Frequency Spectrum of the Bass Guitar

an important point.
I would describe the chart as the "pitch frequency range"
not "frequency spectrum" which implies all harmonics and timbrel information as well as pitch fundamentals.

 

especially since for low-pitched instruments that fundamental may not even be the loudest frequency happening.

for bass guitar, most of the time the first octave is "area under the curve" louder on the lowest notes, so for an E the 82Hz octave has more real energy than the 41Hz fundamental.

 

yup. the "most audible pitch information" in a bass guitar note is usually not the fundamental, but somewhere in the lower mids, around 250~500 hz.
this is why boosting the lower bass frequencies on an EQ usually generates mud rather than a nice "phat" bass tone

 

This. I do audio mastering on the side and have seen/heard electric bass frequencies that go down as low as 20hz easily. That's frequency spectrum rather than pitch frequency range.

 

It has interesting implications for the utility of a low B at 30.9 Hz,
when most of what we hear as a 'nice, tight low B' is not in fact the fundamental.

 

As the same way of some speakers aren´t capable to reproduce these low frequencies. But in a fact, we have the sense of hearing a nice E and even B too.

 

form the Wikipedia entry on the harmonic series (music)

So we clearly don't need the fundamental to be strongly represented (or even present at all) in order to perceive a strong fundamental pitch. Psychoacoustics is fascinating...

 

What I'd like to see is a practical audio power spectrum for bass guitar from 40-8000 Hz. On the low side most production bass cabs don't have much useable output below 40 Hz. On the high side, the highest fundamental for a G string is around 500 Hz and there is negligible power past the 4th overtone at 8000 Hz. One practical area this comes into play is matching a woofer with the right midrange driver or tweeter. For example, a Faital 15PR400 woofer with 100 dB/watt matches well with a M5N8-80 mid driver at 99 dB/watt. The 15" woofer can handle 400 watts rms while the 5" mid only handles 80 watts rms. This isn't a problem because most of the power is down low. I've seen a reference that every octave down requires another 3dB (double the wattage) because you have to move twice as much air to put out the same sound level. A properly designed crossover dishes out the right frequency band to each driver and blocks what's not supposed to be there so all is well as long as each driver is properly sized and rated for what it is supposed to reproduce. It would be helpful if one had access to a power spectrum with flat eq where you could see for example 75% of the power is below 1000 Hz, another 20% between 1000 to 4000 Hz, and the last 5% above 4000 Hz. I understand that large eq adjustments can substantially alter the balance but it would be helpful to know if you're in the ballpark for proper component selection. Let's take another example. Eminence has an 8 ohm 12" Delta Pro 12-450A driver which looks like a nice one to use in a 212 bass cab. It should have a solid low end in a properly tuned box and a rising mid for presence which drops off rather quickly above 3500 Hz. Sensitivity at that point is about 100dB/watt for one speaker or 103dB/watt for two. On a voltage basis (which Bergantino and some others use), 2.83 V generates 1 watt across an 8 ohm load. With two 8 ohm drivers in parallel to provide a 4 ohm load, this same 2.83 V generates 2 watts. So, 2.83 V apllied to two Delta Pro 12-450A drivers in parallel should generate 106dB just above 3500 Hz.
Speaker Detail | Eminence Speaker
Say you wanted to add a tweeter for some treble extension. Eminence came out with a nice BGH25-8 supertweeter which is optimized for bass guitar. It handles 25 watts rms with a nominal sensitivity of 105.2 dB/watt but by 3500 Hz it puts out 108.8dB/watt. With a hefty 100 watt 8-ohm attenuator to adjust output level and an 18dB/octave 3500 Hz high pass filter to block destructive low frequencies it looks like this should be a good fit.
Supertweeter Detail | Eminence Speaker
The Eminence PXB:3K5 High Pass Crossover Board 3,500 Hz might be a good fit for this DIY project. It's rated 400 watts rms for 8 ohm drivers which is 56.57 volts across the amp output terminals. This 56.57 volts would generate 800 watts across the 4 ohm woofer load which is 50 watts over the combined 750 watt rating for the Delta Pro 12-450A drivers. Everything seems to fit but one question remains: Is there enough power above 3500 to fry this tweeter or would this provide trouble free service?
Having this power spectrum as a start would help sort out questions like this. I know a lot depends on the player, eq choices, etc. I know this wouldn't survive those going for aggressive slap and the Marcus Miller tone but would it be enough for a player who favors a more moderate use of the high frequencies to fill out their sound?

 

It's been a long time since the last post but I think knowing the power spectrum as well as the woofer frequency response might help get a feel for choosing a high pass filter frequency for a HF driver/horn which will match the woofer roll off and provide adequate protection for the HF driver. I recall coming across an old post with a rule of thumb which said a HPF at 3.5kHz could see up to 15% of a bass cabs rated power while a HPF at 5.0 kHz would only see about 5%. If this is reasonable then an 8-ohm cab rated at 400 watts might have peaks of up to 60 watts to an HF driver with a HPF at 3.5kHz. These are usually very efficient and padded back which splits power between the pad and the driver. A 100 watt pad with -6dB attenuation should provide adequate protection for the 30 watt HF driver. If the woofer is 98 db/W and the HF driver is 108 dB/W the HF driver would have to be padded back to match levels so this works.

Here is an image for an extended range bass I found interesting. Ignore everything below 30 Hz which should be filtered out by the amp to avoid speaker damage and even well engineered bass cabinets for a stage rig have a useful low end around 40 Hz. If there are other reference graphs or documents on this topic I'd be interested. I think what this shows is that most of the power (no surprise) is in the fundamental region below 400 Hz with a much less powerful but important harmonic band from 400 to 4000 Hz. Residual treble content, for my lack of a better term, is still audible with quick transients seen in slap and pop and when using rounds instead of flats but is only a minor component of the instrument's power spectrum.