Sure some people have the absolute ear (ability to tell a note from the sound), but those are rare and rarely enjoy music with drums.
That being so, it would make sense to avoid hitting a tom with a low frequency note in unison with, say, a bass guitar playing the same note. That could result in two bassy notes sounding off a semitone apart... yuck.
Whatever sense my theory makes, I didn't read much about it being a consideration. I read about tunings, for example, that just pitched each drum up by exactly 3 or 4 or 5 semitones... seemed weird to me.
Perception of consonance and dissonance is related to the phenomenon of "beats"[0]. If you add two sine waves of similar frequency, you get alternating constructive and destructive interference, sounding like tremolo. As you increase the difference in frequency, the beat becomes faster, until it's no longer heard as tremolo, and becomes a single dissonant tone. Increase it further still and the dissonance vanishes as it's heard as two separate tones.
Importantly, beats depend on absolute difference in frequency, not relative difference. Musical intervals are relative differences, e.g. a semitone higher in equal temperament is 2^(1/12) times higher frequency, not some fixed number of cycles per second. The higher in the musical scale, the bigger the absolute difference per semitone. This means low frequency sine waves a semitone apart will sound consonant, medium frequency will sound dissonant, and at high enough frequencies the dissonance diminishes.
However, this effect applies to all the harmonics/partials of the notes, not just the fundamentals. A smooth bass note will have mostly fundamental, so the pairs of harmonics with frequency differences that cause dissonance will be quiet and unnoticeable. A bright or distorted bass note will have much louder harmonics, so the dissonance will be obvious.
Two bass notes a semitone apart won't necessarily
sound bad; it depends on the timbre.
By relative interval I understand the interval within an octave, so C-D is a second regardless of the octave. The frequencies (notwithstanding fine tuning), double each octave. Of course the absolute difference is proportional to the power of two, depending on the octave.
The picture is different when counting the proportion relative a fundamental frequency of your choice. That's how dezibell is generally defined, arbitrarily over some reference point. This has two interesting consequences. When counting keys not modulo 8 but continuously, the ratio D5 over C5 is much lower than D4 over C4. Second, if you want integer multiples of the fundamental's wave length, the first multiple spans an octave, and only the fourth or fifth octave has a full scale--this chromatic scale worked reasonably well tested on AVR with a buzzer, except that F needed adjustment taken from a frequency table.
This means there can be no second in the lowest register unless you invert the programm and scale the higher octaves down linearly. In that case, the interference from the second (ca. 9/8'th of the fundamental's wave length) sounds extremely grating when played as a chord; the attenuation where the maxima of both waves meet forms the actual fundamental and your notes lie 9 to 8 above it, canceling each other out half the time; this is easier illustrated with a sixth that would be 1.5 of the base key. It is not a good illustration of music theory though, more like information theory while the signal chain is computationally intractable.
Jazz musicians, huh
In modern popular music at least, it's not desirable for the pitch to be constant. You typically want to tune the resonant head (the one at the bottom) a little higher in pitch than the batter head so that there's a slight descending pitch shift.