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.github/images/diagram_hearing_threshold.svg

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··· 1 1 + <svg xmlns="http://www.w3.org/2000/svg" width="900" height="600" viewBox="0 0 900 600"><rect width="900" height="600" fill="#ffffff"/><text x="450.0" y="30" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="26" font-weight="600" fill="#1a1a1a" text-anchor="middle">Hearing-threshold model (ISO 7029 age distribution, ISO 389-7 zero)</text><rect x="180.0" y="56" width="540.0" height="62.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="84" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="20" fill="#1a1a1a" text-anchor="middle" font-weight="600">Age Y, sex, population fractile Q</text><text x="450.0" y="106" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="15" fill="#666666" text-anchor="middle">audiometric frequencies 125 Hz – 8000 Hz</text><line x1="450.0" y1="118" x2="450.0" y2="143.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 152.0 L 446.4 143.0 L 453.6 143.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="152" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1f77b4" stroke-width="2"/><text x="450.0" y="178" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Median deviation from age 18 (ISO 7029, 4.2)</text><text x="450.0" y="199" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">dHmd = a · (Y − 18) ^ b (Table 1, by sex)</text><rect x="140.0" y="244" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="270" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Spread su / sl (ISO 7029, 4.3)</text><text x="450.0" y="291" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">degree-5 polynomials in (Y − 18) (Tables 2–5)</text><rect x="140.0" y="336" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="362" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Fractile threshold (ISO 7029, 4.4)</text><text x="450.0" y="383" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">dHQ = dHmd + z(Q) * s (su if Q &gt;= 0.5, else sl)</text><line x1="450.0" y1="212" x2="450.0" y2="235.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 244.0 L 446.4 235.0 L 453.6 235.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="304" x2="450.0" y2="327.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 336.0 L 446.4 327.0 L 453.6 327.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="396" x2="450.0" y2="421.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 430.0 L 446.4 421.0 L 453.6 421.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="430" width="620.0" height="58" rx="10" fill="none" stroke="#1f77b4" stroke-width="2.4"/><text x="450.0" y="456" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="19" fill="#1a1a1a" text-anchor="middle" font-weight="600">Expected hearing threshold level (dB HL)</text><text x="450.0" y="476" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#1f77b4" text-anchor="middle">referenced to the audiometric zero</text><rect x="140.0" y="506" width="620.0" height="52" rx="10" fill="#f0f2f5" stroke="#d62728" stroke-width="2"/><text x="450.0" y="530" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="17" fill="#1a1a1a" text-anchor="middle" font-weight="600">Audiometric zero = ISO 389-7 reference threshold</text><text x="450.0" y="549" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">free-field / diffuse-field (Table 1) — the dB HL / dB SPL zero</text></svg>

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··· 1 1 + <svg xmlns="http://www.w3.org/2000/svg" width="900" height="600" viewBox="0 0 900 600"><rect width="900" height="600" fill="#0d1117"/><text x="450.0" y="30" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="26" font-weight="600" fill="#e6e6e6" text-anchor="middle">Hearing-threshold model (ISO 7029 age distribution, ISO 389-7 zero)</text><rect x="180.0" y="56" width="540.0" height="62.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="84" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="20" fill="#e6e6e6" text-anchor="middle" font-weight="600">Age Y, sex, population fractile Q</text><text x="450.0" y="106" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="15" fill="#9a9a9a" text-anchor="middle">audiometric frequencies 125 Hz – 8000 Hz</text><line x1="450.0" y1="118" x2="450.0" y2="143.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 152.0 L 446.4 143.0 L 453.6 143.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="152" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#4da3d8" stroke-width="2"/><text x="450.0" y="178" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Median deviation from age 18 (ISO 7029, 4.2)</text><text x="450.0" y="199" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">dHmd = a · (Y − 18) ^ b (Table 1, by sex)</text><rect x="140.0" y="244" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="270" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Spread su / sl (ISO 7029, 4.3)</text><text x="450.0" y="291" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">degree-5 polynomials in (Y − 18) (Tables 2–5)</text><rect x="140.0" y="336" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="362" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Fractile threshold (ISO 7029, 4.4)</text><text x="450.0" y="383" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">dHQ = dHmd + z(Q) * s (su if Q &gt;= 0.5, else sl)</text><line x1="450.0" y1="212" x2="450.0" y2="235.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 244.0 L 446.4 235.0 L 453.6 235.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="304" x2="450.0" y2="327.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 336.0 L 446.4 327.0 L 453.6 327.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="396" x2="450.0" y2="421.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 430.0 L 446.4 421.0 L 453.6 421.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="430" width="620.0" height="58" rx="10" fill="none" stroke="#4da3d8" stroke-width="2.4"/><text x="450.0" y="456" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="19" fill="#e6e6e6" text-anchor="middle" font-weight="600">Expected hearing threshold level (dB HL)</text><text x="450.0" y="476" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#4da3d8" text-anchor="middle">referenced to the audiometric zero</text><rect x="140.0" y="506" width="620.0" height="52" rx="10" fill="#1c2128" stroke="#e46a6a" stroke-width="2"/><text x="450.0" y="530" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="17" fill="#e6e6e6" text-anchor="middle" font-weight="600">Audiometric zero = ISO 389-7 reference threshold</text><text x="450.0" y="549" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">free-field / diffuse-field (Table 1) — the dB HL / dB SPL zero</text></svg>

