Symmetrical Single Increase

 When you want to increase one knit stitch to two, there are not many ways to do it that are symmetrical. If you know of any others, let me know!

This way is probably not ideal, but I've seen none others like it.

If you're familiar with the "knit-one-yarn-over-knit-one" increase, that's the first step in this new increase. K1-yo-k1 is what I'll call it from now on.

K1-yo-k1 is a symmetric increase, but you've added two stitches when you work it. The way to turn this into a single decrease is to decrease away (symmetrically) the yarnover on the return row, leaving just two knit stitches symmetrically arranged.

Here is the increase:

Row 1, right side: Work to stitch to be increased. K1-yo-k1 in next stitch. work to end of row.

Row 2, wrong side: Work to increased stitch. Purl 2 together, the knit stitch and the yarnover. Slip the next stitch to the right needle knitwise, and replace on the left needle. Next work a "purl-2-together through back loops" of the stitch just slipped, using that loop and also using the left needle to pick up the left leg of the yarnover  (that was just worked together in the first p2tog).

This is brand new, so I don't think the instructions are that great. A video would probably help.

I just wanted to stake my claim on this technique!

Knitting axioms

Writing about knitting is not like writing about math. 

 Terms are ambiguous, sometimes in a good way, sometimes not.

A "stitch" is sometimes a loop. Sometimes it is an interaction between loops.

A "course" is a length of yarn pulled through previous loops, creating new loops on the right needle. I'm talking about conventional, right-to-left hand-knitting.

With circular knitting, it's all the same fucking course, man. No, but it is really a spiral with no back-tracking like flat knitting. Or at least, not exclusively back-tracking. Short rounds are a thing, like short rows, I guess.

 A great "aha" moment came for me when I realized that a knit stitch is not a loop. Stitches on the needles are loops.

 Pulling a loop through a loop is knitting a stitch.

 The stitch participates in (usually) at least two courses. Yarnovers are granted an exception.

Suppose you have knitted back-and-forth in one color, in stockinette stitch. Suppose the color is red.

Suppose you knit one course (row) using black yarn. 

You break off the red yarn and recommence knitting with red.

 The fabric, when you're done, has one "row" of black knit stitches.

 Wrong!

The fabric has two rows of knit stitches that are half-black, half red.

 You could legitimately say that there is one course knitted with black, but each course of stockinette stitch participates in two rows of knitting. 

 With few exceptions, each worked stitch participates in at least two courses. Each course is (always) attached to two other courses. Except cast-on or bind-off.

Now when casting on, you're actually creating two courses. With the long-tail cast-on, you are creating a course of e-wraps and a course of loops. The e-wraps are the exception, they are sui generis, not attached to another course at the base. They are their own base.

Every course you knit after that is pulled through a previous course and serves as the base for another course.

Flat, Reversible, Neat Entrelac Joins and Pickups

There are at least a couple of ways to join entrelac motifs. I like the "magical" way. 

Recall that entrelac knitting is knitting with modules (I'll call them squares): small patches of knitting that are either (a) preliminary modules that are unattached to other modules (except by a thread), such as the first row of triangles in traditional entrelac, or (b) subsequent modules that are attached to other modules.

The essence of entrelac is that while you knit you are attaching squares at right angles to previously knit squares. This creates a pleasing effect of strips of knitting that are interlaced, woven together, but without the double-thickness of real interlaced strips of knitting. The only double-thickness in regular entrelac comes when you are joining one square to another. This began to bother me… I was able to figure out the neatest way to pick up stitches for one square from the side edge of another, but not to do the other kind of join, where you are attaching the square-in-progress to another square's live stitches. I eventually solved the puzzle, and while the technique isn't as easy, I believe the results are worth the modicum of extra effort.

I generally start an entrelac square by picking up from an exposed side edge of a previous square. Here is the pickup I use: 

The other attachment used in entrelac is done while you knit the square. You attach alternate (or two consecutive) rows of the current square to a live stitch from a previous square. Generally this is done as a decrease… knit to the end of a row to the last stitch and do a decrease using the last stitch of the row and a stitch being held on the needles from a previously made square.

I prefer another way of attaching the side edge as I go, and it’s an adaptation of the “sliding-loop” technique Ric Mondragon first put forth in Knitter's Magazine of February, 1995. He uses the technique for joining strips of knitting parallel to each other as in intarsia, and I use it for joining squares of knitting perpendicular to each other.

While working on Square B, join it to Square A (which is not usually the square you just finished) as follows: On B, work to the end of the row and *work one more stitch from the left needle (off the held live stitches of Square A). Take that “one more” stitch,  the loop that was just formed, off the right needle, and open it up by pulling yarn through it to enlarge the loop, and use the yarn of that loop to work back and forth over two consecutive rows, pulling through extra yarn as needed. Then, when the two rows are done being worked, pull the excess yarn back through the “one more” stitch. Repeat from * until all the live stitches are from the Square A have been used. When you have used up all of the live stitches from A, you have worked just enough rows to complete B… no need to count rows…. Yay.

Here is Jolie Elder's video demonstrating the join… she explains it better than I can!

This gives a join that is geometrically the same as the “perfecting the perpendicular pickup” technique. Adds to the magic of your knitting, which is somewhat subliminal, but it’s nice when there’s more symmetry for your efforts.

There are some nice effects that you can do once you know this join. True reversibility in entrelac is possible, and I’ve designed and made several hats that use a ribbed or other motif for entrelac, and they look good on both sides. Note that these hats use only knit and purl stitches. The light-green hat looks like it's cabled, but it isn't. Some really nice relief effects happen with these techniques.

Four reversible-entrelac hats

When a reverse-stockinette square joins a regular stockinette square at right angles, the join is smooth… on both sides… and this is true with both the picking-up join and the sliding-loop one. Magic!