Return to circles, knit “pies”, miters and spirals 4

I  have gotten used to seeing charts for crochet in the round, and prefer charts to written instructions in knitting as well. My hand knitting has usually been project oriented in terms of experimentation or exploration. Reviewing information provided by both Zimmermann and Thomas in their early publications has led me to new appreciation and admiration for their efforts and for the knowledge made available to their readers, and not just in their time.

Looking at the additional medallions by Mary Thomas, I thought I would play with attempting to illustrate them, some in rounds rather than individual wedges lining up flat with blank or greyed out squares between them. The first example is my imagined square medallion (straight, geometric), p. 239 in my Dover edition 1972, and created in Excel. The work is begun on 8 stitches, divided evenly among 4 needles, knitting with a fifth. The cast on is equal to double the number of sides of the square geometric shape, 4. A hexagon would begin with 12 (6X2), an octagon with 16 (8X2). In this instance the increases are arranged at the beginning and end of stitches on every needle.  When compiling information on machine knitting, I generally swatch to proof ideas. I am not planning on making accompanying samples or swatches for these.

I knit primarily on the machine, and prefer hand knitting on long straight needles as opposed to rounds, so I find myself often referring to counts as rows rather than rounds. For square medallions cast on 8 stitches, divided on 4 needles, knitting with a fifth. In all patterns after cast on row is divided, first round is knit in back of all stitches to flatten them. Stitch counts after increases sorted high to low are helpful when knitting from the outside edge in, and in that instance they become decreases. For the square medallions they are shown in that order, with counts for many more rounds than those in the illustrations. Beginning with the pentagon, they reflect stitch counts from the start of each segment shown.
The windmill medallion (square, p. 240) instructions given: beginning on round 6 “M1 into the second stitch from the beginning and the third stitch from the end of each needle. Continue thus on all even rounds”

The maltese cross medallion (square, p. 240) lines up the M1 increases side by side, in the center of each wedge. Increases are grouped together at the center of each of 4 needles in use may also be grouped on either side of 2 center stitches they may also be grouped on either side of 2 center stitches In a square medallion (bias, swirl, pp. 241-242) increases are placed on only one side, at the beginning of each wedge. Yarn overs are used to create eyelets for more ease when attempting to keep the square flat, and the increase round is to be repeated “as required”. If double yarn overs are used, drop the second yarn over on the next round. They are made before the stitch. Single increases are to be made each round. Here are the wedge shapes side by sidearound a center core For a pentagonal medallion (pp. 242-43) cast on 10 stitches divided evenly, or as number of segments increase, work 2 sections or more on any one needle. For the swirl double yarn overs may be needed to keep the work flat. Thinner yarns may require additional knit rows between increases. Stitch counts For hexagonal medallions (p. 243) cast on 12  stitches, two sections are placed on each of three needles, knitting is done with a fourth. Each increase round will add 12 stitches; 2 or possibly even 3 rounds may be needed between each increase row to keep the shape flat. STS column reflects their number after increases have been made 
The hexagonal medallion swirl (p. 243) is shown using both M1 and YO increases. Here the rate of increase in rounds is slower than above (2 per needle as opposed to 4), so increase rounds are separated by only one row knitThe octagonal medallions (pp.244-245) are cast on 16 stitches, divided on 4 needles and knit with a fifth. To make a smaller center hole, 8 stitches may be cast on, doubled on the next round, and then divided. The first geometric medallion shows increases (4 per segment, 16 per round) in single rounds, requiring several knitting rounds between the increases. The second medallion uses more frequently (2 per segment, 8 per round), so single all knit rows separate roundsFor the octagonal medallion swirl  (p.245) directions are the same as for the hexagonal one, with a 4th segment providing extra sidesIf the perimeter or circumference of the shape to be knit are known, the process may be reversed from the edge in, with decreases replacing increases. The advantage to working from the center out is that adjustments i.e. extra knit rows between increases, changing increases to yarn over(s) for added ease or decoration, etc. may be made far more easily as the work grows. Considerations should be given to leans of M1 stitches so they point in opposite directions on alternating sides. Motif and pattern placement can only be planned after these building units have been sorted out.

Two online guides for increases in hand knitting and their results:

Return to circles, knit “pies” 3

Elizabeth Zimmermann provided guidelines for circular shawls in her books and publications, including “Knitting Workshop”. For a basic pi shawl (p. 112, Schoolhouse Press, 1984) the assumption is that each section is twice as deep as the previous section and has twice as many stitches. Below CO row represents cast on stitches if the work is to begin from the center out, Column A the row count on which the increases take place, column B the number of rows knit just prior to increase row (A-1), and C the number of rows available for any planned repeat (A-2), thse are constants. The columns directly below each cast on (CO) number (orange) counts represent the number of stitches when increases are complete. The stitch count doubles when the number of rounds has doubled.Mary Thomas’s Book of Knitting Patterns, Dover 1972, p.p. 245-247 provides guidelines for circular medallions. She calls her first a “disc” medallion. In executing it the aim is to scatter increases so they are less visible and do not form spokes. Four stitches are cast on, with 4 stitches increased in the total count every other row. The number of stitches between M1s increases by one on every other row. My chart happens to read from left to right. As with any knitting in the round, the process may be reversed, starting at the circumference and moving toward center. I personally like charts to help visualize results, and have revised her counts in the illustration below so increases are at the same rate, but placed a bit differently within the rows. On rows with even numbers between decreases, start row with half that number of knit stitches before the first increase. Because one is knitting in the round, with knit side facing, all rows are knit. If the work were knit on 2 needles, knitting every row would produce garter stitch.what happens if increases “line up”For her circular “radiant” medallion after the first 2 rows increases are made every 4th round. My chart is renumbered excluding the first 2 rows, so the increase rounds would occur on numbers divisible by 4, making it easier for tracking them. Each “building” round increases the number of stitches by 16.