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.github/images/diagram_hearing_threshold_es.svg

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··· 1 1 + <svg xmlns="http://www.w3.org/2000/svg" width="900" height="600" viewBox="0 0 900 600"><rect width="900" height="600" fill="#ffffff"/><text x="450.0" y="30" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="26" font-weight="600" fill="#1a1a1a" text-anchor="middle">Modelo del umbral de audición (ISO 7029 por edad, cero ISO 389-7)</text><rect x="180.0" y="56" width="540.0" height="62.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="84" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="20" fill="#1a1a1a" text-anchor="middle" font-weight="600">Edad Y, sexo, fractil poblacional Q</text><text x="450.0" y="106" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="15" fill="#666666" text-anchor="middle">frecuencias audiométricas 125 Hz – 8000 Hz</text><line x1="450.0" y1="118" x2="450.0" y2="143.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 152.0 L 446.4 143.0 L 453.6 143.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="152" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1f77b4" stroke-width="2"/><text x="450.0" y="178" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Desviación mediana respecto a los 18 años (ISO 7029, 4.2)</text><text x="450.0" y="199" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">dHmd = a · (Y − 18) ^ b (Tabla 1, por sexo)</text><rect x="140.0" y="244" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="270" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Dispersión su / sl (ISO 7029, 4.3)</text><text x="450.0" y="291" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">polinomios de grado 5 en (Y − 18) (Tablas 2–5)</text><rect x="140.0" y="336" width="620.0" height="60.0" rx="10" fill="#f0f2f5" stroke="#1a1a1a" stroke-width="2"/><text x="450.0" y="362" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#1a1a1a" text-anchor="middle" font-weight="600">Umbral del fractil (ISO 7029, 4.4)</text><text x="450.0" y="383" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">dHQ = dHmd + z(Q) * s (su si Q &gt;= 0.5, si no sl)</text><line x1="450.0" y1="212" x2="450.0" y2="235.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 244.0 L 446.4 235.0 L 453.6 235.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="304" x2="450.0" y2="327.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 336.0 L 446.4 327.0 L 453.6 327.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="396" x2="450.0" y2="421.0" stroke="#1a1a1a" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 430.0 L 446.4 421.0 L 453.6 421.0 Z" fill="#1a1a1a" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="430" width="620.0" height="58" rx="10" fill="none" stroke="#1f77b4" stroke-width="2.4"/><text x="450.0" y="456" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="19" fill="#1a1a1a" text-anchor="middle" font-weight="600">Nivel del umbral de audición esperado (dB HL)</text><text x="450.0" y="476" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#1f77b4" text-anchor="middle">referido al cero audiométrico</text><rect x="140.0" y="506" width="620.0" height="52" rx="10" fill="#f0f2f5" stroke="#d62728" stroke-width="2"/><text x="450.0" y="530" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="17" fill="#1a1a1a" text-anchor="middle" font-weight="600">Cero audiométrico = umbral de referencia ISO 389-7</text><text x="450.0" y="549" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#666666" text-anchor="middle">campo libre / campo difuso (Tabla 1) — el cero dB HL / dB SPL</text></svg>

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.github/images/diagram_hearing_threshold_es_dark.svg

