The treadles of the original tie-up correspond to treadles
or pairs of treadles in the reduced tie-up according to the
following table:
| Original |
Reduced |
| 1 |
1 |
| 2 |
5+9 |
| 3 |
6+10 |
| 4 |
7+10 |
| 5 |
4+10 |
| 6 |
5+10 |
| 7 |
2 |
| 8 |
3 |
| 9 |
4 |
| 10 |
5 |
| 11 |
6 |
| 12 |
7 |
| 13 |
8 |
| 14 |
9 |
You'll need to modify your treadling draft accordingly.
|
Every column in the original tie-up is either a column
in the reduced tie-up or a combination of 2 columns there. The rest of the
output is a table showing the translation.
Looking at the two tie-ups, you can see that this makes sense. The effect
of pressing treadle 1 in the original tie-up is the same as the effect of
pressing treadle 1 in the reduced tie-up: shaft 8 gets lifted. (Treadles
are numbered left to right; shafts are numbered bottom to top.) Similarly,
the effect of pressing treadle 2 in the original tie-up is the same as the
effect of simultaneously pressing treadles 5 and 9 in the reduced tie-up:
shafts 1 - 7 get lifted. Use this translation on every line of the
treadling draft, and you have a complete recipe for weaving the 14-treadle
pattern on your 10-treadle loom.
Just to be concrete here: Suppose the original
treadling draft for the 14-treadle loom began like this:
In the reduced draft for the 10-treadle loom, the treadling draft should
begin like this:
|
|
When there is one solution, there are often others (sometimes
thousands of them.) Given one solution, though, you may be able
to find others. You may also be able to modify this solution,
by doing things like rearranging the treadles in order to get
a tie-up which is easier to weave.
Need to change your input? Your browser's Back button
will take you back to the previous screen and save you a lot
of retyping.
Questions or comments? Do, please
mail them to me. Here's
how to contact me.
|
The warnings at the end here are serious. There may be
other possible reductions that are easier to weave than the one shown here.
For instance, you might well want to rearrange the order of the treadles in
the reduced tie-up if you found it awkward to press treadles 8 and 9
simultaneously. Swapping treadles 9 and 2 might make for easier treadling.
Obviously, you should use what the machine tells you as a starting point,
using your judgement as a weaver to find improvements that a computer and a
mathematician cannot.
There are 3 other possible outcomes of using the Treadle Reducer.
- You get some kind of an error. This is never supposed to happen, but
then, one is never supposed to have to unweave, either. Do let me know if
you get an error, telling me what input you used. I'll try to fix it.
- The computation takes too long. This is often because there is no
reduction to the number of treadles you requested, but it may also be that
there is a reduction that is just taking a long time to find. You could try
specifying a longer time limit. You could also try asking for a reduction
with one more treadle. If the Treadle Reducer finds one, maybe it will give
you a hint as to how to eliminate the extra treadle by, for instance,
depressing 2 treadles with one foot and one with the other.
- There may be no solution, and the Treadle Reducer may finish its search
and tell you so. If this happens, then you're really out of luck. The Treadle
Reducer has made an exhaustive analysis, and the reduction you were hoping
for really isn't there to be found. The tie-up above, for instance, can be
reduced to 10 treadles or to 9, but it cannot be reduced to 8
treadles. If this happens, it may be worthwhile to try a reduction to one
more treadle than you actually have, and to see if you can see how to reduce
further by being willing to press 3 treadles at once. Other solutions
include picking a new pattern, or buying a new loom.
|