This is one of the most beloved of Vermeer’s paintings. During his lifetime he kept it close to himself, using it to exhibit his prodigious capabilities. This painting, like others, is full of evidence of his use of the Grail Geometry to guide the composition. On a limited platform such as a website only a few of the features coinciding with the Grail Geometry can be exhibited. The interested Vermeer enthusiast is referred to Robert A. diCurcio’s book “Vermeer’s Riddle Revealed”, AETERNIUM Publishing, 2001, ISBN 0917358139 for an in-depth treatment.

The artist represented here is held to be Vermeer himself.  Look at the trumpet or trombone in the hand of “Clio”, the Muse of History.  The trumpet is symbolic of fame – fame for the artist who brings fame to his birthplace of Delft, Holland.

Look at the "maul stick" used by the painter to steady his hand. The orange tip of the maul stick and the ferrule on the trumpet (just to the right of her finger tips) play an important role in establishing the geometry upon which this masterpiece is based. See below.

Vermeer divided this painting into quarters:

A line drawn from the orange tip of the artist's maul stick through the ferrule on Clio's trumpet divides the image exactly in half horizontally. A vertical line drawn from the corner of the chair divides the image exactly in half vertically. Note how the figure of the female model is positioned with respect to these two lines. At this juncture we are encouraged to look for more geometric guidelines -- perhaps to find once more the Grail Geometry.  See STEP 1 below.                                                          (But let's not forget the artist's brilliant orange stockings -- might this favorite color of Vermeer's have something to do with the House of Orange that ruled Holland in Vermeer's day?)

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STEP 1.  TROMBONE LINE.

STEP 1.  The obvious place to draw an exploratory line is along the trombone, which we do from 1 (the arrow pointing to the beginning) slanting up to 2, an inside corner of the easel. Along the way, this line hits 3, where Vermeer painted the corner of Clio's collar, and 4, where he placed the intersection of the artist's beret with his hair. This could be coincidence -- but after observing how Vermeer placed certain features to divide this painting in exactly equal quarters (see above) it's likely we'll find a Tilted Triangle, so we'll proceed to search for that in the next steps below.

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STEP 2.  The TILTED TRIANGLE.

STEP 2. Building on STEP 1, we try an exploratory line (2--5--A) from 2 up to the left to point A -- so as to be tangent to the cartouche at 5 on the map. (If you're wondering how I know to do this right away -- let me say right away -- that I spent weeks doing trial-and-error lines before arriving at STEP 2 as I shall present it -- sparing you from going through all that!) Note that Vermeer has painted a bright area at A -- bright where there's no reason for brightness -- except that it's where his layout sheet called for it. Look closely and you'll see a faint, elongated, and anomalous "V" on the drapery at the apex marked A.  (What did he do that for?) Now another line starting at A and drawn down through 1 (where we began this -- see above) turns out to make an exact 60 degree angle with line 2--5--A !  We have the makings of our equilateral Tilted Triangle -- lacking now just one more line to complete it. See below.

STEP 2 (continued). The line that completes our triangle is drawn from 2 at the required angle of 60 degrees to line 2--5--A.  We hope that this line will be confirmed -- and we are not disappointed. This third side of the triangle goes through 6 on the edge of the artist's sleeve. And the significance of 6? It's exactly half way -- a line from A to 6 splits the triangle exactly in half! So we label our Tilted Triangle A--V1--V2 as has been done in the Grail Geometry Section. (Please go to this section to refresh your memory, if need be.)

As a check, we draw another bisecting line from 5 down through vertex V1 and are gratified to see it hit a decorative upholstery tack on the chair at 7!  Note the exact center of the Tilted Triangle -- Clio's chin was painted just vertically above it! Look at the highlights on the blue garment under Clio's book -- the pattern is precisely guided by the 5--V1 line! All doubt is removed by now -- Vermeer used the Grail Geometry on his greatest masterpiece!  

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STEP 3.  The TILTED SQUARE.

STEP 3. Having established the equilateral Tilted Triangle in this painting, we may follow the rules (see the Grail Geometry section) to readily draw the associated Tilted Square to see whether Vermeer has placed any features according to that figure. Yes, we note that the corner M falls on the right edge of the map -- or more properly: Vermeer painted the right edge of the map to coincide with the top right-hand corner of the Tilted Squareof his layout. (more below . . .)

STEP 3 (continued). The artist's right knee is guided by the side M--N. But the diagonals A--N and M--O tell the story: their intersection PX is exactly on the gutter of the open book on the table! The orange tip of the maul stick has been painted at Q -- right on Diagonal M--O! A line of black tiles has been painted along the line of diagonal A--N -- and the last of those tiles exits the bottom edge of the image at R, where the diagonal A--N intersects that bottom edge.

The intersection point of the diagonals A--N and M--O is the objective of the whole exercise. It is hard to say exactly what symbolism Vermeer had in mind for the 'X Marks the Spot' , which falls on the open book on the table. Since experts contend that the female model represents Clio, the Muse of History, and since Vermeer painted Clio looking down at that open book, we may speculate that his message is that the artist was making history by painting masterpieces that would bring credit to his native land -- and fame for himself. Note that he is shown at work on the crown of laurel leaves, symbolic of victory and fame. Holland at the time had emerged victorious in a struggle with Spain. This could well have been in Vermeer's mind -- and satisfactory it must have been to him, even though this and many other of his riddles would have to wait for centuries to be revealed.

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STEP 4.  The HEXAGRAM.

