Fundamental frequency VS real world amplification

[holllowbody]

At east once on this site I have seen someone say something along the line of this...

"The low B string produces very little of it's 30hz fundamental. The low B string is really going to generate frequencies at about 60hz (open). So don't be concerned about coming up with a rig that will play down to 30 hz + / - 1 db"

...thats not word for word what I read, but thats the jist.

Now, how does one look at the fundamental frequencies that a given instrument will produce and then put together a rig to amplify the said instrument?

If the fundamental for a 4 string bass is 41 hz, how low do I need the rig to play + / - 1 db??

What about an instrument with a fundamental of 80 hz?

What about an instrument with a fundamental of 100 hz?

Thanks!

 

[fdeck]

There's no universal answer. Very few bass speakers have a response curve that can be meaningfully described, solely in terms of a +/- 1 dB tolerance band, because their response varies by more than that amount over most of the spectrum. You can probably define a 3 dB low frequency cutoff point, which can be as high as 100 Hz on some bass speakers, and possibly down to 40 or even 30 Hz on some specialized models. Where you want that cutoff to be depends on how you want your bass to sound, and probably also how you are using it, e.g., indoors or outdoors.

Nothing is simple.

 

[seanm]

I agree with fdeck. While I like debating cabs as much as the next guy....... I chose cabs based on how they sound. In the end, that is all the matters.

 

[holllowbody]

I agree with fdeck. While I like debating cabs as much as the next guy....... I chose cabs based on how they sound. In the end, that is all the matters.

OK, but, cabinet debating aside, is it true to say that the fundamental frequency is far lower than the frequency that the user ought to consern themself with?

My main point of confusion is figuring out how I can look at a fundmental frequency then determine how low the sound amplification needs to be able to play. Not necessarily in the context of bass guitar alone for discussion sake. The low E on a guitar has a fundamental of 80hz. If the sound system is + / - 3db at 80hz will it be able to reproduce the sound of the guitar just as well as a anything else or will it be lacking on the lower end??

 

[Steve]

Now, how does one look at the fundamental frequencies that a given instrument will produce and then put together a rig to amplify the said instrument?

One looks at the fundamental as just one of a long series of frequencies contained in any given note, realizes that it is of lessor importance than some of the others in the series and doesn't obsess about it.

IMHO

 

[seanm]

Let's put it this way..... a low E is about 40Hz. The classic Ampeg 8x10 fridge is about 60Hz at -3dB. I have never heard anybody say it had a weak open E

 

[knuckle_head]

OK, but, cabinet debating aside, is it true to say that the fundamental frequency is far lower than the frequency that the user ought to consern themself with?

No it's not true to say that. Most instruments are fully represented by either dedicated amplification or a PA. Bass is a challenge whether it comes from strings or keys or anywhere else though, and often times the instrument can produce frequencies that speakers are not ACTUALLY able to reproduce, but your brain fills in where the speakers leave off (most of the time).

My main point of confusion is figuring out how I can look at a fundmental frequency then determine how low the sound amplification needs to be able to play. Not necessarily in the context of bass guitar alone for discussion sake. The low E on a guitar has a fundamental of 80hz. If the sound system is + / - 3db at 80hz will it be able to reproduce the sound of the guitar just as well as a anything else or will it be lacking on the lower end??

Bass amplification specifically has always lagged behind the instrument from the very beginning. It is only very recently that bass rigs have even approached the E fundamental. That said, bass sounds pretty good the way we know it by and large so the specifics of it don't matter all that much.

It is optimal to ask of speakers to address the full spectrum they are fed regardless of instrument. When in doubt reproduce it all and EQ out what offends. In your guitar example I would personally prefer to see +/- 0dB at 80 Hz because humans can full distinguish 80 Hz as a frequency when heard. It starts getting dicey to the average human ear at 45 to 50 Hz, and calls for familiarity/training/experience much below that.

My $.02

 

[edbutler3]

OK, but, cabinet debating aside, is it true to say that the fundamental frequency is far lower than the frequency that the user ought to consern themself with?

My main point of confusion is figuring out how I can look at a fundmental frequency then determine how low the sound amplification needs to be able to play. Not necessarily in the context of bass guitar alone for discussion sake. The low E on a guitar has a fundamental of 80hz. If the sound system is + / - 3db at 80hz will it be able to reproduce the sound of the guitar just as well as a anything else or will it be lacking on the lower end??

The simple answer to your question is "double the fundamental frequency". That's because if you look at the harmonic series you see that the 2nd harmonic is an octave above (AKA 2 times the frequency of) the 1st harmonic (AKA the fundamental).

