20min read: "Subwoofer Camp" for best audio system distortion

S. Olive

One subwoofer “camp” believes in traditional full-range-in-a-box loudspeakers.

However locating speakers within one’s room, resonant echoes create over-loud peaks & silent valleys, uneven note-by-note, and differing at each listener location.

The other “camp” redirects deep bass to one or more lower distortion subwoofers (SW) positioned for milder boosting\canceling. Relieved of deep bass, main speakers generate lower distortion: harmonic (HD), intermodulation (IMD), & multi-tone (MTD).

Perhaps not for those who prefer overly-bright, compressed electric popular music, but for critical listening by audio recordists, musicians, & acoustic music enthusiasts, good sound requires one or more low distortion SWs rated within 16~125Hz (C0~C3).

This brief reviews what produces VLF, then reveals how best to enjoy VLF on replay.

Sources and acoustics that produce low bass Musical instruments that produce VLF include double bass viols, bassoons, tuba, orchestral bass drum, piano, organ, etc. Large reverberant concert halls strengthen these VLF sounds. True also for augmenting sources in a large recording studio.

Replay on VLF-deficient speaker systems denies listeners thrilling deep bass.1

San Diego Symphony’s 100 members under Rafael Payare perform at Lehigh University in Bethlehem PA the evening before its debut at Carnegie Hall in New York City 2023. Live & recorded spectra are overleaf.

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With weak VLF we perceive phantom fundamentals by their unique harmonics, original or distortion, cf. FN#6.

Fig.1 - Live real-time analysis (RTA) midway in a 1003-seat hall shows a natural “tilt” of 1~3dB/octave.

Of about 10 octaves audible 16~16kHz (or 20~20kHz as some prefer), subwoofer(s) are tasked with the difficult lowest 2+octaves, where floor-standing ‘tower’ speakers are less capable of low distortion.

Fig.2 - Playback RTA of the above recording on a studio-quality system shows lifelike 100SPL peak lines 10dB above averages. “Tilt” is due to powerful deep bass instruments + room support, preserved compared with the spectrum heard live and expected on replay. Demands above 8kHz are far lower.

Why a subwoofer (or two?) and Bass Management for best audio reproduction?

That ‘bass accounts for 30% of listener enjoyment’ is certainly true at a live acoustic concert. And at home in stereo or surround sound with a subwoofer, even with typical panned-mono content. Audio-video receivers (AVR) with DSP and main speakers set to “small” provide properly filtered signals to speakers, but the bass is monophonic no matter how many SWs are paralleled. (Later we explore more lifelike stereo bass.)

Main speakers – ‘bookshelf’ or floor-standing ‘towers’ – can be over-burdened with VLF in 2+ octaves of hearing’s total range of 10 octaves from 16Hz to 16kHz. ‘Mains’ struggling with VLF generate bogus harmonics, buzzing multi-tone artifacts, and the ‘semi-clipping’ of compression when cone motion cannot follow the loudest audio signals. Active SWs usually do not high-pass filter (HPF) audio passed on to main speakers, which then generate distortion throughout their range (discussed later).

A subwoofer’s own distortion is post-crossover, thus is not filtered by it. The extent a SW itself distorts is determined by its quality (cost), and by playing it at too high a sound pressure level (SPL).2 SW distortion artifacts reach well above crossover to cause it to be localizable, smearing the soundstage, masking mains speaker sounds, and adding to the mains bogus harmonic (HD), intermodulation (IMD), & multi-tone (MTD) rubbish. Each issue is dealt with in turn, based on normal human hearing.

2 dB sound pressure level (SPL) ranges from the “threshold of hearing” at 0dBSPL to a painfully loud 120dBSPL.

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What we hear is not what the wattmeter says The brain transposes sound (the cause) to perceived hearing (the effect). Watts measures power from amplifier to loudspeaker, reproduced acoustically as Sound Pressure Level, in dBSPL. But we hear sound differently, in dBPHON.3 Fletcher & Munson's 1932 Equal-Loudness Contours (updated in ISO:226), sound power in dBSPL relates to perceived hearing in dBPHON at a one-to-one ratio by definition at 1kHz. This relationship is illustrated in Fig.3, transposed for clarity as Equal-SPL Contours that represent an average ears’ frequency response. If unmasked by room noise, this dynamic range spans 105 dBSPL, from the threshold of hearing at 0 to 105 at full scale (FS) in digital recordings played at lifelike SPL, compared in Fig.1&2. Above 500Hz it also spans 105 dBPHON in perceived Loudness. However for bass, Fig.3 shows that as frequency decreases and SPL reduces, human hearing exhibits worsening ‘deafness.’

