Music as Divine Order
Read More![Vitruvius' discussion of theatre design provided the context for a survey of ancient Greek harmonic theory. These diagrams show the arrangements of notes within the Greek system of tetrachords. (A tetrachord is a series of four notes separated by three intervals and spanning a perfect fourth (4:3)). According to the Greeks, tetrachords fell into three categories, determined by the intervals between the notes within them. The three categories of tetrachord were: diatonic, chromatic, and enharmonic. Vitruvius argued that the human voice undulates according to the musical intervals contained in tetrachords and that knowledge of the mathematical basis of these musical intervals was relevant to the acoustic and design of theatres. <br><br>
<b>Author:</b> Marcus Vitruvius Pollio<br>
<b>Title:</b><i> De architectura libri decem </i> decem [Ten books on architecture] (Venice, 1567) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21394501550003606"> F.2.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-SB9dzCG/0/5cd0177b/M/F-002-024-008-M.jpg)
Vitruvius' discussion of theatre design provided the context for a survey of ancient Greek harmonic theory. These diagrams show the arrangements of notes within the Greek system of tetrachords. (A tetrachord is a series of four notes separated by three intervals and spanning a perfect fourth (4:3)). According to the Greeks, tetrachords fell into three categories, determined by the intervals between the notes within them. The three categories of tetrachord were: diatonic, chromatic, and enharmonic. Vitruvius argued that the human voice undulates according to the musical intervals contained in tetrachords and that knowledge of the mathematical basis of these musical intervals was relevant to the acoustic and design of theatres.
Author: Marcus Vitruvius Pollio
Title: De architectura libri decem decem [Ten books on architecture] (Venice, 1567)
Shelfmark: F.2.24
![Gregor Reisch's representation of the art of Music. Alongside Lady Music and a vivid picture of practical music making, Pythagoras is shown in the foreground weighing hammers. According to legend, Pythagoras had discovered the mathematical basis of music (and the universe) when he passed by a blacksmith’s shop. Hearing musical consonances between the sounds made by the different hammers as they struck the anvil, he later found that octave intervals had been achieved by hammers whose weights differed by a ratio of 2:1; the fifth by a ratio of 3:2; the fourth by 4:3. Whilst in reality these musical ratios reflect the differing lengths of sounding strings rather than the weights of hammers, this tale nevertheless proved influential. <br><br>
<b>Author:</b> Gregor Reisch<br>
<b>Title:</b><i> Margarita philosophica </i> [Pearl of wisdom] (Basel, 1583) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21574072500003606"> C.14.24</a><br>
<b>Provenance:</b> Gift of Edward Martin, President of Queens’ College 1631](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-hkf2HZH/0/0d4b527b/Ti/C-014-024-003-Ti.jpg)
![Written in the fourth century by the Roman author Macrobius, this commentary on Cicero’s <i>Dream of Scipio</i> became one of the most widely cited books of the middle ages. Its discussion of the musical philosophy of Ptolemy, Plato, and Pythagoras played an essential role in securing the idea of universal harmony a central position in medieval and Humanist education and thought. In the Dream, Cicero (106-43 BC) presents an imagined ‘high place full of stars, shining and splendid’ from which his main protagonist, Scipio Aemilianus, looks down on the city of Carthage. Scipio sees that the universe is made up of nine celestial spheres. The Earth is the innermost, whereas the highest is heaven. In between lie the Moon, Mercury, Venus, Mars, Jupiter, and Saturn (which proceed from lowest to highest). As he stares in wonder at the universe, Scipio Aemilianus begins to hear a ‘loud and agreeable’ sound. Scipio’s grandfather (Scipio Africanus) identifies this as the ‘music of the spheres’. According to Macrobius, this harmony resulted from the arrangement of the heavenly bodies according to Pythagorean harmonic ratios. This much-read late sixteenth-century edition by the famous French printer Henri Estienne (1531-98) was given to the college by Queens’ president, Henry James (d.1717).
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<b>Author:</b> Macrobius Ambrosius Theodosius<br>
<b>Title:</b><i> Commentarii in somnium Scipionis </i> [Commentary on the dream of Scipio] (Paris, 1585) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21402154100003606"> D.20.64</a><br>
<b>Provenance:</b> Henry James, President of Queens' College (1675-1717)](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-DwcPp9G/0/b234ca6d/Ti/D-020-064-001-Ti.jpg)
![An early reader has marked up key passages in this book by inscribing octothorpe symbols in the margins.<br><br>
<b>Author:</b> Macrobius Ambrosius Theodosius<br>
<b>Title:</b><i> Commentarii in somnium Scipionis </i> [Commentary on the dream of Scipio] (Paris, 1585) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21402154100003606"> D.20.64</a><br>
<b>Provenance:</b> Henry James, President of Queens' College (1675-1717)](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-2fc5FXD/0/5587fd72/Ti/D-020-064-002-Ti.jpg)
![It was largely through the work of the Roman statesman and educational reformer, Anicius Manlius Severinus Boethius (c.480–c.524), that medieval musicians and scholars discovered Greek music and the philosophy associated with it. The presence at Queens’ of his treatise, ‘On the organization of Music’, in an edition acquired in the sixteenth century reflects the continuing role it enjoyed across Europe as a standard text for schools and universities. Assisted by Boethius’ mathematical view of music, medieval scholars and musicians inferred two interconnected ideas: that music mirrored the essential harmony of the cosmos and that it had a decisive influence on human health and behaviour (the doctrine of ethos). For Boethius audible music (<i>musica instrumentalis</i>) was merely a gross metaphor for the two higher forms of music: harmony of the human constitution (<i>musica humana</i>) and, most importantly, harmony of the cosmos (<i>musica mundana</i>). In Boethius’ view it was necessary to have mastered mathematical music in order to truly judge the work of a musician, whether composer or performer.
