The five biggest audiophile mistakes: measurements, loudspeakers and rooms
The Five Biggest Audiophile Mistakes: Measurements, Loudspeakers and Room
Five ideas that sound reasonable and yet lead to choosing and setting up a playback system badly. This report explains why they fail, what evidence corrects them and how to apply that correction in a domestic room.
Starting point: The 5 Biggest Audiophile Mistakes, by Erin's Audio Corner. Case study: Børresen X3 measurements, with data on Spinorama and cross-checked in the Hi-Fi News laboratory.
The five mistakes are not absolute lies but half-truths turned into universal rules. The fault lies not in the intuition but in applying it without context. The report explains why they fail, what evidence corrects them and how to apply that correction in a domestic room. The discipline of evidence labels allows measured data to be distinguished from derived calculation and from causal explanation, and leaves uncertainties documented rather than forcing conclusions.
METHODOLOGICAL NOTE — HOW THIS REPORT WAS PRODUCED
Methodological note
This report was produced with cross-auditing by several AI tools (DeepSeek, Meta, ChatGPT, Claude) and manual verification of primary sources by the author. The tools were used for cross-checking and error detection; the final claims are the author's responsibility. Agreement among several AI tools does not amount to independent verification: they may share biases or starting errors. Traceability rests on the cited primary sources, not on the number of tools that agree.
What the tools contributed. They cross-checked calculations, detected inconsistencies and proposed corrections. Those incorporated include: acoustic summation and voltage sensitivity, the distinction between on-axis response and PIR, the effect of cable resistance, nuances about valve amplifiers, the scope of time-windowed measurement, inclusion of Re, the minimum-phase/non-minimum-phase distinction, the EPDR context, the nearfield warning, the MMM method, valve/solid-state differentiation, vertical directivity and lobing, FDW, the RT60 myth in multisub and thermal compression. Details are in Annex D.
What was discarded. Corrections whose formulas could not be reproduced or that exceeded the available evidence were discarded. Full details — corrections incorporated, discarded and their status — are in Annex D.
What was corrected after the cross-audits. The audits identified conceptual errors and over-strong labels, corrected in the text: double counting of Re, the divider table, EQ and modal decay, the nearfield warning, EPDR out of tuning, Q-cycles, THD and pair matching, phase and current, loudspeaker/room separation, RT60/EDT, PROBABLE/HYPOTHESIS consistency and the cable effect. Rev. 2.1 additionally corrects the burn-in label, the biwiring formulation following Lesurf's model, the X3 THD with values per frequency, and the dating of the price. Rev. 2.2 adds the geometric nuance of SBIR with active filtering and a subwoofer in III.1.2, with the boundary-gain counterpart and a cross-reference from I.3. Rev. 2.3 reorganises navigation cross-references with the Acoustic calculators page (V8.5.1): sidebar converted to "Links" (Acoustic calculators + Index of reports), direct links to the tools in the bridge callout and in the sections that use them, and validation of the existing links in Annex C against the new anchor architecture. Details in Annex D.
Additional sources consulted and discarded or qualified. Popular audio sources have been reviewed: The Ten Biggest Lies in Audio and What I have learned after six decades in audio by Peter Aczel (expert opinion, cited as OBSERVED); the Audiocostruzioni article on beginner mistakes (popular, cited as REPORTED-EXT); the PCP Audio page on the V1 and V2 loudspeakers (workshop narrative without measurements, cited as OBSERVED); and the Wikipedia entry High fidelity (tertiary source, cited as REPORTED-EXT). Only elements that provide verifiable nuances have been incorporated — burn-in, biwiring, port location, sensitivity per way, the definition of hi-fi, the logical nuance of ABX — and dogmatic or anecdotal claims without control have been discarded. The biwiring analysis also draws on the model by J. C. G. Lesurf (University of St Andrews), which quantifies the electrical variation and its dependence on cable resistance. Details in Annex D and Annex E.
Structure of the annexes. A (labels), B (formulas and glossary, with FDW and MSO), C (REW protocol, including FDW in step 5b), D (uncertainties and discrepancies, including thermal compression, burn-in, biwiring and THD by frequency) and E (references and credits). The Schroeder frequency of the example is quoted as ≈192 Hz for the 4.8 × 3.6 × 2.5 m room and T60 = 0.4 s; it is a statistical estimate, not an abrupt boundary. The SBIR figure of ≈85.8 Hz corresponds to the simplified model with d = 1 m and c = 343 m/s.
How it was verified. The Børresen X3 data were cross-checked against the published primary sources (Erin's Audio Corner, Hi-Fi News, Spinorama). Explicit calculations were reproduced with the stated formulas. Discrepancies between sources are documented in Annex D rather than forcing an unjustified reconciliation. Evidence labels indicate the level of support for each claim.
The central idea. None of the five mistakes is an outright lie; they are half-truths turned into universal rules. The fault lies not in the intuition but in applying it without context.
The five mistakes and their trap:
- Price: Believing that "the more it costs, the better it sounds".
- Anechoic vs. room: Believing that "the loudspeaker's curve is what I hear".
- Placement: Believing that "position is an aesthetic detail".
- Drivers: Believing that "more cones mean more sound".
- Measurements: Treating them as dogma ("if it measures well, it sounds well") or as decoration ("if I like it, the curve doesn't matter").
The report has five parts and five annexes. Depending on what you are looking for:
- If you came for the five mistakes → Part I (15-20 min). Each mistake ends with a "X3 case" callout summarising the relevant data and pointing to Part II.
- If you came for the Børresen X3 → Part II (dossier, 10 min). Essential data, verdict and technical details.
- If you came for the theory (modes, SBIR, PIR, DF) → Part III (reference). All the "why" in one place.
- If you came to replicate measurements → Part IV + Annex C. All the "how" in one place.
- If you came to audit sources → Annex D + Annex E.
This report develops the formulas for SBIR, axial modes, Schroeder frequency, sensitivity, power/SPL, critical distance, damping factor and source summation in Part III and Annex B. Those formulas are also available as interactive calculators on a separate page: Acoustic calculators →. Each result carries a CALCULATED label and its scope note, as in this report.
Direct links: 1 · SBIR + boundary gain·2 · Modal explorer·3 · Sensitivity + dB·4 · Power / SPL·5 · Damping factor·6 · Q_res·7 · Delay, phase and summation·8 · Dc + Sabine·9 · Time window.
PART I — THE FIVE MISTAKES
Each mistake follows the same scheme: why the intuition seems reasonable, what physical mechanism refutes or qualifies it, what concrete evidence supports it and what practical consequence it has for anyone about to choose or adjust a system. Each section ends with an "X3 case" callout summarising the relevant Børresen X3 data and pointing to Part II for the detail. The detailed physics (PIR, SBIR, DF) is developed in Part III; the evidence labels, in Annex A.
I. The five mistakes
I.1 Mistake no. 5 — Confusing price with performance
Why the intuition seems reasonable. In many products, price correlates with quality: a more expensive car usually brakes better, a more expensive watch usually lasts longer. Transferring that logic to audio seems natural: if a loudspeaker costs five times more, it should sound five times better — or at least better. The intuition fails because the price of a loudspeaker is not primarily determined by its acoustic quality, but by a combination of factors including materials, labour, finish, brand, distribution and margin.
What actually determines the price. A high-end loudspeaker may use drivers made of exotic materials, machined aluminium cabinets, leather finishes or multi-layer paint, and a manufacturing process in countries with high labour costs. All of that makes the product more expensive without guaranteeing a flatter frequency response, more coherent directivity or lower distortion. Price also buys aesthetics, durability, after-sales service and social prestige. None of those attributes is "sound", but all are legitimate if the buyer values them.
What the evidence says. A loudspeaker's frequency response can be measured accurately in an anechoic chamber or with nearfield scanning systems such as the Klippel NFS. That measurement is independent of price. When loudspeakers from very different price brackets are compared with the same method, cases appear in which the more expensive product shows tonal irregularities that the cheaper one does not. That does not prove the cheaper one is always better, but it does show that price is not a reliable predictor of neutrality.
The specific case that motivates the video. The author compares a Børresen X3 at ~$11,000 per pair (price quoted in the video, October 2026; US market) with a Wharfedale Super Linton at ~$3,000 per pair. According to his description, the X3 shows a peak near 80 Hz of about 7 dB and several consecutive irregularities between 2 and 3 kHz, and he prefers the Wharfedale. That is the author's observation, not an independent laboratory measurement: the Erin and Hi-Fi News data used in Part II allow part of that picture to be cross-checked — bass emphasis, crossover notch, midrange depression — but not the complete set nor the direct comparison with the Super Linton. The X3 price is historical and market-dependent; Hi-Fi News documents a subsequent UK reduction from £10,000 to £8,000 per pair. The ~$11,000 figure should not be interpreted as a universal current price.
I.2 Mistake no. 4 — Confusing anechoic response with in-room response
Why the intuition seems reasonable. If a loudspeaker measures flat in an anechoic chamber — a room without reflections — it seems logical to assume it will sound flat in any room. The intuition fails because a domestic room is not anechoic: walls, floor, ceiling and furniture reflect sound, and those reflections reach the ear with delays and levels that modify the perceived tonal balance. Moreover, at low frequencies, the room's dimensions impose their own modes (resonances) that can reinforce or cancel particular notes.
What happens physically. The sound reaching the listener is a sum of the loudspeaker's direct radiation and the reflections from surfaces. The anechoic response describes only the former. The in-room response includes both. The difference between the two depends on the loudspeaker's directivity — how much energy it emits towards the walls at each frequency — and on the room's acoustic properties. A loudspeaker with a flat on-axis response but irregular directivity can sound very different in two different rooms, even though its anechoic curve is identical.
How in-room response is estimated. Standard CTA-2034 defines a method for predicting in-room response from a weighted combination of the listening window, early reflections and total sound power: the PIR (Predicted In-Room Response). It is a normalised estimate derived from the loudspeaker's radiation curves: it does not simulate a specific domestic room nor calculate the response of a real room. The full methodology, with weights and limitations, is in III.1.3. The room's own modes, which the PIR does not predict, can be explored with the 2 · Modal explorer.
