The Defect in René Ouvrard’s Harmonic Proportions

In 1679, René Ouvrard published a pamphlet about the relationship between musical harmonies and architectural proportions called Architecture Harmonique, ou Application de la Doctrine des Proportions de la Musique à l’Architecture. The pamphlet presents a normative system of correlations between musical harmonies and architectural proportions, based on an analogous understanding of hearing and vision. Ouvrard claims that the system is infallible. In this paper, evidence regarding problems associated with Ouvrard’s normative system based on the correlations between musical harmonies and architectural proportions presented in Architecture Harmonique is showcased, implying that the system to a certain extent is fallible. Based on the argument, the problems are made possible by Ouvrard’s philosophical framework.


Introduction
I thought I explained myself well enough in the previous writings, regarding the marriage between music and architecture, so that no one would doubt that our soul, which is as harmonious in its eyes as in its ears, would be satisfied in its vision by the same harmonies which satisfy its hearing. 1 In 1679, the music theorist René Ouvrard (1624Ouvrard ( -1694 published a pamphlet about the relationship between musical harmonies and architectural proportions called Architecture Harmonique, ou Application de la Doctrine des Proportions de la Musique à l'Architecture. There is a consensus among architectural historians about the importance of Ouvrard's thinking to architectural theory, despite his relatively moderate precedence as a music and architectural theorist in his time. For instance, Joseph Rykwert argues in favor of Ouvrard's work regarding its significance in establishing a body of theory within the Académie Royale d'Architecture of the late seventeenth century (1980: 15). Hanno-Walter Kruft (1994: 132) makes similar assessments of Ouvrard's work. François Blondel, one of the most prominent figures of the Académie, demonstrated the authority of Ouvrard's thinking by using Ouvrard's theories directly in his Cours d'architecture (Blondel 1683: 756-760). Although Architecture Harmonique was Ouvrard's sole theoretical work regarding the intersection between music and architecture, he made several contributions to the field of music theory exclusively (Cohen 1974: 338). In addition to his theoretical oeuvre, Ouvrard occupied the position as Maître de musique at the Sainte Chapelle between 1663 and 1679, after being nominated as the Maître de Chapelle at the Cathedral of Bordeaux (1657Bordeaux ( -1660 and Chef de la Maîtrise at the Cathedral of Saint-Just in Narbonne (1660-1663) (Cohen 1974: 337), which illustrated Ouvrard's sturdy and prominent practical foundation in music.
In short, one can postulate that Ouvrard in Architecture Harmonique presents a normative system of correlations between musical harmonies and architectural proportions, based on an analogous understanding of hearing and vision. According to Ouvrard, all the possible consonances are to be found by various combinations of the first six numbers, 1, 2, 3, 4, 5, and 6 (Ouvrard 1679: 6). For instance, the proportion of 2 to 1 denotes the octave, 3 to 2 the fifth, 4 to 3 the fourth, and so on. His normative system, as he describes in Architecture Harmonique (Ouvrard 1679: 6), is founded on his work on arithmetic, l'Art et la Science des Nombres (1677), and he claims it infallible (Ouvrard 1679: 7, 30). Elaborations on the normative system are to be found in the ensuing sections.
This paper presents evidence of problems associated with the normative system of correlations between musical harmonies and architectural proportions in Architecture Harmonique, implying that Ouvrard's system to a certain extent is fallible. The problems, as it will be argued, are made possible by Ouvrard's philosophical framework, which in this case points to the basis of the judgment of aesthetic quality underlying the normative system of correlations between musical harmonies and architectural proportions, referring to the soul with its corresponding senses. The problems are cited or paraphrased, with attached commentary about the nature of the problem. For the sake of being systematic, the problems are denoted as "Example 1," "Example 2," etc., in addition to the references as to where in Architecture Harmonique they can be found. However, first, it is critical to elaborate on the core of the philosophical framework of the Architecture Harmonique, the soul.

