Hi Rodney, 

I don't understand the sentence referring to BoatUS.   

My thoughts are that the important thing to consider is if the masts are being held so they are straight. While bermudian rigs commonly bend their masts to flatten the mainsail, I don't think that is ever done on gaff rigs.

The triatic does look a bit loose, but that could be related to the tension of the spring stay below it--the spring stay could be overly tight.

Looking at the pictures in your profile (pretty schooner!), it doesn't look like there are running backstays, which, if they were loose, could account for the triatic being loose.

As I'm sure you know, adjusting the triatic is much easier with one person aloft and another on deck able to look up the masts for straightness.

If you're doing this solo, you could tie together the sail ends of the fisherman peak halyard and the fisherman throat halyard, and also tie a long line to the two halyards (to pull them back down), then hoist the halyards aloft. This gives you a line between the top of the mainmast (fisherman peak halyard) and the top of the foremast (fisherman throat halyard), like the triatic, that you can tension from the deck.  That would let you experiment with tightening the halyards (may need a block and tackle) and sighting up the masts to check they are straight.  This could save you some trips aloft to tighten the triatic, come down, sight up the masts, go back up, repeat.   Just make sure to have a long line tied to the halyards so you can pull them back down to the deck again.

Good old AutoCorrect :)

I am thinking your schooner has swept-back spreaders and the after shrouds (with deadeyes) go to the top of the mainmast, and are far enough aft that you don't need running backstays.

In the picture under sail, it looks like the triatic is straight when sailing.

I see a line from the aft end of the main gaff to the top of the mainmast, that I'm thinking is part of the way the peak halyard is rove. So the main peak halyard goes thru blocks both where the spring stay attaches and at the top of the mainmast.

Setting the mainsail is going to tension the top of the mainmast via the peak halyard, pulling the mainmast a bit aft above the spring stay (the spring stay will prevent the lower part of the mast from going aft).  That will tighten the triatic when sailing.

When not sailing, only the after shrouds pull the top of the mast aft, and the after shrouds are not far aft, so don't pull aft much. The triatic will be under less tension when not sailing because of this, so I'd want to avoid overtightening the triatic (that would cause the top part of the mast to bend forward when not sailing).

I would want to sight up the mainmast both with no sails and when the mainsail is set to see if the mast is straight, and use that to determine how to tension the triatic. I'd aim for a straight mast (or within a couple of inches of straight) both when sailing and not sailing. The tension of the aft shrouds (pulling the top of the mainmast aft) is probably involved in this, so you might want to start by ensuring the aft shrouds are tight.