Hello fellow crafty people. :)
In knitting and crochet I often hear people wondering how to go about evenly spacing increases and decreases and wondering if there is a formula. The following is the method I use.
Method for Working Out the Spacing of Increases
I imagine that my increases and decreases are like fence posts and I want them evenly spaced. If I'm working all the way around a piece it doesn't matter where I put the first one (provided it is within the multiple) but if I'm making two pieces that will be seamed it does make a difference.
In that case I must have the posts at each end only half of a multiple from the selvedge. Then when the seam is done the two units join together to make a spacing of a whole multiple.
If dividing the stitches you have by the number of increases you need does not produce a whole number you will need to stagger your increases. There is a method to figure this out.
Let's say that I want to increase 8 stitches over 36 so that I end up with 44. 36/8 = 4.5. Now, I can't do an increase every 4.5 stitches so I multiply up the answer by whatever it takes to get to a whole number. The multiple I used becomes the number of increases I must do for every whole number of stitches I just calculated.
Here it would be 2 increases for every 9 stitches (2 x 4.5 = 9). I can see immediately that the sequence would be:
4 # 5 # 4 # 5 # 4 # 5 # 4 # 5 # where every # is an increase and there are two of them to every 9 stitches (4 # 5 #).
There - that used 36 stitches and produced 44 - but I don't like the 'balance' at the end of the rows - or trying to increase after the end of the row!
So, I do what I said above and do the first increase at half of the first spacing and come up with this instead:
2 # 5 # 4 # 5 # 4 # 5 # 4 # 5 # 2 where every # is an increase.
That also used 36 stitches and produced 44 but the balance is better and I don't have to do an increase after the end of the row.
The Increase Method in a Nutshell
Divide the number of stitches you have (A) by the number of increases you need to do (B). The result is (C). If (C) is a whole number do one increase for that many stitches as your spacing. Do the first increase at half that spacing (rounded to a whole number if the number is odd) to balance the placement.
If (C) is not a whole number multiply it by a number (D) that produces a whole number (E).
Work out a sequence to do (D) increases for every (E) stitches. It will always be a combination of the rounded up and rounded down versions of (C). There will always be at least one even number in the sequence. Put an even number first in the sequence because it is easy to halve for the next step.
Place your first increase at half of the first spacing you just worked out and do the rest of the increases spaced according to that sequence. At the end there will be some stitches left over - that is as it should be.
Method for Working Out the Spacing of Decreases
There is also a method for working out decreases when the division does not lead to a whole number.
Let's say that we have 100 stitches and need to reduce to 85, a decrease of 15 stitches.
100 / 15 = 6.6666.
Multiply 6.6666 to get a whole number - multiplying by 3 gives us 20.
We need to do 3 decreases for every 20 stitches we have. Since 3 decreases will use up 6 stitches (2 x 3 = 6) that leaves 14 stitches to make up the sequence. 20 - 6 = 14.
Because we are decreasing we need to decrease our first result by two (the decrease uses two stitches) to find the numbers we will combine in our sequence. 6.6666 - 2 = 4.6666. Rounding this up and down we find that the numbers we combine will be 4 and 5.
Notice that there will always be an even number in the sequence, use this number first in the sequence because it is easiest for the final balancing step. The sequence of 4's and 5's that adds up to 14 is 4#5#5# where # is a decrease. If we repeat that sequence 5 times (5 x 20 = 100) we get this:
4 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # Which uses 100 stitches, has 15 decreases and produces 85 stitches. However I don't like the 'balance' of the decreases - or trying to do a decrease after the end of the row!
To balance the sequence and correct this problem halve the first number of the sequence like this:
2 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # 4 # 5 # 5 # 2
The Decrease Method in a Nutshell
Take the number you have (A) and divide it by the number of decreases you need to do (B). The result is (C). If (C) is a whole number then you do a decrease within that number of stitches, repeating all the way along. Halve it (rounding if it is an odd number) for the first repeat so that the whole sequence balances. There will be stitches left over after the last decrease, they are the balance from the first repeat you halved so that is correct.
If (C) is not a whole number then find a number to multiply it by (D) to get a whole number (E).
(C) - 2 = (F), the number you round up and down to find the components of your sequence.
(E) - 2x(D) = (G), the number you make your sequence add up to.
Using a combination of (F) rounded up and down create a sequence that adds up to (G). Put an even number first in the sequence.
Halve the first number in the sequence and then continue it as you have already done. There will be stitches left over at the end (the balance of the first number you halved) and that is as it should be.
Some Handy Multiples
If (C) ends in .25 or .75 then multiply by 4
If (C) ends in .3333 or .6666 then multiply by 3
If (C) ends in .2, .4, .6 or .8 then multiply by 5
Go forth and multiply... Megan