The Consonance of the Soul
Ouvrard justifies the claim about the correspondence between musical harmonies and architectural proportions by referring to the composition of the soul as being principal (1679: 15). At Ouvrard's time, this line of reasoning was not new within the sphere of architectural theory. One of the predominant rules Italian Renaissance architects and architectural theoreticians should follow was the subsuming of buildings and all their parts to a system of mathematical ratios based on the ratios of the human body (Wittkower 1971: 101). As Wittkower claims, the use of Vitruvius was crucial in bolstering the acceptance of this system as an axiom. Although Vitruvius partly obeys the same principles as Ouvrard describes in his doctrine (concerning mathematical ratios), Vitruvius did not use the specific terms related to musical analogies (Ouvrard 1679: 16). In other words, Vitruvius did not justify the ratios through the utilization of music. Obviously, the mathematical ratios were not chosen by chance but rather given by God, through-as indicated-the human body, following His divine system (Wittkower 1971: 101-102). Therefore, to express divinity most exquisitely, architecture must implement similar proportions as those of the human body and soul. God's presence in the mathematical ratios was also justified through the use of the examples given by Scripture, e.g., the Temple of Solomon, the visions of Ezequiel, etc. Throughout the Renaissance, these directions were fused with Neo-Platonic ideas. At that time, such worldviews were prominent not only in an Italian context, but also in French architectural theory. Although not addressing the matter systematically, Philibert de l'Orme  in the introduction to his Premier tome, proclaims that everything which is well unified, connected and positioned to each other, will create "… a perfect [architectural] body in complete symmetry, proportion, and harmony, …" similar to the strings of an instrument, thereby creating harmonious chords. 2 Ouvrard pursues the notion of the composition of the soul being principal, stating that the soul desires these harmonic proportions, "… based on the analogy of our two noblest senses …". 3 By accepting this analogous principle, Ouvrard states, it is impossible to achieve proper architecture unless it follows the rules of harmonic proportions. This logic is sustained throughout the doctrine. For instance, it is argued that what is hurtful to the ear in a similar manner will be irritating to the eye. Thus, no real architectural beauty is possible unless the building is obedient to the same rules as the musical consonances (Ouvrard 1679: 5-6). All this taken into account (the soul, composed in harmonious proportions, being pleased via the senses by the same harmonious proportions of which it is composed), it must be remarked that several passages exist in Architecture Harmonique which give rise to problems connected to the system that Ouvrard claims to be infallible.

Sensuous Malconduct
As implied in the previous section, the way for us to recognize the musical harmonies and architectural proportions, according to Ouvrard, is through our hearing and vision, respectively. His first example, a hypothetical façade of an arcade, illustrates the importance of sensuously founding the relationship between musical harmonies and architectural proportions (Ouvrard 1679: 10-12). The height and width of the façade of the arcade are 32 and 24 feet, respectively. The height and width of the arch are 10 and 8 feet, respectively. The second floor is 16 feet above the bottom of the arcade and 24 feet wide. A centralized cross-window 4 on the second floor is 12 feet high and 6 feet wide. The cross-window is flanked by one half-cross-window on each side, each being 12 feet high and 3 feet wide. The distances from the respective edges to the half-cross windows are both 2 feet. The distances from the cross-window to the two flanking half-cross-windows are both 4 feet. Ouvrard then speculates on the hollowing out of the mullions and transoms of the cross-window and half-cross-windows similarly to organ pipes, in addition to adding gutters to receive air through them. And as the mullions and transoms receive wind, they will make audible consonances. He even concretizes the actual consonances by denoting the height of 32 feet as Ut, and proportions the other parts accordingly (Ouvrard 1679: 10).
His example shows an aesthetic legitimization of the proposed ratios of the doctrine through the factual audible consonances the oeuvre of architecture in question may produce if being concurrent to them, i.e., the proportions. Refer to Fig. 1 for a schematic illustration of Ouvrard's first example. The ratios of the parts are noted on the figure.