In her “target” circular medallion, the building increases are arranged in concentric circles. Each increase row begins with a M1. Once RC 20 is reached, a stitch is added between increases on each increase round. This chart reflects the knitting progress, but not the shape. STS column on right reflects the total number of stitches after increases have been made. Each building round after RC 6 increases the count by 32. Formulas for more, varied geometry based medallions are also offered in the book.  I finally “discovered” actually using formulas in Excel! The video that clearly and quickly helped me learn how to: at the flow in table form for the first 2 medallions

These formulas do not take into account changes in gauge, or stitch type within bands. For similar shapes to be achieved in machine knitting, the number of transfers would be prohibitive. In order to achieve similar shapes one begins with the radius of the finished circle and the shapes in the family may be knit sideways, using holding.

Handknitters can work with 4 double pointed needles, one or 2 (or more) circular needles, and crocheters can follow similar shaping methods. The advantage to long circulars is less bunching up as the work grows, and if you like working flat or want to try the garment on while shaping it, you can use more than one long needle, making the piece or the try on manageable. Working from the top down when knitting such shapes may give one more control over the size of the finished piece i.e.. on length of body and sleeves, height between bands, extending a yoke into a shoulderette or cape. Stitch pattern size and repeats add to the math calculations. Garter stitch is the only hand knit stitch that approaches a square gauge, could be used in combination with patterned bands.

The charted patterns above rely on M1 to increases. Yarn overs may be used for decorative holes at increase points. If preferred, the hole may be diminished by twisting the stitch when picking it up on the next round.

When knitting in stripes, the “jog” at the color change in knitting can be eliminated by slipping the old color purl-wise, and starting to knit the second stitch. TECHknitting provides more alternatives in her posts: For a method using yarn ends and a needle when yarn is cut

For shawl shapes and their geometry using YO increases, see the posts and publications by Holly Chayes.

To start it all from center out: I am used to doing the magic loop cast on with a crochet hook, and then moving on from there, Kitty Falol shows it worked with DPNs.

Return to circles, knit “pies” 2

Just as other knitwear styles have varied in style, ease and fit over the years, round yoke sweaters have also done so. Yokes can be wide or narrow, in patterned or textured stitches, and in varied proximity to the neckline. This is not generally a tailored style. Ease in knits can be calculated on the basis of fashion or personal preference. With some familiarity with slopers measurements may however, be adjusted in this style as in any other sweater. Neckline measurements do not reflect the measurements achieved after adding finishes i.e. turtle or round. Depending on the size of the yoke, shaping can begin at the armhole level bind off (seen in the early hand knitting directions in the 70s), while smaller yoke shaping can begin at whatever point is desired, extending to the neckline, or simply to create a design band. The shaping is created by decreases if the garment is knit from the bottom up, and with increases if worked from the top down. In most styles the same number of rows are worked from the armhole bind off or held section to where yoke sections meet. At that point if hand knitting on circulars the 4 sections: i.e. left sleeve, front yoke, right sleeve, and back yoke may be picked up and joined for completing the yoke. My illustrations have been created using Mac’s Pages lines and shapes.  They are not to scale.

Beginning to visualize process: yokes are generally superimposed on raglan shaping

they form part of a flat circle; here is how they might appear in a partially seamed cardigan without front bands. They may be created in varying widths or patterns,

and in a pull over with shaping in back that raises the rear neckline. Some of the early patterns were executed with front/ back and both sleeves sharing equal measurements and slopes

separate the elements: the yoke 

the front and back can be begin to consider shaping at breasts, waist, and those wedges under where the yoke “circle” meets the sweater may be short rowed on each side with the intent of achieving a much better personal fit


Hand knitters are probably familiar with Elizabeth Zimmermann and her daughter, Meg Swansen. Handknitting with Meg Swansen 1995, and Elizabeth Zimmermann’s Knitting workshop 1981, Knitting around 1989, Knitting without tears 1971 are classical references that include information on yoke creation, including these guidelines

Other authors suggest 1/4 of total body and sleeve measurement in stitches (excluding armhole) for a tighter neckline (turtle neck), one third for a more open style (crewneck). Original circumference/ body measurement should include any ease. Though decreases for the yoke: first halfway up 25%(one out of every 4), second 3/4 up 33% (one out of every 3), and last 1/2 inch before full depth is reached 40% (two out of every 5) are the most common, they can be placed and varied to suit your own design.

