Frequency Response

[tim126]

What-ho chaps. In a recent idle moment I was pondering the curious array of terms and specifications we use to describe our rigs. Mine includes a 5-string Ibanez (SR505), a MarkBass Little Mark II and a Schroeder 410L.

So: the amplifier/cab spec includes a rating of the frequencies it'll handle... bottoming out at 40Hz. The bottom "B" string on a 5-string bass has a fundamental frequency of 30.87Hz.

Now I have heard about harmonic frequencies and stuff (not sure I understood it, mind you!)... but, putting it in really dumb terms, if the bottom B is producing a frequency below the rated/stated capabilities of the amp and the cab, how come I can still hear it when I play it?... And how come my rig makes by bass (esp the bottom end) sound so nice?!

I suspect the discussion may have a lot to do with why the amp/cab specs a frequency response of up to 20KHz, when the highest note the guitar can play is G2, at 392Hz... But maybe some intelligent being out there can put an explanation together for a simple-minded plucker?...

[krazy_olie]

aha! I learned this last year! Thought it would come to some use

The ear/brain works in a very weird way, you can actual hear a fundamental even if it is not physically present! pitch is not frequency, it's perceived frequency .

If you take a sound sample, and actually filter the fundamental you still hear it

Edited July 14, 2011 by krazy_olie

[tim126]

Oo! Well Bagger me! How bizarre!

I need to ponder that for a while.... Ta for the response!

[Noisyjon]

I think Alex's 'Issue #6' and 'Issue #7' editions explain what you're asking:
[url="http://barefacedbass.com/bgm-columns.htm"]http://barefacedbass.com/bgm-columns.htm[/url]

Cheers,
Jon

[tim126]

Now that is a collection of some bloody useful stuff!

Cheers, chums... Stuff to read, ponder and learn from...

[Bill Fitzmaurice]

[quote name='tim126' post='1303547' date='Jul 14 2011, 09:12 AM']Now I have heard about harmonic frequencies and stuff (not sure I understood it, mind you!)... but, putting it in really dumb terms, if the bottom B is producing a frequency below the rated/stated capabilities of the amp and the cab, how come I can still hear it when I play it?... .[/quote]Because you're mainly hearing said harmonics. They dominate the output below roughly 80Hz. You perceive the fundamental being louder than it is as the second harmonic is the same note an octave up. And what you perceive as 'deep bass' is typically an octave higher than you think it is.

[Phil Starr]

Bill is right. Funnily enough I was driving home today listening to Lou Reed's 'Walk on the Wild Side' and I thought If anyone asks this question they should listen to this. The Bass sounds amazingly deep because it is played on an upright, even though the bottom frequencies are no lower than a four string the different mix of harmonics gives it a rich deep sound. There are loads of signal generators online and if you are deeply boring (like me)it is quite interesting to listen to a 40Hz (roughly bottom E) pure tone and realise just how low that is. If your speakers can go that low of course.

[Bill Fitzmaurice]

[quote name='Phil Starr' post='1303710' date='Jul 14 2011, 11:29 AM']There are loads of signal generators online and if you are deeply boring (like me)it is quite interesting to listen to a 40Hz (roughly bottom E) pure tone and realise just how low that is. If your speakers can go that low of course.[/quote]You may still be hearing a lot of harmonics, as your speakers create them. If you play a pristine 40 Hz or lower sine wave through a capable speaker with very low THD you can't even discern pitch.

[zero9]

[quote name='Bill Fitzmaurice' post='1303817' date='Jul 14 2011, 05:41 PM']You may still be hearing a lot of harmonics, as your speakers create them. If you play a pristine 40 Hz or lower sine wave through a capable speaker with very low THD you can't even discern pitch.[/quote]


I guess that is 'getting to the bottom of it'...

