Hearing threshold (age and reference zero)

Two standards describe where the hearing threshold sits. ISO 7029:2017 gives the statistical distribution of the hearing threshold with age for an otologically normal population: the slow, high-frequency-first loss known as presbycusis. ISO 389-7:2005 fixes the reference threshold of hearing, the audiometric zero (0 dB HL) expressed as a sound pressure level under free-field and diffuse-field listening. Here both are returned on the same eleven audiometric frequencies, 125 Hz to 8000 Hz, so they combine band for band.

$The hearing-threshold model: age, sex and a population fractile feed the ISO 7029 chain (the median deviation from age 18, the upper and lower spreads su and sl, and the fractile threshold), giving the expected hearing threshold level in dB HL, referenced to the ISO 389-7 free-field or diffuse-field audiometric zero$

For a person older than 18, the median hearing threshold deviation from the value at age 18 grows as a power law of age (ISO 7029 clause 4.2, Table 1):

Δ H_{m d} = a (Y - 18)^{b},

with coefficients $a$ , $b$ per frequency and sex. The spread around the median is modelled by two half-Gaussians whose standard deviations $s_{u}$ (worse than the median) and $s_{l}$ (better) are fifth-degree polynomials in $(Y - 18)$ (clause 4.3, Tables 2–5). Any population fractile $Q$ follows from the standard-normal quantile $z (Q)$ (clause 4.4): $Δ H_{Q} = Δ H_{m d} + z (Q) s$ , using $s_{u}$ when $z \geq 0$ and $s_{l}$ otherwise.

from phonometry import hearing

# Median threshold shift of a 65-year-old man, all audiometric frequencies.
result = hearing.age_threshold(65, "male", fractile=0.5)
print(result.median.round(1))     # [ 6.6  7.6  8.  9.  10.4 13.4 16.3 21.6 26.2 33.7 39.5]
print(result.median[8].round(1))  # 26.2 dB at 4000 Hz

# The worst-hearing decile (90th percentile) at 4000 Hz:
print(hearing.age_threshold(65, "male", fractile=0.9).threshold[8].round(1))  # 50.3

result.plot()   # the median with the 10-90 % fractile band (needs matplotlib)

The loss is largest at the high frequencies and grows with age: the classic downward-sloping presbycusis audiogram. Men and women follow different coefficients (the sex argument), and a subset of the audiometric frequencies can be requested with frequencies=.

Where the model stops. ISO 7029:2017 specifies its coefficients for ages 18 to 80 years over the audiometric frequencies 125 Hz to 8000 Hz (clause 4.1), and adds a caution of its own: from 3000 Hz to 8000 Hz the values above 70 years are informative only, because at those frequencies the threshold of many of the oldest subjects could not be measured at all — it ran off the audiometer’s scale — so the fitted spread there rests on a truncated sample. The power law is anchored at 18 years, where the median deviation is zero by construction, and an age below that is refused outright, since the quantity is defined as a deviation from 18. Nothing stops it at the top, though: age_threshold(90, "male") returns 106.7 dB at 8 kHz, silently, and that is an extrapolation the standard does not support. Quote such a value as an extrapolation or stop at the limit. The fractile inherits the same weakness: it describes a screened population of finite size, so the far tails are least supported exactly where the far ages are.

Who counts as “otologically normal”. The ISO 7029 population is not the general population: it is people screened to be in a normal state of health, free from signs or symptoms of ear disease and wax obstruction, and (the demanding part) with no history of undue noise exposure, ototoxic drugs or familial hearing loss. The model therefore isolates pure ageing: it is the baseline that other standards subtract from. A real, unscreened workforce tends to have higher thresholds on average (not necessarily at every age or frequency), which is why ISO 1999 supplies an unscreened population as an alternate reference (its “database B”) for studies whose goal is comparison with an actual population rather than isolating the noise effect.

Reading the percentiles. A fractile is a population statement, not a prediction for a person: fractile=0.9 returns the threshold that 90 % of otologically normal people of that age and sex are better than (only the worst-hearing tenth exceeds it), and fractile=0.5 the median: half above, half below. The spread is deliberately asymmetric (two half-Gaussians, with $s_{u} > s_{l}$ over most of the range): ageing drags a minority far down while the better-hearing half stays bunched near the median, so the far percentiles on the bad side move much faster with age than the good side ever improves. An individual audiogram can sit anywhere in that fan; the model tells you how surprising it is, not what it should be.

