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This title is available in an enhanced iBook version through the iTunes iBook store. On an iPad or Mac, this enhanced version gives seamless and easy access to the text and illustrations; you need merely touch a sound example to hear and see it.
Sound example 1.1: An octave (ratio 1:2).
Sound example 1.2: The fundamental Pythagorean intervals: a perfect fifth (2:3), a perfect fourth (3:4), and the interval between them, the whole tone (8:9).
Sound example 1.3: A visit to Shehan Prull's blacksmith shop to hear whether or not hammers of different weights sound different pitches, as Boethius asserts.
Sound example 1.4: The tritone (three whole tones).
Sound example 1.5: A scale formed by six successive whole tones (8:9), which slightly overshoots an octave (1:2).
Sound example 2.1: Philippe de Vitry, "Garrit Gallus/In nova fert/Neuma." This motet is an early example of ars nova written about 1317 by a noted composer with whom Oresme was in contact. As indicated by its title, the voices of this motet have different Latin texts, drawn from the Roman de Fauvel, a fable about a donkey whose is the corrupt ruler of a disorderly world. The text "Garrit Gallus" is a political allegory that condemns the fox (the finance minister Enguerran de Maringny) who devours the chickens (the French people) while the old lion (King Philip IV) turns a blind eye. (Note that the left button allows you to stop and resume the recording at any point; the right button restarts the performance from the beginning.)
Sound example 3.1: Gregorian chant "In exitu Israel de Aegypto" in tonus peregrinus (the "wandering tone"), which moves from reciting on A to reciting on G.
Sound example 3.2: The church modes, along with the new Ionian (modern major) and Aeolian (modern minor) modes introduced by Glarean. Note that adding a B♭ to the Lydian mode results in an Ionian (major) scale based on F.
Box 3.1 (sound examples 3.3a–e): How Josquin transforms modes: Part one of De profundis.
Box 3.2 (sound examples 3.4a–c): Arriving at the Phrygian: Part two of De profundis.
Here you can listen to Josquin's entire De profundis motet as a whole; the left button allows you to stop and resume the recording at any point; the right button restarts the performance from the beginning.
Box 4:1 (sound examples 4.1a–c): Pythagorean tuning, just intonation, and equal temperament.
- Sound example 4.1a: Pythagorean tuning for a major third (ditone = two tones, 64:81), minor semitone (243:256), and minor third (semiditone = tone plus minor semitone, 27:32).
- Sound example 4.1b: Just intonation for major third (4:5) and minor third (5:6)
- Sound example 4.1c: Comparison of Pythagorean, just, and equal tuning for a major third and for a minor third.
Box 4.2 (sound examples 4.2a–c): The three ancient musical genera.
- Sound example 4.2a: Vicentino's example of a melody in the diatonic genus, which is based on the pattern S T T: semitone | tone | tone.
- Sound example 4.2b: Vicentino's example of a melody in the chromatic genus, which is based on the pattern S S S3: semitone | semitone | trihemitone (= 3 semitones).
- Sound example 4.2c: Vicentino's example of a melody in the enharmonic genus, which is based on the pattern D D T2: diesis (= quarter tone) | diesis | ditone (= 2 tones).
Sound example 4:3: "Johannes thüt uns schreiben," the first of fifty-two stanzas Michael Stifel wrote using the melody of the popular song "Bruder Veyt" to propagate Luther's teachings (1522).
Sound example 4:4: Vicentino's motet "Musica prisca caput," which he calls "a demonstration of a composition made from all three genera" of music: diatonic (measures 1–16), chromatic (16–30), and enharmonic (29–48). Text: "Ancient music of late has raised her head out of the darkness, / So that, with antique and sweet numbers, to compete with ancient deeds, / Your great deeds, Hyppolitus, she might send high above the heavens." In the score, a dot above a note indicates that the pitch should be raised in pitch by a diesis (quarter tone).
Sound example 4:5: A passage from Act II of Claudio Monteverdi, La favola d'Orfeo, in which the messenger tells Orfeo the dying words of Euridice: "And calling on you, Orfeo, Orfeo, after a deep sign expired in these arms." The arrow marks the dissonance on the word "grave" (deep) between voice (B♭) and continuo (C♯), a diminished seventh that Artusi felt was "irrational."
Sound example 5.1: Kepler's transcription of the singing of a "Turkish priest."
Sound example 5.2: Kepler's version of the Gregorian chant "Victimae paschali laudes." Text: "Let Christians offer sacrifical praises to the Passover victim. The lamb has redeemed the sheep; innocent Christ has reconciled sinners to the Father."
Sound example 5.3: Kepler's melodic skeleton of the Gregorian chant "Victimae paschali laudes."
Sound example 5.4: Orlando di Lasso's motet In me transierunt. Text: "Thy wrath has swept over me; thy terrors destroy me. My heart throbs; my strength fails me; my sorrow is ever before me. Forsake me not, O Lord; O my God, be not far from me.” The first page gives definitions of the rhetorical terms that appear in the score (according to the rhetorical analysis by Joachim Burmeister, 1606).
Sound example 5.5: The beginning of Lasso's motet In me transierunt, as rendered by Kepler and in a modern edition.
Sound example 5.6: Kepler's version of the songs of the planets. By touching each planet's song you can hear it separately or hear all together by touching the indicated button.
Sound example 5.7: A passage from Carlo Farina's Capriccio stravagante (1627), the earliest notated use of glissando in Western music, here imitating the meowing of cats.
Sound example 5.8: An example of a deceptive cadence in Lasso's motet In me transierunt, measures 6–7 (slowed down to highlight the cadence). On the downbeat of measure 7, the altus (second) voice delays or avoids the cadence to the tonic (E–G–B) by substituting a C for the expected B.
