5ths are the backbone of chords
The 5th is possibly the most important interval in music. In fact, when 3rds are combined with 5ths we not only get major and minor chords but also the default notation for diminished and augmented chords, which are the foundation of much of popular music and also the fundamentals of traditional music.
These are the intervals we need. Anything else is rare and in almost all cases not needed:
- 5 or P5 (perfect 5th), used for root position major and minor chords
- b5 or dim 5, also a tritone, used as the default spelling for diminished triads.
- #5 or aug 5, used as the default spelling for augmented triads.