The tao of tenons

Last post we made a mortise in a piece of 4x4. But something has to fit in that mortise, and that something is a tenon. A tenon is a tongue-shaped piece that goes at the end of a post -- or a brace. The easiest tenon to make is a post tenon. So let's look at it first.
Here is a post mortise. My standard post mortise is 6cm long. I made it just as I did the last one. Drill and clean. And there is Mr. Ferret, as I promised, sitting on top of the 4x4. Wonderful tool to clean out the bottom of a mortise. Better call it 88x88 mm, not 4x4. Got to watch the tricky gringos. They do you out of lumber at every chance. But note that at the right end of the mortise is a space. This is called the relish, for reasons that are obscure to me. So I am allowing a 2cm or so relish. Now we need to cut a tenon that will fit this mortise. This is a mark and saw job. You use the same marking gauge settings you used to do the mortise, but you saw inside the lines a hair. You want a looseish fit. Later you will drawbore the tenons. That is, you will put a peg through them. On the tenon you will offset the hole a bit (2-3mm) toward the shoulder. This will pull the mortise and tenon tight. So we saw out the tenon. It looks like this:
Now on to a more complex tenon. Since I did a brace mortise in the last post, it is only fair to show you how to cut one. A brace runs at 45 degrees between (usually) a post and the piece on top of the post, called a plate if it is a one-story thing, such as I want to do. Because things are at 45 deg the lengths of mortises are longer. For instance, the length of the brace mortise is 12.2 cm. Why? Well, Pythagoras. He worked the problem. Most things on a brace are multiplied by the square root of two. This is 1.4142... and on forever. I could do a whole post on the square root of two. But you may rest at ease; I won't (now, that is. I may still inflict it on you). However, to the nearest millimeter a 90-mm wide brace requires a 122 mm mortise. Slight error here, because "4x4" stuff is really 87-90mm wide, but it is better to overcut than undercut; it is very difficult to lengthen a mortise. So let's do the tenon.

First job is to lay it out. All angles are 45 deg. I use a Japanese framing square. In a real Japanese square, one of the scales is in plain old centimeters. Another, however, is multiplied by the square root of two. Alas, I have a gringified Japanese square. Inches, so help me, on one side. Shame on Lee Valley tools. Here's the end of the layout phase:
All 45 degrees. Can be done with a framing square very easily. Now we have to lay out the amount we have to saw away from the tenon. We want the edges of the brace to line up with the outsides of post and plate. Many ways to do this, including YAMG, or Yet Another Marking Gauge (This is why I have so many marking gauges. Pain to set up, so you have many of them, because I set them up once. But then I have to select the right one. Sigh). This time, I used a vernier plastic calipers for the task.
I am using a pencil here because this is where I don't want mistakes. On the other stuff I used a felt-tipped pen. Not the best thing but it shows up very clearly in photographs. Remember, a pencil lead is 0.5 or 0.7 mm. A felt-tip is perhaps 2 mm so marking with a felt-tip is asking for imprecision. The Japanese framers use (traditionally) bamboo markers, chisel-tipped, and india ink. Modern Japan has ersatz markers, very nice. Unavailable in Alaska.

Now we take the saw to our layout lines. I use (natch) a Japanese Ryoba saw. I have a real affinity for Japanese tools. We cut the ends all the way through, but we have to be very careful with the depth we marked out with the vernier callipers. That's the one I'm sawing here. You must saw only down to the marked depth on this cut.
And now we have to get rid of the upper portion if the cut, where my right hand is sitting. Some people use a chisel for this. I find it easier to rip it out. Just turn the Ryoba over!

Now if you want to do this for real you need a book. A good book will tell you how to cut all these joints. It will tell you a lot of things that make your life much easier. My bible is called Build a Classic Timber-Frame House, by Jack A. Sobon, ISBN 978-0-88266-841-3. I invented none of this; the old Saxons did this kind of stuff a thousand years ago and some of their buildings still stand. Much more than you can say for basic California ticky-tacky, nailed construction.