In drafting your own patterns and partnering with someone, a tape measure or string can be laid on shoulder line, etc. for an idea as to preferred placement and measurement. Necklines finished by bound off stitches whether machine or hand knit, do not stretch, so measuring your head with something that does not as well gives you a guideline. Yokes end in open stitches, so the thing to consider there is what method is used to finish the neckline, and its own stretch factor after bind off. Hand knitters have the added benefit of splitting the work on 2 circulars and trying on the sweater or its pieces on while in progress to double check fit.

Japanese designers began to publish patterns that often included yokes that were constructed on the top of the drop shoulder line, with the back yoke placed higher than on the front. Such yokes also began to be represented in stepped figures showing decreases. In the round calculations are gauge based, not relying on the pi formula.

modified raglan for higher placement of yoke on back of body

full pattern with traditional full cap sleeve

pieces meeting at dropped shoulder line: dotted line represents back collar placement, note difference in height between back panel on lower back, and front panel on lower right

a sample diagram from a Japanese magazine 

Yoke shaping may be indicated in stacked format. The final count and frequency of decreases is shown, publishers may vary in language. On the first row here 4 sts – 2X means there is a group of 4 stitches followed by a decrease 2 times, then 5 stitches followed by a decrease 23 times, etc.

Two online calculators are available to help with DIY:  1. the Yoke-U-Lator, and 2. for Lopi, Icelandic styles. The image below is a screenshot from the latter website, indicating a sample possible result.

Jessica Tromp offers free circular knitting patterns with round yoke, dimensions in inches and ounces.

There are endless possibilities for combining math formulas, gauge, and pi. There are many ways to do decreases. With planning so that much more frequent intervals happen between decrease rounds, the decreases themselves can be fabricated to line up in line, and the resulting texture creates the interest in the sweater as opposed to any color patterning (i.e. along white lines)

“pie wedges” may be placed on neckline, yokes, sweater parts, various silhouettes and garment pieces, or full shapes (red dots outline possible dolman sleeve)from a Japanese magazine a hint of detail that must be calculatedand the pie may be oriented in different locations on any one piece 

from a Japanese knitting magazine, an idea for long sleeve and side details merging with and becoming part of a circular yokeFor some of the math  calculations please see:

“Decreases” in rib sometimes can be achieved through changes in needle size if hand knitting, or tension changes on the machine. The yoke in machine knitting would need to be split in 2 parts or knit sideways. Plain colored rows between bands of FI may appear noticeably lighter in weight, so using a 1X1 one color FI pattern or double strand of one of the pattern colors may improve the look.

Before transferring stitches on the machine in the single color rows, make your transfers. The lace carriage may be used after selecting appropriate needles and putting them in position. Knit the following row before removing knitting on waste yarn or garter bar. If stitches are tight for garter bar use sometimes the row after transfers may be knit at a looser tension to facilitate the process, and the difference may not be noticeable when knitting at “normal tension” is resumed. The carriage should be set to plain knit for row prior to and after transfers. It may be easier to work toward the center from each side when returning stitches to the needle bed. In order to match the pattern at the shoulder seams or when motifs need to stack in position on separate bands, the stitches need to be rehung at specific positions on the needle bed that take into consideration the size of the repeat and its location within the stitch count. Also, take into account the seam allowance. One stitch extra on each of the meeting seam sides will allow the end needle selection stitch or an extra patterning needle to be hidden within a full stitch join. Working on machines that preselect needles or pushers makes tracking a bit easier. It is possible to combine knitting pieces in both directions. For example, knit yoke up toward neck, join shoulders, and then pick up appropriate stitches to knit body and sleeves from the top down. Top down makes any adjustments in length easier prior to finishing the sweater. Short rowing in garment segments underneath the yokes makes for a better fit at bust line and upper back.

Calculators to help with all that math: online

for purchase:

Going low tech: if gauge works out to whole numbers, shapes can be plotted out on square grid graph graph paper (or grid created within software to suit) where each square represents one stitch, one row. Draw connecting lines, follow outline, filling in squares (or removing them) as the edge moves a whole unit (k2 tog). Here the goal is to go from 39 stitches to 5 over 60 rows. Color bands could be added and planned between decreases, which should occur on single color rows. Once a gauge is obtained, charting on graph paper or within programs can be boiled down to connecting dots and following outlines as above. Some simple breakdowns for outlines of garment pieces/ shapes 

Return to circles, knit and crochet “pies” 1

I began a series of posts on miters and spirals created on the knitting machine back in 2011. The oldest posts, 12, and 3 begin to address creating flat circles in machine knitting using holding techniques.

Hand knitting in circular format and crochet share some similarities. There are 2 methods of constructing circular work in crochet. 1: in rounds, (akin to knit miters in shape) where the end of each circular row is joined up to its own beginning to form a ring. A new starting chain (s) is formed to take the row up to the proper height for the next row to remain constant. Depending on the pattern, one has the option of continuing by turning the work or not at the end of each row. Doing so allows the opportunity of altering textures and working in the fronts or backs of stitches. 2: in spirals. Rather than joining the ring, one continues on by going into the tops of the posts in the previous row.

With spirals it is useful to mark the beginning of each round. Knitting markers shaped like safety pins are handy for that purpose. A line of contrasting color can also be created using a separate strand of yarn and alternating carrying it back or to the front prior to forming the first stitch in the new row.

