Ellen if you don't have any problem with doing the above then this is similar but even better. After tuning a 1/2"
straight tenon on one end of the blank between centers, remove the spur center and instal a
1/2" draw-bar style collet into your headstock, insert the 1/2" straight tenon into the collet, bring up your tail-stock live center to the blank and tighten until the collet "clamps" the tenon(you don't really need a draw-bar). This will save you from having to try to turn a fitted/tapered tenon. Oh you don't have one of these collets you say? Well, I just happen to have one that I don't use and would be glad to send it to you if you would like to try it. Just PM me with a shipping address.
Edit: the link is only to give you an idea of the device I am talking about.