Sister billets are lams/slices cut off the same board one right after the other. In other words they were right beside each other in the board so they will have pretty much the same characteristics.
Purple heart for a belly I am not sure.
Tillering for equal limb timing is tillering the bow on the tiller tree so both limbs bend in harmony.
My tree is setup to replicate where the shooters hand will be when shooting the bow. The black vertical line on the right is for split finger shooting and the line in the middle is for 3 under shooting. The bow sits in the tree cradle with the arrow shelf aligned with the right side end of the cradle. I can move the bottom pulley of the tree to align with either of those vertical lines so the tree rope pulls straight down.
In the video below you will notice the trees pull rope tracks right down the black line on the wall when I pull the bow string downward. That tells me both limbs are bending in sync, " equal limb timing". Which means when the bow is shot, both limbs return to brace at the same time, that equals zero hand shock. If one limb gets back to brace before the other, that is what causes hand shock and erratic arrow flight and noise.
You start out on the tree only pulling the bow down a few inches, maybe 5 or 6 inches. You want a string on the bow that just fits into the string grooves of the bow so the string lays snug up against the belly of the bow.. You don't just string up the bow to a 6 inch brace right off the bat. As you pull the trees pull rope down, the limbs will start to bend. You want to keep the pull rope tracking the vertical line on the wall. If it drifts to one side or the other, it will "ALWAYS" drift towards the stronger limb.
So you need to remove wood from that stronger limb in order to get the pull rope tracking the line. Tillering a wood bow is a slow tedious process. You need a good eye to see where wood needs removed. If you seen any hinges, " areas where the bow is bending too much in one spot", stay away from that area and do not take any wood off there. Mark it no with a pencil.
As I start tillering the bow, my first goal is to get the pull rope tracking the line. So I see which limb is stronger and start removing a LITTLE wood where it needs removed. Don't go hog wild removing wood or you will cause a hinge. Once the rope is tracking the line, I'll exercise the bow about 25 times to a certain draw length down the tree, there are numbers the whole way down the wall on the lines. If the rope keeps tracking the line, I'll pull another 25 times to 2 inches further. EVERYTIME after removing wood from the bow, exercise it 25 times to the same distance before. Once all is good pull another 2 inches more down the tree. When you remove wood from the bow, it needs exercised to get the bow bending and for the wood removal to set in.
Once the limb tips are bending down to 6 inches, I will brace the bow up to about a 4 inch brace height. Then continue tillering as we did above, 2 inches more down the tree @ 25 pulls. Once the tips are bending to 9 inches, I'll brace the bow to about 6 inches and tiller on out to the intended draw length. But your goal is to keep that tree pull rope tracking the black line and you may need to make adjustments by removing wood the entire way down the tree to do that. But once the rope is tracking the black line, it will stay pretty close and only minor wood removal is needed.
You don't want any nicks or scratches in the wood when tillering, so after removing any wood, sand that area with 220 paper.
There is so much to tell you about tillering that it would take pages and pages. Go to you tube and do a search for tillering a wooden long bow, there should be many there.
Notice in the video below how the pull rope tracks the black line on the wall. This bow is tillered for equal limb timing.
I don't care if the tiller is positive or negative, whatever it ends up as is what the bow likes. It's usually even tiller or slightly negative.
My tree is setup, " those black vertical lines on wall ", replicate where my middle finger will be on the bow string when shooting. The line on the right is for split finger, line in the middle is for 3 under and line on the left is for if I want to setup for a fixed crawl nocking point. My pulley at the bottom can be moved to align with either of those 3 lines to keep straight downward pressure on the bow.
I assume my nocking point on the string is going to be set at 3/8th above the shelf, and that's how I set it on my bow string. I nock the arrow under that nocking point, an arrow nock is about 1/4" high, so I figured out where my middle finger will be and set the tree up according to that. So my bows are tillered for equal limb timing according to where I am going to hold the bow string.
People who just tiller a bow for the old 1/4" positive idea, then have to keep adjusting their nocking point to get the arrows to fly right up and down when tuning the bow. I never have to do that and the bow is tillered to shoot perfect from the start of tillering.
In the above video, that bow is being setup for shooting split finger. Notice the tree pull rope travels straight down the black line on the right. That tells me those limbs are bending exactly the same way, balanced! And when I shoot an arrow, those limbs hit brace at the exact same time. No hand shock, very little noise, and great accuracy.