Sound power (dBSPL) v. perceived loudness (dBPHON)

Fig.3- Equal-SPL Contours of ISO:226 (Fletcher -Munson updated) here transposed to Equal-Loudness Contours, the average human “ears frequency response.” The graph shows that until playing above 60 SPL on the ▪ ▪ ▪ ▪ ▪ curve, a 30Hz fundamental is inaudible (at 0PHON, the chart’s bottom line). However a 60Hz tone representing its 2nd distortion harmonic is audible 28dB lower at a far softer 32 SPL, and a 90Hz tone representing its 3rd harmonic has been audible since 38 dB lower, at a softer still 22 SPL. 3 For clarity, values are color-coded as frequency, actual physical dBSPL, & perceived loudness in dBPHON.

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Below 500Hz along steepening, diverging Contours, 4 fewer dB change in SPL causes greater dB change in PHONS. In Fig.3 a 30Hz fundamental is too soft to hear until it is above 60SPL. At 30Hz, a change of only 45dBSPL, from the 60 SPL ▪ ▪ ▪ ▪ curve to 105, causes a change of 70dBPHON, from its threshold of hearing (“a mosquito at 10ft”) to the 70dBPHON intercept along the 105dBSPL curve. Where above 500Hz a change in SPL higher by +10dB about doubles perceived loudness and –10dB halves it, at 30Hz only about –5dBSPL change sounds half as loud; –10dBSPL is a quarter as loud! The insensitivity to SPL at very low frequencies (VLF) is evolutionary to allay human fear of low and infrasonic booms from thunder and earthquakes. But with audio replay, it causes unwanted changes in musical tone color in the form of added distortion.

VLF “inflated THD” and other distortions alter tone color (timbre) Distortion is objectionable for acoustic classical, jazz, & movie music if listeners have experienced it live and undistorted. Distortion matters less if listeners have not heard the processed sounds in a studio. Even played softer than live SPL, distortion causes complaints of fatigue, and “The sound is too loud.” Harmonically-related THD may be forgiven, but not accompanying burr-sounding IMD and buzzing MTD.

Fig.4 – (Derived from Fig.3.) Listening to a fundamental at lifelike 85SPL, 2nd & 3rd distortion harmonics are perceived louder than a measured %THD implies. For a 60Hz fundamental, a measured 3% THD is perceived as 10%. At 30Hz, 3% sounds like 25%. Driver distortion is mechanical, post crossover.

4 “Diverging” is especially apparent in the VLF range of the SW by counting vertical divisions between contours.

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We’ve seen how a musical fundamental of 30Hz is inaudible until its sound power reaches 60dBSPL. But an equal 2nd harmonic at 60Hz is audible far softer, since 32SPL, and its 90Hz 3rd harmonic softer still, since 22SPL. 5 These conditions are graphed as each pair of in Fig.3. Consider a musical diminuendo falling in SPL. The fundamental diminishes faster than its higher harmonics, as it fades manifesting as unnatural brightness that is bogus tone color (timbre). The total harmonic distortion (THD) mimics a higher % than measured. In Fig.4, a 60Hz tone’s THD measuring 3% can sound like 10%. At 30Hz, 3% THD sounds like 25! Artifacts of harmonic distortion can be audible even after the ancestor fundamental is no longer heard! 6 Intermodulation Distortion (IMD) requires two tones, even if one or both are too soft to be audible! G1 at 49Hz and its 7th F2 at 87Hz create a difference of 38Hz and a sum of 136Hz that we direction-find, diverting attention undesirably to the SW. Between music’s many tones, all combinations may produce “burr”-sounds of IM and buzzing multi-tone distortion (MTD). Most active SW’s do not high-pass filter (HPF) signals passed to main speakers, thereby stimulating ruinous MTD, as shown in Fig.5.

