Note the subject sung forward, then backward (retrograde) in the altus, measures 7–8, making a palindrome. Text: "And peace on Earth to men of good will."
sound example 6.11: Josquin, the beginning of the Credo from Missa La sol fa re mi, performed by The Tallis Singers. The tenor sings the subject (transposed to begin on E) in greatly slowed form ("augmentation"). Text: "[I believe in one God], Father Almighty, maker of heaven and Earth."
sound example 7.1: The opening of Alessandro Striggio's motet Ecce beatam lucem, performed by the Huelgas Ensemble, conducted by Paul Van Nevel. The forty voices are organized into five choirs of eight voices,. The opening statement by choir 1 is answered by choirs 4 and 5 (measures 2–5), then by choirs 2 and 3 (measure 5). Note the additional (forty-first) voice, a continuo that underlines the harmony of the whole. Text: "Behold the blessed light."
sound example 7.2: The climactic entry of all forty voices simultaneously in Striggio's motet Ecce beatam lucem (measure 107), performed by the Huelgas Ensemble, conducted by Paul Van Nevel. Text: "Draw us from here straight to Paradise."
sound example 7.3: The opening eighteen measures of Thomas Tallis's motet Spem in alium, showing the gradual entry of the first twenty voices. Performed by the Huelgas Ensemble, conducted by Paul Van Nevel. Text: "[I have] no other hope."
sound example 7.4: The simultaneous entry of all forty voices, after a general pause (measures 121–2), from Tallis's Spem in alium, performed by the Huelgas Ensemble, conducted by Paul Van Nevel. Text: "Look upon our lowliness."
sound example 8.1: The first four overtones above the fundamental note C, as observed by Marin Mersenne, showing their corresponding ratios.
sound example 8.2: Giovanni da Palestrina, Kyrie I from Missa Papae Marcelli (1562), performed by New York Polyphony. Note that all dissonances between voices are carefully prepared and resolved, always approached and resolved by stepwise motion. These dissonances are often passing notes (between two consonances) or neighboring notes to a consonance. Palestrina restricts himself to the use of only those notes lying in what we would now call C major (with the exception of one possible accidental, the F# in measure 4). Text: "Lord, have mercy."
sound example 8.3: William Byrd, the end of the Agnus Dei from Mass for Four Voices, performed by New York Polyphony. Text: "Grant us peace." Note the dissonant suspensions on the syllable "do-" of dona.
sound example 8.4: Carlo Gesualdo, Tristis est anima mea from Tenebrae (1611), performed by Cantores Antiquae Musicae, conducted by Jeffery Kite-Powell. Text: "You shall run away, and I will go to be sacrificed for you."
sound example 8.5: Chorus of Sirens from the first intermedio of the Florentine wedding celebrations for Ferdinando de' Medici and Christine of Lorraine (1589), performed by the Huelgas Ensemble, conducted by Paul Van Nevel. Music by Cristofano Malvezzi; poem by Ottavio Rinuccini. Text: "We by whose sweet song the celestial spheres are made to wheel around."
sound example 8.6: Orfeo's monody from act 2 of L'Orfeo by Claudio Monteverdi, performed by Nigel Rogers. Text: "Farewell, Earth, farewell, Heaven, and Sun, farewell."
sound example 8.7: The opening of the final chorus from act 3 of L'Orfeo (♪), from a recording directed by Nigel Rogers. Text: "Nothing undertaken by man is attempted in vain."
sound example 8.8: Johannes Kepler's planetary songs (including also the Moon); note the song of the Earth (Terra). By touching each planet's song you can hear it separately or hear all together by touching the indicated button.
sound example 9.1: Johann Joseph Fux's first example of species one counterpoint.
sound example 9.2a: Fux's example of species two, in which two notes of the counterpoint appear against each note of the cantus firmus. Note that in each case, the downbeat must be consonant, while the other note can be either consonant or dissonant. In measures 8 and 9, the master marks with a cross Joseph's violations of the rule forbidding parallel fifths, which are not "hidden" by the skip of a third between them.
sound example 9.2b: Fux allows the dissonant fourth F to appear as a passing tone between the consonances G and E, a third apart—a technique he calls diminution.
