Sometimes i see people on talkbass asking something like:
"i'm going to audition for a band but they play in lower tuning. Can i get away with my standard tuned bass?". I'll try to explain here, why you can't (at least in rock/metal music).
It's not a rule or law, just my opinion (expressed not very clearly) and i'd like to discuss it.
You may need some
basic understanding of harmonics.
I've recorded five sounds (you can hear them
there) and made the spectrogram of them.
There are spectrograms of first three sounds:
1. First sample is low D bass note (3rd fret on a B-string). You can see fundamental tone (36.7 Hz or D1 in scientific pitch notation) and overtones, which are multiples of it.
2. Second sample is higher D bass note (5th fret on A-string). Its fundamental tone is one octave higher and overtones are scarcer (but they extend somewhat higher).
3. Third sample is distorted guitar playing low D5 power chord (three bottom strings on Drop-D tuned guitar). Its lowest note is D2 (73.4 Hz) but in combination with fifth degree (A2 note) and distortion it generates additional overtones and undertones, lowest one being one octave lower than lowest power chord's note (tonic).
As you can see, guitar power chord starting from D2 note has similar harmonic content to D1 bass note: 36.7 Hz and its multiples.
Now let's take a look (and listen) to sounds #4 and #5:
4. Fourth sample is D5 guitar powerchord & low D bass note (sounds #1 and #3 together). It's nice, powerful blending of two instruments (or rather it would be if i made better recording

). Guitar gives it cutting roar and the bass gives it powerful low-end support and clear definite tonic.
5. Fifth sample is D5 guitar powerchord & high D bass note (sounds #2 and #3 together). It sounds not that good: bass is one octave higher than lowest guitar undertone and guitar has richer harmonic content than bass (just compare spectrograms #2 and #3 from first picture). So this sound begs for either higher power chord or lower bass note.
So if you are going to play with downtuned guitars, you will need to downtune your bass so your lowest bass note would be at least one octave lower than lowest note of the guitars.
Otherwise, if you will play higher B note (2 fret on A-string) against low B5 chord, you are going to sound like sample #5 and the band will lack bass power overall. It's just like playing standard tuned rock/metal music without touching the E-string: it won't sound right.
So my opinion is:
in rock or metal context downtuned guitars require downtuned bass. You can't play standard tuned 4-string with downtuned band and sound good (in my opinion).
P. S. There are some heavy bands (Meshuggah and recent Deftones come to mind) that have downtuned guitar and bass tuned in unison with that guitar. But when they do it, they never play powerchords (they don't sound good that low anyway) so the problem described here doesn't occur.
P. P. S. Some may say that one can use octaver pedal on standard tuned bass to play in downtuned band. But IMO octaver has obviously artificial sound. It is nice tool to blend some low-end to your sound or nail some low synth-like sounds in a cover band but it will never sound like real low-tuned bass note. And I've never heard of low-tuning band using octaver on bass.