The ±60° preference proposed in the video. The author states a preference for loudspeakers with intermediate horizontal dispersion, around ±60°, over narrower or wider designs. That is not a universal optimum angle nor a boundary that guarantees one image or another: directivity varies with frequency and design, and ±60° is not a figure that by itself summarises angular behaviour. Assessing dispersion requires looking at the window, off-axis, vertical and sound-power response curves, not a single figure.
I.3 Mistake no. 3 — Not optimising placement and toe-in
Why the intuition seems reasonable. Loudspeaker placement is often treated as an aesthetic detail: where they look good, where they don't get in the way, where they fit with the furniture. The intuition fails because position determines two things that directly affect the sound: the distance to the walls, which modifies the interference between direct and reflected radiation, and the orientation angle, which changes the response reaching the listener directly and the level of early reflections.
What happens physically. When a loudspeaker is close to a wall, the direct and reflected sound reach the ear with a small delay. That delay produces interference that, depending on frequency, adds or subtracts. In the simplified geometric model, the first null appears at f = c / (4d). With the woofer 1 m from the front wall, the first null falls at 85.8 Hz. This phenomenon is called SBIR (Speaker Boundary Interference Response). The formula, the distance table, the geometric diagram and the model's limitations are in III.1.2; the interactive calculator with editable distance and boundary gain is at Acoustic calculators → 1 · SBIR + boundary gain.
Toe-in and asymmetry. Toe-in is the angle at which the loudspeakers are aimed at the listening position. Changing it modifies the direct response and the level of side reflections. In a symmetrical room, symmetrical toe-in is usually the logical starting point. In an asymmetrical room — with one wall closer than the other, or with a piece of furniture that reflects differently — aiming the two loudspeakers differently can stabilise the mid-treble balance and centre the image better. It is not a universal rule, but it is a possibility worth trying.
The case described in the video. The author describes a client with a stereo image off-centre despite equalisation, solved by aiming the two loudspeakers differently: one almost straight at the listener and the other with less inward angle. That is an individual experience, not a demonstration that asymmetry is always superior; to evaluate it one would need to measure both channels, check the stability of the phantom centre and repeat the listening with matched levels. Geometric symmetry remains a good starting point, not an absolute obligation when the environment is asymmetric.
I.4 Mistake no. 2 — Assuming more drivers equal better sound
Why the intuition seems reasonable. More cones look like more capability: more radiating area, more distributed excursion, more possible level. The intuition fails because sound quality does not depend on the number of drivers, but on how they are integrated. A system with many poorly integrated cones can sound worse than a well-designed two-way.
What happens physically. Adding drivers does not increase sensitivity on its own. Three things should be distinguished. First, acoustic summation: two identical, coherent, in-phase sources can produce up to +6 dB of sound pressure in a specific direction. Second, sensitivity per unit of power: under ideal conditions and with a comparable configuration, doubling sources can give around +3 dB of efficiency, but the actual gain depends on how total power is distributed, on the electrical connection, on the impedance of the combination and on acoustic coherence. It is not a rule that allows the sensitivity of any cabinet with two woofers to be deduced from that of a cabinet with one. Third, voltage sensitivity: it also depends on wiring and electrical load, and cannot be deduced from the number of cones alone. The separation between radiation centres affects angular summation and lobing; as separation grows relative to wavelength, the possibility of pronounced angular interference and lobing increases. Moreover, more drivers imply more transitions between ways, greater filtering complexity and more opportunities for integration to fail. The 7 · Delay, phase and summation tool allows the coherent, incoherent and vectorial cases to be explored with a given phase shift.
I.5 Mistake no. 1 — Using measurements as dogma or dismissing them
Why the intuition seems reasonable. Measurements look objective: a curve is a curve. The intuition fails in two opposite directions. On the one hand, believing that an isolated figure is a verdict: if a loudspeaker measures badly in one parameter, it is dismissed outright. On the other, believing that measurements say nothing relevant: if it sounds good to the ear, the curve doesn't matter. Both positions oversimplify.
What measurements say and what they do not. Complete anechoic measurements — frequency response, directivity, distortion, compression — contain perceptually relevant information. Normalised anechoic measurements allow preference indicators to be calculated that have shown high correlations with the results of certain controlled listening tests. That predictive capacity depends on the model, the data and the validation conditions; it does not turn a score into an absolute verdict. A measurement does not say how a loudspeaker will sound in a specific room, with a specific musical programme and at a specific level. Controlled listening — with matched levels — remains necessary to assess the perceptual relevance of a technical difference. The specific levelling methodology is detailed in IV.2.
Three concepts not to be confused.
| Concept | What it assesses |
|---|---|
| Electroacoustic fidelity | The extent to which the system reproduces the signal without introducing relevant alterations. |
| Subjective preference | Which reproduction a listener likes more under given conditions. |
| User satisfaction | The combination of sound quality, aesthetics, ergonomics, reliability, price and context of use. |
They need not coincide. A reproduction with emphasised bass may please more than a more neutral one without that proving the emphasis is more faithful: it proves that preference and fidelity are different variables. And a loudspeaker that measures well may not satisfy someone looking for a particular spatial dispersion or tonal balance.
The percentage figure proposed in the video. The video author suggests a certain proportion for the weight of measurements in the evaluation. It is a personal estimate, not a demonstrated result: it does not specify which variables are weighted or how the percentage is calculated. The report does not adopt universal figures; what is defensible is that measurements allow problems of response, directivity, extension or distortion to be ruled out quickly, and products to be compared without relying only on subjective impressions. The detailed critique of contribution and budget percentages is in Annex D.8. (ND as a universal figure.)
The three technical concepts most often misinterpreted.
- Sensitivity: 1 W is not 2.83 V. Comparing figures without stating the reference produces errors of 3 to 6 dB, of the same order as many differences discussed as audible. The conversion table is in Annex B; the interactive converter is at 3 · Sensitivity + dB. The X3 case illustrates it in II.1.
- Decay: time-domain representations, including burst decay where applicable, can make it easier to interpret resonances or transient behaviour already visible in the frequency response, but they are not necessarily independent evidence of them. In a minimum-phase system, the time response and the frequency response are related, so burst decay should not be treated as independent proof of an anomaly already visible in magnitude. The development is in II.4; the second-order resonator model is at 6 · Q_res.
- Impedance: an impedance peak does not automatically identify its physical cause. It may reflect a driver resonance, an interaction with the cabinet or ports, or a filter characteristic. Attribution requires relating impedance to nearby acoustic responses, vibration measurements, filter data and controlled tests. The X3 case illustrates it in II.4.
PART II — THE BØRRESEN X3 CASE (DOSSIER)
Dossier of the case study. Readers who came for the X3 will find the essential data, the verdict and the technical details here. Room theory and electronics are in Part III; the measurement protocol, in Part IV. Uncertainties and discrepancies are documented in Annex D.
II. The Børresen X3 case
The X3 is used as a case study because published measurements from two independent laboratories are available: Erin's Audio Corner (with Klippel NFS, a nearfield scanning measurement system) and Hi-Fi News. For directivity, Spinorama derives from Erin's data and does not constitute a second independent laboratory.
II.1 The essential measurements
Both laboratories agree on the essentials: bass emphasis around 80 Hz, roll-off below ~50 Hz, midrange depression and a ~6 dB notch centred on the crossover (~2.5 kHz) (a notch is a narrow depression in the response). Hi-Fi News adds a midwoofer cone mode near 2 kHz and a general ~3 dB increase when the ribbon tweeter comes in, which together with the crossover notch explains the ±5.0/±5.3 dB on-axis errors. The catalogue's 35 Hz–50 kHz extension does not equate to a response within tolerance, but the laboratory publishes an extension of 25 Hz at −6 dB relative to 200 Hz: the loudspeaker goes lower than the catalogue suggests, albeit with the tonal imbalance described.
Sensitivity. The manufacturer states 88 dB/1 W/4 Ω; Erin publishes an average of 85.9 dB (300 Hz–3 kHz, 2.83 V/1 m); Hi-Fi News publishes 89.2 dB at 1 kHz, 87.8 dB average and 86.2 dB IEC, all at 2.83 V/1 m. Conversion between conventions depends on nominal impedance (table in Annex B; converter at 3 · Sensitivity + dB). All three figures are retained with their stated condition; the exact reconciliation between methods remains ND.
| Source | Sensitivity | Stated condition |
|---|---|---|
| Manufacturer | 88 dB / 1 W / 4 Ω | Per commercial specification |
| Erin / Spinorama | 85.9 dB | Average 300 Hz–3 kHz, 2.83 V/1 m |
| Hi-Fi News | 89.2 dB / 87.8 dB / 86.2 dB | 1 kHz / average / IEC, 2.83 V/1 m |
II.2 Directivity, listening angle and lobing
The most serious objection to the X3 analysis is not about the room, but about the intended listening angle. Hi-Fi News shows that at ±15° the response error drops from ±5.0/±5.3 dB to ±4.1 dB, and that the crossover notch and several resonances are reduced. The manufacturer specifies toe-out: the axes of the two loudspeakers cross behind the listening position, not in front of it. The front on-axis measurement therefore does not correspond to the intended listening axis.
The cost of the angular improvement. The improvement at ±15° is not free: Hi-Fi News also publishes a ~1 dB sensitivity loss at that angle relative to on axis. Tonal balance improves at the cost of a slightly lower level.
Vertical directivity and interference lobing. The angular objections above focus on the horizontal plane, but the physics of multi-way systems imposes severe constraints in the vertical plane. The X3 uses a crossover filter to make the transition between the midwoofer and the ribbon tweeter around 2.5 kHz. In that crossover region, both drivers radiate the same signal simultaneously.
What happens physically. Because of the real physical distance between the acoustic centres of the two motors, the emitted waves reach the ear with subtle path differences if the listener deviates from the optimal vertical axis. This generates constructive and destructive interference phenomena (lobing).
The impact on the X3. The ~6 dB notch measured on axis by Hi-Fi News indicates a native challenge in the filter integration. Off the vertical axis, it is PROBABLE that this spectral cancellation will change or shift its centre frequency, altering the tonal balance in the presence region if the listener's ears end up above or below the design axis. The exact degree of this worsening depends on the filter slope and the temporal alignment at the crossover, not only on vertical displacement.
