Sonic mapping in Leonardo's disegni

Michael Eisenberg

Columbia University

In the 1568 edition of his Lives of the Artists, Giorgio Vasari casts Leonardo as a proficient performer, teacher and improviser on the lira da braccio. Even if Vasari’s account is somewhat mythologized, evidence of Leonardo’s expertise in music emerges from his disegni and from his discursive reflections on musica and the properties of sound.

Seen through the Neo-platonic prism of the Renaissance, musica ordered the cosmos. Beginning from the macrocosm with its harmony of the spheres (musica mundana), to the microcosm (the body’s musica humana), to its ultimate reification in musica instrumentalis, music was understood as the means that synchronized all layers of the physical world.

While Leonardo denigrated himself as an omo sanza lettere or unlearned, we know that he owned Marsilio Ficino’s commentaries on Plato, in which the neo-platonic philosopher discussed in depth the harmony of the spheres. Leonardo also designed the illustrations for De divina proportione, the book on the golden section that his friend the mathematician Luca Pacioli wrote in 1496-98. Leonardo’s recourse to musical proportions is certainly a topic worth exploring in its own right. Some of his paintings are built on the golden ratio (the Annunciation and the Adoration of the Magi) and it has been argued that the Last Supper is structured visually according to the Platonic proportions that generate the three perfect musical consonances.

Leonardo was also most likely acquainted with Franchino Gaffurio, the maestro di capella of the cathedral of Milan and the author of the music treatise De harmonia. It is possible that Leonardo referred precisely to Gaffurio’s De harmonia when formulating an analogy between the trachea and a wind instrument based on a libro delli strumenti armonici, a book of harmonious instruments he owed. The music treatise of this Milanese composer drew extensively on Boethius, the leading expositor on musica, and the aural ordering of the microcosm in medieval thought. But for Leonardo, it was the visual expression of the microcosm that permeated his imagination, ranging from his Vitruvian man to the anatomical drawings of embryology.

As with all his investigations into the physical universe, Leonardo goes beyond analogy to describe sound in technical terms as the percussione dell’aria, adopting Boethius’ exact terminology. In his musings on sound, he discusses such acoustic phenomena as the enchanting harmony emanating from the fountain at Rimini, a specific instance that provides a window into the artist’s “acoustical world.” Acoustic phenomena also display Leonardo’s intriguing investigation into the commutation of physical materials like air and water to sound. As with other topics, he is absorbed with understanding the mechanics of sound. Similarly, Leonardo’s precise calculation of the decay of sound through space correlates to his study of diminishing perspective and optics. Though rare, music is even occasionally extrapolated to its medieval connotations of the microcosm. In fact, one of the anatomical studies on embryology appears on the same folio where Leonardo compares the visual harmony of the painter's brush to the aural harmony of music (fig. 1).

To understand how Leonardo worked out critical technological problems with subtle references to this larger epistemological framework, a drawing of a bell from his Madrid Manuscripts is particularly interesting (fig. 2). In general, Leonardo’s Madrid Manuscripts are a rich source for music as he portrayed there numerous music instruments, but the section of Manuscript Madrid II that contains folio 75 is particularly significant.

On folio 75 of Manuscript Madrid II, Leonardo drew a bell without a clapper struck by two hammers at its base. The bell utilizes levers with heads operated mechanically on a tracker action initiated by keys. The lever heads are intended to alter the pitch of the bell. Leonardo added a commentary to his image of the bell:

The same bell seems to be four bells. Organ keys with the bell held fast and struck by two hammers, and it will have a change of tones similar to the organ.

Normally a bell can only sound one pitch, but in this drawing Leonardo is charting sonic space on the surface of the bell. He is aware that the bell has regions which produce different pitches based on the instrument’s series of overtones, and that by dampening other areas he is able to isolate an alternate pitch. This experiment with how to produce multiple pitches on the surface of a bell parallels his experimentation with pitched drums.

The bell is a commonplace image for Leonardo as it appears a total of 40 times in his notebooks. Many reasons may be suggested for his interest in designing or producing bells, but it is worth recalling that bells carry a particular Pythagorean resonance in the Renaissance.

At least in Renaissance reception, Pythagoras is depicted as conducting his acoustical experiments with bells. The pitches Leonardo is seeking to generate from this one bell correspond to these proportional acoustical experiments but localize them on one bell. This mapping of distinct pitches derived from musical proportions is not described specifically in spatial terms but envisions a cartography, albeit tenuous, of acoustical space. Thus in this simple invention, Leonardo elegantly coalesces innovative organological experimentation with a larger philosophical interrogation into how one might chart sonic space.

Fig. 1 Leonardo da Vinci, The foetus, and the muscles attached to the pelvis, c.1511,pen and ink over red and black chalk, 30.4 x 21.3 cm, Windsor, RL 19101. (Royal Collection Trust / © HM Queen Elizabeth II 2012).

Fig. 2 Leonardo da Vinci, Manuscript Madrid II, fol. 75v.

Fig. 3 Leonardo da Vinci, Manuscript Madrid II, fol. 75v, detail.

NEH Institute

Sonic mapping in Leonardo's disegni