<Home J. Vermeer "The Concert" |
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STEP 1.. Introduction. This painting is famous for having been stolen from the Isabella Stewart Gardner Museum in Boston in 1990. With two pictures hanging on the wall, this painting looks very much like one of those geometrically-based paintings that Vermeer loved to do. I will focus on the singer’s right hand; it is in an awkward position, and her left hand seems to point towards it. The palm of her right hand will play a central role in my analysis. Exploratory lines are always drawn on a trial-and-error basis until a promising geometric possibility develops. In this painting, the palm of the right hand is central to an equilateral triangle used by Vermeer -- as will be shown in STEP 2.
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2. The First Equilateral Triangle.
One confirmation is that the side 1-2 comes very close to going through the left eye of the singer (white arrow). But the dramatic confirmation is that the palm of the hand is exactly in the middle of side 1-2, so that a line from 3 to A divides the triangle exactly in half! Two exploratory lines are then drawn -- one from the corner of the picture frame to the corner of the female figure’s chair. Note the confirmation where this line intersects line A-3 -- right on the top of the open instrument cover! Note also how that same line just touches the ‘V’ of the white ribbon in the seated female’s hair. The other exploratory line goes from the bump on top of the right-hand picture frame to the corner of the male figure’s chair. Note the confirming intersection – right on top of the male figure’s head! ----------------------------------------------------------------------------- STEP 3. The Hexagram. A circle has been circumscribed around the First Equilateral Triangle A-1-2, so that a Hexagram may be tried. The second triangle is drawn to form a regular hexagram, and then we inspect the result for confirmation that Vermeer indeed used this geometric figure as a guide. Note how the circle hits the corner of the female figure’s chair (black arrow); and how the circle establishes the position of the top of the painted image (black arrow to the left of B, the apex of the second triangle). Note 4, the corner of the picture frame, has been placed on a line that just clips the bottom of the white upside down "V" ribbon in the seated figure's hair, and runs parallel with the line on the second triangle, which completed the Hexagram. This dashed line also clips the bottoms of the white "V" sleeves on the standing figure.
A remarkable confirmation results from a walking stick (white arrow) that Vermeer positioned, leaning against the male figure’s chair. A line extended up along the line made by this walking stick -- all the way up to the top -- hits the apex B of the second triangle exactly! There is no way that this could happen by chance – Vermeer was obviously guided by this geometry from the outset -- and he pointed to it repeatedly! ----------------------------------------------------------------------------- STEP 4. More Exploratory Lines. A roof-like maze of lines results by connecting comparable features painted by Vermeer to exhibit how he positioned the two picture frames geometrically. I have designated as X-Y-Z the isosceles triangle (two equal sides, two equal angles) that he used. This triangle will play an important role in the analysis at STEP 5.
These exploratory lines further prove that Vermeer positioned the features of his composition according to a geometric pattern. Lines have been drawn from feature to feature, yielding this distinctive roof-shaped pattern – so harmonious an arrangement for this composition! ----------------------------------------------------------------------------- STEP 5. A different Final Tilted Triangle gives rise to the correct Tilted Square. STEP 5. The isosceles triangle designated X-Y-Z in STEP 4 now forms the basis of a search for a Tilted Square, which may be found by locating the proper equilateral Tilted Triangle -- provided that Vermeer actually used a tilted square to guide this composition. We will find he did exactly that. It is remarkable, to say the least, that the First Equilateral Triangle A-1-2, which gave rise to the Hexagram of STEP 3, is not the Final Tilted Triangle PNW--V1--V2 that will give rise to the proper Tilted Square PNW--M--N--O. The complexity of these seemingly disparate geometric figures blending together to guide this composition is nothing short of a stunning tour-de-force.
Note that the Final Tilted Triangle PNW--V1--V2 (see above) is bigger than -- and built upon -- the previously discovered First Equilateral Triangle A-1-2. Once the Final Tilted Triangle is established, the Tilted Square PNW--M--N--O is easily drawn according to Grail Geometry principles (see that section of this website). The question is -- is it confirmed? -- i.e. can it be demonstrated that Vermeer used it? The answer is yes, he used it, because when we draw the diagonals of the square PNW--N and M--O we find they intersect on a symbolic rectangle. This time it's the rectangle on the back of the seated male strummer. It's a section of a sash he's wearing, but we see that Vermeer shaded it so that effectively it's a rectangle symbolic of the top of a crypt. I have highlighted this intersection, PX, with an 'X Marks The Spot'. Note how the line from 4 (see Step 3) goes precisely through PX! Some coincidence! Note how the diagonal line M--O hits point Y exactly! And note further how it goes right through the singer's right palm! The conclusion is inescapable -- the geometric pattern was drawn first -- the painting was composed so that all these features would coincide with and be guided by that pattern.
Vermeer was devoted to perfecting his compositions with the perfection of geometric figures. |
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