As with knitting, crocheted circles are not true circles, but rather, they are polygons. The way to make shapes more circular is to scramble the increase points, putting them in different starting positions in each round (always spacing them equally and keeping the formula). Within limits one may make the starting number of stitches in the first round a multiple of the number of segments in the finished shape.

With the creation of a flat circle in mind, the number of stitches needed depends on the height of the stitch. The taller the stitch, the greater the number of stitches required. If the stitch stays the same throughout, the number of stitches added on each round is constant. Test work regularly at intervals as the work grows by placing it on a firm, flat surface, to see if working only one stitch into each stitch is required / enough at that point to maintain the shape. The more segments, the smoother the circumference.

Unlike in hand knitting, the first loop on the hook does not count as a stitch until you make it into something.

Spirals or miters knit on the machine begin with their radius; one possible construction method may be inferred from these images

Spreadsheet programs such as Excel and Numbers have pie charts and other tools that can help visualize or even plan the work with symbols. Unlike machine knitting, both crochet and hand knitting may begin and grow from the center out or from the outside in. Calculated shaping with increases or decreases along circumferences at different points on the pie create the desired shape. For the purposes of this discussion I will address stitches in US terms. There are various published guidelines with some variations. Fiber content and matching gauge (if required) may need editing of the numbers, but, as starting points:
Single Crochet [sc] : Start with 6 sc and increase 6 sc in each round so that the total stitch count in each round is a multiple of 6
Half Double Crochet [hdc] : multiple of 8
Double Crochet [dc] : Multiple of 12
Treble [tr]: multiple of 16

Some symbols and number of stitches required in base rows in table form, for working from center out:
the more wedges in the pie, the smoother the circumference no matter what the method. Single crochet is worked in 6 wedgesdouble crochet in 12 wedgeswedges may be reduced to simple line segments rounds may also be created to log in and track more details adding wedge outlines before filling in symbols

single crochet worked with slip stitch at the end of each row will produce  points similar to those seen in miters in machine knitting

spirals produce a rounder shape double crochet echoes the forms 

Building your own charts requires vector programs to allow for rotation of symbols around an axis. My chart was quickly produced in Inkscape, which is free to download for both Mac and PC users. Mac users in addition will also need to download XQuartz to run the program. I created the chart with my own symbols and freeform laid them down while viewing the grid. It turned out however, that there are 2 published videos on how to use the program for charting crochet stitches, part 1 and part 2 by

Two YouTube videos on topic:  using Illustrator CS 5.1, Marnie Mac Lean’s video, and using StitchWorksSoftware. An online generator by Stitch Fiddle, and its associated video.

if donuts are the goal: find your round 

An example: in single crochet, if round 3 had been completed, there would be 18 completed stitches. Chain 18, either slip stitch or continue in spiral to match count at that point. For round 4: increase every 4th, round 5: every fifth, round 6: every 6th, round 7: every 7th stitch.

A few sites to see for crochet tutorials:
magic ring start : no chain stitches, no center hole
working in spirals
a nice ending
crocheting a flat circle in single crochet: note the start “magic circle”
changing colors

I tend to swatch in easy to see colors, “friendly” yarn, and use tools that allow moving in and out of stitches easily until I have techniques sorted out. When knitting circles in the round, things get a bit more complex, particularly if one begins to introduce items such as round yokes with patterns into garments where gauge matters significantly.

Some of the same principles may be used in hand knitting. For magic loop start with circular needles: KNITFreedom, and on DPs Webs yarn

Seaming, joining, picking up stitches on knits 2

I have an extensive library on both hand and machine knitting. I am not the originator of the base drawings for these illustrations. They have been however,  accumulated from various decades old sources, edited by me for content, color, size, etc. My editing program is gimp. I will review, alter, or add to this library over time.

sewn bind offs on machine

on knit taken off on waste yarn 

joining a hem crochet bind off through top or bottom of stitches in last row respectively

weaving in yarn ends across a row on purl side

Mattress stitch: work a few rows with loose stitches so entry and exit points are visible, then pull on yarn and tug on finished segments as you go to adjust stitch size

  1. under single bar between a full knit stitch on either edge of knit, best for bulkier knits
  2. under double bars between a full knit stitch on either edge of knit, faster on smaller gauge knit
  3. worked half a stitch away from the edge, every  row, under bar on left, loop on right
  4. running stitch along and through center of edge stitches, alternating sides every row
  5. running stitch one full stitch away from the edge, alternating sides every row
  6. joining purl stitches every row

garter stitch

  1. mattress stitch, knit side out, one full stitch away from edge, adding second strand of yarn to finish join
  2.  weaving in joined yarns along inseam, traveling in opposite directions

2 X 2 rib ending with one knit stitch2 X 2 rib ending with 2 knit stitchesrib join through “edge loops” of knit stitches

 2 X 2 rib join ending with 2 knit stitches, 1 full stitch from edge 

2 X 2 rib join ending with 2 purl stitches, 1 full stitch from edge 

picking up stitches to continue knitting or joining on machine: straight edges curved edges 

open sts to bound off          bound off sts to bound off  (steps 1 and 2)knit to purl                                        knit to ribgarter stitch 

decreasing evenly at intervals across a row purl side facing if you are left handed or yarn end is on alternate piece,  rotating the image or flipping it horizontally or vertically will provide guidelines GIMP (free) download  for further DIY image processing

Single bed slits aka horizontal “button holes”

There are many good instructions online for producing buttonholes in doubled over knit bands. This version is from the Brother Knitting Techniques Book, now downloadable for free online


Many hand knitting patterns are published, often in garter stitch, using slits that one may think of as larger “buttonholes” to create a range of interesting fabrics. Trying to produce such slits single bed, without the use of additional strands of yarn and in turn having yarn ends to weave in, leaves few options.

