My Approach to Bass Horn Design

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Written by: Bjørn Kolbrek
Category: Horns
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My Approach to Bass Horn Design

Many starting points for bass horns are built by the equations given in a paper by the late Marshall Leach [1]. These equations are built on certain assumptions, and will give you either a horn system based on driver parameters, or driver parameters and system based on a set of specifications. These assumptions are:

  • The impedance match is designed for maximum sensitivity
  • The low frequency corner is set by the rear volume
  • The horn cutoff is set at the same frequency, and the T-value of the Hypex horn selected to provide reactance annulling with the specified rear volume
  • The upper corner frequency is set by the mass of the driver
  • The front chamber is used to extend the HF response slightly before it starts to roll of quicker
I don’t like Leach’s approach to reactance annulling. For some reason he believes that it is the rear chamber that should set the LF -3dB point, presumably this is in order to preserve space, as it sort of sets the minimum chamber volume for the specified LF extension. But by doing this he paints himself into a corner: Reactance annulling using a plain exponential horn becomes impossible, and he is forced to use a Hypex horn, with a T-value that often ends up around 0.5.
Another thing I don’t like with this approach is the way reactance annulling is considered to just equating the horn reactance with the system compliance at the cutoff frequency, essentially resonating the horn air mass with the system compliance. This approach comes from Plach and Williams [2], who combined the concept of reactance annulling, originally invented by Albert Thuras, with the Hypex horn. With an exponential horn, reactance annulling works perfectly, since the shape of the horn reactance curve perfectly matches, or conjugates, (in the case of an infinite horn) the reactance of a compliance. The system reactance is therefore effectively nulled out above horn cutoff, increasing power output. With a Hypex horn, horn reactance is less above cutoff, but greater near cutoff. The lower the T-value, the worse the reactance annulling above cutoff. This is clearly illustrated by the fact that the total system compliance becomes zero with T = 0.
The original Bell Labs approach to reactance annulling was not to resonate the horn reactance with the compliance, but to create a conjugate impedance match between driver and horn. This is possible to do with Hypex horns too, which I have shown in a paper.

A More Basic View

Instead of just going by a set of formulas form a paper, it can be useful to instead look at some basic horn-driver interaction. For a bass horn, there are three important relations:
  1. The midband impedance match between driver and horn. This sets the efficiency, sensitivity and, since the product of efficiency and bandwidth (EBP) is constant, also the bandwidth of the system. In the midband, the horn can be considered a resistive load having a value of
    Ral
    while the driver presents a source impedance of
    Rat
    These two impedances should be equal for maximum sensitivity, while maximum efficiency requires a maximum throat area. In many cases, we just equate these expressions, solve for throat area St, and are done. But we don’t have do go about it that way, as we will see.
  2. The total system compliance relative to the horn reactance. This has to do with low frequency extension, driver protection from subsonic diaphragm excursion (since the horn doesn’t load the driver below horn cutoff), and efficiency above cutoff due to reactance annulling.
  3. The diaphragm mass relative to the horn resistance RAL. This sets the upper -3dB corner frequency of the power response. But since the horn has typically started to beam in that frequency range, unless the mouth is very small, the on-axis response doesn’t roll off at this point. But we should still pay attention to the mass corner frequency if we want to use the horn in the resistance controlled frequency range, where the driver is truly horn loaded. If we want to roll off the power response, we can add a front chamber. But this makes the power response roll off at 12dB/octave, and it may be harder to cross over. One reason to add a front chamber, though, may be to filter out nastiness from the driver, like distortion products and cone breakup, but this should hopefully not be a problem in a domestic setting.
The importance of the impedance matching described by relations 1 and 2 is that it reduces the variations in power output (and therefore creates a smoother response) when the acoustic load varies. This allows us to use a smaller mouth area than would otherwise be required, but more importantly, it helps in dealing with room modes. A bass horn in a small room will operate in the modal region of the room, with large fluctuations in radiation impedance. Even when placed in a corner, the throat impedance will be ugly. Thuras has show that the variation is smallest when
Rat2
i.e. the geometric mean of the minimum and maximum throat resistance values in the working range. This factor is usually close to 1, so RAL = RAT is a useful starting point.
The relations also show us that we have many levers to pull in order to achieve an impedance match: compression ratio Sd/St, driver motor system parametersBl and RE, and amplifier output impedance RG.

