Woodcut illustrations of cornetts (left page) and a serpent (right page). Author: Marin Mersenne Title: Cogitata physico-mathematica [Physico-mathematical thoughts] (Paris, 1644) Shelfmark: C.14.3
C.14.3
![Woodcut illustrations of cornetts (left page) and a serpent (right page). <br><br><b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-q998wvR/0/5a27b3c0/M/C-014-003-003-M.jpg)
![In his treatise entitled <i>Physico-mathematical thoughts</i>, Mersenne includes a lengthy section on music, in which he explores musical harmony, instruments, tuning and temperaments. As both cleric and scientist, Mersenne prized music as an art reflective of mathematical perfection and divine order. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-h3qvGRV/0/ead9194d/Ti/C-014-003-007-Ti.jpg)
![‘Is Music a science? Does it have evident, certain principles?’ These were questions Mersenne had in mind when he became fascinated by instruments, tuning and temperaments. Mersenne prized music as an art reflective of mathematical perfection and divine order. Unfortunately, the twelve-note octave as played on organ and harpsichord keyboards was (and is) not consistent with that ideal. No matter how it is tuned, it is impossible for more than a few of the degrees of the scale to act as the bass for harmonies that are pure and mathematically correct. For Mersenne this was not simply a musical problem, but also a philosophical one that required debate and research. One solution to the tuning problem, shown here, was to design keyboards with more than twelve notes per octave. By adding extra notes the number of playable keys and harmonies would be increased. Another way, known as ¼ meantone temperament, is described a few pages earlier. This was achieved by tempering (or adjusting) the intervals of the twelve-note scale so that the most used keys would sound (and be) almost perfectly in tune, with the imperfections distributed amongst less used keys. <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-GskCJqp/0/3b0d2e88/Ti/C-014-003-002-Ti.jpg)
![Mersenne’s many descriptions of musical instruments here and elsewhere provide detailed and invaluable insights into this aspect of seventeenth-century music. Influenced by his interest in the then emerging science of acoustics, the inclusion of instruments in this scientific work reflects Mersenne’s conception of them as a new means through which to explore the principles underlying music. Here we see an illustration of a recorder together with accompanying music and tablature (a form of music notation). <br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-dKm2KdR/0/c52cf2f1/Ti/C-014-003-005-Ti.jpg)
![Woodcut illustrations of cornetts (left page) and a serpent (right page). <br><br><b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-q998wvR/0/5a27b3c0/Ti/C-014-003-003-Ti.jpg)
![A bell and tabor.<br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-6kHvSVK/0/b992ec60/Ti/C-014-003-004-Ti.jpg)
![The second of fourteen psalm settings for two or three voices by the French composer Antoine Brion. Mersenne included these as a means to demonstrate each of the twelve modes of music (as discussed by Renaissance theorists).
<br><br>
<b>Author:</b> Marin Mersenne<br>
<b>Title:</b><i> Cogitata physico-mathematica </i>[Physico-mathematical thoughts] (Paris, 1644) <br>
<b>Shelfmark:</b> <a href="http://idiscover.lib.cam.ac.uk/permalink/f/1nnjft8/44CAM_ALMA21573621010003606"> C.14.3</a>](https://photos.smugmug.com/Exhibitions/Heavenly-Harmony/Sympathy-Occult-Gallery/i-Wcfxvm3/0/181aaf5f/Ti/C-014-003-001-Ti.jpg)