This method may be used when creating multiple slits across a row as well. Holding is used to break the knitting into segments. The drawn illustrations show steps taken, not needle positions.

COR, for the bottom of the slit: 1. transfer the first stitch in the buttonhole group onto the adjacent needle to its right

bhole_012. transfer pair of stitches together onto the now empty needle to their left. The knit carriage, holding the yarn, will be on the right


3. push the needle forward until the first stitch (green) passes over the needle’s latch bhole_044. push needle back to work position


5. the forward stitch (red) is now knit through the one behind the latch


This essentially binds off a stitch. Repeat steps 1-5 until for the number of bound off stitches required; the last stitch in the group is then transferred onto adjacent needle to its left. The bottom edge of the “buttonhole” is now complete. bhole_06aTo make the top edge of the buttonhole/ slit bring its corresponding needles out to hold, cast on desired number of stitches with latch tool from right to left.bhole_07aIn order to best accomplish this with COR set KM for holding, push empty needles back to A position, knit up to now empty “buttonhole” needlesimg_4069bring empty needles out to hold img_4070insert latch hook from back to front through below the last stitch now knit on the right screenshot_36twist tool clockwisescreenshot_37bring empty needles out to holdimg_3966come up between the first 2 needles on the group’s right screenshot_38continue with latch tool bind off, last loop in chain is hung on needle already holding 2 stitches from the last bind off transferimg_4071tighten up loop 
return “buttonhole”  stitches into needle hooks, back to B position
img_4073COL: set KM to slip in both directions, move to right img_4074COR: cancel holding, adjust tension, knit across remaining stitches to Limg_4075COL: cancel slip <–>, continue knitting screenshot_08



For hand knitters: my new favorite hand knit buttonhole in video format
in written/ illustrated form
two fabrics using slits: a free Ravelry pattern 
my blog post in response to a Pinterest request: variations in rib with holes

Charting shapes for short row knitting and programming

In machine knitting, stitches are usually brought into hold opposite the carriage. If multiple stitches are brought out to hold on the carriage side, floats are created. Triangles stacked vertically as seen in the previous post, will create a spiral curve along the line where stitches are held. The carriage needs to get to the opposite side and back after each ‘decrease’ or ‘increase’, so pairs of rows are used to execute and reverse angles in short row shaping. When multiple rows are knit independently from the rest of the knit, slits are created. In two row sequences these are generally similar to holes created in lace, in longer sequences much larger slits are produced. The latter are often used as planned design elements. The small holes being visible may not pose a problem for the knitter. If they do, wrapping the adjacent needles can help eliminate them, but the doubled yarn in the wrapped needle may create small, sometimes visible bumps on the knit side of the finished piece, creating a secondary pattern.

Reducing eyelet size: in traditional wrapping  required needle(s) are brought out to hold, the yarn is wrapped under and around the last needle in hold on the carriage side before knitting the next carriage pass

                        COR                                                              COL                                both

The “automatic method” for wrapping

Decreasing: if COR (COL), to hold 1 stitch at a time, set the machine for holding. Bring one needle on the same side as the carriage into hold position. Pass the carriage to the opposite side. COL (COR) repeat if shaping is 2 sided, or if shaping is only on the starting side, knit back to it, and with COR (COL) repeat process. Increasing single stitch : bring 1 needle always opposite the carriage into work position.

Decreasing:  more than 1 needle or stitch at a time: if COR (COL), place 1 needle less than required into hold on the opposite side as the carriage, knit 1 row to left (right), toward the needle in hold. When COL (COR), bring into hold the last, additional needle. COL (COR) repeat if shaping is 2 sided, or if shaping is only on the starting side, knit back to it, and with COR (COL) continue decreases on the single, opposite side.

Increasing:  to remove stitches from holding , COR (COL) place the desired number of needles into working position on the side opposite the carriage, knit one row, repeat with COL (COR) if shaping is on both sides, or knit back to starting position COR (COL) and continue increases on the single, opposite side.

Charting out shapes knitting or programming stacked equal triangles / spirals: the wedge illustrated in the previous post single spiral wedge“Air knitting” is often used to think out fabric issues before swatching using yarn. Drawing lines to follow carriage movement direction required to keep the knitting continuous, whether or graph paper or within software programs, can help sort out shapes that will work in short rowing. Holding needs to happen in 2 row sequences. Below, black lines and arrows indicate the direction of knitting for each row, in this instance beginning with COR. Blue = knit stitches, yellow = all knit rows at the completion of each wedge (2 or multiple of 2, depending on planned design). This repeat is suitable for knitting a continuous strip with ruffling/spiraling at various degrees, not for ‘pie’ shapes.