Practical consequence. Vertical directivity suggests an adjustment of listening height. Aligning the tweeter axis with ear height at the listening position can be achieved by tilting the baffle, if the geometry of the cabinet and base allows it, or by adjusting seat height. Decoupling spikes are one possible means of tilting the cabinet, not a universal solution nor a guarantee of eliminating the notch: the result depends on the filter design and the complete vertical response. It should be described as a geometric adjustment to be verified, not as a demonstrated solution for this model without a specific vertical measurement. (OBSERVED as a geometric possibility; no specific vertical measurement of the X3 is available to demonstrate elimination of the notch.)
II.3 Operational verdict
- It is not neutral: two independent laboratories agree on the bass emphasis around 80-85 Hz, and Hi-Fi News additionally documents a ~6 dB notch at the crossover and a midrange depression. The possible reinforcement or attenuation of the observed emphasis depends on the room's dimensions, the loudspeaker and listener positions, and the boundary conditions. Without those data and without in-room measurements, any specific scenario must be presented as a hypothesis.
- It has a characteristic sonic presentation: Hi-Fi News describes the bass tuning as characteristic of the model and considers that its priorities do not correspond to a flat axial response. That laboratory interpretation is compatible with a deliberate design choice, but it does not by itself prove the manufacturer's intention nor that each specific irregularity — in particular the crossover notch — is intentional. A buyer seeking neutrality will find flatter alternatives for less money; one seeking that marked bass sound and willing to work on the room and EQ has a product with a rationale.
- The right decision depends on whether the buyer wants neutrality or wants that specific sonic presentation, and on whether they can control the room.
The bridge between 500 Hz, 2 kHz and 2.5 kHz. The measurements describe irregularities in three regions: temporal persistence around 500 Hz in Erin's graph, a midwoofer cone mode near 2 kHz and a pronounced depression at the crossover around 2.5 kHz in Hi-Fi News measurements. The laboratory also notes a difference between units of up to 1.9 dB in that region. Taken together, these results justify examining with particular attention the behaviour of the midwoofer path and its integration with the tweeter. Without individual driver responses, the filter schematic and comparable measurements from both laboratories, it cannot be asserted that the four indications share a physical cause. The association between them remains a HYPOTHESIS.
II.4 Decay, impedance and causality
Temporal decay. Erin describes a persistence of 6-8 cycles at −20 dB around 500 Hz in his burst decay graph, against an orientative expectation of 2 cycles at the same threshold. At 500 Hz one cycle lasts 2 ms: 6-8 cycles are 12-16 ms. It is a description of the graph, not an autonomous measurement of the driver's Q. The persistence is an indication worth examining; the "2 cycles" reference is an orientative comparative criterion, not a standardised limit.
Loudspeaker decay and room reverberation. Burst decay and waterfall show how the measured response evolves over time and allow resonances or persistence in particular bands to be located. RT60 and EDT, for their part, describe the decay of sound in a room and are estimated by bands from a suitable impulse response. They are not equivalent quantities. To characterise the room, REW needs an appropriate impulse measurement, without a short time window. The protocol is in IV.1 and in Annex C.
Minimum phase and decay. Decay is a time-domain representation of the system response and is not, by itself, an independent measurement of the frequency response. Comparing measured phase with reconstructed minimum phase allows excess-phase components to be identified. The fact that a loudspeaker has a bass-reflex port does not by itself imply that it is non-minimum-phase: if the port delay is small relative to the period, the system may remain approximately minimum-phase. The non-minimum-phase label must be derived from the phase comparison, not from the enclosure type.
Impedance and EPDR. Hi-Fi News publishes a minimum impedance of 3.1 Ω at 20 Hz, with the modulus rising with frequency and reaching a maximum of 20.3 Ω at 1.55 kHz. The minimum EPDR (Equivalent Peak Dissipation Resistance) is 1.1 Ω at 20 Hz and 1.5 Ω at 55 Hz, and the laboratory notes that those minima fall outside the passband of the bass system. Its literal conclusion is that the X3 "is not a particular challenge to drive".
Context of the electrical minima. The EPDR minima of 1.1 Ω at 20 Hz and 1.5 Ω at 55 Hz lie well below the port tuning, around 87 Hz. In that region, the port's acoustic contribution decreases and cone excursion may increase. The effective demand on the amplifier depends, however, on the signal reproduced, the level, the complex impedance and the current capability of the output stage. Hi-Fi News concludes that the X3 does not represent a particular driving challenge; that laboratory assessment must be kept separate from any extrapolation to specific amplifiers. (PROBABLE as physical context; CONFIRMED as the laboratory's assessment.)
Reactive phase. The laboratory also publishes phase: −25° at 3.4 kHz and +54° at 69 Hz. Complex impedance matters because modulus and phase angle together determine the electrical load seen by the amplifier. At equal applied voltage and impedance modulus, the phase angle does not by itself increase the magnitude of the current, but it modifies the relationship between voltage and current and can raise instantaneous dissipation in the output devices. EPDR attempts to express that demand as an equivalent resistance. The published angles describe the load, but they do not allow a specific stage to be declared problematic without knowing its capabilities.
Speakerranking, summarising Erin's measurements, states that the measured minimum impedance stays at about 6.1 Ω above 80 Hz. That figure refers to a different band and does not contradict Hi-Fi News's 3.1 Ω minimum at 20 Hz: in the useful band, the load is comparatively benign. It is retained as a secondary REPORTED-EXT, pending direct verification in Erin's curve.
Harmonic distortion. Hi-Fi News publishes THD of 0.3% at 100 Hz, 0.2% at 1 kHz and ~3.5% at 10 kHz, at 90 dB SPL/1 m. In the text, the laboratory describes distortion as "a high 3-4% above 8 kHz". Both formulations are compatible: the first gives point values at specific frequencies; the second describes a frequency region. No complete THD-versus-frequency curve is available for the whole upper band. The ~3.5% value at 10 kHz is worth noting, but it does not by itself predict a specific audible character. Perception will depend on the distortion spectrum, the content reproduced and the listening level. Without a complete curve and without controlled listening tests, it cannot be concluded that it necessarily produces harshness or hiss. It is retained as MEASURED-EXT.
Pair matching. Hi-Fi News publishes a 1.9 dB difference between the two units (pair matching), and places that deviation in the same region as the 2 kHz mode and the crossover. A difference in response between units can alter the stereo image and tonal balance, especially if it affects the presence band. The specific effect depends on the bandwidth of the discrepancy, its shape, the musical content and the room. A maximum figure of 1.9 dB does not by itself indicate the magnitude of the image shift. For 1.9 dB at 2-3 kHz to audibly shift the phantom centre, the discrepancy must be broadband and coherent between channels; if it is narrow (a notch), the effect is more of timbre than of image. It is retained as MEASURED-EXT.
PART III — THEORETICAL FOUNDATIONS
All the "why" in one place. III.1 covers the room as a system (modes, SBIR, PIR, target curve, multisub). III.2 covers the electrical chain (power, damping factor, cable, valves, biwiring). The formulas, tables and figures mentioned in Part I without development are here.
The formulas in this part are also available as interactive calculators at Acoustic calculators →. It includes SBIR + boundary gain, modal explorer + Schroeder, sensitivity + dB converter, power/SPL, damping factor, Q_res, delay/phase/summation, Dc + Sabine and time window. Direct links in the bridge callout at the top of the page.
III.1 The room as a system
III.1.1 Modes and Schroeder frequency
The axial mode of a rectangular dimension is approximated by:
where n is the mode number, c the speed of sound (≈343 m/s) and L the dimension. Floor area in square metres is not enough: length, width and height are needed. The 2 · Modal explorer calculates the first axial modes and the Schroeder frequency for your room.
| Dimension L | n = 1 | n = 2 | n = 3 |
|---|---|---|---|
| 2.1 m | 81.7 Hz | 163.3 Hz | 245.0 Hz |
| 3.0 m | 57.2 Hz | 114.3 Hz | 171.5 Hz |
| 4.3 m | 39.9 Hz | 79.8 Hz | 119.7 Hz |
| 6.4 m | 26.8 Hz | 53.6 Hz | 80.4 Hz |
The 80 Hz mode is not exotic: a 4.3 m room has its second axial at 79.8 Hz and a 6.4 m room has its third at 80.4 Hz. The relevant question is not "is there a mode at 80 Hz?" but "which regime are we in?". The Schroeder frequency (with T60 in seconds and V in cubic metres) estimates the transition between the modal region and the statistical region:
For 60 m³ and T60 = 0.5 s: fs ≈ 183 Hz. At 80 Hz we are clearly below it: the room's own modes manifest individually and the response can vary considerably with position. The "modal region" is a statistical approximation, not a rigid boundary.
Concrete example. A room of 4.8 × 3.6 × 2.5 m (43.2 m³) has its first axial modes at 35.7 Hz (4.8 m, n=1), 47.6 Hz (3.6 m, n=1) and 68.6 Hz (2.5 m, n=1). With T60 = 0.4 s, the Schroeder frequency is around ≈192 Hz. The X3's 80 Hz emphasis falls clearly in the modal region; none of the first three axials coincides exactly with 80 Hz, but higher axial, tangential and oblique modes, and interference between paths, can contribute to the response around 80 Hz. Proximity between a modal frequency and 80 Hz does not by itself prove that the measured emphasis comes from the room: the loudspeaker peak, the room modes, SBIR and source and listener positions are distinct phenomena that can superimpose. To see the axials of your room, use the 2 · Modal explorer.
III.1.2 SBIR and boundary gain
SBIR (Speaker Boundary Interference Response) connects placement and bass response. Direct and reflected radiation from a nearby wall arrive with a delay that produces a first null at:
With the woofer 1 m from the front wall: 343/(4·1) = 85.8 Hz, almost exactly the X3's emphasis region. At 0.5 m: 171.5 Hz. At 1.5 m: 57.2 Hz. The interactive version with editable distance and boundary gain is at Acoustic calculators → 1 · SBIR + boundary gain.