Driver

In many cases we have selected a driver to design a horn around, based perhaps on a figure of merit (EBP, Bl, etc), word-of-mouth or availability. I have a pair of Altec 515-8G, which are great bass horn drivers (it actually says so on the back), but I also work in a loudspeaker factory, so I could design and build a suitable driver for my horn. There is also the option of calculating some parameters and then look for a suitable driver that matches those parameters. Let’s have a look at the impedance matching relations.
Ignoring RMS,
St1
and we see that a driver with a strong motor results in a small throat. We may increase the throat area by using a weaker motor, larger diaphragm, or higher amplifier output impedance. So using a tube amplifier is not out of question either, if we play our cards right.
Rearranging the equation to give us Bl, we get
Bl1
Another factor in choosing throat area is horn distortion. A smaller throat means more power per area, i.e. higher intensity in the throat, and this leads to higher pressures and higher distortion. So we don’t want to make the throat area too small. For domestic use, however, horn distortion is not a major concern.
When it comes to driver mass and compliance, this is linked to driver fs and Q values. But these compound parameters obscure the relations between the horn and the driver parameters, and can make the whole thing more confusing than need be. For instance, the mass corner frequency is set by the system resistance and moving mass:
fH1
But if the various electromechanical parameters are expressed by Thiele/Small parameters, and we assume impedance matching and that all system compliance is provided by CMS, this equation can be rewritten as
fH2
The relation
fH2
is called EBP, efficiency-bandwidth product, as it is the product of the mass corner frequency and the conversion efficiency, and is a driver figure of merit. But EBP may put too much emphasis on the raw driver having a high resonance frequency, since the influence of the rear chamber is left out of the picture: the lower corner frequency is left out of the picture. Actually, with a soft suspension and a small rear chamber, a low resonance frequency is perfectly acceptable, as long as MMD gives the correct mass corner frequency. This is one reason I don’t like T/S parameters for horn design: their use rely on assumptions that are not satisfied in horn speakers. They were originally devised to aid in the design of direct radiator speakers, where the system can easily be represented by a few lumped elements. Additionally, they lump the air load mass in with the driver parameters, which are allowable in direct radiators where you know exactly the acoustic load the driver will face, but it is not in horn design. T/S parameters can be misleading in this case.
Driver compliance (CMS or VAS) work together with the rear chamber to provide the system compliance for reactance annulling. The exact value is insignificant, as long as it is large enough to not require an overly large (or negative) cabinet volume. It may be advantageous to make the rear chamber provide much of the compliance rather than a nonlinear suspension, although this may be a problem in high power design where the cabinet compliance becomes to stiff at high levels. With the low displacement possible with high efficiency horn speakers, the chamber compliance should be very linear. Looking at the driver CMS(x) (or KMS(x)) curves, one will often look for linearity and symmetry, but it should be kept in mind that it is the total compliance, including the nonlinear box, that should be evaluated, not the raw driver.

The Design

My preferred way of going about a bass horn design and driver selection is to design the horn first, based on a set of choices dictated by the acoustical performance of the horn. This approach is for a traditional wide-band bass horn, which is designed to be the only low frequency channel of the system, covering from the lowest frequency of interest (usually determined by how big a horn you can accept) up to 3-400Hz or so. So not a horn subwoofer, which is quite narrowband and can have a small mouth and be aggressively folded, nor a midbass horn designed for better MF extension and LF extension usually not below 80-100Hz.
  • A mouth large enough to reduce reflections to an acceptable level, creating a well-behaved and not too resonant throat impedance.
  • Set throat area based on distortion, and also considering the size of the driver and suitable compression ratio. A too high compression ratio may put too much stress on a thin, light cone, so a ratio in the range 2-4 is fairly safe.
  • Use an exponential horn. The reason for this is that if the mouth isn’t large enough, a Hypex horn (T<1) will have larger impedance peaks than an exponential horn. Also reactance annulling becomes more challenging.
  • Select a driver based on the desired impedance matching ratio, usually as good a match as possible. This determines driver (Bl)2 ⁄ RE.
  • Further the selection of drivers is narrowed down by looking at the mass corner frequency and resulting rear chamber size.