On another TB thread it was demonstrated using waterfall plots (if I recall the term correctly) that for a bass guitar, the output level of the fundamental frequency is naturally quite a bit lower than the 2nd harmonic. Keep in mind that the relative level of the various harmonics in a musical instrument's sound is one of the defining elements of the instrument's timbre, or to put it another way, it's a big part of what makes a bass a bass, or a flute a flute, etc. So when you ask your question in general for all instruments, there's not a clear answer, because maybe some instruments (the pipe organ comes to mind) would need a strong fundamental. But for the bass guitar, a reasonable guideline is, for a low B, you need solid output down to at least 60 Hz, and for a low E, you need solid output down to at least 80 Hz. Whether or not you can get by with a complete absence of the fundamental is a point of contention. Personally, I like to have some of the fundamental even if it's down 10db or more, but many argue it's fine for it to be totally absent.

 

[fdeck]

It is optimal to ask of speakers to address the full spectrum they are fed regardless of instrument. When in doubt reproduce it all and EQ out what offends. In your guitar example I would personally prefer to see +/- 0dB at 80 Hz because humans can full distinguish 80 Hz as a frequency when heard. It starts getting dicey to the average human ear at 45 to 50 Hz, and calls for familiarity/training/experience much below that.

This sounds good in principle. However, it creates a practical problem, due to Hoffman's Law. Suppose there is a bassist whose idea of good tone is an 80 Hz cutoff frequency. What are his options?

1. Design a speaker that is flat down to 40 Hz, and then apply EQ to achieve the 80 Hz cutoff.

2. Design a speaker with an 80 Hz cutoff.

To achieve the same volume level, the first speaker has to be roughly 4x bigger than the second, with no audible benefit. The second option wins on cost and portability.

 

[DukeLeJeune]

In my opinion, the ability to reproduce the first harmonic (twice the frequency of the fundamental, as edbutler3 points out) at full power or close to it (no lower than -2 dB) is a good practical goal.

Again just my opinion, but optimizing the design for loudest possible deep bass trades off some low-end clarity and pitch definition. So even if all manufacturers measured their -3 dB points under identical conditions, the raw numbers alone would still fail to paint a complete picture.

fdeck I agree with your analysis, but my understanding is that it's even worse than you describe; extending the bass one octave deeper calls for either an eightfold increase in box size or a 9 dB reduction in efficiency, or some combination thereof. But it's been a while since I ran the numbers, so my recollection could be wrong.

 

[knuckle_head]

The simple answer to your question is "double the fundamental frequency". That's because if you look at the harmonic series you see that the 2nd harmonic is an octave above (AKA 2 times the frequency of) the 1st harmonic (AKA the fundamental).

On another TB thread it was demonstrated using waterfall plots (if I recall the term correctly) that for a bass guitar, the output level of the fundamental frequency is naturally quite a bit lower than the 2nd harmonic. Keep in mind that the relative level of the various harmonics in a musical instrument's sound is one of the defining elements of the instrument's timbre, or to put it another way, it's a big part of what makes a bass a bass, or a flute a flute, etc. So when you ask your question in general for all instruments, there's not a clear answer, because maybe some instruments (the pipe organ comes to mind) would need a strong fundamental. But for the bass guitar, a reasonable guideline is, for a low B, you need solid output down to at least 60 Hz, and for a low E, you need solid output down to at least 80 Hz. Whether or not you can get by with a complete absence of the fundamental is a point of contention. Personally, I like to have some of the fundamental even if it's down 10db or more, but many argue it's fine for it to be totally absent.

I agree with this - bass specific applications are well served to have the second harmonic supported fully. Bass guitar frequency response suggests that there is two to three times the sonic energy at the second harmonic vs the fundamental or more, and it is that way coming out of the bass.

That said, having a rig that can get close to 40 Hz and pumping a 40 Hz E through it is awesome. If it is flat response from the enclosure, the bass guitar is solid, and good strings are on it, it won't boom or be murky.

This sounds good in principle. However, it creates a practical problem, due to Hoffman's Law. Suppose there is a bassist whose idea of good tone is an 80 Hz cutoff frequency. What are his options?

1. Design a speaker that is flat down to 40 Hz, and then apply EQ to achieve the 80 Hz cutoff.

2. Design a speaker with an 80 Hz cutoff.

To achieve the same volume level, the first speaker has to be roughly 4x bigger than the second, with no audible benefit. The second option wins on cost and portability.

Pick your poison here. 80 Hz would serve the majority of bassists quite well and is far closer to the norm in traditional rigs than you may realize.

That said, portability vs flexibility will have to win out. An adroitly placed High Pass Filter would serve most bassist quite well, especially if it is a combo amp that is being relied on. Said filter can be applied to a deeper tuned cab with the same result but, as you suggest, it will be bigger and heavier.

No right or wrong here - just two very different options.

... just my opinion, but optimizing the design for loudest possible deep bass trades off some low-end clarity and pitch definition. So even if all manufacturers measured their -3 dB points under identical conditions, the raw numbers alone would still fail to paint a complete picture.

fdeck I agree with your analysis, but my understanding is that it's even worse than you describe; extending the bass one octave deeper calls for either an eightfold increase in box size or a 9 dB reduction in efficiency, or some combination thereof. But it's been a while since I ran the numbers, so my recollection could be wrong.