Sound example 7.1: The series of overtones (petits sons) observed by Mersenne (extended to include the controversial seventh overtone, which lies between A and B♭).
Sound example 9.1: A major triad (C–E–G) compared to a major seventh chord (C–E–G–B).
Sound example 9.2: Euler's first eight species of harmony, arranged in decreasing order of agreeableness (see figure 9.3a).
Sound example 10.1: A chord progression cited by Euler to show how the dominant seventh chord asserts the key of C.
Sound example 10.2: A dominant seventh chord (C–E–G–B♭).
Sound example 10.3: A tritone (F–B) resolving outward to a minor sixth (E–C).
Sound example 11.1: The pitch 26 Hz (lower than the lowest C of a piano, 32 Hz), which Thomas Young cites as the "distinct clicking sound ... of an extremely grave pitch" that a human glottis can produce.
Sound examples 11.2, 11.3: The beginning of the introduction to the final movement of Ludwig van Beethoven's Piano Sonata in C, op. 53 ("Waldstein," composed in 1804), played in Thomas Young's temperament (1800) and in equal temperament.
Sound example 17.1: Planck's example of a passage from a motet by Heinrich Schütz, "So fahr ich hin zu Jesu Christ" (SWV 379). Text: "Thus I fall asleep and rest soundly."
Sound examples 17.2, 17.3: Planck's first example, performed in a synthesized rendition, in which the voices readjust to just ("natural") intonation around each successive sustained note, compared to a live performance.
Sound examples 17.4, 17.5: Planck's second example, comparing a synthesized rendition to a live performance.
Sound example 17.6: A video of the Hertz oscillator in operation. Note that his vibrating buzzer both generates a sonic tone and the intermittent spark that gives off electromagnetic waves. Hertz later used this device to demonstrate that these electromagnetic waves could be reflected and refracted, like light; his experiments corroborated Maxwell's claim that light was an electromagnetic wave.
Sound example 17.7: The "Planck frequency," which is actually a pitch 135 octaves higher than this quite flat A (426 Hz). Because the Planck frequency is many orders of magnitude higher than the limits of human hearing, this example tranposes it into a comfortable range for hearing.
Sound example 18.1: The eight-measure theme on which J. S. Bach constructed his Chaconne, the final movement in his solo violin partita in D minor (BWV 1004).
Sound example 18.2: A video of a wine glass whose resonant frequency is 454.72 Hz, which is then excited by an audio oscillator producing a variable frequency that reaches the glass's resonant frequency, causing the glass to move sympathetically in its fundamental mode of vibration.
Thanks to Alexei Pesic for the design and execution of all the animations, videos, and the iBook.
Sound example credits
1.3: Courtesy of Shehan Prull (Shihan Fine Knives, Santa Fe, NM).
2.1: Courtesy of Benjamin Bagby, from Phillipe de Vitry: Motets and Chansons (Deutsche Harmonia Mundi/BMG Classics RD 77095), Sequentia, directed by Benjamin Bagby (1991).
3.3a–d, 3.4a–c: Courtesy of Paul Hillier, from Josquin Desprez: Motets and Chansons.
(Virgin Classics CDM61302), The Hilliard Ensemble, Paul Hillier, conductor (1984). Complete score of "De profundis clamavi" (NJE 15.11) courtesy of the Josquin Research Project (josquin.stanford.edu), with special thanks to Jesse Rodin and Craig Sapp; score excerpts in boxes 3.1 and 3.2 reproduced by permission of the American Institute of Musicology, Inc., Middleton, Wisconsin, from Musicological Studies and Documents, vol. 6, pp. 447–54.
4.2a–c, 4.4: Courtesy of Manfred Cordes, from Nicola Vicentinos Enharmonik: Musik mit 31 Tönen (Graz: Akademische Druck- und Verlags-Anstalt, 2007) and its accompanying CD.
4.5: Courtesy of Nigel Rogers and Charles Medlam, from Monteverdi, L'Orfeo (EMI Records Ltd. CMS 7 64947 2), Chiaroscuro directed by Nigel Rogers, with the London Baroque directed by Charles Medlam (1984); Messiaggiera: Guillemette Laurens, mezzo-soprano.
5.4, 5.5b, 5.8: Courtesy of Alexander Blachley and Christopher Greenleaf, from The Flemish Masters, vol. 1 (Classic Masters CMCD-1007), Pomerium Musices, Alexander Blachley, conductor (1988). Score courtesy of Anne Smith, The Performance of Sixteenth-Century Music (2011), by permission of Oxford University Press, USA.
5.7: Courtesy of Vincent Bernhardt, from a live performance in Lyon, France, by Il delirio fantastico, directed by Vincent Bernhardt (May 2011).
11.2: Courtesy of Edward Foote, from Beethoven in the Temperaments: Historical Tunings on the Modern Concert Grand (Gasparo GSCD-332), Enid Katahn, piano.
17.1: Courtesy of Emmanuel Music, from The Motets of Heinrich Schütz (Koch International Classics KCH 7189), The Chorus of Emmanuel Music, Craig Smith, conductor (1991).
17.2, 17.4: Courtesy of The Plancktones (Anne Matthews, alto; Logan McCarty, tenor; Michael Barrett, tenor; Darrik Yee, bass); recorded live at Harvard University, November 18, 2013.
18.1: Courtesy of Ariel Winnick, violin.
18.2: "Wineglass That Won’t Break” video courtesy of Harvard University Natural Science Lecture Demonstrations, Faculty of Arts and Sciences Science Division.
All other sound examples were played, sung, or generated by the author.