Fig.5 With no SW, main speakers can have buzzing multi-tone distortion (MTD) of 30% as measured in red caused by VLF. Reduce MTD to ~20% using bass management that HPF-ers main speakers above 100Hz, or reduce MTD to ~7% above 200Hz. Data Erin Hardison https://youtube.com/watch?v=i1sa50hzEcM.

A good subwoofer reproduces clean low bass AND cleaner main speaker sound The topic of room acoustics could fill a library. Suffice to say absorptive treatment especially below ~300Hz is thick and expensive. Alternatively, placing subwoofer(s) where mains can’t go effectively position-EQ’s a room’s VLF at more listeners’ seats.

More directional higher frequencies render sound images via the main speakers.

But we can also direction-find a SW in error by its distortion. Heard from two angles instead of one tears auditory events away from main speakers. Bass management 5

Most musical sounds exhibit harmonics that can be equal significantly higher in SPL than their fundamental.

Organ builders for centuries have played this “trick” to save cost of 32ft pipes. A “Resultant” relies on listeners’ “filling-in” missing fundamentals, hearing only 2nd & 3rd harmonics with pipes ½ & ⅓ as long. (Also boom boxes.)

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redirects to the SW tones lower than its crossover frequency. But generated after bass management so not filtered by it are the SW’s own distortion harmonics and IMD\MTD sums up-spectrum. Some audiophiles decry using a SW when its distortion smears what they term “soundstage.” They have yet to experience clean low bass.

AVR bass management also high-pass filters signals to the main speakers when set to “small,” reducing mains’ distortion, as in Fig.5. But SW distortion also masks main speaker sounds. Masking is a loud tone concealing softer usually higher pitch tones within its critical band. Popular music spawns a lot; less with dynamic soft-as-wellas-loud acoustic music or movies. In Fig.7L, no masking occurs in the single critical band of VLF if the masking artifact is inaudible up to ~70SPL,7 equivalent to a low 3% distortion subwoofer at 105SPL. Or louder instantaneous peaks that are fleeting, e.g. from the LFE. Faced with all these issues, savvy enthusiasts use a low distortion SW. Deep bass Loudness is affected by playback volume Many recording, mixing, mastering, and motion picture studios respect a listening level standard for monitoring of 85dBspl. This maximum average reference coincides with the OSHA exposure to workplace noise over an 8hr shift. Except for the abusive level compression of popular music and broadcasting, lifelike audio needs up to 20dB added “headroom” for dynamic peaks, now a full scale (FS) SPL of 105, as used here.

And 10dB more for explosions in the sparsely used LFE channel brings movies to 115.

While some play their music louder, most consumers play softer than the standard, at ~75dBspl. This somewhat relieves migraines due to compression & distortion. Per Fletcher-Munson (ISO226), listening at 75dBspl weakens deep bass. Fig.6 illustrates how playing at 75dBspl, 40Hz needs 6dB of boost for bass intended by the musicians & producers. Or to attenuate 40Hz by 8dB playing at 95dBspl, unless addicted to it.8

Fig.6 – Listening at SPL different from the equalization baked into the recording by its producers.

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L. Fielder & E. Benjamin “Subwoofer performance…” 1987;

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Early audio equipment featured Loudness compensation for users to adjust any level for proper tone color. p6 of 10 - Subwoofer Camp

F. Toole “Sound reproduction…” 4th ed. p96.

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No masking below threshold of 70SPL at 50Hz

Fig.7 – L: Fielder & Benjamin found no masking of main speaker sounds for up to 70SPL of a low distortion SW. R: block diagram of a “binaural bass manager” (BBM) to redirect VLF in 2.0 stereo or 5.1 via low pass filters (LPF) to two (or four?) SWs along left & right walls. The BBM high pass filters (HPF) main channel outputs to optimize SW “splicing” with mains and reducing mains’ multi-tone distortion (MTD).