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<b>Author:</b> Boethius<br>
<b>Title:</b><i> De Institutione Musica</i> in <i>Opera omnia </i> [Works] (Basel, 1570) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21392221580003606"> F.1.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-BDPc2fB/0/502acb31/Ti/F-001-024-007-2-Ti.jpg)
![<b>Author:</b> Boethius<br>
<b>Title:</b><i> De Institutione Musica</i> in <i>Opera omnia </i> [Works] (Basel, 1570) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21392221580003606"> F.1.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-dgWLWXB/0/340d88fc/Ti/F-001-024-008-2-Ti.jpg)
![In Book 1, Chapter 11 of <i>De institutione musica</i> Boethius explains 'in what ways the ratios of consonances were variously considered by Pythagoras.' These diagrams illustrate Pythagoras's conception of music as an art founded on the ratio 6:8:9:12.
<br><br>
<b>Author:</b> Boethius<br>
<b>Title:</b><i> De Institutione Musica</i> in <i>Opera omnia </i> [Works] (Basel, 1570) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21392221580003606"> F.1.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-CfMzdtj/0/51b7111f/Ti/F-001-024-005-Ti.jpg)
![<b>Author:</b> Boethius<br>
<b>Title:</b><i> De Institutione Musica</i> in <i>Opera omnia </i> [Works] (Basel, 1570) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21392221580003606"> F.1.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-vC5CTJz/0/1ffca66d/Ti/F-001-024-006-Ti.jpg)
![Discussion of the composition of the Greek musical scale in terms of varying sizes of semitones, tones (tonus), fourths (diatesseron) and fifths (diapente).<br><br>
<b>Author:</b> Boethius<br>
<b>Title:</b><i> De Institutione Musica</i> in <i>Opera omnia </i> [Works] (Basel, 1570) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21392221580003606"> F.1.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-2MvpLMP/1/2c0e6f5e/Ti/F-001-024-008-Ti.jpg)
![Dedicated to Emperor Augustus, the <i>Ten books on architecture</i> by the Roman architect Marcus Vitruvius Pollio (c.90-c.20 BC) is the only treatise on architecture to have survived antiquity. Rediscovered in 1414, numerous editions published over the subsequent century confirmed Vitruvius’ importance as an authority not just on ancient architecture, but also on aspects of music. Owing to the fact that Vitruvius' original illustrations had not survived, the woodcuts that occur throughout this edition by the famous humanist Daniele Barbaro (1514-70) are derived from the text.
<br><br>
<b>Author:</b> Marcus Vitruvius Pollio<br>
<b>Title:</b><i> De architectura libri decem </i> decem [Ten books on architecture] (Venice, 1567) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21394501550003606"> F.2.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-fPK9xC8/0/42e4c7fe/Ti/F-002-024-001-Ti.jpg)
![Vitruvius' discussion of theatre design provided the context for a survey of ancient Greek harmonic theory. These diagrams show the arrangements of notes within the Greek system of tetrachords. (A tetrachord is a series of four notes separated by three intervals and spanning a perfect fourth (4:3)). According to the Greeks, tetrachords fell into three categories, determined by the intervals between the notes within them. The three categories of tetrachord were: diatonic, chromatic, and enharmonic. Vitruvius argued that the human voice undulates according to the musical intervals contained in tetrachords and that knowledge of the mathematical basis of these musical intervals was relevant to the acoustic and design of theatres. <br><br>
<b>Author:</b> Marcus Vitruvius Pollio<br>
<b>Title:</b><i> De architectura libri decem </i> decem [Ten books on architecture] (Venice, 1567) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21394501550003606"> F.2.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-SB9dzCG/0/5cd0177b/Ti/F-002-024-008-Ti.jpg)
![<b>Author:</b> Marcus Vitruvius Pollio<br>
<b>Title:</b><i> De architectura libri decem </i> decem [Ten books on architecture] (Venice, 1567) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21394501550003606"> F.2.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-FkqXRx3/0/0f17c45c/Ti/F-002-024-014-Ti.jpg)
![Vitruvius explains how bronze vases (echea) tuned to resonate to specific musical harmonies (the fourth, the fifth, the octave) can enhance acoustic properties of theatres. According to Vitruvius, vases were placed in niches under the seats in Greek and Roman theatres. When the voice of an actor fell in unison with any of the vases its power would be increased so that it reached the audience with greater clarity. Vitruvius’ belief that the proportions of the human body provided a universal model of beauty applicable to architecture was adapted by Renaissance architects who proposed a corresponding model based on Pythagorean ratios.
<br><br>
<b>Author:</b> Marcus Vitruvius Pollio<br>
<b>Title:</b><i> De architectura libri decem </i> decem [Ten books on architecture] (Venice, 1567) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21394501550003606"> F.2.24</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Divine-Order-Gallery/i-fzhgGsB/0/a348cd44/Ti/F-002-024-009-Ti.jpg)