sound example 9.3a: Fux's example of species three (suspensions), in which the counterpoint is staggered rhythmically against the cantus firmus, so that (in measure 2) a dissonant seventh on the downbeat is resolved downward to a sixth.
sound example 9.3b: Fux's examples contrasting the "good" resolution of dissonance downward against the "bad" resolution upward.
sound example 10.1: The triple canon in six voices (BWV 1076) that Bach holds in his portrait by Elias Haussmann (1748).
sound example 10.2: Variation III of Bach's canonic variations on "Vom Himmel hoch," performed by Robert Costin, organ: the pedal and left hand play a canon in eighth notes at the seventh based on the hymn tune, which appears in half notes in the soprano. The alto voice (marked cantabile, singable) freely intertwines between these other voices.
sound example 10.3: The concluding three measures of Variation V of Bach's canonic variations on "Vom Himmel hoch," performed by Robert Costin; in this compressed passage, all four phrases of the hymn tune are played in close overlapping (stretto), some in eighth notes (alto and bass), others in sixteenth notes (soprano and tenor). Note also the huge stretch in the right hand in the third beat of measure 55, spanning a tenth (A–A–C) and the presence of Bach's musical signature B♭–A–C–B♮ (= H in German notation) in the final measure.
sound example 10.4a: The beginning of Christian Erbach's Ricercar (ca. 1625) played in the original fingering specified by the composer, in which the thumb is used only by the left hand, while the right hand plays scales using mostly the index and middle fingers.
sound example 10.4b: The beginning of Christian Erbach's Ricercar (ca. 1625) played in modern fingering, using the thumb freely in both hands.
sound example 10.5a: Couperin's fingering for an octave scale, from L'art de toucher le clavecin (1717), in which the right hand begins on the thumb but then uses the alternation of third (middle) and fourth (ring) fingers (1 2 3 4 3 4 3 4 5) ascending; the descending pattern is different; compare this fingering with the modern 1 2 3 1 2 3 4 5.
sound example 10.5b: Couperin's fingering for his pieces "Les sylvains," in which the expressive grouping of two notes is underlined by the use of adjacent fingers, the third finger sliding between groups to make a slight articulation. Here, using the thumb would have created too much connection between groups.
sound example 10.6: J. S. Bach's Applicatio (BWV 994), using the composer's own fingerings, written to teach his eldest son, Wilhelm Friedemann. Note the use of finger crossing (3 4 3 4) in the right hand (measure 1) and thumb crossing (3 2 1 2 1 2 1) in the left (measure 3); the right hand uses thumb crossings in measure 7, when three voices are heard.
sound example 10.7: The initial entrance of the six voices in J. S. Bach's Ricercar à 6 from his Musical Offering (1748, BWV 1079).
sound example 10.8: The opening of the Prélude of Bach's Fifth Suite for cello solo, performed by Wayne Foster-Smith.
sound example 10.9: The beginning of the fugue in Bach's Fifth Suite for solo cello as virtual polyphony. performed by Wayne Foster-Smith. Note that the initial notes G–A♭ (measure 27–28) in one "voice" are answered by C–D–E♭in the other "voice" (indicated by dotted parentheses in figure 10.9), and so forth. There are other entrances at measures 35 and 48, separated by episodes.
sound example 10.10: The conclusion to the fugue in Bach's Fifth Suite for solo cello, performed by Wayne Foster-Smith.
sound example 11.1: Ludwig van Beethoven, Symphony no. 3 ("Eroica"), from the coda of the first movement (measures 655–663), performed by the Czech National Symphony Orchestra; though the full orchestra is playing, there are essentially only two distinct contrapuntal voices (the melody in violas, celli, and basses, against a countermelody in the winds), plus textural and rhythmic material in the brass and violins.
sound example 11.2: Johannes Brahms, Symphony no. 2 in D major, op. 73, first movement (measures 204–212), performed by the Czech National Symphony Orchestra. Note the main melody in the first violins, against the countermelody in the violas; meanwhile, the celli and basses play another countertheme, answered in inversion by the clarinets. The second violins add another answering motive, rhythmically displaced by accents.
sound example 11.3: The beginning of Franz Schubert's "Wasserfluth," from his song cycle Winterreise (1827), following the rhythmic notation indicated in his manuscript. Note that he lines up the last note of the triplet with the last sixteenth note, showing that he wished there to be no difference between these rhythms as played here.