Vasco Zara explains, through the utilization of Ouvrard's second example, the Temple of Solomon, that Ouvrard portrayed a direct correlation between the architectural proportions (from musical ratios) and audible sounds (Zara 2011: 415). The second example is congruous to the first example in this regard. However, in the second example, Ouvrard explicitly advocates the need for knowledge on comprehension of the tones to be able to experience the exact sensuous pleasure of the correctly proportioned temple (Ouvrard 1679: 13). Consequently, in practice, one can imagine a tone-deaf architect claiming that his designed, erected building is unimpaired, proportionally speaking, even though it is not, according to the doctrine of harmonic proportions stipulated by Ouvrard. This is not necessarily a problem 5 but it is undoubtedly an apparent result of Ouvrard's sensuous prerequisites for aesthetic judgment. As previously mentioned, an analogous joining of musical harmonies and mathematical ratios with divine ties was nothing new during Ouvrard's time. According to Claude Palisca, Gioseffo Zarlino argues in favor of celestial harmony being constitutional for the construction of the soul (Palisca 1985: 178-179). Palisca refers to Zarlino claiming that the spirit is the medium making the soul able to experience the mundane manifestations of celestial harmony, e.g., audible music, through the bodily senses (Palisca 1985: 181). This taken into consideration, no explicit evidence exists in Architecture Harmonique of an established connection between the soul and the bodily senses by the spirit. Whether such connection should be assumed implicitly is not apparent, as-regarding this issue-one resides in a watershed moment at the time of the publication of Architecture Harmonique, since the importance of theological reasoning, following Enlightenment thought, consequently was decreasing. 6 Albert Cohen argues against assuming an implicit theological reading of Ouvrard. He writes: "The corpus of writings left by Ouvrard projects him as a true exponent of the Age of Reason" (Cohen 1974: 337). The arguments Cohen presents are based on Ouvrard's scientific manner of systematizing his theoretical endeavors, through the weightage he puts on lexicography, etymology, the utilization of original sources, and his acknowledgment of the importance of the Académie for the status of science (Cohen 1974: 337-338). The above-mentioned instance-the legitimation of the normative system through audible proof, and thereof the possibility of deviating from it-is hereby categorized as the first example (Example 1) of a problem in Ouvrard's normative system of harmonic proportions. With this as a foundation, the forewarned descriptions of the problems in the doctrine of harmonic proportions are continued in the following.
Example 2 And as in music all the sounds which are not following these proportions, or which do not have these ratios, are unpleasant and irritating to the ear, we also claim that in architecture, all the dimensions or measures which do not follow these proportions, or do not have these proprieties, will shock the vision and be disagreeable. What is different [between music and architecture], is that the proportions of the music consist so much in an indivisible point, so that on the monochord, the thickness of a hair, which lacks the accuracy of the harmonious sound, can be felt. In contrast, the vision is not so precise in perceiving the small proportional defects; and the habit of seeing few well-ordered ones 7 makes bearable those that are not. 8 Ouvrard uses this passage to clarify significant divergences between the receptive accuracy of the two senses. The sensibility of hearing is more precise than vision. Although not directly advocating it, Ouvrard implies the possibility of diverging from the doctrine of harmonic proportions, by using vision as the judgmental parameter. This is an instance of a problem with the doctrine. One can argue against such an interpretation by referring to a consequently strict application of the doctrine. However, when the stated imprecise visual sense is the fundamental 7 "Well-ordered ones" is translated from "régulières," directly meaning ones that are "in accordance with rules" or "regular." In this context, Ouvrard is referring to works of architecture which apply the doctrine of the proportions of music. 8 Et comme dans la Musique tous les sons qui ne sont pas dans ces proportions, ou qui n'ont pas ces rapports, sont desagreables à l'oreille et l'offensent, nous pretendons aussi que dans l'Architecture toutes les dimensions, ou mesures qui ne seront pas dans ces proportions, ou qui n'auront pas ces convenances, choqueront la veuë, et ne seront aucun agréement. Ce qu'il y a de difference, c'est que les proportions de la Musique consistent tellement dans un point indivisible, que sur le Monochorde l'épaisseur d'un cheveu qui manqueroit à la justesse du son harmonieux se sait sentir; au lieu que la veuë n'est pas si subtile pour appercevoir les petits défauts des proportions; et que l'accoûtumance d'en voir peu de régulières, rend supportables celles qui ne le sont pas (Ouvrard 1679: 9, my Eng. trans.). 6 As Palisca remarks, even Zarlino did fortify the sensuous inaccuracy, in so much as the spiritual mediation between the bodily senses and the soul is dependent on a harmonious structuring of the faculties in the brain relevant for the judgment of harmony (Palisca 1985: 181). parameter in the judgment of the beauty stemming from the architectural oeuvre, unwanted ramifications may occur.

