3rds go with 5ths.
The 3rd is the second most important interval in music. In fact, 3rds work together with 5ths to make major and minor chords, which are the foundation of almost all popular music and also the backbone of traditional music. Without 3rds we have no music, for the most part. 3rds are also important in aug and dim chords, but less so because there are alternate spellings for these other chords
These are the intervals we need. Anything else is rare and in almost all cases not needed:
- 3 or M3
- b3 or m3
- bb3 or dim3, which in chord notation is assumed to be 2 and never marked