Tuesday, October 18, 2011

"Multiple of X plus Y"--stitch pattern notation explained

How's this? "Cast on a multiple of 12 stitches plus 5."  Or how about "pattern is a multiple of 9 stitches plus 3"?  Does that sound horribly like high school algebra?  Does it confuse you? If my e-mail is anything to go by, you are not alone.
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Suppose we are working a cable over 6 stitches.  Another way of saying this is that the cable is a multiple of 6.

a single 6-st-wide cable

For each cable we want to cast on, we have to have six stitches.  That seems simple enough.  But, if we only cast on 6 stitches, we'll have a cable, yes, but no fabric on either side.  If we want, let's say, three cables, it would be awfully tight (and not that pretty) to have nothing but cables sitting right next to one another--here, see for yourself.

three 6-st-wide cables, stacked next to one another

So, let's set each cable against its own little patch of background fabric.  In other words, we'll add a little fabric on each side of the cable to set it off, 3 purl columns, say.

a 6-st-wide cable (purple) set off by two 3-st-wide columns of purl (blue)

The original 6-stitch cable with its two new 3-stitch-wide side flaps is going to take up 12 stitches: 3+6+3.  This LOOKS like we've developed a 12-stitch-wide stitch-pattern. And, indeed, if we just wanted to make a skinny single cable scarf, we'd say "cast on 12 stitches." So far, so good.

But, suppose we want a scarf with two cables. If we simply double the 12-stitch-wide stitch-pattern we've developed, we get trouble.

two 12-st-wide cable patterns, side by side

As you can see, doubling twelve (casting on 24) means the cables aren't centered in the fabric.  Instead of being framed on both sides by THREE columns of purls, the two cables are separated from one another by SIX columns of purls.  Now the edge-columns are looking a little skimpy, the fabric is unbalanced, and the cable placement is not symmetrical.

The problem, of course, is that we really only needed THREE purl columns between the two cables, not SIX.  The three purl columns in the middle of the fabric ought to be SHARED between the cables.  In order to share these columns, however, we're going to have to think about this stitch pattern in a different way.

a nine-st-wide stitch pattern
What if we think of this particular stitch pattern as being NINE stitches wide as shown above, instead of TWELVE stitches wide?  When we stack up these nine-stitch-wide patterns side-by-side, we can see that the cables are sharing the center three purl columns just fine.

two nine-st wide stitch patterns, side by side
Conceptualizing this as a nine-stitch-wide stitch pattern has certainly solved the problem of sharing the purl columns between the cables. Yet it clearly leaves us with a different problem.  That second cable?  The one to the left?  It's naked on its left edge.  We're going to have to add three more purl columns to complete the pattern repeat to the outer left edge.

two nine-st-wide stitch patterns PLUS a 3-st-wide purl column (shown in red)

Now we're finally there: two 6-stitch-wide cables, each framed by 3 purl columns, and no naked knitting.  In fact, we have a pattern of two multiples of 9, plus the three red edge stitches we just added.  Our stitch pattern turns out to be a multiple of 9 plus 3.

looks like a twelve stitch pattern, but it actually
turns out to be a multiple of 9, plus 3

Stated otherwise, when we flanked our original 6 stitch cable with two 3-stitch-wide purl columns, we weren't developing a 12-stitch-wide pattern.  It did have 12 stitches, true, but it was actually a pattern constructed of a single multiple of 9 stitches plus the 3 red edge stitches, as shown above.

By notating the pattern in this manner, we can stack any number of repeats side-by-side without throwing the pattern off.  Further, this notation makes it quite easy to mathematically work out any number of pattern repeats very quickly. For example, a stitch pattern which is a multiple of 9 plus 3, such as this one, can be
  • 12 stitches wide [1x9=9+3=12)  which is one repeat of the pattern,
  • 21 stitches wide [2x9=18+3=21] which is two repeats, or
  • 30 stitches wide [3x9=27+3=30] which is three repeats, or
  • 39 stitches wide [4x9=36+3=39) which is four repeats,  and so on
where the large red numbers are the multiples--the number of pattern repeats and
the small red numbers are the "catch up" stitches required to complete the last
repeat of the pattern to the outer left edge.

You have been reading TECHknitting blog on stitch pattern notation: "Multiple of x plus y."