How to enjoy spatially real-sounding stereo deep bass at home (or mixing studio) Since the 1980s, much enjoyment awaits in most digital recordings that are found to contain “stereo bass,” proven perceivable to 45Hz [R. Miller 2005 9 ]. New since stereo’s early days, when VLF was kept monophonic to avoid a stylus jumping the groove. Captured by a microphone placed at the critical radius of a fine performance space, the energy of the sum of myriad reflected “sonic events” equals the energy of the direct sound that travels by line-of-sight from each instrument. Deeper in the hall, most attendees receive more indirect energy than direct. Enroute at the speed of sound, the room reflections travel along different pathways, each with its own “flighttime.” Finally the sounds arrive at various times as a sum at each ear or mic channel.

When played or sung with vibrato (frequency modulation), each instrument’s or voice’s sounds are produced in time sequence, and thus are at different frequencies.

Acoustic instruments that with vibrato produce binaural VLF include bass viols, bassoons, bass drum, organ, contra-anything. All augmented by reverberant concert hall acoustics. Or electric sources in a large recording studio, notably the spinning Leslie speaker of a Hammond B-3. What arrives at any instant at each ear and each microphone is a unique mix of many frequencies – a “chorus.” Artificial reverberation can simulate the effect; of all music content, live or recorded, it is most engaging.

Say a bass plays vibrato at 90Hz shimmering with 91Hz. The 90Hz version arrives after reflection from a side wall at the same instant the 91Hz sound arrives directly at an ear or mic. One instrument heard as two, then three from another reflection, etc.

Or at ¼ of an orchestra’s total power, a 40in bass drum’s “batter head” when smacked produces an attack at say 35Hz, its “resonant head” sustains as tuned at say 32Hz. The profusion of these sonic events arrives simultaneously at each listener’s ear or 9

“Physiological and content considerations for a 2nd LF channel…” AES, ASA, CAA, VDT demo & 2005 paper at www.filmaker.com. Most movie and acoustic music recordings contain stereo deep bass that is lifelike in spatiality, but often not popular music when electric bass guitar and kick drum are panned center (mono). p7 of 10 - Subwoofer Camp

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mic channel, each source a chorus in itself. As in live hearing, it’s crucial that these sounds arrive from the same hemisphere. Thrilling when heard in a concert hall live... … or recorded. Using passive SWs along L & R side walls, a binaural bass manager (BBM) is inserted between control and power amplifiers, as shown in Fig.7R. Sadly few new consumer BBMs survive, e.g. an Outlaw Audio ICBM, but professional units can be found (e.g. a Sound Technology 65 BBM). Or feed two active SWs by an AVR’s respective L or R speaker or line level outputs, while feeding SL or SR to each side’s other input (mixed internally). Again, active SWs may not HPF signals, as in Fig.5.

There’s a relatively simple DIY method that can both approximate HPFing signals to mains AND provide spatial deep bass by a simplified BBM. It works with active main speakers and two active subwoofers along side walls. Feed the Left (and Surround Left) channels at line level to the L & R inputs of the SW on the left, and the Right (and Surround Right) channels to the SW on the right.10 Additionally, insert a polypropylene capacitor Cc at the input of each corresponding main speaker. The value of Cc in µF (micro-Farads) is determined by the input impedance of each main speaker, and the desired crossover frequency. For an 80Hz filter and resistive input Rin of 10kΩ, capacitor Cc is 0.2µF. Other values of Rin & Cc inversely vary the HPF’s fc. The calculation is Cc = 1 / (2π fc Rin).

Takeaways from “Subwoofer Camp” Subwoofers should be heard but not seen. But subwoofers can be ‘seen’ (localized) by their audible distortion. Unseen are the silenced sounds of main speakers masked by strong broad-range SW distortion. However a SW without Bass Management HPFing for main speakers causes mains compression (semi-clipping) and MTD as in Fig.5.

Lifelike sound requires linearity. Loudspeakers, excited simultaneously with myriad tones across the full range of sound power levels (SPL), generate more distortion than any other link in the audio chain, from mic to ears. Consumer SW makers strive for less than 3% THD; professional models less than 1%, plus IMD & MTD. SW distortion is mechanical, post crossover electronics, so distortion artifacts are not filtered by it.

For best sound, do not push a SW to overload, and share the load with two (four?).

A single subwoofer channel, being mono regardless of how many SWs are driven in parallel, loses the stereo cues present in most music recordings & movies. Binaural Bass Management (BBM) preserves stereo deep bass difference in each hemisphere.

