Carrière et vie professionnelle

Music, Machines and Theology (II)

Mersenne’s organ: Theory, experiment and artisanal knowledge revealed

To Mersenne the organ was simply one of the most admirable pneumatic machines ever invented. And strictly that. Not once in the treatise on organ was he tempted by the art of allegory, portraying the organ as a symbol of God’s creation, for instance, as Athanasius Kircher did in his 1650 Musurgia universalis. Yet any reader could tell the organ represented more than a musical instrument. Even browsing Mersenne’s description of the

God playing on his celestial organ, giving birth to the world. From Kircher's Musurgia universalis

God playing on his celestial organ, giving birth to the world. From Kircher's Musurgia universalis

organ gives incredible insights into the practice of natural philosophy, which in addition to a thorough knowledge of music theory, now involved experimental data gathering and hands-on savoir-faire from the mechanical arts. Actually making the organ, nonetheless, had less importance to Mersenne than the rigorous account entailing its construction. The organ’s comprehensive description, as we will see, reified the practices of the mechanical philosophy into an admired and altogether Christian material entity. The organ was thus not only a powerful religious symbol to Mersenne: it epitomized and materialized the role that theory, experiment, and the mechanical arts played in the overall notion of harmonie universelle.

Length of organ pipes, and how they sound, from Mersenne's Harmonie universelle.

Length of organ pipes, and how they sound, from Mersenne's Harmonie universelle.

Mersenne’s experimental research with organ pipes is traceable to the early 1620s. In correspondance with Rouen honnêtes hommes like Robert Cornier, and in situ, Mersenne sought to have experiments with organ pipes done by other parties in order to confirm his own results. Mersenne was chiefly interested in the standardization of organ-pipe making. Mersenne, for instance, discovered in a series of experiments that if one used small diameter pipes, say of three lines (roughly 6 mm) and a base length of half a foot, Pythagoras’s explanation of consonances was approximately verified-i.e. if you double the length of this small pipe, it will sound an almost perfect octave lower. But what Mersenne discovered, and Vincenzo Galilei before him, was that with bigger sounding pipes this scheme did not stand anymore. In a series of numerical examples, Mersenne demonstrated that doubling the length of a pipe while at the same time keeping its cross-section constant did not produce the required octave; the sound was off by half a tone, a tone, or even more. Similarly, the Minim was able to report numerous experimental results proving that keeping the length of organ pipes constant while varying their cross-section did not produce either the required consonances. Here he used five half-foot pipes of diameters ranging from three lines to four inches, always doubling in size following the geometrical series. The experiments showed that it was virtually impossible to reach an octave when keeping the pipes’ length constant while modifying the cross-section. Mersenne wrote that to reach a sound an octave lower, one would have to add two inches in diameter and two feet in length to the biggest pipe. Mersenne’s description of the pipes’ dimension was precise to make sure that if “one encounters other intervals in pipes larger or smaller, he will have occasion for seeking the reason.”

From such experiments Mersenne was able to generate a universal table of organ-pipe making, containing he said “all that can be reasonably desired on the subject [the division of the octave], aside from which there is nothing for the makers to know.” In this full-page table, Mersenne combined knowledge acquired from experiments, artisanal practices and the theory of mathematical proportions. This table — drawn to scale, the height being one foot (pied de roy) — contains eleven columns showing the precise length and cross-section of organ pipes corresponding to several divisions of the diapason. This table, however, did not solve all there was to know about the production of sound in organ pipes. Why, for example, did organ pipes sing different intervals when air pressure varied? What was the relationship between air pressure, musical intervals and the material components of pipes? For Mersenne the “manufacturers can help out Philosophy by preparing a catalogue of the pipes which rise only a semitone, or a third, or a fourth, or a fifth, etc., for it will be easier to find the reason when one understands the qualities of the pipes which cause the difference of these pitches…” Musical instrument makers were truly central to Mersenne’s work. Because they were actually making these pneumatic machines, which involved all kinds of matter, object and craftsmanship, they were the best providers of raw data regarding the nature of sound production. Finally, as Mersenne reminded his readers, due to the great and multifaceted complexity of the organ “whatever one may say and whatever figures one can give to explain everything that concerns the construction of the organ, it is very difficult to have it understood when one has not seen one made, or has not considered the pieces in the large as well as in detail.” To fully understand how an organ worked, one had to watch and scrutinize in situ how it was put together. If natural philosophers were serious in their quest to become lord and master of nature, they had to tackle head-on the mechanical arts. The novel experimental practice, in other words, went hand-in-hand with the traditional artisanal practices.