Enclosure design will determine clarity and pitch definition. The best thing that can happen to instrument amplification in general is for MI guys to take a class or two from SR or Audiophile guys.

If the speaker enclosure gives you back what you put in and the sound isn't there then the offending piece lives in a different component (bass, pre, amp, etc.).

If the speaker enclosure IS your sound you are screwed if the enclosure fails as no two cabs from any manufacturer are identical, and cabs from different manufacturers will leave you chasing your tail (at least for a while).

 

[greenboy]

Been said in so many threads about precisely the same, but it's all about tradeoffs. If you can get the SPL you want for live sound for your low fundamentals and are willing to carry the extra weight and bulk, go for it. You might be surprised how much extra bulk and weight that really is as it entails more enclosure space and more power (amps), and if you are tuning lower than normal, even more so. And at the end of it all, in live performance you might also find it creates additional sets of acoustic and stage mix problems.

The other issue that needs to be underlined is that excursion is really a bigger issue than a low f3. If you have enclosures with a low tuning but they run out of excursion before you can reach the desired SPL at low frequencies, then all is for naught.

 

[JustDavid]

Hollow, you're going to want to keep in mind that discussions on this are very instrument-dependant. Word's coming through that the fundamental can be skipped for bass guitar (arguably, for 'bass guitar as we are used to hearing it'), but keep in mind that doesn't mean you can extrapolate that to any other instrument.

An extreme example is a synthesizer running a patch that's mostly fundamental; that's not going to work with a rig that's missing the fundamental.

 

[alexclaber]

A rig that can strongly go down to your lowest note fundamental can sound very good but there is a huge cost in efficiency and power handling. For equal size optimised bass rigs one that has F6 @ 60Hz will indeed be 9dB more sensitive than one with F6 @ 30Hz. Also the lower a bass cab goes the lower it must be tuned - this does protect the cone from unloading below its tuning frequency but it greatly increases the excusion demands in the more critical (IMO) region around 60Hz. If you're playing in less loud situations or are willing to cart the extra power/speakers required then a rig that is strong on your lowest note fundamental can be a lovely thing. As the scenarios require more SPL or you want a more lightweight rig then you'll have to trade off some extension.

Bear in mind that all the extension in the world is of no use if the speakers can't move enough air to support those lowest notes at sufficient SPL. This requires some pretty specialist high excurision woofers.

Alex

 

[alexclaber]

I see greenboy and I have paraphrased each other with remarkable similarity whilst posting simultaneously!

Alex

 

[greenboy]

Hollow, you're going to want to keep in mind that discussions on this are very instrument-dependant. Word's coming through that the fundamental can be skipped for bass guitar (arguably, for 'bass guitar as we are used to hearing it'), but keep in mind that doesn't mean you can extrapolate that to any other instrument.

An extreme example is a synthesizer running a patch that's mostly fundamental; that's not going to work with a rig that's missing the fundamental.

Actually few synthesists will use patches that are almost entirely fundamental because they go largely UNHEARD unless layered in with other bass note sources, especially in live settings. Whether talking individual keyboard monitoring or SR, that's the case. Bass sounds are usually chosen for their character, but if there is little content above the fundamental, there is little character.

 

[greenboy]

Word's coming through that the fundamental can be skipped for bass guitar

Let's put that in context. If a fundamental averages 10 dB below the octave harmonic for the duration of a note, and it's in the range the ear is 10 dB less sensitive, then it is in effect 20 dB below! How much extra power and enclosure (and driver sensitivity tradeoff) does it take to even make up part of that gap? Remember, 10 dB is a difference of 10 times the energy.

Link Removed


Thus, it makes more sense to develop drivers that don't easily run out of excursion when reproducing that octave harmonic, and that until recently was not the case.

 

[alexclaber]

This thing about 'skipping the fundamental' is fundamentally confusing!

Yes, you don't need the fundamental on the lowest notes but as you go higher it becomes much more important. Play B on the second fret A string and the fundamental is a big part of the depth of the note. Play B on the fourth fret of the G string and the fundamental is a big part of the fatness of the note (not much depth by that point).

Alex

 

[greenboy]

Yep, that fundamental comes into its own as you go up in pitch, especially as you go up the neck. Several things are at play here. First, the fundamental actually becomes more present at the instrument due to pickup position along the vibrating string. Second, the fundamental is now at a higher frequency where the ear finds it easy to hear. It then supplies more of the "bass voice" function that in lower pitches was supplied mainly by the octave harmonic and the octave-and-a-fifth harmonic.

 

[Rick Auricchio]

Aside from the quality of information in this thread, I find the quality of the writing refreshingly good!

Here are two drawings I cobbled up last week.. The graph inverts the 100dB Equal-Loudness curve, to show its effect on required SPL.

The second drawing shows the overlap of guitar/bass frequencies; this helps us understand why bass-heavy electric guitars wreak havoc with electric bass, especially when the bass' fundamental is at a low SPL. High-pass the guitars!