STEP 4. Going back to STEP 2 and the Tilted Triangle A--V1--V2, we add a second equilateral triangle VH1--VH2--VH3 to form a regular hexagram. The obvious question -- did Vermeer lay out this hexagram on his canvas first and then paint features to fall on it and be guided by it? Our answer -- yes -- we have already confirmed triangle A--V1--V2. But what about the rest of the Hexagram -- triangle VH1--VH2--VH3? Yes, again -- consider confirmations 1, 2, 3, and 4 to begin with -- see below.

STEP 4 (continued). Confirmations: 1 -- the corner of the book painted at line VH1--VH2;  2 -- the left edge of the artist's long hair painted on line VH2--VH3; 3 -- the rectangular cartouche on the map painted on line VH3--VH1;  4 -- the edge of the hanging drapery painted to coincide with the intersection of lines A--VH2 and VH3--VH1. Note how the top edge of the map is painted to fall precisely on the apex VH3! Note also how the extension of line A--VH2 arrives exactly at the lower right corner of the image, suggesting strongly that Vermeer established this corner of his canvas on the line! No coincidence could explain all of this -- Vermeer used the Tilted Triangle, The Tilted Square, and this Hexagram -- and yet another hexagram! See below.

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STEP 5.  Another HEXAGRAM!

STEP 5. This hexagram A-B-C--D-E-F is bigger than the previous one (A-V1-V2--VH1-VH2-VH3) identified in STEP 4. This one (see below) is governed by the slant of the maul stick, line C-1-4-B.

(It is one thing to draw lines on Vermeer's work -- but yet another to contemplate the preparation and planning that must have gone into Vermeer's achievement of this geometric tour de force.)

STEP 5 (continued). As for confirmations, four of several are circled above: Vermeer painted 1, the orange tip of the maul stick on line B--C, the bottom side of the large tilted triangle A-B-C;  he painted 2, a strong confirmation, the vertical line on the map on the intersection of lines A-C and D-E;  he painted 3, the corner of the table, on line B-E, a diagonal of the hexagram. Note that 4 is also a comparatively strong confirmation, being the edge the model's gown, painted on the intersection of the two lines B--C and D--F.

The edified observer can probably identify a few more features whose positioning was guided by the lines, nodes, and angles of this larger hexagram. For example, look at E, the apex of the hexagram. Does it not appear that Vermeer positioned the center of the chandelier precisely there? Look at line A-B. Does it not appear that the artist positioned on that line the edge where the drapery covers the trombone or trumpet? Follow the lines and the circle -- and you'll be struck by how strictly this composition is adjusted to this geometric pattern (as well as to all the other ones discussed above).

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STEP 6.   MORE EXPLORATORY ANALYSIS.

STEP 6. Vermeer went beyond the Grail Geometry in this painting, but first let's refer back to STEP 4 and the first hexagram. I have exhibited it in dashed lines (below) and labeled the relevant diagonal V1--VH3 as was done in STEP 4.  I have extended this diagonal upwards, and I find that Vermeer painted 2, the top part of the chandelier, exactly on the diagonal! (STEP 6 continued below...)

STEP 6 (continued). Extending diagonal V1--VH3 downward, I find that Vermeer painted 3, a corner of the chair, on that line. The back of the chair is emphasized by line 3--5; while the seat of the chair is emphasized by line 3--4 , which I've terminated exactly at the corner of the black tile -- where Vermeer painted that feature.

Beyond the usual Grail Geometry, Vermeer arranged the position and angle of the artist's easel supports along the lines X--Y and Y--Z (above). The lower two of the four small white arrows (above) pointing to the easel lines X--Y and Y--Z call attention to more confirming intersections -- one at the top of the beret and the other at the top of the artist's canvas. (I have used the top two small white arrows above to emphasize the slant of both the easel supports.) Both points X and Z call attention to the fact that the artist positioned the easel according to the tile pattern (or vice-versa) on the floor.

Note that Y, the apex of the angle X-Y-Z falls almost exactly on the top of the map. I have no doublt that Vermeer intended it that way. After about 350 years, this canvas, like all the others, must have distorted at least slightly. Moreover, we have the distortions of photography and the scanning of the image into the computer. Consequently, we must be judicious and allow a bit of leeway with these confirmations, accepting "very close" in some cases where it is obvious that this is justified.

Vermeer did not need to use geometry to compose a masterpiece. In some of his paintings, I find no evidence of a geometric basis. But in this one, only a die-hard skeptic would question the use of a geometric pattern here -- the Grail Geometry is without question in evidence in this masterpiece of masterpieces.

Since this Grail Geometry was not only still secret in Vermeer's time (being divulged by publications only in the latter half of the 20th century) -- it was also considered heretical at that time by the Church. For Vermeer to have known it and used it is a significant revelation concerning his hitherto murky apprenticeship. He was clearly instructed by a secret society -- most probably The Priory of Sion.

Furthermore this sheds some light on, and raises questions about his supposed adherence to the Catholicism that he, a Protestant, embraced on marrying a wealthy Catholc girl. They did raise their many children as Catholics. Vermeer's Delft, Holland, was a 17th century community very much riven by relgious differences -- yet it was a progressive city whose shining lights were on the cutting edge of the technologies of the times: cartography, optics, instrument-making, and tile-making to name a few famous specialties -- not to mention marvelous masterpieces of Dutch genre painting by Delft's most famous denizen -- Johannis Reynierszoon Vermeer.

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