Two panels at 4000 Hz against age from 18 to 80 years. Left: the ISO 7029 median deviation for men and women, both rising from zero at 18 to 50.0 dB and 43.2 dB at 80, the shaded gap between them widening from 4.9 dB at 60 years to 6.8 dB at 80. Right: the upper and lower spreads for men, the upper spread rising to a peak of 18.8 dB at 64 years and then falling back until it crosses under the lower spread at 75 years, with ages above 70 shaded and marked informative only

Both claims of the paragraph above, drawn at 4 kHz. Left: men and women follow different coefficients, and the gap grows with age — 4.9 dB at 60 years and 6.8 dB at 80 — so a fractile statement without a sex attached is meaningless. Right: the asymmetry is real but not permanent. $s_{u}$ pulls away from $s_{l}$ until about 64 years, then falls back and crosses under it at 75. That reversal is an artefact with a name: from 3 kHz upwards the threshold of many of the oldest subjects could not be measured at all, which is why ISO 7029 clause 4.1 marks everything above 70 years at those frequencies as informative only.

Show the code for this figure

import matplotlib.pyplot as plt
import numpy as np

# `hearing` is the import of the first snippet on this page.
ages = np.arange(18.0, 81.0)
i = 8   # 4000 Hz, the ninth audiometric frequency

fig, (ax_sex, ax_spread) = plt.subplots(1, 2, figsize=(12.5, 5.4))
for sex, style in (("male", "-"), ("female", "--")):
    med = [hearing.age_threshold(a, sex, 0.5).median[i] for a in ages]
    ax_sex.plot(ages, med, style, label=sex)
ax_sex.legend()

res = [hearing.age_threshold(a, "male", 0.5) for a in ages]
su = np.array([r.spread_upper[i] for r in res])
sl = np.array([r.spread_lower[i] for r in res])
ax_spread.plot(ages, su, "-", label="s_u")
ax_spread.plot(ages, sl, "--", label="s_l")
ax_spread.axvline(70.0, linestyle=":")      # informative only above here
ax_spread.legend()
plt.show()

AgeThresholdResult.plot() draws that fan directly: the median, the requested fractile and the 10 % to 90 % fractile band, on an audiogram axis.

$ISO 7029 hearing-threshold deviation of a 70-year-old man on an inverted audiogram axis from 125 Hz to 8000 Hz: the median deepens from about 10 dB at 125 Hz to 50 dB at 8000 Hz, the requested 90 % fractile from about 22 dB to 74 dB, and the shaded 10 to 90 percent band between them widens steadily toward the high frequencies$

Show the code for this figure

import matplotlib.pyplot as plt
from phonometry import hearing

# A 70-year-old man, worst-hearing decile: the median presbycusis slope with
# the population spread around it.
res = hearing.age_threshold(70, "male", fractile=0.9)
print(res.median.round(1))
print(res.threshold.round(1))     # the 90 % fractile

# One line: the median, the fractile and the 10-90 % band.
res.plot()
plt.show()

The band is the whole point of the model. At 500 Hz the fractiles of a 70-year-old span a handful of decibels, so an individual audiogram there is informative; at 8 kHz they span tens of decibels, so a single measured value says little about whether that ear is unusual. Any statement of the form “this person has lost more hearing than their age explains” is a statement about where they sit in this fan, and it needs the fractile, not the median.

Where the age component goes next. ISO 7029 is not only an audiology reference: it is the age input of the noise-induced-hearing-loss model. ISO 1999:2013 calls it database A and its clause 6.1 Formula (1) combines the age threshold $H$ with the noise-induced shift $N$ into the threshold a real audiogram would show, $H^{'} = H + N - H N /120$ , at the same fractile. In practice that means the two guides chain: pick the population and fractile here, add the exposure there, and compare the result, never the noise component alone, against a measured audiogram. The noise-induced hearing loss guide picks the chain up at that point.