Working out the repeat: the red line represents the starting, selection (KC), knit  row, the numbers at the bottom the width of the repeat, the numbers to the side its height. The first repeat A, results in the fewest punched holes, drawn squares or programmed pixels, requires being knit double length. The remaining repeats (B, C) are drawn double length, standard card rotation is used. Eyelets form at the held edge. C takes automatic wrapping to decrease eyelet size at held edge into account. When any sequences are programmed for knitting using slip stitch, the end needle selection is always cancelled by using KCII, or turning non needle selection cams in punchcard models.

A                                 B                                    Crufflethe start of a miter shape: blue repeat, extra knit rows in yellow, auto hold on bottom rightscreenshot_45

Going 3D: in many designs the original repeat may simply be mirrored to be executed. If this is done here, one can see there is no longer a continuous knitting line, directional arrows are moving in opposite directions or toward each other from center point

offset1restoring continuity offset 2shifting rows around to create a workable repeat offset 3one shape 3 different ways:  red row = KC II, all knitdouble spiral

An executable 24 stitch, 26 row repeat:  black arrows alone indicate movement of carriage on the first row of the repeat, black arrows on red line indicate starting point and direction of movement of carriage for KCII rows. A begins to knit repeat with COR, B with COL. whole repeatsThe triangle’s vertex can be squared off, the height of the repeat shortened, to make 3D shapes much rounder ball1X8ball1X8

Not just for electronics: some punchcard repeats to try (also suitable for any machine). End needle selection is cancelled.  Selection rows are always toward the first pair of rows knit in holding pattern, so for the first 2 cards they would be from right to left. Single rows are punched but 2 row sequences are needed, so cards must be elongated X 2; miter shaping repeat is shown on the left, spiral on the right. Narrower shapes may be created and knit on the appropriate segment of the 24 stitch repeat needle positions. Use needle tape markings as guides for placement. Selection row is from right to left, the pattern repeat begins with COL. All punched, extra series of pairs of rows of knitting may be added at the top. Note: just a few rows may not be added with a small a segment of an additional card with clips, the whole repeat may have to be split in sections to allow for the extra rows and its smooth passage through the card reader. As an alternative, more rows of all holes could be added to the original card when first punched, tested, and then trimmed if not needed. It is useful to try out the repeat as a hand technique first in any of these instances, to determine personal preference.


Going 3D: punch only actual holes (black pencils marks were originally used to mark squares that needed to be unpunched for auto wrap on right, not the best choice for B/W scans). Two row sequences are punched, so no elongation is needed for either repeat. Miter shaping is shown on left, spiral on right; mem <– indicates direction for KC row; decreasing angles are auto wrapped, increasing angles need not be as seen in the top of miter on left, where needles are returned back to work to create the reverse shape.3Dmiter_spiral corrected

Some ruffle possibilities: all knit rows were added to the card on left with snaps, and are composed of all punched holes. The number of all knit rows  between held segments determines the spacing between wedges and the degree of spiraling of final fabric. KC row needs to be R to L for A, left to right B. Holding sequences are now staggered, changing the angle of the resulting curves. Where 2 stitches are brought to hold on the carriage side, a short  float is created.                                                      

A: elongate X 2                              B: use as is         ruffle-pair-

The recommended minimum for punchcard length is generally stipulated to be 36 rows. Card A without the added rows is 28 rows high (last 2 rows are for card overlap when adding snaps), so the repeat below, with extra segment removed, would need to be punched twice

A single_correctedeyelet pattern reflects shaping500668



B: dotted lines outline segment: yellow dots on purl side, the 1 needle floatsruffle_floatone possible card revision: red dots indicate punched holes, stitches in hold as carriage moves from left to rightruffle16_CORany difference in the swatch, in this yarn, was almost imperceptible; results would vary depending on yarn thickness and fiber content.

rufle not floatthe swatch as a “ruffle”ruffle_show

Revisiting miters, spirals, going square, round, and more

I am working on updating my flickr photostream albums, including “all things holding” and will be revisiting posts on this topic over  the next few weeks, possibly adding edits.

There are times in knitting when math becomes a necessity. With online libraries, tools, and fairly intuitive software, drafting angles and shapes is now much easier. I will be teaching a class that includes miters and spirals at a seminar next month, leading me to revisiting the topic. Most published pattern instructions will give starting carriage locations, but shapes may be constructed counter clockwise or clockwise depending on preference. With understanding of how the shapes are formed and stacked, they may in turn be automated (depending on their size and the type of km) using the slip stitch setting. Stitches that are to be knit on each row are programmed as pixels, black squares, or punched holes.

Miter shaping may occur on side or in center of each triangular shape; a minimum of 2 knit rows usually occur at designated spots. Adding more knit rows and playing with angles of triangles will create ruffling effects, other angular shapes, pleats, and more. I have returned to using  Mac Numbers, their shapes and charts to generate most of the images below. Here the colored areas represent knit stitches, white negative (white) spaces stitches in hold. Red lines represent all knit row(s)/ spots for seaming at top and bottom of sequences. Seaming is easiest when done by joining all knit rows. Stitches are always brought into hold opposite the carriage side, returned to work on carriage side. In shaping guide, COL= carriage on left, COR= carriage on right.

knitting each segment

COR                                   COLwedges

Yellow triangle segment: bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Green triangle segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold.