References

[1] Leach, W. M.: “On the Specification of Moving Coil Drivers for Low-Frequency Horn-Loaded Loudspeakers”, J. Audio Eng. Soc. , Vol. 27, 1979, No. 12 p. 950-959
[2] Plach, D. J.: “Design Factors In Horn-Type Speakers”, J. Audio Eng. Soc. , Vol. 1, 1953, No. 4 p. 276-281

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Horn Loudspeaker Simulation

Horn Loudspeaker Simulation

Many readers may be familiar with the free software Hornresp, which, given driver parameters and some geometrical parameters for the horn and cabinet, can simulate a wide variety of horn, direct radiator and bandpass systems. This may be enough for most people, while others (like me) are curious about the math and algorithms behind it

Simulating horns and horn loudspeakers has interested me for a long time. I found Hornresp back at the time when David McBean first made it available (around 2000 I think). At first you could only get the full functionality by paying a small fee, otherwise the throat area of the first segment was fixed. He later told me that he actually ended up giving the full version for free to those who asked, and if I had known that I'd probably started using it in earnest earlier. But my first midbass horns were designed using Hornresp (with the original limitation), as was my later horn subwoofer and other horns. But around 2005-2006 I got interested in horn theory and other methods of evaluating horn performance, like power factor (the cosine of the phase angle between resistance and reactance of the throat impedance). First I made a program that would read the data exported from Hornresp and plot the power factor. Later I started looking into wave fronts in horns, and combination of horn types (like multiple segment horns with Hypex segments), and for that I needed to write my own horn simulation software. 

I first made contact with David McBean in 2004, and we started corresponding regularly, discussing many aspects of horn simulation. This was extremely helpful when I started writing my own horn simulator, and I can't thank David enough for making Hornresp available, and for guiding me through the rough terrain of horn simulation. Although he never showed me more than a couple of snippets of code, through discussion and references I was able to make things work and learn things from the ground up. 

My horn simulator, HornCAD™, evolved into a complex program that could use the Mode Matching Method (MMM), simulate all types of segments, rectangular horn, and curved horns. It could use measured compression driver data, and export dxf files for CAD use. Thanks to the MMM, directivity simulations were quite accurate, and I used it extensively during my time at Celestion. 

But since HornCAD™ was born as a tool to learn horn simulation and to explore various ways to simulate horns, it is full of unfinished functionality and bugs that are hard to track down due to the size of the code base. Therefore it has never been released to the general public. That may change in the future, though... But enough about my background as a horn simulator writer!

Simulation Basics

The point of this article is to give an introduction to horn loudspeaker simulation. While it may seem like black art for most people, it is more similar to electrical circuit simulation. So in this little series, I plan to explain how to implement a simple "Hornresp-ish" code in Octave/Matlab. It will of course not have all the bells and whistles of Hornresp, but will be able to simulate the power response, electrical impedance and diaphragm displacement of a basic horn loudspeaker. 

Horn loudspeaker simulation typically consists of simulating:

  1. The radiation from the horn, especially radiation impedance, but also directivity.
  2. The horn itself: throat impedance as a function of mouth radiation impedance, and the output volume velocity as a function of the input volume velocity.
  3. The acoustical circuit apart from the horn: front and rear chambers, vents etc.
  4. How the loudspeaker driver behaves when connected to the acoustical load made up by the horn, chambers, vents etc and thereby the power delivered to the horn, the electrical input impedance of the system, diaphragm displacement etc. 

We will cover all of this, but also things like simulating multiple segment horns, horns with special profiles like the tractrix, and maybe even look at tapped horns. 

Glossary

The list above contains many words that may be unfamiliar, but if you want to learn horn simulation, you need to know what they mean. So here is a short glossary:

  • Radiation impedance: When something vibrates with a certain velocity, it pushes the air, and the air pushes back with a certain force. The ratio of this force from the air to the velocity of vibration is the mechanical radiation impedance. In this analogy, force is analoguous to voltage and velocity to current, and just like voltage divided by current gives electrical impedance, force divided by velocity gives mechanical impedance. 
  • Volume velocity: velocity times area, cubic meters per second.
  • Acoustical impedance: A similar analogy can be made in acoustics: with pressure analoguous to voltage and volume velocity analoguous to current, the ratio between them is acoustical impedance. It relates to mechanical impedance through the area of the vibrating surface (which may not be solid, but can be an imaginary surface, for instance the horn mouth). Mechanical impedance is acoustical impedance times area squared.
  • Acoustical circuit: an analoguous circuit of acoustical components like ducts, horns and volumes. It can be drawn like an electrical schematic, and we can calculate its performance based on electrical circuit theory. This is a fundamental method for simulating electroacoustic systems.