Boundary gain is the complementary phenomenon: a radiator in half-space receives up to +6 dB relative to free space; in quarter-space, up to +12 dB. These are idealised upper bounds: in real rooms, with finite walls, furniture and absorption, the effective value is lower and depends on frequency.
| Distance to wall | First SBIR null | What it implies |
|---|---|---|
| 0.5 m | 171.5 Hz | Null in the midbass; may be masked or modified by other modes and reflections. |
| 1.0 m | 85.8 Hz | Coincides with the X3's emphasis region: adds or subtracts depending on geometry. |
| 1.5 m | 57.2 Hz | Null in the extension region; may compensate an excess or create a hole. |
When a high-pass filter is applied to the main monitors and the bass is delegated to a subwoofer, the monitors can be placed at a short distance from the front wall (for example, 20-30 cm). In the simplified SBIR model (fnull = c / 4d), reducing the distance to 25 cm shifts the first boundary-interference null above ~343 Hz, outside the critical midbass region. (CALCULATED under the point-source, flat infinite-wall model.)
Counterpart. Moving the loudspeaker closer to the wall also increases boundary gain: the radiator in half-space receives up to +6 dB relative to free space, and in quarter-space up to +12 dB, as idealised upper bounds. The high-pass filter reduces the monitor's contribution in the low modal region, but it does not necessarily eliminate the excess in the crossover region (80-120 Hz). The effective result depends on the crossover frequency, the filter slope and the actual distance.
The strategy is an orientative geometric approximation, not a universal guarantee. In a real room, the presence of multiple boundaries (floor, ceiling, side walls) and interaction with the room modes modify the effective response. Displacing the null reduces the destructive notch in the low modal region, but it requires verification through acoustic measurements in the listening space. (PROBABLE as a placement strategy; the specific result in a given room is not predicted by the simplified model.)
III.1.3 PIR, directivity and target curve
PIR: definition and scope. The PIR (Predicted In-Room Response) is a normalised estimate of in-room response obtained by combining the loudspeaker's radiation curves with energy weighting: one works with energies (pressures squared), applies the weights (12% Listening Window + 44% Early Reflections + 44% Sound Power) and converts the result to decibels. A direct arithmetic average of levels in dB is not equivalent to an energy combination. The PIR is not a measurement of a specific room nor a universal target curve: it is an estimate derived from the loudspeaker's curves.
Limitations of the PIR. It allows loudspeakers to be compared using a normalised criterion of off-axis behaviour, but it does not predict the room's own modes or nulls. At low frequencies, the response at the listening position depends especially on room dimensions, loudspeaker and listener positions, and boundary conditions. The PIR therefore does not replace a measurement in the real room.
Directivity and Directivity Index (DI). If a loudspeaker maintains a coherent tonal response as the angle varies, side reflections retain a colouration similar to that of the direct sound and the room does not alter the balance too much. If the response changes abruptly off axis, the room receives spectrally different energy and modifies the perceived balance. The DI summarises that coherence, but does not replace looking at the curves.
PIR, target curve and in-room response are not synonyms. The target curves used in preference studies are a different reference: their shape depends on listening conditions, measurement procedure and adjustment method. The actual in-room response is the one resulting from the interaction between loudspeaker, enclosure, position and listener.
Domestic target curve. A frequent reference in domestic reproduction is a smooth curve with a downward tilt towards the treble and a moderate bass emphasis, on the order of +4 to +6 dB below ~100 Hz relative to the midrange. It is an example of a domestic target curve, not a universal recommendation nor a figure automatically attributable to Harman: Harman's preference research supports that the preferred response depends on listening conditions and on the relative bass and treble adjustments; it does not turn any specific slope or emphasis into a general rule. Without a specific published curve, it is more rigorous to say "a moderate bass emphasis, whose magnitude depends on the chosen target curve".
Note on Harman. The target curve associated with Harman's research describes a preferred response that, in general terms, shows greater relative level in the bass and a progressive fall towards high frequencies. Its exact shape depends on the measurement method, listening conditions and equalisation procedure. A qualitative tendency should not be confused with a universal slope expressed in dB/octave. The figure of −0.8 dB/octave has circulated in the literature and in technical discussions, but no primary prescription fixing it at that exact value under the relevant conditions has been located here; therefore no fixed numerical slope is assigned. The interactive illustration of what a slope means is at Acoustic calculators → A · Target curve slope.
Note on EBU Tech 3343. No response slope for loudspeakers in domestic rooms is attributed to EBU Tech 3343. The document deals with headphone monitoring in programme production; a headphone target curve does not by itself constitute a recommendation for in-room loudspeaker response.
Minimum and non-minimum phase as models. The viability of equalisation in the acoustic domain depends on the mathematical nature of the room's behaviour in each spectral region (Toole, Sound Reproduction, 3rd ed., 2017). A peak dominated by a resonance can be approximated by a minimum-phase model; a cancellation null is usually difficult or impractical to correct with EQ. Not every peak or null in a real room should be automatically classified as belonging to a particular mathematical category:
- Modal peaks (approximately minimum phase): in resonance regions where the room accumulates energy, the system behaves approximately as a minimum-phase system. There is a direct mathematical link (Hilbert transform) between magnitude and phase. Applying a parametric equalisation filter that attenuates the magnitude of the peak simultaneously corrects the phase response and reduces the excess level and the energy injected into the mode. EQ here is effective at reducing the peak. In regions of modal overlap, the approximation may lose accuracy.
- Cancellation nulls (approximately non-minimum phase): deep valleys caused by destructive interference (such as SBIR or acoustic cancellations between walls) are better approximated by a non-minimum-phase model. The magnitude drop is due to a geometric subtraction of wave vectors in antiphase, not to a resonator. Applying a boost filter in EQ does not alter the destructive interference and degrades the temporal response, injecting excess energy with a phase that does not correspond to that of the null: it increases distortion and imposes useless work on the amplifier, without filling the null at the listening position.
The response of a real room combines its own modes and multiple acoustic paths, so this approximation does not describe all frequencies or all listening positions equally. Precise classification of a specific case requires analysing its magnitude and phase response.
HRTF and preference. Even with the same PIR, two listeners may prefer different target curves because each has their own head-related transfer function (HRTF). The PIR is an average; it does not guarantee that the response preferred by a specific listener will match the average.
III.1.4 Multisub optimisation (theory)
The interaction of a single bass emission point with the room boundaries (SBIR and axial modes) produces an irregular response that depends on position. Multisubwoofer optimisation distributes between 2 and 4 subwoofers in geometrically distinct positions, with independent gain, EQ, delay and all-pass filters (MSO, Multi-Subwoofer Optimizer), to improve the spatial uniformity of the bass response in a listening area.
The combination of a loudspeaker with moderate emphasis and a well-integrated multisub system is, in practice, more robust than that of a neutral loudspeaker with a single poorly located subwoofer. Practical configuration is detailed in IV.3.
III.2 The electrical chain
III.2.1 Power and SPL
The power required depends on the target SPL, the loudspeaker's sensitivity, the listening distance and the crest factor. The formula and a complete numerical example, with explicit assumptions, are in Annex B. The interactive calculator, with acoustic scenarios and crest margin, is at 4 · Power / SPL.
III.2.2 Damping factor
The damping factor is defined as DF = Zload / Zoutput. A high number impresses, but what matters is how much the response varies when the loudspeaker impedance changes with frequency. The approximate deviation, for a resistive voltage divider, is:
| Zoutput (amplifier)† | DF with 4 Ω load | Variation with Z from 4 to 16 Ω |
|---|---|---|
| 0.1 Ω | 40 | ≈ 0.16 dB — small in practice |
| 0.5 Ω | 8 | ≈ 0.76 dB — small in practice |
| 1.0 Ω | 4 | ≈ 1.4 dB — potentially audible in direct comparison |
† Amplifier output impedance only. The following section develops the effect of the cable, which adds to the total series resistance and modifies these figures significantly in the first row: with 0.1 Ω of cable, the variation goes from 0.16 to 0.32 dB (Ztotal series = 0.2 Ω), from 0.76 to 0.89 dB (0.6 Ω) and from 1.4 to 1.53 dB (1.1 Ω). The interactive calculator with Zoutput, Rcable (manual or by geometry) and Zmin/Zmax is at 5 · Damping factor.
The cable counts too. The previous table considers only the amplifier's output impedance. A typical loudspeaker cable adds 0.05-0.3 Ω in series, depending on length and gauge. That resistance adds to the amplifier's Zoutput and increases the total series resistance of the circuit. In the resistive model, this increases the difference in voltage applied to loads of different impedance: the response variation with load impedance is greater, not smaller, than that calculated with Zoutput alone. A DF of 40 with 0.1 Ω of amplifier and 0.1 Ω of cable is, in practice, a DF of 20 with 0.2 Ω total. At high frequencies, the cable also adds a small inductive reactance: above 10 kHz, 3 m of braided cable can add on the order of 0.2 Ω reactive. It is harmless in most cases, but it closes the argument that DF is not the whole story.
The complete electrical model and the role of Re. To analyse the effect of the amplifier's output impedance and the cable resistance on the response, it is useful to represent the circuit with the loudspeaker's terminal impedance:
where Zloudspeaker(ω) is the complete impedance of the loudspeaker at its terminals, which already includes the DC resistance of the voice coil (Re), the coil inductance, the electromechanical contribution of the resonance and the elements of the crossover filter as applicable. Re must not be added again as an external series resistance with Zloudspeaker(ω): doing so would count the same component twice.
Why differences between very high DFs are usually small in solid state. In a modern solid-state amplifier, Zoutput is typically tiny (on the order of 0.004-0.04 Ω in certain designs; the range depends on design, feedback, frequency and measurement conditions). The total external series resistance (Zoutput + Rcable) is small relative to the modulus of Zloudspeaker(ω) over most of the band. That is why differences between very high DF figures usually translate into small changes in effective voltage across the loudspeaker, and therefore into small response variations. This is not because Re imposes a universal audibility threshold, but because of the smallness of the external series resistance relative to the load impedance. (CALCULATED under the resistive model; PROBABLE as a generalisation to real loudspeakers.)
