Tuning-fork type piezoelectric vibrating pieces having similarly shaped vibrating-root and supporting root portions

A piezoelectric vibrating piece, comprising:

• a base having a first end and an opposing second end;
• a pair of vibrating arms extending from the first end of the base in a first direction, each vibrating arm progressively narrowing from the first end to a respective constriction located distally in the first direction;
• a vibrating root portion situated between the vibrating aims;
• a pair of supporting arms extending, outboard of the vibrating arms, from the first end of the base in the first direction, each supporting arm progressively narrowing from the first end to a respective constriction located distally in the first direction;
• and
• a respective supporting root portion situated between each vibrating arm and respective supporting arm;
• wherein the vibrating root portion defines a void extending in the first direction between the vibrating arms from the first end of the base, where the vibrating root portion is wider, to the constrictions where the vibrating root portion is narrower;
• each supporting root portion defines a void extending in the first direction between the respective vibrating arm and respective supporting arm from the first end of the base, where the supporting root portion is wider, to the constriction where the supporting root portion is narrower;
• and
• the vibrating root portion and supporting root portions have substantially identical shapes.