sound example 11.4: The first page of Frédéric Chopin's Nouvelle étude, no. 1 (1840), in which the right hand begins alone by playing steady triplets (three quarter notes in the time of the half note of the piece's tempo), then separately the left hand plays four eighth notes per half note. At measure 9, the two rhythms are combined, each hand having assimilated the independent feeling of its own rhythm.
sound example 11.5: The beginning of Igor Stravinsky's Étude, op. 7, no. 1 (1908) for piano; the left hand begins playing quintuplets, joined then by the right hand playing first triplets, then duplets. In measures 5–6, all three rhythms are combined.
sound example 11.6: Arnold Schoenberg's Chamber Symphony no. 1, op. 9, at rehearsal number 38, performed by The Black Diamond Ensemble, conducted by Max Artved.
sound example 11.7: The polyphony of timbres in Arnold Schoenberg's "Farben" ("Colors"), the third of his Five Pieces for Orchestra, op. 16 (1909), performed by the Gustav Mahler Jugendorchester, conducted by Jonathan Nott.
sound example 11.8: Anton Webern's orchestration of the opening of Bach's Ricercar à 6, performed by the Münchener Kammerorchester, conducted by Christoph Poppen. A muted trombone plays the first (diatonic) element of the theme; the second (chromatic) element is passed sequentially between muted horn, trumpet, and trombone; the harp adds its timbre to accent the middle of this element; the third (closing) element uses horn, trumpet, and harp. In measure 6, the overlap between horn and trombone notes allows the fusion of their timbres.
sound example 11.9: The end of the scene with three orchestras from the finale to act 1 of Wolfgang Amadé Mozart's Don Giovanni, performed by the Baroque Orchestra of New Jersey, conducted by Robert Butts.
sound example 11.10a: The beginning of Charles Ives, The Unanswered Question (1908), showing the strings as "the Druids" and the solo trumpet stating "the Question." Performed by the University of Cincinnati College-Conservatory of Music Concert Orchestra, conducted by Oliver Ochanine.
sound example 11.10b: The conclusion of Charles Ives, The Unanswered Question (1908), including "the fighting Answers" given by four flutes. Performed by the University of Cincinnati College-Conservatory of Music Concert Orchestra, conducted by Oliver Ochanine.
sound examples 11.11a: An excerpt from the beginning of György Ligeti, Poème symphonique (1962) for one hundred metronomes, as performed by Forum andere Musik.
sound examples 11.11b: The conclusion of György Ligeti, Poème symphonique (1962) for one hundred metronomes, as performed by Forum andere Musik.
sound example 11.12: The opening of Conlon Nancarrow's Study no. 33—Canon for player piano (1965–69).
sound example 12.1: The opening of Glenn Gould's The Idea of North (1967), its four spoken voices entering one by one.
sound example 12.2: The ostinato from the final movement of Jean Sibelius's Fifth Symphony, which accompanies the final section of Glenn Gould's The Idea of North.
sound example 12.3: The beginning of Franz Schubert's melodrama "Abschied von der Erde," D. 829 (1826). Text: "Farewell, thou beautiful Earth! I can only now understand how joy and suffering come to us."
sound example 12.4: A passage from Glenn Gould's The Latecomers (1969), including the strikingly monotonous voice of a female speaker.
sound example 12.5: The passage from Glenn Gould's The Quiet in the Land (1977) that includes takes from an unidentified recording session of a children's chorus and harp.
sound example 12.6: A passage from a performance of John Cage's Radio Music (1956) by The Curiosity Cabinet.
sound example 14.1: A video showing that five metronomes sharing a common suspension will become entrained and come into phase with each other.
sound example 16.1: Excerpts from a performance of John Luther Adams, Sila: The Breath of the World by members of the Department of Music of the University of North Carolina at Chapel Hill on April 3, 2016.
sound example 16.2: Drummer Tom Grosset plays over 1,200 strokes in one minute, averaging over 20 beats per second (2013).
0.1, 0.2: Performed by the New England Conservatory Philharmonia, Hugh Wolff, conductor.
1.1: Courtesy of Nino Tsitsishvili.
