I'm 100% sure you do not have a 127 - either you are misreading the number on the machine, or the chart is wrong.
BTW - Singer started producing the 127 around 1912-1913 (based on earliest manual I've seen).
Both are 28's. If you put them side by side, you will see they are the same size. The 27/127 is quite a bit larger.
But it's also very easy to tell by the way the tension sits on the head of the machine
This is a 27 - notice the amount of cast that is visible below the tension. The 127 (updated version of the 27) but has the high bobbin winder.
