- history, drum set evolved kind of organically bringing marching band percussion, orchestral percussion and other drums into the theater / concert halls / dance halls
As a consequence things like temple blocks were often placed above the bass drum which, before toms were really a thing. They were loosely pitched in similar way.
As the drums evolved they became a thing unto themselves and not just a collection of percussion instruments.
3 or more toms was rare historically. The "floor Tom" and "high tom" allowed a drummer to make a high and a low sound with their hands, which has numerous musical applications
Then as kits got more toms key factors become:
- reach (you cannot fit a low tom above a bass drum)
- style: rock generally suited looser and lower tension tunings, bigger drums, jazz tended to be more tightly tuned toms, and smaller sized drums, more open resonance, pop and funk generally wanted more dampened staccato sounds.
- feel. Drummers balance tuning of their drums with how it feels to play. You will not pick a tuning that feels bad, or sounds bad to you.
- mountings: you can either mount toms directly on bass drum, with legs on the floor or off cymbal stands (and the latter option was bolstered by modern hardware), but so to balance space, mount points and reach there isn't really many other places for them to go.
I'm being brief here, and the musical motivation was sort of natural and evolutionary and not prescribed by music theory.
Finally, if you play tuned percussion like timpani, you go to great lengths to retune them quickly between different passages and pieces. You cannot re-tune toms to an exact pitch while playing it with 4 limbs, and so it would be repeatedly out of tune with the music, and that would be worse than the approximate high mid low you get today!
Hope that makes some sense.
(says owner of seven)
Toms are pretty tonal, as far as drums go, yet, as far as I could tell from my research there's no standard tuning for them. That would make sense if pop musicians all tuned their toms according to the music they were playing, but to the extent that they do, the tunings I read about were mostly flakey (ie: ungrounded in music theory)
So instead of having a neat more-or-less integer-based harmonic series like a 1D resonant object (i.e. a string) they have multiple complex resonant modes which are triggered simultaneously, and which decay at different rates.
So they're semi-pitched. There's usually a fundamental, but the other frequencies can be almost as loud. So if you tune the fundamental you can still get dissonance with the other modes.
All of this makes the idea of tuning a bit and miss.
I know a drummer that is very particular about tuning his drums, and he gets mad when people change it, thing is, he also plays other instruments, so I guess he DOES choose what notes he wants from his drum.
I don't blame him.
I often keep my acoustic guitar tuned down a whole tone, and use heavier strings as a result, because it fits my voice better when I sing. You better believe I get grumpy with people when they pick it up and ignorantly retune it to standard.
As another commenter mentioned, it's also about timbre and not only tuning for a song. I've noticed I got particular about tuning at least my kick and bass layer to the scale of the lead of a track (if there is a noticeable key), in techno is easy to break almost any rule but to me, personally, is much easier to start a new idea with the kick and bass in tune.
I haven't played in ages, so I'm not sure where I settle at, but I imagine there's a few notes that come up in music frequently enough to leave the toms in those tunings.
They also have to match the cymbals
Source - learned for several years
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
I don’t think GP is denying this. They are simply saying that an interval at a lower frequency is generally more dissonant than the same interval at a higher frequency.
The problem is, if you have only two tones, the lower one is essentially the base frequency in my address. But I'm assuming you have somewhat of a natural buzz, or resonant frequencies from the environment that command the base frequency for you, so you can't take any two intervals and compare them as if they were relatively same. This should be relevant especially if you play them one after another to compare, no?
I don't have a bass guitar, but if somebody does they might want to try playing those G# and A notes together, and check how consonant they sound with the tone knob turned all the way up and all the way down. I predict that the brighter tone will sound more dissonant.
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.