Music and the Scientific Revolution
Read More![Benedetti challenged orthodoxy further by means of the musical examples displayed here. Through them, he correctly argued that it was impossible for both the harmony and melody of a musical work to proceed according to intervals that are at all times both musically pure and mathematically perfect. The conflicts that always arise between melodic steps and harmonic intervals require musicians to make occasional adjustments to interval sizes. In contrast to those who expected musical art to conform to number, Benedetti realised that this was not always possible.
<br><br>
<b>Author:</b> Giovanni Battista Benedetti<br>
<b>Title:</b><i> Diversarum speculationum mathematicarum, & physicarum liber</i> [Book of various mathematical and physical ideas] (Turin, 1585) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21397918030003606"> D.1.26</a> <br>
<b>Provenance:</b> Gift of John St George, Queens’ Fellow (1570s)](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-sw9dxXC/0/97867327/M/D-001-026-005-M.jpg)
Benedetti challenged orthodoxy further by means of the musical examples displayed here. Through them, he correctly argued that it was impossible for both the harmony and melody of a musical work to proceed according to intervals that are at all times both musically pure and mathematically perfect. The conflicts that always arise between melodic steps and harmonic intervals require musicians to make occasional adjustments to interval sizes. In contrast to those who expected musical art to conform to number, Benedetti realised that this was not always possible.
Author: Giovanni Battista Benedetti
Title: Diversarum speculationum mathematicarum, & physicarum liber [Book of various mathematical and physical ideas] (Turin, 1585)
Shelfmark: D.1.26
Provenance: Gift of John St George, Queens’ Fellow (1570s)
![The French polymath and cleric, Marin Mersenne (1588–1648), believed that the universe was a perfect creation based upon God’s design, hence it was rational, orderly and harmonious. However, Mersenne’s conception of cosmic harmony rejected Pythagorean number mysticism to propose a universe comprising extended matter governed by precise mechanical laws. Music became one of the most important models for Mersenne’s cosmology as it manifested more clearly than anything else this mechanistic-harmonic order. Intended as a compendium of everything the musician need know, Mersenne’s <i>Harmonicorum libri</i> provides invaluable insights into both the practice and philosophy of music in the seventeenth century. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-VRjc6nq/0/54acf914/Ti/D-001-017-024-2-Ti.jpg)
![The so-called ‘Guidonian hand’ used in the late middle ages as a mnemonic device to enable singers to sight-sing. Each portion of the hand represents a specific note within the hexachordal system. Mersenne referres to it as the 'harmonic hand'. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-M2Wf5gt/0/7aba297d/Ti/D-001-017-017-Ti.jpg)
![The many illustrations and detailed descriptions of instruments and tunings in <i> Harmonicorum</i> speak to Mersenne’s interest in music as a means to discover and measure nature’s hidden properties. By using musical instruments as scientific instruments, he was able to determine the laws that govern the vibration of musical strings, now known as ‘Mersenne’s Laws’. <br><br>
The diagram above demonstrates the so called ‘Mersenne test’, used to determine the quality of a musical string. The sounding vibrations of a ‘Bonne Corde’ are regular and distinct at the outer sides and free from fuzzy lines in the middle. Modern methods of gut string manufacture obviate the need for this test. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-BxP2pG3/0/42f5e5cd/Ti/D-001-017-018-Ti.jpg)
![<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-VGmRXdK/0/c14b281a/Ti/D-001-017-019-Ti.jpg)
![Woodcut illustration and description of a viol, including details of its range. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-wwPcTMr/0/4e7d42b6/Ti/D-001-017-020-Ti.jpg)
![In Book 8 of his <i>Harmonicorum</i> Mersenne deals with the theory of composition. These are the twelve modes of music, as described by Renaissance music theorists.<br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Harmonicorum</i> [Harmonics] (Paris, 1636) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21586143390003606"> D.1.17</a> <br>
<b>Provenance:</b> Bequeathed to Queens’ College by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-vKCccHj/0/59376b39/Ti/D-001-017-024-Ti.jpg)
![Two letters from Giovanni Battista Benedetti (1530–90) to the famous Flemish composer Cipriano de Rore (1515–65) mark a turning point in perceptions concerning music’s basis in number. Famous for his daring use of chromatic harmony and melody in his madrigals, de Rore was the ideal composer to consult on this matter. In his letters published in his treatise on mathematics, Benedetti argued that musical ratios should be measured in terms of vibrations rather than string lengths (as the Pythagoreans had done). In so doing, Benedetti’s new thinking helped to reposition music in the realm of acoustical science. In the new system, the significance of numbers had shifted from that of mystical cause to being descriptive of physical phenomena. Yet, in both systems the small number ratios used to express musical intervals were in fact the same as before (in either system an octave, for example, is expressed as 2:1).
