130 705H (Schmetz or Bernina)and 15x1 (Singer) and HAx1 (Organ) all have the same configuration. Which means they are the same length from the top of the needle to the top of the eye. The Singer needles are thinner at the top of the shaft, and can fall out of some machines.
Actually, most vintage Singers take a normal needle. Except for the "slant" machines.