Valve amplifiers. In a valve design, the output impedance is usually much higher than in solid state — on the order of 2 to 3 Ω as an orientative example, depending on the transformer tap, feedback, frequency and load. This figure is comparable to the loudspeaker's own impedance in some regions. As a consequence, the voltage reaching the loudspeaker varies with frequency, modulating the response. The full development, with the corresponding divider schematic, is in Annex B.
Measuring damping factor at 1 kHz. Damping factor is usually stated by measuring output impedance at 1 kHz. This frequency is usually in a region where the loudspeaker impedance is relatively stable. However, an amplifier's output impedance can vary with frequency, and in a valve design it may rise at the band edges. A DF figure at 1 kHz does not necessarily describe behaviour across the whole range. The resistive divider table (0.16 / 0.76 / 1.4 dB) and Figure 10 are applicable when the output impedance can be modelled as a constant resistance under the measurement conditions and the load is treated according to the calculation's assumptions. A published DF is incomplete without knowing the reference load, the frequency and the measurement method.
PART IV — PRACTICE AND PROTOCOL
All the "how" in one place. IV.1 is the REW + UMIK-1 protocol. IV.2 is levelling for comparisons and prior diagnosis before upgrades. IV.3 is the practical configuration of a multisub system. The corresponding theory is in Part III; protocol details, in Annex C.
The tools at Acoustic calculators → complement the protocol in this part: ms ↔ m converter for the REW ETC, modes and Schroeder for sizing the room, dB converter for levelling and window → Δf for frequency resolution.
IV. Practice and protocol
IV.1 REW + UMIK-1
A Klippel NFS is not needed to replicate the logic of this report. With a USB interface, a calibrated microphone such as the UMIK-1 and REW (free), a preliminary inspection can be done in 10-15 minutes with practice and the equipment ready; the full protocol takes longer. The protocol distinguishes two objectives that must not be confused:
A. Loudspeaker response. Reconstructed by combining the nearfield responses of cone and port (with complex transfer functions, radiating areas and distance and phase reference) and splicing that sum with an appropriate far-field measurement, verifying the overlap region.
B. In-room response. Obtained with full-range measurements at the listening position and several nearby positions, interpreted bearing in mind that the bass includes interaction with the room. Combining these measurements with the nearfield must not be presented as a direct reconstruction of the loudspeaker response.
- Nearfield of the bass cone separately, with the microphone 1-2 cm from the surface.
- Nearfield of the port separately, if the enclosure is bass-reflex.
- Sum of cone + port with complex transfer functions and splice with an appropriate far-field measurement to reconstruct the loudspeaker response. The in-room response is measured separately, at the listening position.
- Measurement at 1 m with a time window that excludes the first reflections (typically 3-5 ms).
- Measurement at the listening position with at least 6 averaged positions (for example, 30 cm around the central position), saving and examining the six curves separately as well as the average.
With those data, the 80 Hz emphasis, the midrange depression, the crossover notch and, above all, whether the loudspeaker sounds as the curve suggests in a specific room can be checked. The protocol does not replace a laboratory, but it does allow the separation between loudspeaker behaviour and room contribution to be guided. The step-by-step development, with checks at each stage and the FDW complement, is in Annex C.
(1) Define the listening position and the real furniture constraints. (2) Calculate the modes from the dimensions and estimate the Schroeder frequency; check response and decay at several points. (3) Try distance to walls and separation between cabinets, changing one variable at a time; check SBIR. (4) Adjust toe-in and evaluate tonal balance, centre image and side reflections; in asymmetric rooms, try different angles. (5) Apply moderate equalisation to response problems, avoiding attempts to correct deep cancellation nulls. (6) Consider one or more subwoofers if more extension or spatial uniformity is needed; adjust level, phase/delay and crossover. (7) Repeat measurements and listen at matched level with known recordings.
IV.2 Levelling and comparison
Comparing amplifiers or DACs must include output level matched precisely, absence of clipping, noise and distortion low enough, frequency response with the real load, current and voltage capability, and absence of dynamic limiting. An isolated SINAD figure or a low output impedance does not by itself prove equivalence under all conditions.
The practical reference in comparative listening tests is matching levels within 0.1 dB. Above that tolerance, level bias can decide the result instead of the equipment. Toole and Olive's research supports that very small level differences can be detected in blind tests; 0.1 dB is a methodological tolerance, not a universal boundary between a valid and an invalid test.
Home levelling protocol (5 minutes). Without a professional ABX switcher, levelling can be approximated with an SPL app with C weighting, playing pink noise filtered between 500 Hz and 2 kHz, with the phone on a tripod at the listening position. Adjust the amplifier or AVR gain until the reading matches within 0.1 dB between channels and between devices. It does not replace an ABX switcher, but it reduces level bias, which is the main confounding factor in uncontrolled comparisons. To convert magnitudes between dBu, dBV, dBm, Vrms, Vpeak and Vpp, use the "Universal dB converter" tab at 3 · Sensitivity + dB.
- Invest first in a loudspeaker that satisfies the needs for response, directivity, extension and maximum SPL.
- Verify electrical compatibility and the amplifier's real capability with the load.
- Reserve budget and time for location, bass control and, where appropriate, subwoofers.
- Compare electronics through tests levelled within 0.1 dB and equivalent conditions, not by price, weight or topology.
- Value finish, aesthetics, ergonomics and personal satisfaction as legitimate attributes, but separate them from the claim of unproven sonic superiority.
IV.3 Multisub configuration
The theory of multisub is in III.1.4. This section is the practical configuration: what to adjust, in what order, what to check.
- Geometrically distinct positions. Distribute 2-4 subwoofers in locations that are non-symmetrical relative to the room and the listener. Avoid two subwoofers being at the same distance from the main walls.
- Individual measurement. Measure each subwoofer separately at the listening position and at several nearby positions. Save the curves.
- Gain and delay. Adjust gain, delay and all-pass filters with MSO (or an equivalent tool) to optimise the vector sum in the listening area. Optimisation is on the combined response, not on each subwoofer in isolation.
- Crossover with the monitors. Adjust crossover frequency, slope and phase/delay between subwoofers and monitors. Apply a high-pass filter to the monitors to reduce their excursion in the bass.
- Verification. Measure the combined response at several positions and check spatial uniformity. Check that RT60 has not degraded (it should not, because MSO adds no absorption).
- Matched listening. Repeat the listening with matched levels and known recordings. Adjust if necessary.
PART V — CLOSING
Balance and decision table.
V. Closing
V.1 Balance
What we know with grounds.
- Price does not guarantee neutrality or superior performance.
- The on-axis response does not fully describe the loudspeaker's radiation nor its interaction with a room.
- Placement, toe-in and distance to the walls are real acoustic variables; asymmetry can be a reasonable solution in an asymmetric environment. The combination of an active high-pass filter, a subwoofer and moving the monitors close to the wall shifts the SBIR null in the simplified model, with the boundary-gain counterpart.
- More drivers can improve dynamic capability, but they do not by themselves guarantee better integration or greater sensitivity.
- The X3 measurements published by Erin, cross-checked with Hi-Fi News, allow its tonal balance to be criticised on firm grounds: bass emphasis, crossover notch and midrange depression. What they do not prove is that the loudspeaker is inferior in all respects, for all listeners or in all rooms.
- Impedance, phase, decay and acoustic response must be interpreted together, without assigning unproven causes.
- Sensitivity and electronics comparisons require declaring the convention and matching levels.
- In solid-state amplifiers with very low Zoutput, differences between very high DF figures usually translate into small response variations, because the external series resistance is small relative to the load impedance.
- In valve amplifiers, high output impedance can interact with the loudspeaker's complex impedance, modulating the frequency response according to Zloudspeaker(ω). The DF measured at 1 kHz does not necessarily describe the whole band.
- Biwiring can produce small, frequency-dependent electrical differences, but there is no evidence of a universal audible advantage; biamping can make sense depending on the topology.
- Burn-in has a plausible mechanism in loudspeakers (mechanical devices) and no demonstrable change in performance in electronics and cables in a well-designed device. The claim of progressive sonic improvement over hundreds of hours is unproven.
- Equalisation can effectively reduce moderate response peaks and resonances whose behaviour approximates that of a minimum-phase system, within the limits of the signal, the system and the listening position. It does not replace control of prolonged decay.
- Vertical directivity and interference lobing at the crossover region are real variables; adjusting baffle tilt is a geometric possibility to be verified, not a demonstrated solution.
- FDW is a useful visualisation and filter-design complement, but it does not replace the nearfield sum nor reconstruct the loudspeaker's anechoic response.
- Multisub optimisation improves the spatial uniformity of the bass response, but does not reduce the room's physical RT60; reduction of energy excited in specific modes is probable, not guaranteed.
What remains undetermined.
- The exact contribution of each physical mechanism to the X3's measured irregularities.
- The audibility of each persistence at any level, musical programme or room.
- The exact response of the X3 in a specific room without knowing dimensions, position and treatment.
- The commercial motive that might lie behind a tonal emphasis, beyond Hi-Fi News describing a specific sonic presentation.
- A universal percentage of the budget that should go to loudspeakers, room or electronics (see Annex D, entry 8).
- The exact reconciliation between the different sensitivity measurement methods and the resolution of the discrepancy between the Preference Score figures published by Spinorama and those reproduced by Speakerranking.
- The band-by-band breakdown of the X3's 1.9 dB pair matching, beyond its concentration in the crossover region.
- An exact percentage dividing the contribution to perceived sound between loudspeaker and room (see Annex D, entry 8).
- The exact magnitude of thermal compression in the X3's ways, the real asymmetry of its dynamic behaviour and its audibility under a given musical programme (see Annex D, entry 9).
- The complete verification of Part II and Annexes A–E against the primary sources (see Annex D).
