Tuesday, March 24, 2009

Darjeeling Limited: Border Numero Uno - Part Numero Uno

This is partly the story of the first border of my medallion quilt inspired by the Wes Anderson film The Darjeeling Limited. It is also partly a song of praise for Jinny Beyer's book Quiltmaking by Hand: Simple Stitches, Exquisite Quilts. Don't let the title fool you, this book is about so much more than making quilts by hand. In fact, I would go so far as to say it is the most comprehensive resource on how to draft pieced quilts from blocks to borders. The book applies the tips and tricks of drafting to quilting. This can be intimidating to the math averse. But she explains her math thoroughly so it's not too difficult to follow along at home.

Jinny Beyer (who is totally one of those people whose first and last names you have to say together) is known for, among other things, her medallion quilts. In fact her quilt "Ray of Light," one of the One Hundred Quilts of the 20th Century, brought medallion quilts to the attention of the quilting revival of the 1970s. So it's no surprise that her book goes into great detail describing how to draft the kind of pieced borders that appear so frequently in medallion quilts.

Now, as quilt historians like Gwen Marston will show you, pre-20th century quilters didn't get overly fussy about planning their pieced borders to make sure that the same portion of the design falls in exactly the same place at each of the corners of the quilt. Often borders just ended where they ended. But as a challenge to myself I wanted to see if I could piece a border where the design did fall exactly the same place at each of the corners of the quilt. I also thought it would be easier to test drive a pieced border on a small quilt rather than a large quilt. So, while the effort will be ENTIRELY lost on the infant recipient and their parents, I am doing it anyway . . . for me . . . for the experience.

Preliminaries

If you'd like to follow along, turn to pages 150-156 in Quiltmaking by Hand: Simple Stitches, Exquisite Quilts. First, the unfinished size of my center (as measured through the centers of the center, not along the edges) is 24 inches long by 12 1/4 inches wide. That makes the finished size of my center 23 1/2 by 11 3/4 inches.Second, the border unit looks like this. It is a non-directional symmetrical, square unit (though it will be pieced out of quarter square triangles, because what is life without a challenge). Because it is a non-directional symmetrical unit the edge of a full unit or the edge of a half unit could fall in the center.

Corner Unit
Designing a pieced corner unit seems really difficult until you draw the two possible endings (full units or half units) at right angles to one another. Then you just play around with how those units would continue. For example, if the pieced borders end with a full unit, the corner might look like this.If the pieced borders end with a half unit, the corner might look like this.

Determining Border Unit Size

Beware: this way there be mathematics!

Getting a pieced border to fit the center of a quilt is THE challenge of pieced borders (unless you take the traditional pre-20th century "wherever it lands, there shall the border end approach"). How many border units will fit along the sides of the quilt? About how big would you like each border unit to be? In my case, I'd like each border unit to be about 2 inches (my border unit is square so the width and height will be the same). Let's start with the shorter finished dimension of my center: 11 3/4 inches. If I divide 11 3/4 inches by 2 inches, I find that 5 7/8 units fit along the short side of my center. 7/8 unit is not going to cut it. So I can either go down to 5 units along the short side or up to 6 units along the short side. Either way, the size of each unit will have to deviate from my ideal size of 2 inches in order for the pieced strip to end with a whole or half unit.

Let's imagine I want 5 units along the short side of my center. If I divide 11 3/4 inches by 5 units, I find each unit will have a finished size of 2 7/20 inches.

Let's imagine I want 6 units along the short side of my center. If I divide 11 3/4 inches by 6 units, I find each unit will have a finished size of 1 23/24 inches.

Now, neither of those measurements are going to show up on your standard ruler. And neither of them are my ideal 2 inch unit size. So how do you pick between the two? In a rectangular quilt like mine, it's easy: see which unit size fits best along the longer side of the quilt.

Let's imagine I want 5 units along the short side of my center. We determined that the finished unit size would be 2 7/20 inches. If I divide the finished length of the center's longer side, 23 1/2 inches, by the finished unit size, 2 7/20 inches, I find that exactly 10 units fit along the longer side of the center.

Let's imagine I want 6 units along the short side of my center. We determined that the finished unit size would be 1 23/24 inches. If I divide the finished length of the center's longer side, 23 1/2 inches, by the finished unit size, 1 23/24 inches, I find that exactly 12 units fit along the longer side of the center.

Well, huh, both ways it works out to be a whole number of units. All things being equal 1 23/24 inches is closer to 2 inches than 2 7/20 inches, so I'm going with a unit size of 1 23/24 inches, which results in 6 units along the short sides and 12 units along the long sides.

Now, this is not the end of my problem. I have the finished length of the hypotenuse of a quarter-square triangle. So how do you draft a template for a quarter-square triangle whose finished hypotenuse is 1 23/24? Now, part of me wants to skip it and just draft one with a 2 inch hypotenuse. But over the twelve units of the long side, that would be off by half an inch. If you were a drafting rockstar like Jinny Beyer, you'd probably plug the decimal version of 1 23/24 into your little CAD program and churn out a template.But I just used ye olde pencile, papere, and rulere to draft a 1 23/24 inch square. Then I drew a line 1/4 inch outside one edge. Then I drew lines through the corners of the square through the external line. Measuring the distance between the intersection of the diagonals with the external line gave me the length of the square I would have to cut to make quarter-square triangles with 1 23/24 inch hypotenuses: 2 1/2 inches.


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2 comments:

Thalia said...

Between the Olde Tyme materials, and the wizard math, I am suitably impressed.

I can imagine being presented with such a dilemma, and taking the lazy way out by saying, "I'll do it the traditional way. Old school!" and let the border pieces fall where they may.

You are tempting me with quilting. Now I must knit through half my stash so I can start working on a new hobby.

Bob said...

I love the painstaking calculations, of course. Some observations on them:

First: your center is _brilliantly_ sized. Because the rectangular center is twice as long as it is wide, your square border units will always fit evenly on the long side, if you make them fit the short side. To get exactly 2-inch border units to fit, you could use a center with unfinished size 12 1/2 by 24 1/2. (I don't know how controllable the size of a center is.)

Secondly, it seems to me that technically the length for your square to make triangles with 1 23/24 inch hypotenuses is 2 11/24 inches. So long as your (beautifully drafted) square is actually square, the diagonals you drew go out 1/4 inch as they extend up 1/4 inch to your external line. The total added from drafted 1 23/24 inch square to external line is therefore 1/2 inch, and 1 23/24 + 1/2 = 2 11/24.

(I don't know if this is possible either, but alternatively you could cut 2 1/2 inch squares and do whatever it is you do with an extra 13/48 inch, instead of the 1/4 inch you usually use. Or maybe the extra 1/48 inch is immeasurable.)