Twenty-seven-key organ clavier invented by Mersenne, depicted in the Harmonie universelle.

Twenty-seven-key organ clavier invented by Mersenne, depicted in the Harmonie universelle.

As convinced as Mersenne was of the utility of artisanal knowledge and experimental practices, he likewise believed the mathematical foundation of music could greatly improve the practice of organ playing. This he showed by studying the “science of organ claviers.” In fact, Mersenne explained that “[Gioseffo] Zarlino would not have taken so much pains in explaining the syntone of Ptolemy, which misses many degrees, if he had had an understanding of the keyboards that I propose in the treatise on the spinet and the organ.” Mersenne, in brief, tried to relocate the complete knowledge of musical genres into a mechanical device-the organ clavier. Since experiments and mechanical knowledge showed how best to build organ pipes, a keyboard based on the theory of music now had to match their perfect diapason, so that theory and practice could ultimately work in unison.

Proceeding methodically, Mersenne started with two thirteen-key claviers differently tempered, neither of which displaying perfect major and minor thirds and sixths. In order to produce all the just intoned consonances, these two claviers had to be combined into a seventeen-key clavier. Yet even this keyboard was insufficient to exhibit the just intonation of the complete diatonic genre, which needs at least eighteen tones (hence nineteen keys). The latter, although exhibiting the three musical genres, did not do so perfectly for the chromatic and enharmonic ones, yet would be the best-tempered nineteen-key organ keyboard one could imagine, matching the third column of the organ-pipe table presented previously. To fully render the perfect harmonic diapason, a clavier would need twenty-seven keys, the first row of keys for the diatonic genre, the second row for the chromatic and the last row for the enharmonic. The table that accompanies the clavier’s drawing was the real thing though, displaying at a glance (says Mersenne) the perfection of the harmonic diapason, such that one could straightforwardly extract from it this twenty-seven-key clavier.

Drawn from the most exact theory of music, Mersenne’s twenty-seven-key clavier had great advantages over the conventional ones, and because these claviers were so perfect, nothing should stop organists using them, even if it meant learning anew how to play the organ:

For it is of no importance that the difficulty of playing them is greater, inasmuch as it is not necessary to feel pity for the pains nor to avoid the work which leads to perfection. To this I add that they will be played as easily as the others when the hands become accustomed to them, because they follow the infallible rule of reason.

In this case, musicians and the mechanical arts had to meet the terms of the music theorist, for only through the latter’s science would a better musical instrument be designed and built-and consequently would music approach the long lost perfection of Antiquity.


Mersenne’s twenty-seven-key organ clavier became a true mechanical representation — an embodiment — of the most perfect musical harmony attainable by any of God’s creation. Yet without the precise craftsmanship of organ pipes, which was brought to light by experiments on the width and height of pipes, organ claviers were simply useless. Theory was thus no longer enough. Boethius’s rational musicus was replaced in the seventeenth-century by a perfect musician whose knowledge encompassed, besides the theory of numbers, physiology, philology, poetry, anatomy, metallurgy, the mechanical arts and even magic.

The organ epitomized better than any other musical instrument the strong relationship between religion and secular knowledge. In fact, the same way Lutherans and Catholics claimed organ music assisted the population in praising the Lord Almighty, Mersenne used the detailed description of the mechanical organ to help artisans and savants understand the production of natural philosophical knowledge. The ecumenical virtues of the church organ were transformed, in the secular and material world of natural philosophy, into epistemological virtues. By keeping the organ as mechanical as possible, without imposing on it any allegorical or religious connotation, Mersenne was able to use the organ as the most worthy secular object of knowledge, which could be studied by Christians of all faiths. The same piece of machinery, I would claim, symbolized both the best religious and secular practices. Organs were the reification of Mersenne’s universal harmony, an harmony juxtaposing the spiritual and the worldly, the music of pure consonances with the levers, gears and bellows of a mechanical device. To worship God while listening to the music of an organ or to discover God’s natural creations by means of the latter’s mechanical parts was not that incongruous to someone like Mersenne.


March 15, 2009 - Posted by | Epistemology, Instrument | , , , ,


  1. I’d like to arrange for a high-quality scan of Mersenne’s twenty-seven-key organ clavier. What do you think?

    Comment by What Music Really İs | August 10, 2015 | Reply

    • I do not own a copy of Mersenne’s book (unfortunately!). You will have to request a scan from a library.

      Comment by jfgauvin2008 | August 10, 2015 | Reply

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