Monday, December 7, 2015

Los Libros de Sánchez Cotán

That would have been the galactic music that has not been heard by anyone. Not by men whose ears, for many reasons, those sounds cannot reach, nor by those spirits who move the stars because they do not have ears nor need them.”—Francisco de Salinas
            According to Sarah Schroth, the earliest collectors of the still life genre were a small group of intellectual clergymen at the Toledo Cathedral. (Schroth 1985) The interests of these collectors are reflected in the work of one of their beneficiaries, the painter Juan Sánchez Cotán.
In 1603, prior to entering a Carthusian monastery as a lay brother, Sánchez Cotán gave testimony before the notary public Miguel Díaz de Segovia about outstanding debts owed to him by clients and colleagues, and an inventory of the goods of his house and studio. In his studio there were three books: a book on painting by Sánchez Cotán’s instructor Blas de Prado (now lost), a book on perspective by Vignola identified by scholars as Le Due Regole della Prospettiva Pratica, and a book of music identified only as “de Música.” (Orozco Díaz 1993, 291) The connections between these texts and the works of Sánchez Cotán have been noted but not explored in-depth by scholars. This article makes specific links between these texts and specific works by Sánchez Cotán. It also proposes that the unknown music book is Francisco de Salinas’ De Musica libri septum of 1577. Finally, the paper explores how geometry connected the artistic practices and religious beliefs of both Sánchez Cotán and Salinas.
Figure 1
Le Due Regole
Vignola’s Le Due Regole is the text we can be most sure that Sánchez Cotán owned and used. According to Ramón Soler i Fabregat, it was a very common book in Spanish artist’s studios at the time. (Soler i Fabregas 1995) The direct influence of Le Due Regole in Sánchez Cotán's work has been noted by Orozco Diaz, and can perhaps be seen most dramatically in the refectorio or dining hall of the Carthusian monastery at Granada in the form of wooden crosses depicted on canvases and on the testero. Chapter XI of the second rule, entitled "Come si disegni di Prospettiva con due righe, senza tirare molte linee" provides detailed instructions for depicting the form of a cross in space (Figure 1). Sánchez Cotán seems to have completely assimilated this technique displaying his virtuosity in the canvases Cristo con la Cruz a Cuestas and Los tres priores cartujos y Richard Reynolds arrastrados por caballos camino de su ejecución and the painted cross high on the testero, all in the refectorio. The effect is particularly compelling in the four distinct attitudes of the crosses carried by the doomed monks. The power of the illusion of the painted cross on the testero has already been noted by Orozco Díaz.
Le Due Regole provides clear and simple instructions for creating the pictorial space necessary to depict a narrative scene of multiple figures. Correctly constructing “storia di figure” was an essential skill for successfully completing the religious encargos or commissions which were simultaneously the economic lifeblood and life-purpose of the Spanish painter in the beginning of the 17th century. Therefore, the book would have been invaluable to Sánchez Cotán.
Figure 2
There appears to be a direct connection between the formal structure of Sánchez Cotán’s bodegones and the diagram connected to Teorema XXIIII. Prop. XXX. on pg. 36 (Figure 3). This diagram perhaps represents the crux of the text for the working artist, that is to say a perspective technique that is simpler and faster than the Albertian costruzione legitima, which “in its complete form is obviously unwieldy. Not only does it require two preparatory drawings, the plan and the elevation, but also it involves a tedious procedure of plotting the points obtained from these.” (Kitao 1962, 177)
A composition based on the diagram from Teorema XXIIII. Prop. XXX. only requires one drawing, and if a regular triangle is used as the basis for the construction (as in the diagram), the perspective may be simply transferred and enlarged from a preparatory drawing to a painting support with only a compass and straight edge. Both of these advantages would be desirable to a working artist. Furthermore, the diagram is simple enough that it does not require the artist to fully comprehend the Italian text in order to grasp the basics of the technique.