While some prefer the “brighter” sound resulting from distortion, especially benign 2nd harmonic, distortion is anathema for listeners who have remembered references of live tonality. As presented, distortion is “inflated” as low frequency fundamentals fade and higher frequency distortion artifacts take on a higher percentage. Not using the knowledge in this brief, audio enthusiasts may not fully enjoy clean deep bass.

The author has enjoyed 60+ years of recording & mixing music to dramatic features, and as a studio, cinema, and home theater engineer who shares expertise with clients and readers of his publications at www.filmaker.com. Reputable loudspeaker makers devote considerable resources to reducing distortion. Are they foolish for doing so?

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Appendix – not an ephemeral shoppers’ guide, but a reference for subwoofers at four price points The technically-minded find “a picture (graph) worth 1,000 words.” Frequency decreases leftward; SPL or % harmonic distortion are on vertical axes.11 This paper advocates users consider distortion along with frequency response: both are plotted in these examples. Fig.8→ compares the four SWs below, showing acceptable THD by application in the useful octave 40~80Hz. All but the “small home 10in” are at high SPL for LFE, so THD would be lower at average level. “Spinorama” reviews by Amir (Audio Science Review) or Hardison (Erin’s Audio Corner) are mostly of main speakers, but they usually recommend using subwoofers for reasons given throughout this paper.

Low-priced active 10in SW 95SPL for small home stereo or THX-certified home theater (THD <5% at 110SPL PORTED, 100SPL SEALED 22~80Hz; THD <3% at 95SPL ¼-space, est’d )

Fig.9 - From manufacturer’s data, a budget SW well-controlled at 2% of more objectionable 3rd harmonic distortion down to <20Hz. Less objectionable 2nd HD dominates THD at 4% 22~80Hz .

Mid-priced active 13in SW 105SPL for medium home stereo or THX-certified home theater (THD 3~9% at 117SPL 30~100Hz Ported\sealed; THD <2% at 105SPL ¼-space, est’d )

Fig.10-L: Depicted in the banner p1, a long-excursion driver VLF-optimized (data not from manufacturer).

C: “Highly rated” (based on “acceptable THD 20%”). R: Ported (higher 20Hz SPL) or sealed (rings less).

Data courtesy James Larson - https://www.audioholics.com/subwoofer-reviews/monolith-13201d-thx-ultra 11

105SPL is digital full scale 20dB above standard 85SPL, or home listening at 75SPL with LFE peaks at +10dB. p9 of 10 - Subwoofer Camp

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Mid-priced passive 18in SW max 130SPL for large home cinema, professional music PA system (THD <2.5% at 115SPL ≥35Hz ½-space; <0.5% at 105SPL ¼-space with enclosure, est’d)

Fig.11-L: Even at 115SPL for LFE, this driver “bare” at 70Hz exhibits 1% of the more musical 2nd harmonic, 0.3% of the less musical 3rd harmonic (raised 20dB, the distortion % is 1/10 of the -20 & -30dB ratios shown).

At moderate home levels, distortion drops greatly to <0.5% at 30Hz. R: Factoring in fundamentals boosted by a ported enclosure, response is flat -3dB at 40Hz with no EQ, flat to 30Hz with mild 3dB EQ. [Data: JBL 2268.]

High-priced passive 18in SW max 140SPL for THX-certified cinema, mixing stage, largest home cinema (THD <1.5% at 116SPL ≥29Hz ½-space; <0.3% at 105SPL ¼-space with enclosure, est’d)

Fig.12 – L: This driver “bare (without support of a ported enclosure) reaches 1/3 octave below that in Fig.11, but with enclosure at R the SPL output on the floor is –3dB at 22Hz without EQ. Add +6dB output when also <¼ wavelength from one wall. For +5dB more output, couple 2+ dual-driver JBL 5628, each driven by a 2kw amplifier. Cinema SWs cross over at 80Hz, carry LFE up to 120Hz, but are monophonic. [Data: JBL 2269.] _____________ Dissemination of any of this content beyond brief attributed quotations or a review is prohibited without the author’s expressed permission in writing. More technical papers and books by Robin Miller are at www.filmaker.com p10 of 10 - Subwoofer Camp

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