2. Reference threshold of hearing (ISO 389-7)

The audiometric zero is not a fixed sound pressure level: it depends on how the sound reaches the listener. ISO 389-7:2005 Table 1 gives the reference threshold for free-field (frontal incidence) and diffuse-field listening. That table is a one-third-octave table of 38 rows running from 20 Hz to 18 000 Hz; reference_threshold carries only the eleven audiometric rows ISO 7029 also uses, so the two functions align band for band and can be added without resampling. Any other frequency raises rather than interpolating, because the standard tabulates the threshold and defines no interpolation between its rows.

from phonometry import hearing

print(hearing.reference_threshold("free-field"))
# [22.1 11.4  4.4  2.4  2.4  2.4 -1.3 -5.8 -5.4  4.3 12.6]
print(hearing.reference_threshold("diffuse-field")[4])   # 0.8 dB at 1000 Hz

What the reference zero is referenced to

These values calibrate sound-field audiometry — the loudspeaker-based test methods of ISO 8253-2 — and not earphone audiometry. They hold under the four conditions ISO 389-7 clause 1 lists, and only those:

The field. With the listener absent, the field is a free progressive plane wave with the source directly in front (frontal incidence), or a diffuse field qualified as ISO 8253-2 specifies.
The signal. A pure tone in the free field; a one-third-octave band of white or pink noise in the diffuse field. Up to 8 kHz either column also applies to any other noise band narrower than the critical band.
The measurement point. The sound pressure level is measured with the listener absent, at the point the centre of the listener’s head will occupy — not at the ear, and not with the subject in the chair.
The ears. Listening is binaural.

The values also carry a procedure. Definition 3.1 notes that the whole ISO 389 series rests on the threshold procedure of ISO 8253-1, and that a test procedure with other characteristics can be expected to give thresholds differing by up to several decibels on average. A survey therefore records the procedure it used, not only the levels it obtained.

The trap is the clinical audiogram. 0 dB HL on an audiometer is the reference equivalent threshold sound pressure level of ISO 389-1 (supra-aural), ISO 389-2 (insert) or ISO 389-8 (circumaural) for the earphone actually fitted, referred to an acoustic coupler or an ear simulator, and obtained monaurally. ISO 389-7 clause 1 states outright that its data differ from those and that a direct comparison is not appropriate. reference_threshold("free-field") is the zero of a loudspeaker-based test; it is never a conversion factor for a headphone audiogram.

Three panels of the listening conditions behind ISO 389-7 Table 1. A, free field: a loudspeaker on the reference axis at least 1 m from the reference point at zero degrees azimuth and elevation, a boom-mounted measurement microphone with its capsule exactly at that point, and the listener and chair drawn dashed because both are absent while the level is measured; a dashed square marks the plus or minus 0.15 metre volume that must stay within plus or minus 1 dB up to 4 kHz. B, diffuse field: four loudspeakers around the same absent listener with non-coherent feeds and rays arriving from every direction, the same reference point and microphone. C, for contrast: a listener present, wearing a supra-aural earphone whose level is referred to an IEC 60318-1 coupler, labelled as the reference zero of ISO 389-1, -2 or -8 and never an ISO 389-7 value

The two fields agree at low frequencies and diverge above about 1 kHz, where the ear-canal resonance and head diffraction make the frontal free field the more sensitive condition (a lower threshold) around 3–4 kHz.

From a dB HL threshold to a sound pressure level. Audiometric zero is the sound pressure level of the reference threshold, so a threshold in dB HL becomes a physical level by adding the ISO 389-7 value for the same frequency and the same listening condition, $L_{p} = HL + T_{f}$ :

hl = hearing.age_threshold(65, "male", 0.5).median      # dB HL, the §1 median
free = hl + hearing.reference_threshold("free-field")
diffuse = hl + hearing.reference_threshold("diffuse-field")
print(hl[8].round(1), free[8].round(1), diffuse[8].round(1))  # 26.2 20.8 22.4

The 65-year-old man’s median 26.2 dB HL at 4 kHz is a sound pressure level of 20.8 dB under frontal free-field listening and 22.4 dB in a diffuse field: the same ear needs 1.6 dB less pressure in the free field, because head diffraction and the ear-canal resonance give it more gain there. Three things make that addition legitimate, and all three belong in the report. The ISO 7029 output is a deviation from the median 18-year-old, and it is a hearing threshold level in dB HL only insofar as the reference zero is that same median — ISO 7029 clause 1 says exactly this, and its NOTE 2 warns that the two do not always coincide, because the reference zeros were established on subjects up to 25 or 30 years old whose hearing is on average slightly worse. The two standards also describe different listening conditions (ISO 7029 monaural through earphones, ISO 389-7 binaural in a sound field), so the sum estimates the field level that ear would need rather than reproducing a measurement. And the field is a listening condition, not a measurement option: pick the one that matches how the sound actually reaches the listener, and never mix a diffuse-field threshold with a free-field speech spectrum in the same calculation.