Simulation: The Nitty Gritty Details

Here are links to the parts in the series (the links will go live as the parts are added):

  1. Part 1: Radiation and T-Matrix
  2. Part 2: Adding a driver
  3. Part 3: Multiple segments and more T-matrices
  4. Part 4: Other horn profiles and curved wave fronts
  5. Part 5: A simple tapped horn model

The Bass Transmission Index

The Bass Transmission Index

Evaluating the accuracy of low frequency reproduction isn't as straightforward as one may think. There is talk about "fast bass", and PRAT (Pace, Rythm And Timing) is sometimes mentioned as a description. In such a discussion someone will invariably point out that a 20Hz sine wave isn't "fast", and that the issue of fast or slow bass is meaningless. It may seem that way using these simple arguments, until you experience accurate, detailed bass reproduction. But how do we quantify it? Obviously not by measuring the rise time of a 20Hz sine wave! 

This is actually a very real problem. For the mix engineer, perhaps the biggest problem is how a loudspeaker with poor temporal response alters the perceived balance between rhythm section instruments like kick drum and bass guitar. Though not exclusively the case, loudspeakers with ported cabinets (bass reflex loading) are more likely to exhibit this type of problematic behaviour, due to the use of resonant elements to increase bass extension. An incorrect mix made on loudspeakers like this may not transfer well to other sound reproduction systems, and can't be corrected later during mastering, since the two instruments occupy the same part of the audio spectrum.

Lara Harris, Keith Holland and Philip Newell have done extensive work on quantifying bass reproduction accuracy, resulting in Lara's PhD work and the Bass Transmission Index (BTI). The BTI is an objective measure of a loudspeaker's ability to accurately reproduce low-frequency musical content. The metric aims to describe how well a loudspeaker reproduces the temporal envelope of a dynamic and harmonically-complex signal, something that cannot easily be evaluated from the usual frequency response (magnitude plots). 

Like the STI (Speech Transmission Index), as used in speech intelligibility measurements, the BTI is based on a metric called the Modulation Transfer Function (MTF). MTF-based methods such as these pass an amplitude-modulated signal through the system, varying the rate of the temporal fluctuations across a range of values that are likely to feature in the real-world signals that the system will encounter. The preservation of modulation depth between input and output is used as an indicator of how well the system can reproduce these temporal variations. The figure below illustrates the concept, showing modulation depth for input (mi) and output (mo) signal envelopes.

MTF

The BTI evaluates the MTF in 10 frequency bands from 16-160Hz, with 7 modulation frequencies from 0.8-11.7Hz. The algorithm computes a matrix of modulation index scores between 0 and 1 for each combination of frequency band and modulation frequency. This grid of numbers can be used to calculate an overall average score, and is visualised as a grayscale intensity image where white = 1.00 (perfect reproduction). As a rule of thumb for interpreting these BTI intensity images:

  • Inconsistent shading in the horizontal direction (left-right) indicates variation in the frequency response magnitude (this is variation across frequency bands).
  • Inconsistent shading in the vertical direction (up-down) indicates variation in the faithfulness of envelope transmission (this is variation across modulation frequencies).

The figure below shows an example BTI intensity image and mean score for a bass-reflex studio monitor. Frequency bands (centre frequencies) are on the x-axis, and modulation frequencies on the y-axis.

BTIplot

Recently I have worked with Lara to make her BTI research code production ready, and it has now been officially made available on GitHub. It runs in Matlab and Octave (although not all the advanced options are available in Octave, and some requires certain Matlab tooboxes), and demonstrates a reference implementation. Here are the links:

BTI Toolbox on GitHub

Lara's LinkedIn post about BTI

My LinkedIn post about BTI

 

Big Bend Bass Horn: Driver Update

Big BenD Bass Horn: Driver Update

[Previous: Installation; Main] 

This update is actually long overdue, and related to a project at Celestion I wasn't able to finish: a cone driver specifically designed for bass horns. It follows the ideas I outlined under My Approach to Bass Horn Design, and is a 12" driver designed for a compression ratio of about 1:2. As I wanted it to be easy for Celestion to put it into production, I used as many standard parts as possible, either directly or something that could be easily machined from standard parts. But I also added a feature that aren't easy to find in modern drivers: an underhung edge-wound voice coil. 

Here are a some of the features of this driver:

  • Underhung 3" edge-wound voice coil
  • Copper sleve on pole piece
  • Focused magnetic gap
  • Low moving mass
  • Vented pole piece and back plate
  • 250W power handling
  • Large ferrite magnet
  • Inverted dustcap to allow for phase plugs if desired

And for those who worry about the high power rating being detrimental to other qualities important for horn speakers, rest assured: this power rating was a result of the voice coil size and venting, not of "beefing up" the driver (which typically makes the moving assembly lighter) to take higher temperatures and forces. 

