DIY Single phase transformer to split phase
Just for your consideration, here's a cut away of a transformer that is approximately rated for 240 volts on the primary: -



I estimate it has maybe 800 or more turns on the primary and this would be consistent in achieving a primary magnetization inductance of several henries.


  Would this work? 21 windings on the primary


No, it will catch fire or trip the breakers immediately. However, if you told me that your AC frequency were in fact 100 kHz instead of 50/60 Hz then 21 turns sounds reasonable.