If seaming is desired in miter shaping with resulting eyelets at sides of triangle, the full wedge is split between the top (yellow segment) and the bottom of the piece (green segment). Knitting always starts with at least one or 2 rows of knitting (depending on whether the finished shape is to have a grafted seam.  For the full wedge: * yellow segment, bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work. Reverse shaping with green segment: with all the needles in work, begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold. End with knit rows (red line) across all stitches*. Repeat  from * to * for desired number of full segments, end at top with a yellow segment if needed, followed with knit row(s) (red line) before binding off or seaming.

shaping with resulting eyelets at sides of triangle: the final shape COReyelet at sidethe knitting sequence with top/bottom 1/2 triangle segments shown

COR                                   COLfinal at sides

For miter with shaping and resulting eyelets at center of triangle: begin with all knit row(s) (red line) at the start. To shape full wedge: *green segment is worked bringing stitches into hold opposite the carriage at the determined rate until all the needles are in hold. Shaping is next reversed with yellow segment, pushing needles back at the determined rate until all needles are returned to work. End with all knit rows (red line) *. The sides of this miter are all knit rows, an easier place to seam/ graft joins if needed.

shaping with resulting eyelets at center of triangle: the final shape COReyelet at center2the knitting sequence

COR                             COLfinal at center

a tiny test

shaping at side                              shaping at center



In the following images the red or blue lines indicate seams or joins

segments composing a square shape 
adding squares or rectangles to alter the square
squarextra_seamsadding triangular segments: hexagonpentagon_seamexpanding it with rectangles, shaping at sides
dodecadon extra_seams2shaping at centerhexagon extra_seamsgoing 3D: triangular pocket with point at center 3dmiter

combining shapes: this one is often seen in tams (hats); bottom shaping is on only one side, at the top it occurs on both sides


tam2adding rectangles or squares to alter shape


bringing needles out to hold opposite carriage

Spiral stack 1/ green full triangle : knit row (s), *with all the needles in work begin to bring stitches into hold opposite the carriage at the determined rate until all the needles are in hold, end with all knit row(s) (red line).

COR                                   COLspiral stack1 cor

Spiral stack 2yellow full triangle:  knit row (s), *bring all needles out to hold, push them back into work on the carriage side at the determined rate until all needles are back in work, end with all knit row(s) (red line).

COR                                   COLfull stack 2

3D spiral 3Dspiral

If the object is to construct a circular shape, the greater the number of panels, the smoother the outer edge of the piece . Some of the pie-bilities: so many pies

In all instances above the radius and therefore 2 sides of each wedge remain equal in size, and therefore are composed of the same number of stitches. The triangle knit to achieve these shapes are isosceles triangles, where 2 of 3 sides are equal in length and in this case, number of stitches. The 2 equal sides are usually referred as legs, the remaining one as the base. The 2 base angles are equal as well. The remaining angle is the vertex one. In knitting, this will be the pivot point for the wedges, the center point of the “pie” shape. In the illustrations below the vertex angles are marked by blue dots. Its angle value is the first represented in the numbers immediately below each shape, with the other 2 numbers indicating the remaining, equal 2 angles. The sum of all 3 should equal 180 degrees.all anglesTaking it to a shape: octagon (half the total # of wedges shown). In colored shapes spiral, stacking equal triangles is shown on left; full triangle, divided into 2 segment shaping for miter on right.octagon col

Oh, yes, the math! The desired shape may be drawn to scale using any number of tools. Wedges may in turn be shaped following the scale drawing on any charting device such as knit-leaders, or stitches and rows required may be calculated on actual full drawing measurements. In knitting, the equal sides (AC, AB) of the triangles are formed by stitches, the height of the triangle (CB) by rows. If finished size matters, accurate gauge is required. One approach to calculating the base (CB) is to think of the whole shape as a complete circle, in this case divided into 8 “pie” wedges, with congruent sides (radius) measuring 10 inches each. To find the circumference of the circle, multiply the diameter (20) inches by pi 3.14 = the total in this case, of 62.8, rounded off to 63. Divide that number by the number of sections (8) = 7.85, rounded off to 8 inches (rows). If stitch gauge is 6 stitches and 8 rows per inch, each triangle would be 60 stitches wide, 64 rows high. Holding happens every other row, opposite the carriage, so total number of rows is divided by 2 = 32 for knitting a spiral. The stitches are distributed along one edge over the total 64 rows in height. The goal is to reduce shape down to the next to last group, followed by two rows knit over all the stitches at the end of each section. This will cause a small hole at the center of each completed pie due to extra rows knit. For a miter 2 triangular shapes are required for each wedge, so holding sequences are recalculated with shaping now occurring over 16 rows for knitting a miter. screenshot_09 color

An online calculator is available to help calculate the number of stitches brought into hold opposite the carriage or into work on carriage side, sequence preference should be tested on swatches where gauge is significant

  spiral screenshot_02miter Miter online

Magic formula (X represents times)magic formula

In the photo below I chose to start with all the needles out to hold,  pushing them back into work across the knit for the spiral. For the miter again, I began with all needles in hold, pushing back the required needles into work; for the top half of each wedge needles were returned to hold opposite the carriage at the same rate, forming the upper half of the “pie slice”. The swatch is not worked at the same rate as shapes calculated above. It is shown on its purl side with color changes to highlight the intersections where wedges begin to repeat. The yarns used are random acrylics, in different weights. photo miter spiral