Here's a side view of the driver, without the front segments. It's built on a Celestion FTR chassis. 

New driver

The magnet system:

bigBendDrivers3

The gap flux is slightly above 1Tesla, which is quite good for a gap this size. It takes a substantial amount of magnet to produce that, especially when you lose gap width to a copper cap. 

Comparisons with old DIY driver

Below are a couple of photos comparing the new driver to a DIY project I used to begin with, referred to as 12" DIY driver in the performance measurements. The DIY driver used the motor system from a pair of Celestion NTR08-2009D 8" woofers I found in the bin. They had the cones cut out, but the motor was salvageable (even the voice coil), and I used them to build a pair of 12" drivers using available parts. I used the lightest 12" by 2" cones I could find, and a fairly soft spider. They turned out to be quite good, with the BL^2/Re being a good match for my bass horns. But the new drivers are more robust, and also give a very good performance and produces very clean bass in the Big BenD horns. 

Comparision with old DIY driver

Comparision with old DIY driver (back)

 Parameter  Old DIY driver  New driver
 Re [Ohms]  4.46  5.8
 Le [mH]  0.065  0.086
 BL [N/A]  12.3  17.0
 Mms [g]  39.2  64.5
 Rms  [Ns/m]  3.4  0.63
 Cms [m/N]  4.36e-4

 1.88e-4
     
 

Now I just hope Celestion will finialize this project and put the drivers into production, as I think this would be a good driver for bass and midbass horn use, especially for domestic use.

[Previous: Installation; Main] 

Big BenD Bass Horn: Installation

Big BenD Bass Horn: Installation

[Previous: Performance Measurements; Main; Driver Update] 

Finally, the last article about the Big BendD bass horn! This part will cover the installation and setup of the horn, with some comments on the subjective performance at the end.

Installation

Although the DIY 12" driver showed the most promise during outdoor testing, I still wanted to try the Altec 515-8G when setting up the horn. It was mounted in the rear chamber, the chamber was filled with wool, and the rear wall covered with pieces of an acoustic celing tile. 

RearChamberAltecWoolBackWallDamping

Then came the process of carrying all the parts into the living room, setting it up, adding gaskets, bolting it all together, installing the drivers, wiring it up and put the rest of the system back together. In the process I had help from my good friend Harry. This is really a two-person job, because carrying the big parts into the house isn't easy to do by oneself. The parts were all designed to fit through a standard door, but they are still a bit difficult to move around. 

Setup01Setup02Setup03

Setup01Setup05Setup03

Setup01Setup08Setup03

Setup01Setup11Setup03

With two people working, the setup was done in a couple of hours. There are a lot of bolts, about 70 per horn, so or ratchet spanners got a real workout. 

The complete setup is shown below. The white middle/throat sections blend in with the walls, making the bass horn less dominating in the room. It does work, some people have not recognised it as part of the bass horns.

Axi2050Proto1

The First Test: Where's the Bass?

Just setting up the horn and putting some music on, without any crossover or EQ, left us wondering: Where's the bass? Isn't this supposed to be a bass horn? There's a lot of lower midrange, but the sound was a bit thin. 

Altec95dBInRoomThe measurements made it obvious what the problem was: the output fell below 70Hz, and apart from a peak at 50Hz, the response was more like a midbass horn than a 30Hz bass horn. What was going on? 

We swapped the Altec for the DIY 12", and that helped significantly; the better impedance match between the horn and driver was definitely an issue in the presence of room modes. Which turned out to be the real problem.

Room Modes

 My living room is about 7m long and 3.5-4m wide. This means that the second mode in the length direction and the first mode in the width direction are both at about 50Hz, which is also clear from the measurement above. Between these two modes, energy transfer in the room is quite limited. A wider room would definitely be an improvement, but you have to work with what you've got. 

In the modal region in a room, the response can vary quite a lot from position to position. Some listening positions have a smoother response, while others place the listener at peaks or nulls of modes. To find the best starting point for EQing the response, I measured the response in the room at a 2.5 by 3m grid, every 0.5m. The results for all positions are shown below. 

RoomRespGrid

It turned out that the response was quite smooth about 3m from the horns mouths, somewhat behind the middle of the room. The responses at this line are shown below. Annoyingly, the response drops quite sharply below 45Hz, due to the lack of modes between 25Hz and 50Hz, but apart from rebuilding the room (which I'm sure the landlord wouldn't like), there's not much to be done. 

