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.
* * *
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.

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

18 Comments:

Anonymous Clair St. Michel said...

Wow, I love this! Thanks for the great explanation and illustration! Still might leave algebra alone but this is very helpful!

Your devoted fan,
Clair

October 18, 2011 at 6:12 PM  
OpenID honeysuckleblue said...

Beautifully explained, thank you!

October 18, 2011 at 7:10 PM  
Blogger Stephanie said...

I originally figured out that whole "multiple of a + b" when I started knitting out of Knitted Lace of Estonia. I really like this explanation, though. It's super simple, and the illustrations alone explain it well.

October 18, 2011 at 7:28 PM  
Blogger Artista said...

"eek dress me i'm naked"? LOL thanks for the explanation.

October 18, 2011 at 7:58 PM  
Blogger Ruth C said...

Thanks for this! I knew that the extra stitches plus repeat were for that purpose, but it was hazy in the details. I love seeing it all written out so clearly.

October 18, 2011 at 8:29 PM  
Blogger northernknitter said...

Totally brilliant explanation - thank you!

October 18, 2011 at 9:14 PM  
Blogger Raggedy Sarah said...

Hi had never seen this kind of cast on instruction when I read your post yesterday. And not one hour later I came across a pattern that used it! Thanks for the explanation!

October 19, 2011 at 7:45 AM  
Anonymous JJ said...

I was never clear that it meant add those "plus" stitches just =once=...thanks for the crystal explanation!

October 19, 2011 at 10:54 AM  
Blogger NerdGirl said...

Great explanation. The basic idea of why cast-on instructions are written like that has always made sense to me but the way you explained it is clear enough that I can now confidently switch out cables and motifs to customize a pattern that is close, but not quite what I wanted. Thanks!

October 19, 2011 at 11:02 AM  
Anonymous LKEcroknits said...

Finally, a clear explanation of what this really means! Thank you!

October 19, 2011 at 12:09 PM  
Anonymous Anonymous said...

Yet another masterful explanation. Thank you!

October 20, 2011 at 12:07 AM  
Blogger Carolina said...

Great explanation! Now I get it. Thanks for helping me visualize even lace patterns that have "8+3"
I get it!1

October 20, 2011 at 6:55 AM  
Anonymous Anonymous said...

The beginning illustrations look sort of like multicolored spaghetti! Expertly rendered spaghetti of course though. Oddly knitting-like spaghetti. Do I get pancakes for this comment? (Love you!)

October 20, 2011 at 11:12 AM  
Blogger La Tricoteuse Heureuse said...

This is SO clear and concise. Thank you for explaining this. I expect I'll be directing students to this tutorial. The images really illustrate it beautifully!!!

October 20, 2011 at 12:02 PM  
Blogger Suzanne said...

I'm totally fine with the math part of the pattern but I really enjoyed your visual explanation. It makes even more sense now. Thanks!

October 21, 2011 at 5:58 AM  
Anonymous Anonymous said...

Hey thank you for that! Now I can use my stitch libraries everywhere. They were driving me crazy before. I even have a subscription to Knitting Fool which is a great stitch finder online. You can find patterns by stitch count there, and now that you have explained stitch count so well, I can use that site better. Duh! Thank you so much!

November 6, 2011 at 9:22 PM  
Blogger Jenn said...

Thank you so much I am hopeless when it comes to reading patterns & that was one of the major reasons. I may be able to ween myself off of YouTube how to videos yet! Thank you again

July 1, 2012 at 1:31 PM  
Anonymous Anonymous said...

You're a champ!

July 5, 2013 at 10:46 PM  

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