Example 3
To make the complete comparison of the feeling of these two senses in this matter, it is necessary to know that as, in music, there are only the sounds which strike together, or which one hears at the same time, which must concur and make harmony with each other, and not with those following one another, or which is not perceived at the same time. In the same way, in architecture, there is only what is presented to the vision at the same time, which must follow these proportions: for example, the cross-windows, or windows of the façade of a building; the height, and the width of the same façade, or at least each floor. However, as the vision simultaneously embraces many more things than what can be heard, and it [the vision] being able to see all the parts of the same building façade instantaneously; if all these parts could have proportions in accordance with the relations which we have said to make harmony, their beauty would be charming and felt. 9 With this, Ouvrard proposes that one can limit the application of the normative system of harmonic proportions to a minuscule amount of the building. For example, just the windows, the height and width of a single façade, or the height and width of a single story, as long as they are the only ones seen together. This is another example of a problem. Nevertheless, Ouvrard does not recommend abandoning the system, but he is open to changing parts not seen together. He presents three different possible changes of proportions to retain harmony within the part in question: changing of numbers of a proportion within the genre, changing of the genre, 10 or changing of the species (Ouvrard 1679: 28-30). In the referred segment, Ouvrard poses an example of how to make changes of genre and species 11 of a triumphal arch. He cites that the two masses at both ends of the initial triumphal arch are 9 feet wide. On the respective sides, the two ensuing smaller openings are 18 feet wide and 36 feet high each. Subsequently, two mass parts are noted, each being 13.5 feet wide, followed by one centralized large opening being 27 feet wide and 54 feet high. Above these elements, which comprise the first story, three more above-laying sections each of 18 feet high are added. Thus, the width of the entire triumphal arch is equal to its height. He continues by showcasing that the utilized numbers, 9, 13.5, 18, 27, 36, 54, 72, 90, and 108, denoted as 2, 3, 4, 6, 8, 12, 16, 20, and 24, equals to the following musical consonances: Ut, Sol, Ut 2 , Sol 2 , Ut 3 , Sol 3 , Ut 4 , Mi 4 , Sol 4 , stating that the triumphal arch is consonant, visually speaking. Refer to Fig. 2 for a visualization of the triumphal arch.
Ouvrard outlines that one may find it necessary to change the composition of the triumphal arch, either due to the need for ornamented columns (presumably between the openings in the first story) or simply due to a need for the masses between the arch's openings to appear "stronger" (Ouvrard 1679: 30). He exemplifies how to make such changes by adapting the triumphal arch initially described. Both the end mass areas become 20 (or 24) feet wide. Both of the middle mass areas become 24 feet wide. The two smaller openings become 16 feet wide and 32 feet high. The centralized larger opening becomes 32 feet wide and 64 feet high. The three sections laying above the first story become 16 feet, 16 feet, and 32 feet in height, respectively, from bottom to top. The following proportions are present after implementing the changes: 2, 3, 4, 8, 10, 12, 16. This results in the following corresponding musical consonances: Ut, Sol, Ut 2 , Ut 3 , Mi 3 , Sol 3 , Ut 4 . In other words, the visual consonance of the triumphal arch is retained. Refer to Fig. 3 for a visualization of the triumphal arch after implementing the changes.
One issue connected to changes between different parts in a work of architecture, is that the parts, with these permitted changes, may become dissonant in relation to each other. This is of course with the two above-mentioned examples 1 and 2 in mind. Considering the same problems, another issue is how to decide which changes to implement and on which grounds. Ouvrard does not explicitly describe a systematic method regarding when to implement changes and what type of changes to implement in the relative instances. However, this is a question of complex syntax, which can hardly be expected to be handled exhaustively by any work of architectural theory, except for general guidelines. These problems related to the changes discussed above, facilitating possible visual dissonance in a work of architecture seen as a whole, are hereby categorized as Example 4.
Ouvrard upholds the notion of limiting the application of the doctrine to parts of the building seen simultaneously, another example of a problem, in the ensuing section: Example 5 And if, as we have just stated, all the parts which present themselves together to the vision have consonant proportions, regardless of there being ornament or not, the vision will feel attraction which can even be represented by the ear, as we will see in the example of a building raised on top of an arcade, with all these harmonic proportions. 12 Ouvrard reinstates the conception of the vision's inaccuracy, and the need for competence and experience of the utilization of the doctrine, through the following segment: Example 6 But regarding these things [the proportioning of the building and its parts], great judgment is required to be successful, especially as the vision is not always certain, and that its judgment often deceives us, as we experience in painting, where columns, mutules, and statues appear protruding and jutting out from the painting, which we know is flat. 13 This is another instance of a problem, advocating possible misuse of the doctrine, if our senses instruct us to do so. All the problems with the normative system of correlations between musical harmonies and architectural proportions in Architecture Harmonique have been showcased. This concludes the current section.

