The Magical Number Seven, Plus Two

This DIY loudspeaker system experiments with multiple small wide-range transducers in a multiway configuration. The idea is to join good directional characteristics to coherence and power handling. Another goal is to improve timing by controlling the phase with FIR filters. This is an upgrade to my 2018 system with new filtering and the addition of "cheeks" to the speaker columns.

   

Wide range

The main speakers are based on seven E.J.Jordan JXR6 HD that I picked up from a previous linear array system. Arranged as close together as possible, they form three groups having the same acoustic center:

The whole can be viewed as one coaxial driver.

   

The 20 liter sealed enclosures are made of 30 cm PVC pipes filled with polyurethane foam and a polyester fleece. A tapered internal partition helps reduce the standing waves that start around 600 Hz. The build is simple: just a PVC KGU-socket connecting sleeve (which has rubber rings) and two KGM plugs (no glue). The baffle is covered with a 5 mm felt sheet to reduce diffraction and make the drivers flush.

The graphs below show the magnitude response and group delay measured with a log sweep from 16 to 24000 Hz taking 21.8 s.
The magnitude response stays inside ±3 dB from 200 to 20000 Hz.
Group delay rise below 250 Hz reflects the low frequencies roll-off.


Average measure of the six groups of small drivers at 50 cm.


Group delay (blue), minimum group delay (gray), and excess group delay (black).

Subwoofers

The bass extension is provided by two 20 cm SB Acoustics SW26DAC76-4 per channel. With dual rigid aluminum cone and moderate moving mass, these lightweight (neodymium magnet) drivers can be used in rather small sealed enclosures.
The 21 liter enclosures were very easy to build: PVC connecting sleeve and two plugs. They are arranged up and down the main speakers in a way that the acoustic centers match.
Calculated Qtc=0.86 and F3=35 Hz. Internal standing waves start around 600 Hz, well away from the intended operating range.
The magnitude response is very smooth from 40 to 500 Hz.

 
Average measure of the four subwoofers at 5 cm.

 
Group delay (blue), minimum group delay (gray), and excess group delay (black).

Operating

Digital to analog conversion tasks an 8-channel miniDSP U-DAC8 at its best with iFi Audio iPower and iGalvanic3.0.
A Behringer Ultralink Pro MX882 V2 splits the stereo signal into the dual subwoofers.
Power is supplied by two Rotel RMB-1565 5-channel Class D amplifiers, one for each stereo channel.

Instead of a dedicated DSP, the computer does all the filtering, equalization and phase linearization. I believe it's a better solution because the PC has all the power to compute the FIR filters for phase control. Replacing hardware DSP by computer software is just smarter and can be a lot more economical.
This tutorial may help configuring the PC: Windows PC as a FIR Audio Processor.

The computer is configured with Jonas Thedering's Equalizer APO. The E-APO configuration file looks like this:

Device: USBStreamer - USBStreamer Multi-channels
Eval: mainLevel= -3
Stage: pre-mix
# Channels (7.1)
#   1   2   3   4   5   6   7   8
#   L   R   C  LFE  RL  RR  SL  SR
# 3.1 source
# Copy: 1=L+0.5*LFE 2=R+0.5*LFE 3=L+0.5*C 4=R+0.5*C 5=L+0.5*C 6=R+0.5*C 7=L+0.5*C 8=R+0.5*C
# Stereo source
Copy: 1=L 2=R 3=L 4=R 5=L 6=R 7=L 8=R
Stage: post-mix
# Equal-loudness
LoudnessCorrection: State 1 ReferenceLevel -18 ReferenceOffset 0 Attenuation 0.3
# Convolution
Channel: 1 2
Convolution: IR_sub.wav
Channel: 3 4
Convolution: IR_low.wav
Channel: 5 6
Convolution: IR_mid.wav
Channel: 7 8
Convolution: IR_high.wav
# Levels
Channel: 1 2
Preamp: `mainLevel+3` dB
Channel: 3 4
Preamp: `mainLevel-6` dB
Channel: 5 6 7 8
Preamp: `mainLevel` dB

To generate the finite impulse response stereo WAV files I use Thomas Drugeon's rePhase loudspeaker phase linearization, EQ and filtering tool. With the following impulse settings, precision is 1.46 Hz up to 48 kHz. Including 10 ms for APO processing, total latency is 331 ms.

Crossover

I applied Horbach-Keele filters according to their 2007 paper:
Application of Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers.
The critical frequency of the subwoofers is chosen at 98 Hz with a spacing ratio of 4.24 which brings the critical frequency of the bass to 416 Hz. Given their separation of 70 cm, the subs become directional from 165 Hz while the vertical coverage of the bass drivers is essentially omni directional. The wavelength of the critical frequency of the midrange (1109 Hz) is half the separation of the drivers pair, which provides a vertical beamwidth of approximately 84º that spans three octaves.
I am aware that this speaker arrangement is not entirely within the rules. Yet Horbach-Keele filters give more consistent results than any others I have tried.

Equalization

Low frequencies phase and magnitude responses are linearized by inverted second order filters (rePhase compensate mode). The highest frequencies are adjusted in the same way, not that a magnitude correction is necessary, but it gives the phase a linear trend that improves the balance between midrange and trebble.
Given its abrupt side, the resonance of the room around 110 Hz is attenuated by a cosine type linear-phase filtering.
The following figures show the equalizations with (red) and without (blue) low/high-pass filters. You may copy the settings to clipboard and load them in rePhase.


rePhase settings for low, midrange and high frequencies.


rePhase settings for subwoofers.

Results

For the measures, I used John Mulcahy's REW analysis software.
After equalization, the phase responses are aligned and the magnitude response extends from 25 to 18000 Hz.


Four measures average of the left and right loudspeakers at the listening position.

Conclusion

The light aluminium transducers produce a clear and detailed sound that engages attention. Using them in such a configuration is obviously beneficial to the homogenity of the sound reproduction, so the promise of full spectrum coherence is clearly delivered. Thanks to balanced directivity, the sonic colour remains consistent over a wide listening field. This always feels natural, whether the music is relaxing or energizing. I've had this system for five years and its latest update has given me even more satisfaction.
What about the shortcomings? In theory, the cylindrical enclosures are a weakness and specifically designed baffles might be an improvement. This doesn't negate the benefits of the 7+2 drivers configuration and I would advise the curious hobbyist to give it a try.


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