Figure 3
The essence of the Vignolan technique is il punto della distanza, the distance point (helpfully labeled “D” in the diagram). Kitao writes that by “using a distance point one can establish diminutions of squares in depth by a single diagonal line instead of by a set of visual rays required in the Albertian method. But the most remarkable simplification in the distance-point method consists in the replacement of the checkerboard modules by a more flexible control device—a network of intersecting diagonals and orthogonals converging at two separate vanishing points.” (182)
In practical terms, this means that the artist can easily determine the vertical position of the horizontal lines that intersect the orthogonal lines converging on the “vanishing point” or il punto principale (labeled “A” in the diagram) to cut the Albertian pavimento in a way that is both geometrically correct and convincing to the eye with one simple drawing that is easy to construct with only a compass and straight edge.
The use of this diagram would mean that the triangle is fundamental to the composition of Sánchez Cotán’s bodegónes. According to the American scholar Rebecca Zorach, this would not have been unusual in Renaissance paintings. “Painters were thoroughly trained in the practical geometry of their time; simple plain and solid geometry were their bread and butter, and the task of creating patterns on surfaces was part of the artist’s repertoire. Sometimes an artist makes compositional structure in a figurative work, and we can trace geometric shapes—often triangles—that enclose a figure or arrangement of figures.” (Zorach 2011, 29)
 The Vignolan technique can certainly be said to be predicated on Euclid’s propositions related to the triangle. According to Zorach, this basis on the figure of the triangle is also true of the Alberti treatise from which Le Due Regole is primarily derived. “If we read Alberti’s account of perspective with an eye to triangles, they are everywhere. ‘It is usually said,’ Alberti begins, ‘the sight operates [fieri] by means of a triangle whose base quantity seen, and whose sides are those same rays which extend to the eye from the extreme points of that quantity.’ For Alberti, human perception is the product of nearly infinite numbers of labile triangles composed of elusive ‘visual rays.’ This notion of vision dependent upon triangles coincides with Plato’s view of triangles as the building blocks of the world.” (30)
Zorach also proposes that the figure of the triangle itself was infused with religious meanings for the Renaissance artist. The triangle has an obvious connection to the Holy Trinity. She writes that St. Augustine “sees a vestige of the Trinity in the operations of perception, where the perceiving power joins with the thing perceived, even though their natures are different: thus sight, the thing seen, and their joining together are a triad. He thereby produces a theory of vision based on the trinity, privileging sight as the highest of the perceptual powers.” (58)
Furthermore, Zorach connects the triangle and this Trinitarian conception of sight with marian imagery. Referring to the triangular composition of Fra Angelico’s San Marco altarpiece, she writes that “Taking into account the relational, bidirectional conception of vision in this period, we might say that the hierarchical triangle, or the Trinity, in fact emanates from the body of the Virgin. Mary is symbolically associated with Ecclesia, the female personification of the church. She serves as a support for the expression of many different theological concepts. She is also described in various devotional texts… as the temple or receptacle of the Trinity.” (90)
De Musica
Figure 4