[xgsjx]

[quote name='zero9' post='1303845' date='Jul 14 2011, 06:18 PM']I guess that is 'getting to the bottom of it'...[/quote]
Oh! That's low

[ShergoldSnickers]

Manufacturers should really define the limits within which the frequency response is measured – and also provide an honest plot with a full explanation. Two speakers cabs may still be outputting at 40Hz, but unless you know by how much the output has dropped at this frequency for each cab, then a simple statement like 'Frequency response 38Hz to 5kHz' for example, is meaningless. The following is better, but you'd still want a plot with an explanation of how that plot was derived:
Frequency response 38Hz to 5kHz ± 6dB

Which SPL is that measured at? How far away from the speaker was the mic? Was the mic a properly calibrated Brüel & Kjær or an SM58?
Even having the precise figures and a plot will only be a rough guide as to how the cab actually sounds when put to the intended use, but it is a guide nontheless. Your ears are the final judge.

[tim126]

Understand. In the world of Pro AV install, speaker specs are often given with not only a freq response range, but also a SPL expressed as dB @ xxHz, 1W @ 1m. Which is the technical level of mathmatical/physics/science detail. And I think there is a danger in over-simplifying... speakers (amps, and all the rest of the stuff) can't really be judged by just one criterion - there's loads of measurements and aspects of performance that must be considered as a whole, not in isolation.

But I guess the bottom line... well, I was playing last night (for a primary school production of "Joseph" ... great fun, lots of enthusiasm, the band and cast started together and finished together - mostly - and that ticked all the boxes that needed ticking!)... My ears were telling me that my rig was producing nice big fat deep round sounds when I wanted it to, and more punchy middle-y sounds when played that way. And it was mostly down to how the strings were played. So I think I'm going to put this particular worry to bed ... it's raised a lot of useful info, and may continue to do so, which is all good.

But, as I keep seeing around this forum, there's a certain pragmatic approach, which is: if it sounds good (to your musical/aural taste), then it is good. Tick that box, job done, get on with the main business of life which is having loadsa fun making music! (IMO anyway!)

Keep it moist, chaps and chapesses!

[alexclaber]

The 'frequency response' specs quoted by 99% of cab manufacturers are essentially pointless. We put one of those vague ones on our site just to stop people writing off the cabs because they're not seeing the numbers they want to see and then the useful response specs are in the technical info bit. There is a serious risk that if you put those useful specs out front and centre then bassists (particularly those with a low B or lower) will assume that your cabs can't handle a bass whose lowest string is tuned to ~31Hz. With the Big Series cabs we focused on fantastic performance with lower tunings (F# below low B etc) and in the real world of loud gigs the cabs stomp all over some cabs that are designed specifically for low B by being tuned to 31Hz, because we've considered not just the fundamental frequency but the energy content when you play that note, the inherent highpass filtering in bass amps and power amps and the required tone to work in a mix at high SPL.

Based on the speaker configuration and internal volume of the Schroeder 410L there's no way the -3dB point can be below 70Hz (and there'll be a hump above 100Hz which will make that F3 effectively higher) and by 40Hz it'll be at least 12dB down. I haven't had the time to accurately measure many other cabs (but, having spent enough time listening to ones with whose response plots I know, my ears are pretty reliable at detecting peaks, dips and roll-off points) but their response curves tends to be seriously far from the implied flat from 40Hz-20kHz response suggested by specs.

(Courtest of OldogNewTrick on the fEarful forum) here's a load of plots from a Line6 modeller (so one would hope that these are fairly accurate representations of the following cabs - my ears certainly say so):

'70s Ampeg sealed 8x10"



Acoustic 360 (folded horn 18")



SWR Goliath 1 (ported 4x10"+tweeter)



Fender Dual Showman with JBL D140F (sealed 2x15")



Mesa Boogie 2x15"



Hiwatt 2x12"



Sunn Coliseum 18"+12"



Ampeg B15



Versatone Pan-O-Flex (crazy old biamped dual voice coil 1x12")



EA CXL112 (transmission line coax 1x12")

[Phil Starr]

[quote name='Bill Fitzmaurice' post='1303817' date='Jul 14 2011, 05:41 PM']You may still be hearing a lot of harmonics, as your speakers create them. If you play a pristine 40 Hz or lower sine wave through a capable speaker with very low THD you can't even discern pitch.[/quote]
Fair comment, I should have said there is little point in doing this with your computer speakers. Even with decent hi-fi speakers you will get some audible harmonics but it does give you an idea of just how low the fundamental of bottom E is and it's usually a shock to people who hear it for the first time.

