<Home J. Vermeer "The Music Lesson" |
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STEP 1. Exploratory lines. STEP 1. The usual procedure is to look for an equilateral triangle with which the artist guided his composition. One is readily found: the corner of the instrument cover 1 -- to the corner of the picture frame 2 – to the corner of the beam in the ceiling A – these points connected form the equilateral triangle A-1-2.
STEP 1 (continued). Furthermore, extending the line A-1 downward, we find that it hits 3, the corner of the instrument’s leg. With these four confirmations, we are confident that we are on the right track, and that Vermeer used a geometric pattern to guide this composition. ---------------------------------------------------------------------- STEP 2. The Tilted Equilateral Triangle. STEP 2. A line drawn from feature 3 to feature 4, the corner of the second picture frame, turns out to be parallel to line 1--2! Who could dispute that these features were painted intentionally by Vermeer to conform this triangular pattern? A larger equilateral triangle A-3-6 is thus formed. This is the so-called Tilted Triangle so important to the Grail Geometry.
STEP 2 (continued). Note how the line 3-6-4 has played a role in guiding the composition. Another corner of the instrument (the corner to the left of the female's left arm) has been placed almost exactly on it – and the back of the female’s head has been painted squarely upon it. The general flow of the lower right side of the painting is guided by the slant of line 3-6-4. ---------------------------------------------------------------------- STEP 3. The Tilted Square. STEP 3. Proceeding to build on the confirmed Tilted Triangle A-3-6, we apply the rules of the Grail Geometry (see the section so named) to construct the Tilted Square A-5-7-8. The top side is line A-5, drawn from feature A (the corner of the ceiling beam) through feature 2 (the corner of the picture frame) ending on feature 5 (the edge of the other picture frame). Once this side is established, the square that contains it is readily drawn.
STEP 3 (continued). Now we search for more confirmations – and -- Bingo! We find a dramatic one at 9, the tip of the viola on the floor! This cannot have arisen by chance! Several other features in this image manifest evidence of being positioned by the Tilted Square. Furthermore, the general flow of features on the lower right side of this painting are strongly influenced by the slant of the side of the square designated 5-7. It is clear that Vermeer was using this geometry to guide his composition. ---------------------------------------------------------------------- STEP 4. “X marks the Spot”. STEP 4. The objective of the Grail Geometry, if it can be achieved in a painting, is to indicate an “X marks the Spot” on a symbolic feature of the composition. In this composition we see that Vermeer has carried it to a successful completion. The diagonals A-7 and 5-8 of the Tilted Square A-5-7-8 are drawn. Their intersection is indicated with a cross. Note that the center of the cross (PX) is on a rectangular section of the instrument played by the female figure. This rectangle may be thought of as symbolizing a crypt, a tomb, a burial site – since some legends of the grail suggest a burial.
STEP 4 (continued). (We found the same situation in the analysis of 'Lady Seated ' -- the PX or 'X Marks the Spot' also fell there on a rectangular side of the instrument -- symbolic of a crypt). Note how the male figure’s head is tangent to line 5-8. Note how line 5-8 goes through the lower left corner of the musical instrument. --------------------------------------------------------------------- STEP 5 Another Tilted Triangle Yields Remarkable Results. STEP 5. Now we try a larger Tilted Triangle: A--5--10 -- which recognizes the importance of point 5, the edge of the picture frame that defined the square in Step 4. We may well wonder whether Vermeer used yet another triangle in composing this masterpiece. If he used it -- then its associated Tilted Square should reveal some further insights. To construct the square, we draw a base line A--B at 15 degrees counterclockwise to the side A--5 of the larger Tilted Triangle A--5--10. Extending triangle side 10--5 up and to the right to intersect A--B at B fixes the length of the base line. Then, according to the rules of the Grail Geometry, triangle side A--5 is extended to a point 11 that makes line segment A--11 equal in length to line segment A--B. It is this line segment A--11 upon which we construct the new and larger Tilted Square A--11--12--13.
STEP 5 (continued). Upon completing new Tilted Square A--11--12--13, we immediately note that its right side 11--12 goes through the beautiful white pitcher, and this bodes well. But the most interesting aspect will come from drawing the diagonals A--12 and 11--13. These diagonals intersect at a point I have designated PX2. Now PX2 is remarkable, for it sits precisely on line X--X, which divides the painting in two halves -- upper and lower! We may wonder if PX2 is in the precise center of the canvas (where lines X--X and Y--Y intersect), and while it is not -- we can see what Vermeer has done: he has positioned the image and its features so that PX1 -- the symbolic "X marks the Spot" (of STEP 4) -- falls on line Y--Y, which divides the painting in two halves -- left and right! Note how the bottom of the white pitcher and the bottom of the musical instrument sit precisely on line X--X. Note how the lower right corner of the instrument has been positioned at the intersection of line X--X and the diagonal 5--8 of the smaller square A--5--8. The careful observer will be able to spot other features that Vermeer positioned using this complicated pattern as a guide. --------------------------------------------------------------------- STEP 6. Further Exploration. STEP 6. We take another approach to the geometry that Vermeer used to guide the features in this composition. We observe what looks like an eye painted on the edge of the rug draped over the table. Drawing a line from the circled “EYE” up to point A, we observe that the angle at A (1—A—2) is cut exactly in half – bisected. This is no coincidence.
STEP 6 (continued). We then draw a circle so that the line from “EYE” to A is the diameter of it. Remarkably the center of that circle falls at 11 – right on the edge of the open instrument cover. Another diameter drawn through 11 and perpendicular to the previous diameter goes through 10, the corner of the picture frame, and 12, another corner on the instrument! This could not happen by chance! Next, we try an equilateral triangle A—13—14 inscribed within the circle. Is it not remarkable that the line 13—14 is also tangent to the male's head (see STEP 4), and it intersects the line from “EYE” to A at point 15, an intersection point on the female’s garment in the back? How truly a geometric marvel is this painting of Vermeer’s! ---------------------------------------------------------------------- STEP 7. The Hexagram. STEP 7. Now we try a hexagram built on the previously confirmed geometry. The Tilted Triangle A-3-6 is the basis for the hexagram. The second equilateral triangle is drawn within the circumscribing circle (note that this is a different circle from the one drawn in STEP 6). A convincing confirmation is the intersection of two lines exactly on the back of the female’s head. Other confirmations (see below) of the second triangle are: one vertex falls on the edge of the upright in the window -- and the line of the top-left side of the second triangle establishes where the corner of the lower window frame meets the back wall. Note also how the positions of the female’s elbows have been guided by this pattern of lines and curves.
STEP 8. Putting It All Together. STEP 8. It is instructive -- even though Vermeer did not work with such a complicated combination as this for an overlay -- to put together below most of the Grail Geometry guide lines identified in this masterpiece of geometric design:
The more one studies Vermeer's work with an eye to its geometric foundations -- the more astonishingly are his achievements revealed. All these lines guided Vermeer’s paintings – and his compositions give us that timeless feeling of repose that only a geometrically based painting can give. It is no wonder that Vermeer was so devoted to geometry in general – and to the Grail Geometry in particular. The SPHINX of DELFT grins: "I'm revealed !"
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