Drum sets are pretty weird in general. I play the drums but I don't know much about their history or development and I've always felt the kit feels like an arbitrary arrangement of circles for me to hit. There's nothing "unifying" about it for want of a better term.
I was a pro drummer for years. There is a general balance of factors:
- 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!
That's my impression, too. I once did some research on toms for some audio code.
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)
All drums - including the snare, but excluding the snare rattle - are modal. They're the 2D/3D implementation of a wave equation.
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.
That's not unreasonable. Tuning a drum these days is a function of a huge number of inputs. There are at least 16 tension rods on a drum — often 20 — and you not only need to consider the relationships between each of them (and how simply turning each rod the same amount does not work, given various degrees of inconsistency in the tension rod and lug manufacturing process), but also the relationships between each head (more opportunity for "phase issues" there), the tension of the batter head (the one you hit) so it is playable), and also the relationships between different drums. You don't want the snares under your snare drum to buzz uncontrollably whenever you hit your 12" tom.
Tuning is not just about pitch, it's about timbre, too. On top of that, the feel under the stick changes at different tensions. Most drums have a handful of pitches where they resonate the best (or to the player's taste). It's a lot of effort for many drummers to get the balance they like, and this is often harder on less-expensive kits.
> I know a drummer that is very particular about tuning his drums, and he gets mad when people change it
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.
That happens in electronic music as well. There are some artists who are very specific about tuning their drums, from bass drum/kick (which in my opinion should be tuned to fit with your bass at least), toms and hats.
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 certainly do, but I try to play them in a melodic manner.
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.
Tabla - the Indian percussion instrument (the one usually played by the dominant/right hand) is definitely tuned and often fine-tuned between songs. Professional players often carry a few differently tuned ones to concerts and switches as needed.
A tom has a surprisingly long decay, so I think it's more a matter of the pitch not being entirely constant (neither between hits nor over the span of a single hit).
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.
Two bass notes a semitone apart won't necessarily sound bad; it depends on the timbre. Try it with sine waves and it will sound like a slow tremolo. Try it with sawtooth waves and it will sound dissonant.
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.
Another factor is that the ear wants to makes repetition, in and of itself, work. That likely allows drums to sound good despite their fundamental tones often being 'wrong'. To pick an example at random: the triangle bells in this pop song sound pleasing, despite their key being 'wrong', simply because they repeat https://youtu.be/ZWmrfgj0MZI
That's not how I understand the musical scale, if I even understood you correctly.
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.
> By relative interval I understand the interval within an octave, so C-D is a second regardless of the octave.
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.
I was conceeding to make sure I understood them correctly.
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 think it's likely to be less dissonant at lower frequencies. Try a 51.913Hz sine wave (G#1) played with a 55.000Hz sine wave (A1), at low enough volume that they don't clip when added together. This does not sound dissonant to me. Then speed them up by 16x (increasing the pitch four octaves). This does sound dissonant to me, although not extremely so, because timbre makes a huge difference, and sine waves produce the least dissonance of all timbres.
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.
> I think it's more a matter of the pitch not being entirely constant
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.
