Quality comes from the scale
Every chord here is the same voicing — stack the 1st, 3rd, and 5th scale-steps (and sometimes the 7th):
1 3 5 # triad
1 3 5 7 # seventh
The quality isn’t stored anywhere. It falls out of which scale the voicing is read against:
major triad → scale: major # C E G
minor triad → scale: minor # C E♭ G
diminished → scale: locrian # C E♭ G♭
dominant seventh → scale: mixolydian # C E G B♭
half-diminished → scale: locrian # C E♭ G♭ B♭
Same numbers, several qualities — the projection does the work.