Predicting Headphone Fit-to-Fit Consistency

This short article explains an idea I have for generating a rating system for accoustic fit-to-fit consistency of headphones. I believe this in important as recent research from Sean Olive and Dan Clark (2025) has shown that headphones with high Acoustic Impedances have massively different fit-to-fit consistency across listeners.

So, introducing a new metric for predicting headphone fit-to-fit consistency allows reviewers to give some confidence with their subjective reviews of headphones and allows objective reviews to also subjective headphones where PEQ is possible and headphones where it can only have very limited accuracy.

1. Model the Headphone as an Acoustic Thevenin Source

Treat the driver + front cavity + pad system as a pressure source $(P_s(f))$ in series with a complex acoustic source impedance $(Z_s(f))$.

The listener contributes an ear load $(Z_e(f))$ (pinna + concha + canal + leak).

The ear canal pressure is then:

$$ P(f) = P_s(f) \frac{Z_e(f)}{Z_s(f) + Z_e(f)} $$

If $(|Z_s| \ll |Z_e|)$ over a frequency band, fit differences matter less. If $(|Z_s|$) is comparable or larger, small variations in $(Z_e)$ cause noticeable response swings.

2. Measure $(P_s(f))$ and $(Z_s(f))$ with Two Known Loads

A direct impedance probe isn’t required—measure the headphone’s SPL with two known acoustic loads:

  • Load A (sealed): Standard 711-type ear simulator.
  • Load B (perturbed): The same simulator but with a calibrated leak or extra shunt volume.

From the complex pressures $(P_A(f))$ and $(P_B(f))$, and known loads $(Z_A(f))$, $(Z_B(f))$:

$$ P_s(f)=\frac{P_A Z_A - P_B Z_B}{Z_A - Z_B}, \quad Z_s(f)=Z_A\left(\frac{P_s}{P_A}-1\right) $$

Getting the Load Impedances

  • Use the published impedance curve of your 711 coupler for $(Z_A)$.
  • Model $(Z_B)$ by adding a known leak path (resistive/inertive element).

3. Build a Population of Ear Loads

Once $(P_s)$ and $(Z_s)$ are known, simulate many possible listener ear loads:

Variable Typical Range Notes
Canal length ±5–10 mm Alters resonance frequency
Canal volume ±20–40% Affects midrange coupling
Leak area 0–1 mm² Represents pad leakage or hair
Clamp force ±2 N Changes pad compliance

For each simulated ear load $(Z_e^{(k)}(f))$:

$$ P^{(k)}(f) = P_s(f) \frac{Z_e^{(k)}(f)}{Z_s(f) + Z_e^{(k)}(f)} $$

Compute standard deviations of SPL across these virtual subjects.

Key metrics:

  • σdB(20–200 Hz): Leak sensitivity
  • σdB(2–6 kHz): Placement sensitivity
  • Δ90–10: Spread between 90th and 10th percentile responses

4. Leak Susceptibility Index (LSI)

If the full impedance method isn’t feasible, measure LSI as a simple surrogate:

  1. Measure sealed response on the 711 coupler.
  2. Add a small, repeatable leak (e.g., 0.2 mm feeler gauge, 5 mm wide).
  3. Compute:

$$ \text{LSI} = \text{Avg}(\Delta\text{SPL}_{50–200Hz}) \text{ in dB} $$

Lower LSI = greater robustness to seal variation.

5. Additional Controlled Perturbations

Metric Method Frequency Band Interpretation
Clamp-Force Sensitivity (CFS) Vary clamp ±2 N 100 Hz–1 kHz, 2–6 kHz Pad compliance robustness
Placement Sensitivity (PS) Rotate ±5°, ±10° 3–8 kHz Off-axis concha loading sensitivity

6. Ranking Criteria

Rank headphones by:

  1. Median LSI (LF stability)
  2. CFS (midband stability)
  3. PS (treble stability)
  4. $|Zₛ|/|Zₑ|$ ratio (theoretical consistency metric)

Headphones with lower $(|Z_s|)$ at low frequencies and moderate front-volume resonances perform more consistently across users.

7. Implementation Tips

  • Load control: Use adjustable micro-valves instead of shims.
  • Complex data: Keep phase; don’t rely on SPL magnitude alone.
  • Calibration: Recalibrate your coupler mic before each session.
  • Repeatability: Reseat between runs—fit variation is part of the test.
  • IEM adaptation: Vary insertion depth and canal volume for IEMs.

Conclusion

By measuring and modeling acoustic source impedance using a two-load Thevenin method, and by simulating a realistic range of ear impedances, you can predict a headphone’s fit-to-fit consistency.

For a practical shortcut, a standardized Leak Susceptibility Index (LSI) provides a robust, repeatable indicator of how consistent a headphone’s bass and lower midrange will be across listeners.