RoomResp3m

I have applied some EQ to lift the response a bit, but one should be very careful with EQing dips caused by room modes. And I'm not going to spend the rest of my life in this house, so hopefully my nest home will have a more beneficial distribution of modes int eh listening room!

Listening Tests

So, after all this work, how does it sound? The lack of output below 45Hz is only noticable on music where you know there should be something down there. Apart from that, the response in the listening position is quite smooth, and it has the traits of bass horns that I have been missing for so long: proper impact - even at low volumes -, and responsive, detailed and tight bass. Low frequency details in the recordings are quite easy to hear, and there's no overhang or resonance. It sounds effortless even at very high volumes too. The horn integrates well with the fast and detailed midrange of the Axi2050, making it a good combination. I also tried a delay-derived subtractive crossover, as described in the Horn Book, and it made a worthwile improvement to the coherence and naturalness in the lower midrange.

All in all, I'm very satisfied with the performance. 

[Previous: Performance Measurements; Main; Driver Update] 

Big BenD Bass Horn: Performance Measurements

Big BenD Bass Horn: Performance Measurements

[Previous: Belts and braces pt. 4; Main; Next: Installation] 

 With one horn finished, I took it outside to do some frequency response measurements. First thing to do is to measure the horn under conditions similar conditions to the simulations. This is a very important part of designing speakers, if you want to use simulation tools in the process. You need to verify that your simulation is correct, and if not, in what way. It is especially important if you are writing your own simulation software. I think people are getting better at it, but there have been many cases on DIYaudio of people complaining about their simulations being wrong, when the actual problem is that they have not simulated what they have actually built. 

Corner

The actual condition of a horn built into an "infinite corner" (3 infinite baffles perpendicular to each other) isn't easy to achieve in practice. The best I could do was to use the walls of my house and garage:

Testing1

And then put some extra sheets of plywood between the buildings to try to close the gap.

Testing2

So, finally the first measurements, with and without baffles. The difference isn't huge, This may be because the garage is still close enough in terms of wavelengths to contribute to the baffle effect. (I'm not sure if the levels are actually correct, trying to do the calibration in ARTA gave some confusing results.)

MeasuredCornerTxt

So how well does this fit with the simulations? Actually pretty good, see below. The Response below 200Hz is almost spot on, the  response at higher frequencies deviates, probably because of the simple model used for simulating the curving, and because I used a different driver than in the measurements. 

What I'm quite happy with is that the curving approach worked as intended: there are no sharp dips and peaks or suckouts in the response, and it doesn't roll off until about 500Hz. This creates a nice overlap with the midrange horn. At the lower end, the response starts to fall off rapidly below 30Hz, which was the intended lower limit. The response is a bit uneven, but we'll see that this changes with a different driver.

OutdoorResp

Wall

The second test condition is in front of a wall. Neither of the two are fully representative of the operation conditions in actual use, but it will show the effect of placing the horn in front of, instead of flush with, a wall.

Testing3

The effect of one missing side wall and the increased distance to the back wall is evident: a loss of level at low frequencies that was predicted by both the simulations and scale model measurements. 

MeasuredWallTxt

Driver Tests

The next measurements were done with REW as I found it easier to do a level calibration there than when using ARTA. Four different drivers were tested:

Altec 515-8G, a 15" driver built in a Celestion FTR-3070 chassis, A 12" guitar speaker, and a 12" high efficiency woofer built using various parts available. The results are shown below. 

There is a clear difference between the drivers; the guitar speaker clearly fails and has a very peaky response (not all musical instrument drivers are suitable for bass horn use, even if Dr. Bruce Edgar had good results with EVM-12). The 15" drivers perform about the same. The best results comes from the 12" driver I built. This isn't actually very surprising, since it has the best impedance match with the horn of all the drivers. 

The dips in the response at 483Hz and 870Hz are from standing waves in the empty rear chamber.

FR105dBWall

Distortion

Following is some distortion meausrements of the drivers tested. I measured at 95, 105 and 115dB SPL at a 2m distance. Only the results for 115dB (114dB for the 12" prototype) are shown.
Altec115dB

15inDIY115dB

Guitar115dB

12inDIY115dB

The 15" drivers are quite similar in response, but the Altec clearly has lower distortion. The guitar driver has very high distortion (not surprisingly, since it has a stiff paper surround and only 1mm overhang on the voice coil), and is best left to what it was designed to do: create distortion for electric guitars. 

The 12" DIY driver has the smoothest response, and while the distortion is slightly higher than the Altec, they are both quite at "sane" listening levels.  

Altec95dB

12inDIY95dB

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