In the Sánchez Cotán’s Asunción de la Virgen in Granada (Figure 4), we can see a similar triangular composition. In the foreground, we can see what may be the artist’s own instruments played by angelic musicans on either side of the levitating Virgin. Díaz de Segovia’s inventory tells us that Sánchez Cotán owned  una harpa dentro de una caja” and “una bihuela.” (Orozco Díaz 1993, 291) The term “bihuela” is somewhat broad. Via e-mail, the Spanish musicologist Cristina Bordas assesses the depictions of the instruments: “The harp corresponds with the Spanish models of the time (wide box, with ribs, pegbox not very elevated), its appearance like those of Zurbarán. The term vihuela was used at the time for the vihuela de mano (even though in the 17th century it was falling into disuse in favor of the guitar) as well as the vihuela de arco (the viola da gamba in Italian). The instrument on the left seems to be a vihuela de arco. I cannot see enough detail to see if it has frets, appropriate to the vihuela de arco., but it appears to. Also, the form of the box and the lateral necklines correspond to the vihuela de arco. This does not mean that the models in the painting correspond with those which Sánchez Cotán possessed. It can only be a hypothesis…[1]
In any case, the fact that Sánchez Cotán owned a vihuela and a harp can perhaps help us identify the music book in his studio. Nelly van Reed Bernard presents the case that the two instruments were played with keyboard instruments. “By tecla or key(board) was meant either the organ or the monachordio (the name used for the clavichord). Despite the very low volume level of the monachordio in comparison to the harp and the vihuela, these three instruments seem to have been used ‘in consort’ during the sixteenth century on the Iberian Peninsula.” (van Ree Bernard 1994)
In light of these facts, we can consider that the music book was Hernando de Cabezón’s Obras de música para tecla, arpa, y vihuela de Antonio de Cabeçon published in 1578, L.Venegas de Henestrosa’s Libro de cifra nueva para tecla, harpa y vihuela of 1557, or Diego Pisador’s Libro de música de Vihuela of 1552. The autodidactic nature of these works would seem to fit in with the instructional nature of his other texts. They would also perhaps be amenable to Orozco Díaz’s simple conception of Sánchez Cotán’s intellect. Another possible candidate is Francisco de Salinas’ De Musica libri septum of 1577. The main argument in favor of De Musica is the importance of “chromatic practices” to players of the harp and vihuela in Sánchez Cotán’s time. De Musica integrates the chromatic genus into a triadic system based on geometry.
Francisco de Salinas, blind since early childhood, was a Spanish court musician and professor at the University of Salamanca. The Spanish scholar Amaya García Pérez states plainly that “De Musica libri septem can be considered a manual for the teaching of speculative music in the University of Salamanca.” (García Pérez, Francisco de Salinas y la teoría musical renacentista 2013) Although it is certainly more theoretical and complex than the autodidactic player’s manuals mentioned above, it also contains practical information for the player of the vihuela and the harp. García Pérez tells us that “Salinas’ theory is also very coherent on an external level, that is to say with the musical practice of his moment. Our author refers constantly to his own musical experience and always intends that his theories should be applicable to the music of his era.[2] (55)
The late 16th century was a time of change in music theory and practice. As the American scholar Arthur Daniels notes, “The late Renaissance was a turbulent period in the history of music theory, characterized by full acceptance of triadic harmony, a growing awareness of major-minor tonality, and chromatic practices which led to explorations of the most remote areas within the circle of fifths. While Salinas does not consider these aspects of the music of his own time as compositional procedures, his enharmonic genus and the mean-tone systems of temperament which he recommended for his tuning system (by means of which the twenty-five note octave of the enharmonic genus could be reduced to an octave divided into nineteen notes) do represent an attempt to accommodate the most advanced music of his time, by means of multiple divisional systems.” (Daniels, Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas 1965, 278)
Four chapters of De Musica are dedicated to the tuning of the vihuela, especially in relation to the organ. These chapters are predicated on a mathematical formulation of equal temperament, the most common tuning method for fretted string instruments. Salinas was the first musicologist to correctly formulate this tuning. He relied especially on geometry, rather than arithmetic, to achieve this.