The Defect in René Ouvrard's Harmonic Proportions
As argued through the examples in the previous section, with the second section as a backdrop: Even though the prerequisites for architectural beauty, i.e., the harmonic proportions, in René Ouvrard's Architecture Harmonique are systematically accurate, the sensuous apparatus through which we process the visual impressions of the manifestations of the ratios-to ultimately please our souls-is not. An apparent difference exists between Ouvrard allowing changes of proportional numbers, genres, or species of an entire oeuvre, where he is remaining within the doctrine of harmonic proportions, and him-through encouraging judgment founded on the purely palpable registration of musical or architectural proportions-allowing deviation from the doctrine, through particular changes or other means. Even though Ouvrard, as previously remarked, refers to the presented doctrine as "infallible" (Ouvrard 1679: 7, 30), our judgment may tell us otherwise if we accept Ouvrard's premise of our sensuous apparatus being the judgmental 12 Et si, comme nous venons de dire, toutes les parties qui se presentent ensemble à la veuë peuvent avoir des proportions consonantes, quoy qu'il n'y ait point d'autre ornement, la veuë sentira des charmes qui pourront même estre representez à l'oüie, comme nous l'allons voir dans l'exemple d'un bastiment élevé sur une Arcade avec toutes ces proportions harmoniques (Ouvrard 1679: 9-10, my Eng. trans.). 13 Or en ces choses, il faut un grand jugement pour bien reüssir, d'autant que la veuë n'est pas toûjours certaine, et que son jugement nous trompe souvent, comme on éprouve dans la peinture, où des Colonnes, des Mutules, et des Statuës paroissent saillantes et avancées hors le tableau que l'on sçait estre plat (Ouvrard 1679: 23, my Eng. trans.). parameter. As discussed previously, it is impossible, in Architecture Harmonique, to retrieve explicit evidence of the sensuously founded judgment of divine connotations similar to ones found in Renaissance architectural theory. Thus, one cannot by Architecture Harmonique ensure the infallibility of the sensuously founded judgment similarly. In the utmost consequence, a dissonant chord may strike between our divinely constructed soul and its nourishing senses, and a defect in René Ouvrard's system of harmonic proportions may become apparent.
Some final remarks should be made regarding the role of dissonance, referring to the previous paragraph. Although consonances unquestionably were predominant in the approach to composition in Baroque music theory, fitting application of dissonances to ornate and diversify the prevailing consonances was a desired aesthetic mean (Cohen 1971: 68). In seventeenth-century France, in this respect, the term used for the mastery of dissonance became "la supposition" (Cohen 1971: 64). Specifically, "la supposition" involved replacing selected consonant parts with dissonant ones, as well as comprehending the replacing dissonances as the replaced consonances. "La supposition" was also embraced by Ouvrard in his Secret pour composer en musique (1658: 44-46), with the intention of achieving distinguished melodies and compositional heterogeneity (Cohen 1971: 70-72). However, distinctly contrary to this, in Architecture Harmonique (1679: 28), Ouvrard advocates that one is obliged to perform changes in a composition (according to the above-mentioned methods) if one encounters dissonances in it. Whether this instruction is to be applied in an absolute manner, including to every ornamental detail, or merely to the main outlines of the composition, is not clear. Therefore, in case of Ouvrard, the aesthetic value of dissonance-especially in a visual context-appears seemingly ambiguous. For a discussion of Ouvrard's use of musical dissonance, see Vasco Zara's introduction to the critical edition of Architecture Harmonique (2017: 67-68).
The ramifications and importance of the problems discussed in this paper may be regarded as a segment of the debate on the problem of harmonic proportion in architecture, initiated by Wittkower in the 1940s (1971. As Zara correctly claims, the sphere of seventeenth-and eighteenth-century architectural theory contained systematic ventures on the topic of the correspondence between architecture and music. Thus, Wittkower exaggerated by suggesting that such practices were more or less omitted in the eighteenth century (Zara 2011: 413). Zara uses Ouvrard's Architecture Harmonique as one of his primary examples to argue in favor of his claim. As Zara remarked, Wittkower did not have access to Architecture Harmonique but relied on secondary sources (Wittkower 1971: 144;Zara 2011: 413). Nevertheless, as shown in the present paper, there exist problems with the normative system of harmonic proportions in Architecture Harmonique, which foreshadows the consequential abandonment of such systematic ventures on the correspondence between music and architecture.
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