A previous post on short row knitting from with links to other online sources A category search in my blog roll for miters and spirals will link to blog posts including pies:  breaking and mixing up pie wedges: . A garter bar short row trim: Charting shapes: using Gimp and Mac Numbers:  . Executable charts, shapes, automating with slip stitch:

Hand knit “dragon scales”

detail of half fisherman machine knit version of stitch500_606

My last experiments led to a search for possible hand knit “scale” version. Similar shapes may be achieved through holding, but here the effect is created through use of increases and decreases. The test for the repeat was knit in a 4 ply acrylic. As with the machine knit version, the pockets become more pronounced as the fabric relaxes, without any blocking. Garter stitch was used in the first sample, for both texture and speed. Everyone has their preferred methods for increasing (M1) or decreasing/ combining 3 stitches into one. I tried picking up from row below or casting on single stitches (#1), but found the least noticeable methods to my eye, using this yarn and stitch type, were simply to knit in front and back of the stitch (#3) where an increase was required, and to knit 3 together (#2) for the decreases.

numbered_636the reverse structure curves in a similar way to the machine knit 500_637

The number of stitches remains constant on each row knit; the chart reflect side panels (A, C).The central 18 stitches (B) that may be repeated multiple times to achieve the desired width. The border stitches added may be any number, are also knit on every row.


The fabric changes dramatically when every other row is purled. This swatch was knit with a single stitch garter stitch border, and I experimented with increases and decreases. The M1 sts were created by picking a loop up knitwise from the row below for the increase. The slight shift in the pattern center where decreases and increases meet helps define a point on the “scale” shape. The same yarn and needle size were used as in the above sample. A softer, thinner yarn knit using smaller needle size would benefit either variation. To my eye, the all garter stitch version was more successful and pleasing.

knit as “outside”, default shapeknit frontits reverse500_643purl as “right side” after poking scales out 500_639its reverse


for a less pronounced, “scaly” relative using lace in its design please see

Tuck and garter stitch: from hand knit to machine knit hand tech pattern

A Ravelry question on the possibility of executing a particular fabric on the machine has led to the experiments in this post. The pattern that led to the discussion is  free hand knit one,  shared and published on the Purl SOHO website and on Ravelry. The gauge for their project is 4.75 stitches = 4 inches in stitch pattern, it includes garter rows. Such rows may be executable on home knitting machines by transferring from ribber (Passap front bed) to main bed, alternating with reversing the process at predetermined frequency, depending on stitch type. K1b is the hand knit equivalent of tuck for that stitch on that row, adding to the mix.  Not practical for G carriage use, as the latter does not form tuck loops, and hand retooling would be required for all k1b stitches.

Using holding to create tuck stitches in non auto patterning days was commonly used, and I chose to do so here. As machine knitters we are conditioned to believe that single color rows are impractical to execute, and that the yarn would need to be cut on each side after the one row. Color changers are on one side or the other, making striping with frequent color changes practical if executed in even multiples of rows. Transfer carriages are available that will help move stitches from one bed to the other, I personally have never had the patience to work with them enough to get good at using them without dropping stitches, so I went back to even lower tech than usual, using the garter bar on the bulky, and beginning pattern row 1 with COR.

Before attempting nearly every row turns, it is helpful to have some practice with turning work over using garter bar, develop a sequence to repetitive actions, keeping careful notes as to what works for you, and using contrasting yarns in tests to better understand stitch structure. In my sample the white yarn was thicker than the blue, reversing colors or balancing yarn thickness would change the visual look of the fabric.  Beginning on small samples helps work out issues and the making of the decision to try on a larger project or simply as a border.

Analyzing the pattern repeat:

screenshot_43tools to help with EON needle selection tools

the results of rows beginning with k1 sequence after the row is knit, note the “tuck” loops on top of E position needles, which will be knit off on the next row knit K1_after knit

a row that begins with a k2 sequence, before it is knit; the needles holding the single, blue stitch will form the loops on top of the needles as the yarn moves across to opposite sidek2_before knit

E position prior to transferring stitches onto garter bar, also for free pass to other side to pick up yarn after stitches are removed on bar free pass473

1            begins and ends with K 1; COR select needles, col A * knit row, COL, bring all needles out to hold, remove on garter bar, free pass carriage to opposite side, COR, flip garter bar over, replace stitches onto needles push all stitches against gate pegs *

2            begins and ends with k 2; COR select needles for row 2, col A repeat * to* end COR

3            begins and ends with k1; COR select needles for row 3, change to col B, knit one row, do not turn, do not cut yarn; COL bring all needles out to hold, free pass to right to pick up col A on next knit row, end COR

4            begins and ends with k 2; col A, COR select needles for row 4, repeat from * to *

5             begins and ends with k 1; COR select needles for row 5, col A, repeat from * to * do not turn

6            begins and ends with k 2; COR select needles for row 6, change to col B, repeat from * to *

publisher’s project photo


my swatch, knit on a whopping 9 stitchesrav blanket 300