Garcia Pérez makes explicit the connection between De Musica and the practical playing of the vihuela in Sánchez Cotán’s time: “Fretted stringed instruments, however, presented greater limitations at the time in terms of tuning because the frets effected all the strings equally. In this way, if a fret marked a chromatic semitone, that semitone would be chromatic in all the strings effected by the fret. The problem is that frequently the composers were using the same fret for the chromatic semitone as well as the diatonic. Salinas was plainly conscious of this problem, and for this reason concluded that fretted string instruments must be tuned with equal temperament, a temperament in which both semitones were equal.[3] (García Pérez, El temperamento igual en los instrumentos de cuerda con trastes 2014, 63)
The late 16th century was also a time of great change in the construction and theory of harps on the peninsula. As noted by Bordas, in “the case of the harp, a very particular trend can be noted in Spain from the middle of the sixteenth century. Two highlights of this evolution are a guide to better understanding of their construction, namely: the very early appearance of chromatic harps, about 1550, and the great importance of the harp in Spanish Baroque music. As to the first of these points, evidence of chromatic harps in Spain is perhaps the first in Europe: Juan Bermudo’s reference in Declaración de instrumentos musicales (1555) is sufficiently explicit on the addition of strings specifically to produce chromatic sounds, and it is inferred from his text that some builders were already using five chromatic strings per octave, i.e. the same as double harps with crossed strings, known in Spain as arpa de dos órdenes. With this advance, also according to Bermudo, the harp’s chromatic potential was equal to that offered by any keyboard instrument.” (Bordas, Harp Builders in Madrid (1578-1700) 1994)
Sánchez Cotán’s life falls into this period, so we can say that he would have experienced at least some this transformation of the harp from a diatonic to a chromatic instrument. It should be noted that the harp in the Asunción appears to show only one row of strings, but all the instruments in the composition are somewhat simplified and Bordas explains that iconographic sources “do not provide any relevant information [about the evolution of the harp] either, since the harps portrayed in them appear to have a single rank, even those from the 17th and 18th centuries.” (Bordas, The Double Harp in Spain from the 16th to the 18th Centuries 1987, 151)
Therefore, we can see how understanding chromatic practices was important to a player of the vihuela and the harp. Salinas helpfully describes the chromatic genus as the sounds produced by the black keys on a piano. Daniels more precisely explains that the “word chromatic comes from the Greek chroma, meaning color; the application of the word here indicating a coloring of the original quality of the diatonic. For, just as the Greeks say that color is the mean between black and white, so the chromatic genus strikes a mean between the sparse nature of the diatonic and the density of the enharmonic genera. “ (Daniels, 32)
Figure 5
Salinas understood the chromatic genus as part of an interdependent triadic relationship with the other two harmonic genera, the diatonic and the enharmonic (Figure 5). Like mean tone temperament, this triadic arrangement is not new, it is a continuation of quadrivial music theory. This triadic structure extended to musical instruction in Spain at the time. It also is a reflection of Salinas’ geometric conception of the human soul, as we shall see.
Daniels, translating Salinas: “Further, one also should know that these three genera stand in relation to one another as "good", "better", and "best". For just as only "good" can exist per se, and "better" can neither exist nor be imagined without "good", [and just as] each of these two exists in a more excellent fashion in "best", so the diatonic alone can be found per se. For it forms the foundation for the others, and is annexed to them.
But although it [the diatonic] is more natural than the others, as Boethius says, it is nonetheless too hard, and the chromatic was invented to mollify its harshness. And yet this [chromatic] genus cannot be found without the diatonic, for it is nothing else than the diatonic made dense, so to speak. It receives its name [chroma] because it produces a more gentle and more perfect sound, as if emanating from a more perfect source ...
The enharmonic also cannot subsist per se. But, since it is a combination of the other two genera, it produces the densest and most perfect sound. It is called not the diatonic or chromatic, but rather the enharmonic genus, because it is the best adjusted and most adaptable of all.” (Daniels, Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas 1965, 34)
Finally, we can speculate on the similarity between the composition of the San Diego still life and the musical proportions described by Salinas. The curve created by the suspended vegetables and those resting on the sill of the window has been compared to an Archimedean conic by Soria, and a hyperbola by Orozco Diaz. The harmonic nature of the curve and its relation to the musical proportions has already been noted by Norman Bryson, and may in fact be derived from the diagram of the relative sizes of the lesser intervals presented on pg. 92 of De Musica (Figure 6).
Figure 6
The religious implications of this diagram and his music theory in general are discussed by Salinas the end of Book 1. Salinas reports that the ancients distinguished three classes of music: cosmic music, human music, and instrumental music. Cosmic music is found in the movements of the celestial bodies. Human music is a reflection of this cosmic order found in the human body and soul. Instrumental music is produced by the human voice and musical instruments.