$Two panels. Left: the ISO 7029 median hearing-threshold deviation for men at ages 20, 40, 60 and 80 on an inverted audiogram axis, with the 10 to 90 percent fractile band around the 70-year curve; the loss deepens toward high frequencies and with age. Right: the ISO 389-7 free-field and diffuse-field reference threshold, coinciding below 1 kHz and diverging above, dipping to a minimum near 3 to 4 kHz$

Show the code for this figure

import matplotlib.pyplot as plt
from phonometry import hearing
from phonometry.hearing import AUDIOMETRIC_FREQUENCIES as f

# One line for the age distribution:
hearing.age_threshold(70, "male", 0.5).plot()
plt.show()

# By hand, both panels:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
for age in (20, 40, 60, 80):
    r = hearing.age_threshold(age, "male", 0.5)
    ax1.plot(f, r.median, "o-", label=f"{age} yr")
ax1.set_xscale("log"); ax1.invert_yaxis(); ax1.legend()

ax2.plot(f, hearing.reference_threshold("free-field"), "o-", label="Free-field")
ax2.plot(f, hearing.reference_threshold("diffuse-field"), "s--", label="Diffuse-field")
ax2.set_xscale("log"); ax2.legend()
plt.show()

The AgeThresholdResult carries the median, the spread_upper and spread_lower, and the threshold at the requested fractile, and its .plot() draws the median with the 10–90 % band. The noise-induced permanent threshold shift of ISO 1999, which adds a noise component on top of this age component, is the subject of the noise-induced hearing loss guide.

What this guide covers

Covered
ISO 7029:2017’s age model: the median power-law deviation from age 18 (clause 4.2, Table 1), the asymmetric half-Gaussian spreads $s_{u}$ and $s_{l}$ (clause 4.3, Tables 2–5), and the population-fractile calculation of clause 4.4, all implemented by age_threshold(age, sex, fractile). ISO 389-7:2005 Table 1’s free-field and diffuse-field reference threshold of hearing at the eleven audiometric frequencies, returned by reference_threshold(field), together with the clause 1 listening conditions that define it.
Not covered
ISO 1999:2013 clause 6.1 Formula (1) combines this age threshold with a noise-induced shift into a real audiogram. That combination is implemented, by htlan, but it is documented in the noise-induced hearing loss guide rather than here; this page stops at the age component. Of ISO 389-7:2005, this module returns only the eleven audiometric rows of Table 1. The other 27 — the third octaves from 20 Hz to 100 Hz, the intermediate third octaves between the audiometric points, and the extended high frequencies from 9 kHz to 18 kHz — are not carried, and neither is Amendment 1:2016, so low-frequency and extended-high-frequency work has to read the table itself. The earphone reference zeros of ISO 389-1/-2/-8, the sound-field audiometric procedure of ISO 8253-2, and how the ISO 389-7 values were established, are not implemented.

References

International Organization for Standardization. (2005). Acoustics — Reference zero for the calibration of audiometric equipment — Part 7: Reference threshold of hearing under free-field and diffuse-field listening conditions (ISO 389-7:2005). The audiometric zero of section 2 (Table 1), implemented here through its European adoption EN ISO 389-7:2006.
International Organization for Standardization. (2017). Acoustics — Statistical distribution of hearing thresholds related to age and gender (ISO 7029:2017). The age model of section 1: the median power law (clause 4.2, Table 1), the asymmetric spread around the median (clause 4.3, Tables 2–5) and the fractile machinery and its application (clause 4.4).

Created and maintained by José Manuel Requena Plens ORCID All projects

Hearing threshold (age and reference zero)

1. Age-related threshold (ISO 7029)

2. Reference threshold of hearing (ISO 389-7)

What the reference zero is referenced to

What this guide covers

See also

References