V.2 Quick decision table
| If the priority is… | Guidance |
|---|---|
| Tonal neutrality | Prioritise smooth on-axis and listening-window response, coherent directivity and absence of significant resonances. Also check vertical directivity in the crossover region. |
| High-SPL listening | Check distortion, dynamic compression, excursion and power capability; do not choose on size alone. |
| Deep, uniform bass | Evaluate real extension, room modes, SBIR, location and possible subwoofer integration. In problematic rooms, consider an optimised multisub system (MSO) before a single subwoofer. |
| Asymmetric room | Try different orientation per channel if measurements and reproducible listening indicate an improvement. |
| More expensive electronics | Demand a demonstrable advantage under load and at matched levels before attributing sonic superiority to it. Consider the cable as part of the total series resistance. |
| Product with a serious deficiency | If it contradicts an essential need and offers no relevant compensation, discarding it is rational without proving absolute inferiority. |
ANNEXES
- A. Evidence labels — how to read CONFIRMED, OBSERVED, MEASURED-EXT, etc.
- B. Formulas and glossary — SBIR, Schroeder, sensitivity, DF, PIR, power example, acronyms.
- C. Detailed REW protocol — step by step, with FDW.
- D. Uncertainties and discrepancies — sensitivity, Preference Score, EPDR, thermal compression, burn-in, biwiring, THD by frequency.
- E. References and credits — sources, bibliography, use of graphs.
ANNEX A — EVIDENCE LABELS
Annex A — How to read the labels
The labels indicate the nature of the support, not the importance of the matter nor the subjective probability that the author is right. "MEASURED-EXT" identifies measurements published by third parties; it does not imply that Nauscopio has repeated them. "DIAGRAM" is reserved for the author's own conceptual illustrations that reproduce neither a measurement nor a verifiable numerical calculation. "PROBABLE" and "HYPOTHESIS" both express uncertainty, but they are not interchangeable.
- CONFIRMED: the claim is directly supported by an identified source or by a checked calculation, within the conditions and scope of that evidence. The label does not turn an interpretation of the source into a universal truth.
- OBSERVED: a visible characteristic or a literal statement from the source.
- MEASURED-EXT: external instrumental measurement, with attribution to the corresponding product and laboratory.
- REPORTED-EXT: data published by a third party without the complete primary measurement being available here.
- CALCULATED: result reproducible from the stated data and formula, under the declared assumptions.
- DIAGRAM: the author's own conceptual illustration; it is neither a measurement nor a numerical calculation.
- PROBABLE: interpretation compatible with the available evidence, though not conclusively proven. It characterises the degree of support for an interpretation.
- HYPOTHESIS: specific causal explanation proposed as possible, not verified. It characterises the provisional nature of a causal explanation.
- ND: not determinable from the material examined.
ANNEX B — FORMULAS, GLOSSARY AND POWER/SPL EXAMPLE
Annex B — Quantities, formulas and glossary
The formulas in this annex have interactive calculators at Acoustic calculators →. Direct links: 1 · SBIR + boundary gain · 2 · Modal explorer · 3 · Sensitivity + dB · 4 · Power / SPL · 5 · Damping factor · 6 · Q_res · 7 · Delay, phase and summation · 8 · Dc + Sabine · 9 · Time window · A · Target curve slope · B · ms ↔ m · C · λ ↔ f ↔ T.
Wavelength and period → C · λ ↔ f ↔ T
With c ≈ 343 m/s and f = 80 Hz, λ ≈ 4.29 m. At 500 Hz, T = 2 ms; six to eight periods equal 12–16 ms.
Axial mode and Schroeder frequency → 2 · Modal explorer
In the Schroeder formula, T60 is expressed in seconds and V in cubic metres. The Schroeder frequency is an estimate of transition, not an abrupt boundary between two regimes. In small rooms, the distribution of modes may be irregular.
SBIR → 1 · SBIR + boundary gain
Approximation for a simplified geometry (point source, flat infinite wall, perpendicular incidence). The frequency and depth of the real null also depend on listener position, angle of incidence and the other surfaces. d represents the effective distance between the acoustic source and the reflecting boundary in the geometry considered.
Sensitivity: 1 W versus 2.83 V → 3 · Sensitivity + dB
With R = 8 Ω: 0 dB. With R = 4 Ω: +3 dB. With R = 2 Ω: +6 dB. Comparing figures without stating the reference produces errors of 3 to 6 dB. The conversion assumes a resistive load; the real impedance of a loudspeaker varies with frequency. The formula does not automatically convert a real loudspeaker measurement into another equivalent one: it is a nominal equivalence. As a presentation convention, the report expresses sensitivities at 2.83 V/1 m when the source provides that reference. Figures published under another convention are retained with their original condition.
Decay and Q → 6 · Q_res
Origin relation: N = Q · ΔdB / (8.686 · π). Valid for an idealised second-order resonator, with exponential envelope and a defined threshold. It is not a universal conversion applicable to any waterfall, burst decay or CSD. In the body of the report, cycle figures are always quoted with their threshold (for example, "6-8 cycles at −20 dB").
Damping factor and response variation → 5 · Damping factor
The response variation with load impedance is calculated with the voltage divider, under the assumptions of the resistive model. It is not a complete prediction of a real loudspeaker's response, whose impedance is complex.
Valve amplifiers
In a valve design, the output impedance may be on the order of 2-3 Ω, comparable to the loudspeaker impedance in some regions. The voltage divider is not dominated by a negligible Zoutput: the voltage reaching the loudspeaker is modulated according to Zloudspeaker(ω), altering the frequency response. The DF measured at 1 kHz does not necessarily describe the whole band. The full development of this case requires a specific analysis of the amplifier and the load, beyond the scope of this report.
Energy weighting of the PIR
PIR (Predicted In-Room Response): an estimate of in-room response obtained by combining the curves with energy weighting: one works with energies (pressures squared), applies the weights (12% Listening Window + 44% Early Reflections + 44% Sound Power) and converts the result to decibels. A direct arithmetic average of levels in dB is not equivalent to an energy combination. If the PIR is calculated from curves expressed in decibels, it must be verified that each curve is converted to the energy domain with the correct normalisation conventions and that the weights are applied to the magnitudes intended by the procedure; the result is then converted to decibels. The general explanation does not replace the full specification of the algorithm. The PIR is not a measurement of a specific room nor a universal target curve.
Crest factor → 4 · Power / SPL
In P = 10^((SPLtarget − SPL1W@d − factor)/10), the factor is the stereo gain already obtained: 0 dB in mono (one channel), +3 dB with two uncorrelated channels, +6 dB with two correlated channels. It is subtracted because it reduces the power needed per channel as the other channel's contribution adds. In real stereo music, correlation varies with frequency and content: the +3/+6 dB values are reference cases, not a universal gain.
Numerical example of power and SPL (idealised exercise)
Suppose a loudspeaker of 88 dB/1 W/1 m, a listening position at 3 m, a target of 95 dB SPL sustained and a crest margin of 12 dB. It is a generic exercise with a hypothetical sensitivity, not a prediction of the real power needed for the Børresen X3.
- SPL at 1 W and 3 m: 88 − 20·log₁₀(3) ≈ 88 − 9.5 = 78.5 dB.
- Power for 95 dB sustained: 10^((95 − 78.5)/10) = 10^(1.65) ≈ 45 W.
- With a 12 dB crest margin, the peak power needed is 10^(12/10) ≈ 15.8 times the average power: ~710 W peak, corresponding to a theoretical peak of 107 dB SPL.
This example shows why rated power is not the only variable: the real SPL depends on the musical programme, the crest margin, the distance and the room. Calculated power and effective acoustic capability are not equivalent: excursion, thermal compression and distortion limit the real result below the theoretical value. The 710 W are a theoretical peak from an idealised exercise, not an amplifier specification for the X3.
Glossary of acronyms
| Acronym | Expansion | Meaning |
|---|---|---|
| LW | Listening Window | Average response over a narrow angle around the axis (±10° horizontal, ±10° vertical). |
| ER | Early Reflections | Weighted average of the first lateral, vertical and front/rear reflections. |
| SP | Sound Power | Average of the energy radiated in all directions. |
| PIR | Predicted In-Room Response | Estimate of in-room response: 12% LW + 44% ER + 44% SP, energy-weighted. It is not a measurement of a specific room nor a universal target curve. |
| DI | Directivity Index | Difference in dB between on-axis response and sound power. |
| SBIR | Speaker Boundary Interference Response | Interference between direct radiation and reflection from nearby walls. |
| Q | Quality factor | Quality factor of a resonator. |
| DF | Damping Factor | Ratio of load impedance to amplifier output impedance. |
| Re | Voice-coil resistance | DC resistance of the voice coil. It is not a fixed percentage of nominal impedance: "typically 70-85%" is an orientation, not a rule for deducing Re without measuring it. |
| EPDR | Equivalent Peak Dissipation Resistance | Equivalent resistance associated with the dissipation of output devices under given load and signal conditions. It is not an additional physical resistance nor a direct measure of amplifier incompatibility. |
| RT60 | Reverberation Time 60 dB | Time it takes for sound to decay by 60 dB after the source stops. It is estimated by frequency bands. In the modal region, a single value per band may be unrepresentative because of the discrete distribution of resonances. |
| EDT | Early Decay Time | Early decay time: extrapolates the slope of the initial decay (usually the first 10 dB) to estimate the equivalent 60 dB decay time. |
| MMM | Moving Mic Method | Spatial averaging by moving the microphone slowly through the listening area with RTA in Forever Averaging mode. |
| FDW | Frequency Dependent Windowing | Frequency-dependent time window: wider at low frequencies and narrower at high, to isolate direct sound from late reflections in each band. A visualisation complement; it does not replace the nearfield sum. |
| MSO | Multi-Subwoofer Optimizer | Optimisation tool that calculates independent gain, EQ, delay and all-pass filters for each subwoofer in order to homogenise the bass response in a listening area. It does not reduce the room's physical RT60. |
| SINAD | Signal-to-Noise And Distortion | Signal-to-noise-and-distortion ratio. |
| CSD | Cumulative Spectral Decay | Spectral-temporal representation of accumulated energy. |
| NFS | Near-Field Scanner | Nearfield scanning measurement system, developed by Klippel. |
| HRTF | Head-Related Transfer Function | Individual acoustic response that modifies the perception of sound according to direction of arrival. Two listeners may prefer different target curves. |
ANNEX C — DETAILED REW + UMIK-1 PROTOCOL
Annex C — Detailed REW + UMIK-1 protocol
The protocol of IV.1 developed step by step, with the checks worth making at each stage. The protocol distinguishes two objectives — loudspeaker response and in-room response — that must not be confused. It is useful for diagnosing the domestic system and cross-checking hypotheses, but it does not reconstruct the anechoic response of a Klippel NFS.