            Salinas differs from the ancients by proposing a different tripartite division of music: “the music which is captured by the senses, that which is captured by the senses and the intelligence, and that which is captured only by the intelligence.”
            Salinas links this intellectual perception with Augustine’s triadic concept of the soul, and furthermore the geometric musical proportions he later describes in detail. He states “all that is captured in the conjunction of the natural elements and in the diversity of the seasons, is not learned by ear, but by reason, which constitutes one of the parts of the soul. In these are found, it seems, all the proportions of the consonances. So, the rational faculty distanced from the irascible appetite by one and a half, behold thusly, the consonance of the diapente [perfect fifth]; the irascible distanced from the concupiscible by three and a half, that is to say, a diatessaron [perfect fourth]: Therefore, we have in the soul the perfect diapason [octave]. Further still, in vocal music, as in instrumental, the perfect fifth encloses within itself the perfect fourth, but not the reverse, and the octave contains both, but not the reverse. As well, in the same way the sensitive soul contains within it the vegetative soul, but not the reverse and the rational soul contains within it the other two, but not the reverse. It is the same as when they say that in every quadrilateral there is always a triangle.[4] (F. Salinas 1983, 35)
            Salinas’ comparison of the musical proportions and the Augustinian soul can perhaps provide some insight into the religious meaning, if any, of the San Diego still life. We can speculate that perhaps the vegetables in the San Diego still life are a reference to the vegetative soul mentioned above by Salinas. The vegetative soul is common to all living beings, including plants. It is a generative force, “the power of growth and organic cohesion, of self-nourishment and the conservation of the appropriate balance and measure particular to individual organisms.” (O'Daly 1987, 13). In the Augustinian soul, sense perception or the “sensitive soul” is generated from the vegetative soul. Animals and humans both have this “sensitive soul.” Man is distinguished from animals by reason, or the “rational soul.”
The strong trompe l’oeil effect of the vegetables in the San Diego still life can perhaps be said to underscore the idea that the painting is in part an allegory of sight and sense perception. We can speculate that Sánchez Cotán was attempting a painterly version of Salinas’ music “which is captured by the senses and the intelligence.”
            If this was the case, Sánchez Cotán perhaps also intended for there to be some aspects of the painting that could not be perceived by sight, but a visual parallel to the music that is “captured by understanding alone, is perceived by it and only it, and cannot be heard.”
In the San Diego still life, we can speculate that Sánchez Cotán arranged the vegetables with the proportions of the lesser intervals in mind. For Salinas, the proportions of the lesser intervals can be considered to generate the consonances, as the vegetative soul generates the sensitive and the rational soul. “Music... is constituted by sounds and, finally, by the consonances which are born from the conjunction of the intervals, arriving so to obtain song and melody.” In this way, the proportions of the consonances can be considered an implied or invisible part of the composition much like the Vignolan triangle. Both of those implied or invisible elements of the composition can be interpreted as perceived by reason, in contrast to the visible elements of the composition which are perceived by sight.
By spacing the vegetables in the composition to the proportions of the lesser intervals, Sánchez Cotán was perhaps alluding to the parallel between the generation of the consonances from the intervals and the generation of the sensitive soul from the vegetative soul, and in turn the rational soul from those two, just as in “every quadrilateral there is always a triangle.”