[Bill Fitzmaurice]

[quote name='Phil Starr' post='1305381' date='Jul 15 2011, 07:49 PM']Fair comment, I should have said there is little point in doing this with your computer speakers. Even with decent hi-fi speakers you will get some audible harmonics but it does give you an idea of just how low the fundamental of bottom E is and it's usually a shock to people who hear it for the first time.[/quote]Not as much of shock as it is to have a speaker putting out 15Hz at 100dB and you can't hear it, nor would you even be aware of it if not for a meter telling you it's there. And that's why even for home theater LFE I don't even think about going below 20Hz.

[ShergoldSnickers]

[quote name='Bill Fitzmaurice' post='1305423' date='Jul 16 2011, 03:02 AM']Not as much of shock as it is to have a speaker putting out 15Hz at 100dB and you can't hear it, nor would you even be aware of it if not for a meter telling you it's there. And that's why even for home theater LFE I don't even think about going below 20Hz.[/quote]
This reminds me of a velocity coupled 'infra-bass' cabinet design originally published in H-Fi Answers in the early 80s I think. Going from memory, the design was something like the quickly knocked up diagram below. The lowest reproducible frequency was in single figure Hertz values again if memory serves. Quite what use this was at the time - as CD hadn't yet come out, and having that amount of surplus low frequency energy near a record deck - even a floating sub-chassis one - would be asking for trouble, even if you could get LPs with suitable low frequency information on them. Some keyboards and mega multi-string wideband basses may benefit I suppose if the design is efficient enough.

The original design(s) catered for a 10", 12" or 15" speaker and were adjusted accordingly. A difficult construction job though, and attention had to be paid to rounding off any sharp angles in the horn path and chamfering the holes cut in the shells according to the original author Graham Holliman. If I had the time, money and skills it could be an interesting way to disturb people's digestion I suppose.

[url="http://www.avforums.com/forums/attachments/subwoofers-tactile-transducers/237169d1303471020-graham-holliman-infrasonic-generator-graham-holliman.pdf"]Just found this link to a pdf giving all the details[/url]. The memory wasn't too bad after all, but some details I'd not remembered – for example the hole on top of which the speaker sits needs to be much smaller in diameter than my diagram.

Edited July 16, 2011 by ShergoldSnickers

[Bill Fitzmaurice]

[quote name='ShergoldSnickers' post='1305621' date='Jul 16 2011, 06:33 AM'][/quote]It's a bass reflex cab, nothing special or unusual except for the external driver mounting, and that serves no purpose, it could be inside with the same result. In current parlance it would be called an LLT, for Long (duct length) Low Tuning. The designer was totally in error with regard to the rounding of corners. Ten to forty foot wavelengths aren't the least bit hindered by hard corners.

Edited July 16, 2011 by Bill Fitzmaurice

[ShergoldSnickers]

[quote name='Bill Fitzmaurice' post='1305759' date='Jul 16 2011, 01:42 PM']It's a bass reflex cab, nothing special or unusual except for the external driver mounting, and that serves no purpose, it could be inside with the same result. In current parlance it would be called an LLT, for Long (duct length) Low Tuning. The designer was totally in error with regard to the rounding of corners. Ten to forty foot wavelengths aren't the least bit hindered by hard corners.[/quote]
Does the constriction of the hole immediately in front of the speaker on the top shell - and not shown properly in my rough from memory illustration - serve any purpose other than to speed up air 'squirted' into the resonant chamber in order to excite it? Surely this constriction would radically alter the behaviour of the cone as it is now impeded more by having to move air through a constricted hole?

Edit: Also wondering about how much distortion this set-up would introduce to any otherwise pure signal.

[url="http://www.avforums.com/forums/attachments/subwoofers-tactile-transducers/237169d1303471020-graham-holliman-infrasonic-generator-graham-holliman.pdf"]Link to original plans for this cabinet[/url]

Edited July 16, 2011 by ShergoldSnickers

[Bill Fitzmaurice]

[quote name='ShergoldSnickers' post='1305827' date='Jul 16 2011, 09:31 AM']Does the constriction of the hole immediately in front of the speaker on the top shell - and not shown properly in my rough from memory illustration - serve any purpose other than to speed up air 'squirted' into the resonant chamber in order to excite it? Surely this constriction would radically alter the behaviour of the cone as it is now impeded more by having to move air through a constricted hole?

