“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 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 |
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 |
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.
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.
[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.
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