This idea of an invisible composition may seem somewhat pulp, but it was an important concept for Augustine in his De Trinitate, as Zorach writes:
“If for Augustine the image of the Trinity cannot be found in any visual depiction, the concept of ‘image’… is nonetheless crucial: the image of the Trinity is in the human soul. Because human beings were created in the ‘image and likeness’ of God, and God is triune, human essence must reflect the Trinity. The Trinity, Augustine argues, leaves both images and vestiges in the world. Only the angels and the human soul could boast of being ‘images’ of the Trinity. The Trinity was ‘impressed upon the soul, such that the soul operated in triads (e.g. of mind, knowledge, and love, or of intelligence, memory, and will). Elsewhere in the world there exist vestiges, indexical signs, literally ‘footprints’ of the divine. The Trinity acts on the world through numerous triadic relationships of which it is a template.” (Zorach 2011, 57)
Therefore, we can understand the San Diego still-life as an allegory of sight, perception, the soul, and the Trinity itself. This interpretation of the painting as an allegory of sight is very similar to Norman Bryson’s analysis of the Sánchez Cotán’s still life production. “In much of still life, the painter first arrays the objects into a satisfactory configuration, and then uses that arrangement as the basis for the composition. But to organize the world pictorially in this fashion is to impose upon it an order that is infinitely inferior to the order already revealed to the soul through the contemplation of geometric form: Cotán’s renunciation of composition is a further, private act of self-negation. He approaches painting in terms of a discipline, or ritual… down to its last details the painting must be presented as the result of discovery, not invention, a picture of the work of God that completely effaces the hand of man…” (Bryson 1990, 70)
This idea of a self-negating artistic practice in the service of revealing a universal truth would perhaps be congenial to Salinas. Salinas considered his own theories in this way: “While I was a youth at Rome I was regarded as the inventor of this [true method of tempering organs]. Later I discovered the system of Gioseffe Zarlino, which differed in no respect from my own. Nor should this seem remarkable to anyone, because truth is one and the same and presents itself to all who search after it properly.” (Daniels, Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas 1965, 253)
 Sánchez Cotán and Salinas’ artistic practices were essentially geometric. Art, music, and geometry all communicated not only to the sensitive faculty of the soul, but also the rational. Geometry was also the form of the soul and and the universe, and the purpose of art and music was to reveal this cosmic truth. The triangle was a talisman or vestige of this perfect cosmic order that could not be totally perceived by the senses.

Works Cited

Bordas, Cristina. "Harp Builders in Madrid (1578-1700)." In Aspects of the historical harp: Proceedings of the International Historical Harp Symposium, Utrecht, 1992, by Martin van Schalk. Utrecht: STIMU, 1994.
Bordas, Cristina. "The Double Harp in Spain from the 16th to the 18th Centuries." Early Music (Oxford University Press) 15, no. No. 2 (May 1987): 148-163.
Bryson, Norman. Looking at the overlooked: four essays on still life painting. Cambridge, Massachussetts: Harvard University Press, 1990.
Daniels, Arthur. "Microtonality and Mean-Tone Temperament in the Harmonic System of Francisco Salinas." Journal of Music Theory (Duke University Press on behalf of the Yale University Department of Music) 9, no. 1, 2 (Spring 1965, Winter 1965): 2-51, 234-280.
García Pérez, Amaya. "El temperamento igual en los instrumentos de cuerda con trastes." In FRANCISCO DE SALINAS Música, teoría y matemática en el Renacimiento, by Amaya and PALOMA OTAOLA GONZÁLEZ García Pérez, 61-89. Salamanca: Ediciones Universidad de Salamanca, 2014.
García Pérez, Amaya. "Francisco de Salinas y la teoría musical renacentista." In Francisco de Salinas: De musica libri septum, by Amaya and Bernardo García Bernalt Alonso García Pérez, 37-83. Salamanca: Ediciones Universidad de Salamanca, 2013.
Kitao, Timothy K. "Prejudice in Perspective: A Study of Vignola's Perspective Treatise." The Art Bulletin (The College Art Association) 44, no. 3 (September 1962): 173.
O'Daly, Gerard. Augustine's Philosophy of Mind. Berkeley and Los Angeles: University of California Press, 1987.
Orozco Díaz, Emilio. El Pintor Fray Juan Sánchez Cotán. Granada: Universidad de Granada, Diputación Provincial de Granada, 1993.
Salinas, Francisco. Siete libros sobre la musica. Translated by Fernández de la Cuesta. Madrid: Alpuerto, 1983.