Edit: Also wondering about how much distortion this set-up would introduce to any otherwise pure signal.

[url="http://www.avforums.com/forums/attachments/subwoofers-tactile-transducers/237169d1303471020-graham-holliman-infrasonic-generator-graham-holliman.pdf"]Link to original plans for this cabinet[/url][/quote]The size of the hole is part of the tuning mechanism. The size of the hole has far less to do with the driver excursion than the volume of the chamber. The THD of this box would be similar to a standard bass reflex with similar specs. BTW, the tapering of the ducts would seem to be an attempt at adding some horn loading, but duct length and exit area preclude that, both being far too small.
As my colleague George Augsperger would say [i]"There are many ways to build a bass reflex. This is one of them."[/i]

[ShergoldSnickers]

[quote name='Bill Fitzmaurice' post='1305924' date='Jul 16 2011, 04:07 PM']The size of the hole is part of the tuning mechanism. The size of the hole has far less to do with the driver excursion than the volume of the chamber. The THD of this box would be similar to a standard bass reflex with similar specs. BTW, the tapering of the ducts would seem to be an attempt at adding some horn loading, but duct length and exit area preclude that, both being far too small.
As my colleague George Augsperger would say [i]"There are many ways to build a bass reflex. This is one of them."[/i][/quote]
Thanks Bill, very interesting. Apparently the designer got a patent for the design, but I've not bothered to verify that. Just goes to show there's nothing much really new in cabinet design.

[fatback]

[quote name='Phil Starr' post='1303710' date='Jul 14 2011, 04:29 PM']Bill is right. Funnily enough I was driving home today listening to Lou Reed's 'Walk on the Wild Side' and I thought If anyone asks this question they should listen to this. The Bass sounds amazingly deep because it is played on an upright, even though the bottom frequencies are no lower than a four string the different mix of harmonics gives it a rich deep sound. There are loads of signal generators online and if you are deeply boring (like me)it is quite interesting to listen to a 40Hz (roughly bottom E) pure tone and realise just how low that is. If your speakers can go that low of course.[/quote]


Presumably it's the longer scale length that's allowing for the different harmonics? How does that work?

[Bill Fitzmaurice]

[quote name='fatback' post='1306026' date='Jul 16 2011, 12:35 PM']Presumably it's the longer scale length that's allowing for the different harmonics? How does that work?[/quote]The longer the scale the higher the fundamental to harmonic ratio in the waveform. A string doesn't reach its full potential for fundamental output until it's 1/4 wavelength long. At 30 Hz that's 9 feet, so you'd need one really big bass to create a strong 30 Hz tone.

[escholl]

[quote name='Bill Fitzmaurice' post='1306270' date='Jul 16 2011, 11:04 PM']The longer the scale the higher the fundamental to harmonic ratio in the waveform. A string doesn't reach its full potential for fundamental output until it's 1/4 wavelength long. At 30 Hz that's 9 feet, so you'd need one really big bass to create a strong 30 Hz tone.[/quote]
Err, that's not quite how it works.

A string always oscillates at its fundamental frequency, with a harmonic series superimposed on top of that -- the ratio of harmonics to fundamental, and to each other, depends entirely upon the excitation point and any additional boundary conditions other than the end points. The ratio of harmonics does not, however, depend upon length.

The fundamental frequency of the string is mostly a function of the tension, mass per unit length, total length and boundary conditions. The wave speed on this string will thus be a function of the tension and mass per unit length, and has nothing whatsoever to do with the speed of sound in air.

[Bill Fitzmaurice]

[quote name='escholl' post='1306283' date='Jul 16 2011, 06:16 PM']The ratio of harmonics does not, however, depend upon length.[/quote]I've found that it does, though I've only done very rudimentary testing just to satisfy my curiosity.

[Mr. Foxen]

The ratio of harmonics depends pretty heavily on the sampling point I think. As in the pickup position.