Minimum equipment
- USB audio interface with a microphone input.
- Calibrated measurement microphone such as the UMIK-1 (with calibration file).
- REW software (free).
- Tripod or stand for the microphone.
Step 1 — Nearfield of the bass cone
Microphone 1-2 cm from the cone surface, at the centre. Moderate signal level to avoid compression. Sweep from 10 Hz to 1 kHz (not up to 20 kHz: see the caution warning). This measurement captures the cone response without the room contribution, but it does not by itself represent the complete response of the bass-reflex system.
Step 2 — Nearfield of the port
Microphone 1-2 cm from the port output. Sweep from 20 Hz to 2 kHz (not up to 20 kHz). This measurement isolates the port contribution and allows its tuning to be seen.
Step 3 — Cone + port combination and splice
Sum the cone and port responses with complex transfer functions and their relative phase to obtain the bass system response, considering radiating areas and the distance and phase reference. Splice that sum with an appropriate far-field measurement. Without this step, an emphasis cannot be automatically attributed to "the loudspeaker" or "the room". A sum of magnitudes without phase or correct normalisation can produce an erroneous result. The in-room response is measured separately, at the listening position.
Step 4 — 1 m window
Microphone at 1 m on the loudspeaker axis, with a 3-5 ms time window that excludes the first reflections. Sweep from 200 Hz to 20 kHz (the short time window prevents good measurement below 200 Hz). This measurement is suitable for midrange and treble, but it does not by itself allow the bass behaviour to be validated. It must not be used to calculate RT60, EDT, T20 or T30: that window removes practically all the temporal information needed to assess the room's reverberant decay.
Step 5 — Averaged listening position
Microphone at the listening position and at least 6 positions around it (30 cm left, right, up, down, forward and back). Save and examine the six curves separately, as well as the average, to diagnose spatial variability. Full sweep from 20 Hz to 20 kHz.
Step 5b — Analysis complement: Frequency Dependent Windowing (FDW)
As a complement to static spatial averaging and the MMM method, REW allows an advanced processing called FDW (Frequency Dependent Windowing) to be applied to the impulse response obtained at the listening position.
Step 6 — RT60 and EDT
Reverberation parameters are obtained from a room impulse measurement without a short window, with sufficient dynamic range and appropriate configuration. They must not be calculated from the gated 1 m measurement of step 4. From that impulse measurement, REW calculates RT60 and EDT. Review the curve by octaves or third-octaves. In the modal region, RT60 values per band should be interpreted with caution: the discrete distribution of resonances may make a global figure unrepresentative. A high RT60 does not by itself prove that the sound will be subjectively "muddy"; it is advisable to also examine the decay of each mode using a waterfall, spectrogram or impulse response, and to compare several microphone positions.
- The 80 Hz emphasis may appear in measurements 1, 2 or 4. Correct attribution requires comparing the cone+port sum with the measurement at the listening position. Presence in one or another measurement is an indication compatible with a cause, not an automatic diagnosis.
- The crossover notch will appear in measurement 4. If it appears both in the 1 m measurement and at the listening position, there are indications that it does not depend exclusively on the time window of the first measurement.
- The difference between the nearfield sum and the in-room measurement tells you how much of what you hear is from the loudspeaker and how much from the room, but not automatically: you must splice and compare curves, not label a single measurement.
- Use the microphone calibration file and keep the specified orientation. Document level, position and time reference for each measurement so it can be repeated.
- Keep conditions constant when comparing the two channels (same distance, same height, same level).
- Always distinguish an individual measurement from a spatial average: a single position does not characterise the room.
- RT60 and EDT complete the temporal diagnosis: an acceptable waterfall with a high RT60 in the bass is still a room problem, but a high RT60 in isolation does not by itself prove a specific subjective perception.
- MMM is a valid alternative for obtaining a spatially averaged response and guiding an EQ; it does not replace individual static measurements for diagnosing spatial variability.
- FDW is a visualisation complement, not a measurement of the loudspeaker response. Its main use is to smooth the transition in the Schroeder region and to facilitate the design of stable equalisation filters.
To quickly convert ETC peaks to physical distance, use the B · ms ↔ m converter on the Calculators page. For your room's modal landscape, the 2 · explorer. For the relationship between window and frequency resolution, the 9 · time window.
ANNEX D — UNCERTAINTIES AND DISCREPANCIES
Annex D — Uncertainties and discrepancies
This annex documents the points where sources do not agree or where interpretation requires additional caution.
1. X3 sensitivity
The manufacturer states 88 dB/1 W/4 Ω. Spinorama calculates an average of 85.9 dB (300 Hz–3 kHz, 2.83 V/1 m). Hi-Fi News publishes 89.2 dB at 1 kHz, 87.8 dB average and 86.2 dB IEC, all at 2.83 V/1 m. Converting 88 dB/1 W to ~91 dB/2.83 V assumes a 4 Ω resistive load; the real impedance varies with frequency. Moreover, Erin's average (85.9 dB) and Hi-Fi News's average (87.8 dB) differ by 1.9 dB and that is not reconciled either: they are two independent campaigns with different averaging methods. The exact reconciliation between methods remains ND. The correct approach is to retain each figure with its stated condition.
2. Preference Score
In the query of 21-Oct-2026, Spinorama's page for the X3 shows 2.38 (3.50 with a perfect subwoofer; 5.21 with EQ and 5.99 with EQ and a perfect subwoofer). Speakerranking reproduces the same figures. There is a documented alternative series of 2.04 / 3.16 and 5.52 / 6.30 with EQ that could not be reproduced in the current query. The discrepancy is documented and unresolved: the cause is not determined. The discrepancy remains ND until archived versions, change history or reproducible calculations are available to identify its origin. The indicator is a model-based prediction, not a listening test nor an absolute verdict.
3. Impedance, EPDR and phase
Hi-Fi News: minimum 3.1 Ω/20 Hz, maximum 20.3 Ω/1.55 kHz; minimum EPDR 1.1 Ω/20 Hz and 1.5 Ω/55 Hz, outside the bass system passband; phase −25° at 3.4 kHz and +54° at 69 Hz. Laboratory conclusion: the X3 is not a particular challenge to drive. Speakerranking, citing Erin, states ~6.1 Ω above 80 Hz. They are not contradictory: they measure different bands. An isolated EPDR value is not enough to declare incompatibility; frequency, phase, required level and the current capability of the stage matter.
4. Room modes and numerical example
For 4.8 × 3.6 × 2.5 m, the first axials are 35.7 Hz, 47.6 Hz and 68.6 Hz. None coincides exactly with 80 Hz. The second axial of the height (2.5 m) is 137.2 Hz; the second axial of the 3.6 m side is 95.3 Hz; the second axial of the 4.8 m side is 71.5 Hz. An axial mode alone does not prove an audible problem: higher axial, tangential and oblique modes, source and listener positions, and the measured response must be examined.
5. Cycles-Q conversion
The relations cycles(−20 dB) ≈ 0.73·Q and cycles(−60 dB) ≈ 2.2·Q are approximations for an idealised second-order resonator, with exponential envelope and a defined threshold. They should not be applied indiscriminately to any waterfall, burst decay or CSD representation. In the body of the report, Erin's persistence is described as a description of the graph (6-8 cycles at −20 dB ≈ 12-16 ms at 500 Hz) and is not presented as an autonomous measurement of the driver's Q.
6. Video figures and laboratory figures
The video describes a peak of ~7 dB near 80 Hz and several consecutive irregularities between 2 and 3 kHz, and suggests a specific proportion for the weight of measurements in the evaluation. These are the author's observations, not laboratory measurements. The Erin and Hi-Fi News data allow the bass emphasis, the crossover notch and the midrange depression to be cross-checked, but not the complete set nor the direct comparison with the Wharfedale Super Linton. They are retained with their source condition.
7. Pair matching and THD
Hi-Fi News publishes 1.9 dB difference between units, concentrated in the crossover and 2 kHz mode region. It also publishes THD of 0.3% at 100 Hz, 0.2% at 1 kHz and ~3.5% at 10 kHz, at 90 dB SPL/1 m, and describes distortion as "a high 3-4% above 8 kHz". Both formulations are compatible: the first gives point values at specific frequencies; the second describes a region. The report does not have the numerical band-by-band breakdown of pair matching nor a complete THD-versus-frequency curve for the whole upper band. The figures are retained as MEASURED-EXT. A difference in response between units can alter the stereo image and tonal balance; the specific effect depends on bandwidth, the shape of the discrepancy, the musical content and the room. The published THD does not by itself predict a specific audible character.
8. Loudspeaker/room contribution and budget percentages
The ~75% (measurements in I.5) and ~90% (loudspeakers and room in III.2.1) figures are informal rules, not universal data. No primary source has been located that supports them as general proportions. The report replaces them with an analysis of the system and its limitations. The relative contribution of loudspeaker and room depends on the specific room, position, treatment and musical programme; it cannot be reduced to a single percentage. The Audiocostruzioni article also proposes a budget distribution among loudspeakers, electronics and cables (on the order of 50-60% / 30-40% / remainder); it is a popular heuristic without a primary source located, and the report does not adopt it.
9. Thermal compression and spectral imbalance with SPL
Conductor resistance increases with temperature, reducing driver efficiency. In the X3's midwoofer (voice coil), the mechanism is clear. In the ribbon tweeter (conductive trace bonded to the diaphragm), it also exists, with shorter time constants due to the extremely low thermal mass. If both ways compress at different rates and magnitudes, the tonal balance can shift dynamically with level. The physics of the mechanism is CONFIRMED; for the X3 there are no published compression-versus-level curves: magnitude, asymmetry and audibility = ND.