1.2: Courtesy of Simha Arom.
1.3, 2.3a, 2.3b, 3.6, 6.2b, 6.8: Courtesy of Consuelo Sanudo.
1.4: Courtesy of Ensemble De Organographia, from Music of the Ancient Greeks (Oregon City: Pandourian Records, 1995).
2.1, 6.1,6.2a, 6.3, 6.4, 6.5, 6.6: Courtesy of Paul Hillier and Hyperion Records, from The Hilliard Ensemble, Paul Hillier, conductor, Machaut: Messe de Notre Dame, © 1987 Hyperion Records Ltd. CDA 66358.
2.2, 3.2, 3.3: Courtesy of Antony Pitts and Naxos of America, Inc., from Tonus Peregrinus, conducted by Antony Pitts, Sacred Music from Notre Dame Cathedral © 2015 Naxos Rights International, Naxos CD 8 557350.
3.1: Courtesy of Paul Hillier and Harmonia Mundi, from The Hilliard Ensemble, Paul Hillier, conductor, The Age of Cathedrals © 1996, 1999, 2003 Harmonia mundi HMX2907356.
3.4, 3.5: Courtesy of Lumina Vocal Ensemble.
5.1, 5.2: Courtesy of Eastman Capella Antiqua.
8.6, 8.7: Courtesy of Nigel Rogers, from Monteverdi, L'Orfeo (EMI Records Ltd. CMS 7 64947 2, 1984).
6.7: Courtesy of Lucien Kandel and Ensemble Music Nova.
6.9, 6.10, 6.11: ©1986 Gimell Records (www.gimell,com). The recording of Josquin's Missa La sol fa re mi by Peter Phillips and The Tallis Scholars is available on The Tallis Scholars Sing Josquin (CDGIM 206).
7.1, 7.2, 7.3, 7.4, 8.5: Courtesy Huelgas Ensemble and Paul Van Nevel, © Huelgas Ensemble.
8.2, 8.3: Courtesy New York Polyphony, from Roma aeterna and Times Go By Turns © 2016, 2013 BIS Records.
8.4: My thanks to Jeffery Kite-Powell for the use of this excerpt.
8.8: Animation by Alexei Pesic.
10.2, 10.3: Courtesy of Robert Costin.
10.8, 10.9, 10.10: Courtesy of Wayne Foster-Smith, cello.
11.1, 11.2: Performed by the Czech National Symphony Orchestra (Creative Commons 3.0).
11.6: Performed by The Black Diamond ensemble conducted by Max Artved in the Royal Library in Copenhagen on March 15, 2016.
11.7: Performed by the Gustav Mahler Jugendorchester, conducted by Jonathan Nott, live at the BBC Proms © BBC 2009.
11.9: Courtesy of Robert W. Butts.
11.10a, 11.10b: Performed by the University of Cincinnati College-Conservatory of Music Concert Orchestra, conducted by Oliver Ochanine on November 29, 2009.
11.11a, 11.11b: Courtesy of Forum andere Musik.
11.8: Courtesy of Christoph Poppen, the Münchener Kammerorchester, and ECM Records from Bach/Webern Ricercar(© 2003 ECM 1774).
11.12: Courtesy of Schott Music & Media/WERGO, www.wergo.de. Conlon Nancarrow: Study No. 33 from the album: Studies for Player Piano (WER 6907 2) ©+℗1988–1991/1992 Schott Music & Media Gmbh/WERGO, Mainz, Germany.
12.1, 12.2, 12.4, 12.5: Courtesy of CBC and Primary Wave.
12.6: Courtesy of The Curiosity Cabinet.
14.1: "Synchronization of Metronomes" video courtesy of Harvard University Natural Science Lecture Demonstrations, Faculty of Arts and Sciences Science Division.
16.1: SILA: THE BREATH OF THE WORLD by John Luther Adams © Taiga Press (BMI): Used by Permission. Video courtesy of Lee Weisert and the Department of Music of the University of North Carolina at Chapel Hill, from their performance on April 3, 2016.
16.2: Courtesy of Thomas Grosset.
All other sound examples were played, recited, or generated by the author, who thanks Alexei Pesic for invaluable suggestions and Kristin Waites for her expertise and superb work in preparing this ebook.