<br><br>
<b>Author:</b> Giovanni Battista Benedetti<br>
<b>Title:</b><i> Diversarum speculationum mathematicarum, & physicarum liber</i> [Book of various mathematical and physical ideas] (Turin, 1585) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21397918030003606"> D.1.26</a> <br>
<b>Provenance:</b> Gift of John St George, Queens’ Fellow (1570s)](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-kJZQp6c/0/2e3d7bea/Ti/D-001-026-004-Ti.jpg)
![Benedetti challenged orthodoxy further by means of the musical examples displayed here. Through them, he correctly argued that it was impossible for both the harmony and melody of a musical work to proceed according to intervals that are at all times both musically pure and mathematically perfect. The conflicts that always arise between melodic steps and harmonic intervals require musicians to make occasional adjustments to interval sizes. In contrast to those who expected musical art to conform to number, Benedetti realised that this was not always possible.
<br><br>
<b>Author:</b> Giovanni Battista Benedetti<br>
<b>Title:</b><i> Diversarum speculationum mathematicarum, & physicarum liber</i> [Book of various mathematical and physical ideas] (Turin, 1585) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21397918030003606"> D.1.26</a> <br>
<b>Provenance:</b> Gift of John St George, Queens’ Fellow (1570s)](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-sw9dxXC/0/97867327/Ti/D-001-026-005-Ti.jpg)
![The great German astronomer, Johannes Kepler (1571–1630), believed that the development of music in parts (polyphony) constituted an advance comparable to the Copernican revolution in astronomy. According to Kepler, the perfection of musical harmony as used by musicians stemmed from its correspondence to geometrical archetypes in the mind of God and soul of man.<br><br>
<b>Author:</b> Johannes Kepler<br>
<b>Title:</b><i> Harmonices mundi</i> [The harmony of the world] (Linz, 1619) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21553618360003606"> D.1.35 </a> <br>
<b>Provenance:</b> One of a set of Kepler volumes left to Queens’ by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-6ZTjZLP/0/ccba9253/Ti/D-001-035-017-2-Ti.jpg)
![On the origins of harmonic proportions. <br><br>
In Book 3 of <i>Harmonices mundi</i> Kepler provides the theoretical background to music theory as a precursor to his use of it to explain the works of nature, later in the book. <br><br>
<b>Author:</b> Johannes Kepler<br>
<b>Title:</b><i> Harmonices mundi</i> [The harmony of the world] (Linz, 1619) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21553618360003606"> D.1.35 </a> <br>
<b>Provenance:</b> One of a set of Kepler volumes left to Queens’ by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-C9xhZLM/0/437d03ac/Ti/D-001-035-020-Ti.jpg)
![The five platonic solids. <br><br> In 1596 Kepler had argued that these 'solid figures' could be inserted inside one another to form the distance relationships that separate the six planetary spheres (Mercury, Venus, Earth, Mars, Jupiter, Saturn). This idea played an essential part in his conception of celestial harmony. <br><br>
<b>Author:</b> Johannes Kepler<br>
<b>Title:</b><i> Harmonices mundi</i> [The harmony of the world] (Linz, 1619) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21553618360003606"> D.1.35 </a> <br>
<b>Provenance:</b> One of a set of Kepler volumes left to Queens’ by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-ZPmH7mT/0/8e4c3aff/Ti/D-001-035-015-Ti.jpg)
![This small stellated dodecahedron is an extended version of the dodecahedron, which is one of the five ‘Platonic solids’ (see previous). <br><br>
<b>Author:</b> Johannes Kepler<br>
<b>Title:</b><i> Harmonices mundi</i> [The harmony of the world] (Linz, 1619) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21553618360003606"> D.1.35 </a> <br>
<b>Provenance:</b> One of a set of Kepler volumes left to Queens’ by John Smith](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Music-Scientific-Revolution-Gallery/i-jGx2PmF/0/c0a8667d/Ti/D.1.35-001-Ti.jpg)