10. Burn-in: three distinct phenomena
Burn-in or run-in is often invoked to justify changes in sound after days or weeks of use. Three questions should be separated, as they are not equivalent. First, the mechanical changes of a loudspeaker's suspensions: run-in of a few hours or a couple of days may make sense because they are mechanical devices with moving parts under tension that settle in; the change is usually small, but the mechanism is plausible (PROBABLE). Second, the thermal and electrical stabilisation of a circuit after power-on: it occurs within seconds to minutes, depending on the type of component, the dielectric and the circuit. Aczel's formulation ("capacitors form in seconds; bias stabilises in minutes") is a simplification of expert opinion, not a universal law: "formation", "reforming" and thermal stabilisation are not the same phenomenon, and the time range depends on the component (OBSERVED as opinion; the time range depends on the case). Third, the much more demanding claim that equipment acquires a progressive sonic improvement over hundreds of hours: it is not demonstrated by the previous two, nor is its absolute impossibility proven for every conceivable piece of equipment (ND). The critique of the burn-in myth is maintained in essence — there is no evidence of progressive sonic improvement over hundreds of hours — but the formulation must avoid generalisations about capacitors and fixed times.
11. Biwiring: superposition and the limits of the model
Biwiring consists in running two pairs of cables from the same amplifier terminal to the separate inputs of the loudspeaker's passive filter. The conclusion that "it changes nothing" is too absolute. The superposition principle applies to linear networks, but it does not prove that two cabling configurations have exactly the same series impedance. Connecting conductors in parallel can reduce resistance and modify the effective inductance of the cabling. The practical magnitude of the change depends on length, gauge, geometry and loudspeaker impedance. In a model with an 8 Ω loudspeaker and cables with 0.1 Ω series resistance, the variation is on the order of 0.1 dB; with low-resistance cables, real differences are usually much smaller. There is no evidence of a universal audible advantage. Biamping — with separate power stages and active or passive crossover — can make sense because it splits the signal before the power stage; biwiring, in normal domestic practice, has not demonstrated a universal audible improvement. The 0.1 dB figure corresponds to the model by J. C. G. Lesurf (University of St Andrews) with 0.1 Ω cable and 8 Ω loudspeaker; it is not a general result applicable to any installation. (PROBABLE as a practical interpretation; CALCULATED under the stated model.)
12. Geometric nuance of SBIR with active filtering and a subwoofer
The combination of a high-pass filter on the main monitors and a subwoofer allows the monitors to be physically moved closer to the front wall. In the simplified SBIR model, reducing the distance to 20-30 cm shifts the first null above ~286-429 Hz, outside the critical midbass region. The calculation is CALCULATED under the point-source, flat infinite-wall model; the strategy is PROBABLE as placement. The counterpart is boundary gain: moving the loudspeaker closer to the wall increases the radiated energy in the low region by up to +6 dB (half-space) or +12 dB (quarter-space), as idealised bounds. The high-pass filter reduces the monitor's contribution in the low modal region, but it does not necessarily eliminate the excess in the crossover region (80-120 Hz). The specific result in a given room is not predicted by the simplified model and requires verification through acoustic measurements in the listening space. The development is in III.1.2.
ANNEX E — REFERENCES AND CREDITS
Annex E — References and credits
Primary sources of the video
- Erin's Audio Corner. The 5 Biggest Audiophile Mistakes. Original video and transcript. Open video. (accessed 20 Oct 2026)
Instrumental measurements
- Erin's Audio Corner. Børresen X3 Floorstanding Speaker Review. Measurement with Klippel Near-Field Scanner. Open report. (accessed 20 Oct 2026)
- Spinorama. Børresen X3 — Erin's Audio Corner data. Data derived from Erin's measurements; it does not constitute a second independent experimental campaign. Open dataset. (accessed 21 Oct 2026)
- Hi-Fi News. Børresen X3 loudspeaker Lab Report. Independent laboratory. Open report. (accessed 20 Oct 2026)
- Speakerranking. Comparisons and summaries of third-party measurements (including reproduction of the Preference Score). Secondary source. Open site. (accessed 21 Oct 2026)
Sources consulted and discarded or qualified
- Aczel, P. The Ten Biggest Lies in Audio. The Audio Critic, no. 26, autumn 2000. Polemical article. Cited as OBSERVED for burn-in (loudspeaker/electronics distinction) and biwiring (superposition principle, with the nuances of Lesurf's model). Its dogmatic claims about valves and its rhetorical equivalence between cables are discarded. Open PDF. (accessed 24 Oct 2026)
- Aczel, P. What I have learned after six decades in audio. Translation at hificafe.org. Expert opinion source. Cited as OBSERVED for the idea that an anechoically perfect loudspeaker does not sound good in a real room, and for the distinction between hearing and knowing what to listen for. (accessed 24 Oct 2026)
- Audiocostruzioni. The most common mistakes beginners make in hi-fi (and how to avoid them). Popular source. Cited as REPORTED-EXT for the note on the digital source and prior diagnosis before upgrades (IV.2) and for the critique of budget percentages (Annex D.8). Open article. (accessed 24 Oct 2026)
- PCP Audio. Project V1 and V2. Workshop narrative without systematic instrumental measurements. Cited as OBSERVED for the effect of port location (I.3) and sensitivity per way (I.4). Its design methodology without measurements is not adopted. Open article. (accessed 24 Oct 2026)
- Wikipedia. High fidelity. Tertiary source. Cited as REPORTED-EXT for the canonical definition of high fidelity and the logical nuance of ABX. Not used as a source of primary technical data. Open article. (accessed 24 Oct 2026)
- Lesurf, J. C. G. Biwiring analysis. University of St Andrews. Model that quantifies the cabling impedance variation and its dependence on cable resistance; cited as CALCULATED under its assumptions (0.1 Ω cable, 8 Ω loudspeaker). (accessed 24 Oct 2026)
Complementary tools
- Nauscopio · Acoustic calculators. Nine tools in three sections plus a reference and auxiliaries section: SBIR + boundary gain, modal explorer, sensitivity + dB, power/SPL, damping factor, Q_res, delay/phase/summation, Dc + Sabine and time window. Open calculators.
Normative documentation
- CTA-2034-A (2015). Standard Method of Measurement for In-Home Loudspeakers. Consumer Technology Association.
Scientific bibliography
- Toole, F. E. Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms. 3rd ed. Routledge, 2017.
- Toole, F. E.; Olive, S. E. "The modification of timbre by resonances: perception and measurement". Journal of the Audio Engineering Society, vol. 36, no. 3, 1988, pp. 122–142.
- Olive, S. E. "A multiple regression model for predicting loudspeaker preference using objective measurements: Part I — Listening test results" and "Part II — Development of the model". 117th Audio Engineering Society Convention, San Francisco, 2004. Preprints 6113 and 6114.
- Schroeder, M. R. "The frequency-curve requirements for high-fidelity transmission". Journal of the Audio Engineering Society, 1954.
- Klippel GmbH. Near-Field Scanner (NFS) — System Manual. Technical documentation of the nearfield scanning measurement system. Klippel GmbH, Dresden. Available at klippel.de.
Methodological note
This report combines the video transcript, the measurement pages and listening comments published by the cited sources, explicit calculations and electroacoustic reasoning. Causal interpretations are marked as probable, hypothesis or not determinable when there is no measurement that isolates them. Figures attributed to the video (~7 dB, irregularities 2-3 kHz, ±60°, 75%) are retained with their status as the author's observation and are not presented as equivalent to laboratory measurements. The production process is summarised in the methodological note at the beginning of the report.
On the independence of sources. Erin (Klippel NFS) and Hi-Fi News are the two independent measurement campaigns cited for frequency response and distortion. For directivity, Spinorama derives from Erin's data and does not constitute a second independent laboratory. Speakerranking reproduces or summarises third-party data and should not be counted as a third independent experimental verification. The AI tools used for cross-auditing may share biases or starting errors; their agreement does not amount to independent verification.
On the preference score. The figures published by Spinorama and Speakerranking are cited with their source and query date (21-Oct-2026). In the current query, both sources show 2.38 / 3.50 (5.21 / 5.99 with EQ). There is a documented alternative series of 2.04 / 3.16 (5.52 / 6.30 with EQ) that could not be reproduced in the current query. The discrepancy is documented and unresolved; the cause remains ND (see Annex D.2).
On target-curve conventions. No response slope for loudspeakers in domestic rooms is attributed to EBU Tech 3343. As for the Harman reference, the qualitative tendency is maintained (greater relative level in the bass and progressive fall towards treble) without fixing a universal numerical slope of −0.8 dB/octave.
Source consultation: 20-25 October 2026.
Use of third-party graphs
The fourteen figures in this report are published in their final version. Each caption indicates what the figure shows, the source and the corresponding evidence label: figures 2, 3, 4, 5 and 6 reproduce measurements published by Erin's Audio Corner, Spinorama and Hi-Fi News, and are used with explicit attribution and for the purpose of critical analysis, commentary and teaching; figures 1, 7, 8, 9, 10, 11, 12, 13 and 14 are the author's own conceptual diagrams and are labelled DIAGRAM.
Attribution and critical purpose do not by themselves guarantee that reproduction is authorised in all jurisdictions. Publication on a Spanish blog may be subject to a legal framework different from the US one and to the conditions of the original sources. For any independent redistribution of the report outside this blog, verify the reproduction licence of each graph with its original source.
The author's own diagrams (figures 1, 7, 8, 9, 10, 11, 12, 13 and 14) can be generated in SVG or a vector drawing tool and do not reproduce measured data. They are distributed under the same licence as the rest of the report.
If you want to apply the formulas in this report to your specific room, the page Acoustic calculators → includes SBIR + boundary gain, modal explorer, sensitivity + dB converter, power/SPL, damping factor, Q_res, delay/phase/summation, Dc + Sabine and time window, plus a reference section with ms ↔ m, λ ↔ f ↔ T and target curve slope. Each result carries a CALCULATED label and its scope note, as in this report.
Direct links: 1 · SBIR + boundary gain·2 · Modal explorer·3 · Sensitivity + dB·4 · Power / SPL·5 · Damping factor·6 · Q_res·7 · Delay, phase and summation·8 · Dc + Sabine·9 · Time window.