Salinas, Franciscus. De Musica libri septum. Kassel: Bärenreiter, 1958.

Schroth, Sarah. "Early Collectors of Still-Life Painting in Castile." In Spanish Still Life in the Golden Age, by Willam B. Jordan, 28-38. Fort Worth: Kimbell Art Museum, 1985.
Soria, Martin S. "Sánchez Cotán's 'Quince, Cabbage, Melon and Cucumber'." The ART Quartlery (The Detroit Institute of Arts), no. Summer (1945): 224-230.
van Ree Bernard, Nelly. "Ornamentation in Sixteenth-Century Iberian Music for 'Tecla, Hapa y Vihuela': Quiebros, Redobles, and Glosas." In Proceedings of the International Historical Harp Symposium, Utrecht, 1992, by Martin van Schalk. Utrecht: STIMU, 1994.
Vignola, Ignazio Danti, and Francesco Zannetti. Le Dve Regole Della Prospettiva Pratica. Rome: Francesco Zannetti, 1583.
Zorach, Rebecca. The Passionate Triangle. Chicago: The University of Chicago Press, 2011.

[1] El arpa se corresponde con los modelos españoles de la época (caja ancha, con costillas, clavijero no muy elevado), se parece a las de Zurbarán. El término vihuela se utilizaba en la época tanto para la vihuela de mano (aunque ya en el siglo XVII estaba cayendo en desuso a favor de la guitarra) como para la vihuela de arco (la viola da gamba en italiano). El instrumento de la izquierda parece una vihuela de arco. No alcanzo a ver con detalle si tiene trastes, propio de las vihuelas de arco, pero parece que sí. También la forma de la caja y las escotaduras laterales corresponden a las vihuelas de arco. Esto no significa que los modelos pintados en el cuadro se correspondan con los que él mismo poseía. Puede ser solo una hipótesis…
[2] la teoría de Salinas será también muy coherente a nivel externo, es decir, con la práctica musical de su momento. Nuestro autor remite constantemente a su propia experiencia musical y siempre pretende que sus teorías sean aplicables a la música de su época. paintinga vihuela and a harp can perhaps help us identify the music book in his studio. ruth would perhaps be congenial to Salinpaintinga vihuela and a harp can perhaps help us identify the music book in his studio. ruth would perhaps be congenial to Salin
[3] Los instrumentos de cuerda con trastes, sin embargo, presentan mayores limitaciones a la hora de ser afinados porque los trastes afectan por igual a todas las cuerdas. De esta forma, si un traste marca un semitono cromático, ese semitono será cromático en todas las cuerdas afectadas por el traste. El problema es que es frecuente, que en una misma pieza los compositores estén usando el mismo traste tanto para el semitono cromático como para el diatónico. De este problema es plenamente consciente Salinas, y por eso concluye que los instrumentos de cuerda con trastes se tienen que afinar en temperamento igual, un temperamento en el que ambos semitonos se igualan.
[4] Por tanto, todo aquello que se capta en la conjunción de los elementos naturales y en la diversidad de los tiempos, no le aprende el oído, sino la razón, que constituye una de las partes del alma. En éstas se encuentran, al parecer, todas las proporciones de las consonancias. Así, la facultad racional dista del apetito irascible uno y medio, he aquí, pues, la consonancia del diapente; el irascible dista de concupiscuble tres y medio, es decir, un diatessarón: por tanto, tenemos en el alma el diapasón perfecto. Más aún, en la música vocal, como en la instrumental, el diapente encierra dentro de sí al diatessarón, pero no al revés, y el diapasón contiene a los dos, pero no al revés. Pues bien, de la misma manera el alma sensitiva contiene dentro de sí al alma vegetativa, pero no al revés y el alma racional contiente dentro de sí a las otras dos, pero no al revés. Es lo msimo que cuando se dice que en todo cuadrilátero hay siempre un triángulo.