Calculating total score for a scale including polytomous and dichotomous items [duplicate]

I have a variable that is measured using a 13-item, 4-point Likert scale with the exception of one item (yes $=1$, no $=2)$.

How can I calculate the total score for this variable?

The simple, "classical test theory" approach that weighs every item equally would probably have you just standardize all the items and average the $z$-scores, but I don't think that's a good idea, because four-point Likert scales may not approximate a continuous dimension well enough (and a binary item definitely won't; it might not even make sense), though the average of 12 polytomous items might be approximately continuous enough. I've seen it suggested that each item's Likert scale should have at least five items to approximate a continuous distribution, and at least five Likert scale items should measure the same scale if their simple sum / average is to approximate a continuous dimension. (Can't remember where, but I can look it up and edit it in if you want a source but can't find one yourself; just comment!)