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··· 1 1 + <svg xmlns="http://www.w3.org/2000/svg" width="900" height="600" viewBox="0 0 900 600"><rect width="900" height="600" fill="#0d1117"/><text x="450.0" y="30" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="26" font-weight="600" fill="#e6e6e6" text-anchor="middle">Modelo del umbral de audición (ISO 7029 por edad, cero ISO 389-7)</text><rect x="180.0" y="56" width="540.0" height="62.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="84" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="20" fill="#e6e6e6" text-anchor="middle" font-weight="600">Edad Y, sexo, fractil poblacional Q</text><text x="450.0" y="106" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="15" fill="#9a9a9a" text-anchor="middle">frecuencias audiométricas 125 Hz – 8000 Hz</text><line x1="450.0" y1="118" x2="450.0" y2="143.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 152.0 L 446.4 143.0 L 453.6 143.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="152" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#4da3d8" stroke-width="2"/><text x="450.0" y="178" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Desviación mediana respecto a los 18 años (ISO 7029, 4.2)</text><text x="450.0" y="199" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">dHmd = a · (Y − 18) ^ b (Tabla 1, por sexo)</text><rect x="140.0" y="244" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="270" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Dispersión su / sl (ISO 7029, 4.3)</text><text x="450.0" y="291" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">polinomios de grado 5 en (Y − 18) (Tablas 2–5)</text><rect x="140.0" y="336" width="620.0" height="60.0" rx="10" fill="#1c2128" stroke="#e6e6e6" stroke-width="2"/><text x="450.0" y="362" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="18" fill="#e6e6e6" text-anchor="middle" font-weight="600">Umbral del fractil (ISO 7029, 4.4)</text><text x="450.0" y="383" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">dHQ = dHmd + z(Q) * s (su si Q &gt;= 0.5, si no sl)</text><line x1="450.0" y1="212" x2="450.0" y2="235.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 244.0 L 446.4 235.0 L 453.6 235.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="304" x2="450.0" y2="327.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 336.0 L 446.4 327.0 L 453.6 327.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><line x1="450.0" y1="396" x2="450.0" y2="421.0" stroke="#e6e6e6" stroke-width="1.8" stroke-linecap="round"/><path d="M 450.0 430.0 L 446.4 421.0 L 453.6 421.0 Z" fill="#e6e6e6" stroke="none" stroke-width="1.5" stroke-linejoin="round"/><rect x="140.0" y="430" width="620.0" height="58" rx="10" fill="none" stroke="#4da3d8" stroke-width="2.4"/><text x="450.0" y="456" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="19" fill="#e6e6e6" text-anchor="middle" font-weight="600">Nivel del umbral de audición esperado (dB HL)</text><text x="450.0" y="476" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#4da3d8" text-anchor="middle">referido al cero audiométrico</text><rect x="140.0" y="506" width="620.0" height="52" rx="10" fill="#1c2128" stroke="#e46a6a" stroke-width="2"/><text x="450.0" y="530" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="17" fill="#e6e6e6" text-anchor="middle" font-weight="600">Cero audiométrico = umbral de referencia ISO 389-7</text><text x="450.0" y="549" font-family="Segoe UI, Helvetica, Arial, sans-serif" font-size="14" fill="#9a9a9a" text-anchor="middle">campo libre / campo difuso (Tabla 1) — el cero dB HL / dB SPL</text></svg>

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docs/CONFORMANCE.md

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··· 15 15 16 16 ## Numerical conformance report 17 17 18 18 - &#9989; **73/73 conformance checks pass** across 15 domains and 47 standards - filters class 1 - weightings within IEC 61672-1 class 1. 18 18 + &#9989; **76/76 conformance checks pass** across 16 domains and 49 standards - filters class 1 - weightings within IEC 61672-1 class 1. 19 19 20 20 ### Numerical validation - filters &amp; weightings 21 21 ··· 233 233 234 234 </details> 235 235 236 236 + <details> 237 237 + <summary>&#9989; <b>Hearing threshold (ISO 7029 / ISO 389-7)</b> — 100% (3/3)</summary> 238 238 + 239 239 + | Standard | Quantity | Expected (norm) | Computed | &#916; | Status | 240 240 + |:---|:---|:---|:---|:---|:---:| 241 241 + | ISO 7029:2017 Table 1 | Median threshold, male age 60 at 4 kHz | 20.209 dB (+/-0.001 dB) | 20.208 dB | 0 dB | &#9989; | 242 242 + | ISO 7029:2017 Table 2 | Upper spread su, male age 60 at 1 kHz | 10.153 dB (+/-0.001 dB) | 10.153 dB | 0 dB | &#9989; | 243 243 + | ISO 389-7:2006 Table 1 | Free-field reference threshold at 1 kHz | 2.4 dB (+/-0 dB) | 2.4 dB | 0 dB | &#9989; | 244 244 + 245 245 + </details> 246 246 +

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docs/README.md

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··· 13 13 - [Psychoacoustics and Speech Intelligibility](psychoacoustics.md) — Zwicker loudness, sharpness, STI/STIPA 14 14 - [Speech Intelligibility Index](speech-intelligibility.md) — the ANSI S3.5-1997 one-third-octave-band SII: band-importance weighting (Table 3), self-speech and upward spread of masking, band audibility, and the index in noise and hearing loss 15 15 - [Room-noise criteria](room-noise.md) — the ANSI/ASA S12.2-2019 room-noise ratings: the NC tangency method (Table 1) and the RC Mark II rating with its rumble/hiss/neutral spectral tag (Annex D) 16 16 + - [Hearing threshold](hearing-threshold.md) — the age-related hearing threshold distribution (ISO 7029:2017) and the free-field/diffuse-field reference threshold of hearing (ISO 389-7:2006) 16 17 - [Sound Intensity (p-p)](intensity.md) — two-microphone intensity and field indicators 17 18 - [Room and Building Acoustics](room-acoustics.md) — impulse-response acquisition, reverberation and room parameters, open-plan speech metrics, field airborne/impact/façade sound insulation (ISO 16283-1/2/3), laboratory characterisation (ISO 10140), flanking-transmission prediction (EN 12354-1/2), measurement uncertainty (ISO 12999-1), sound absorption (ISO 354) 18 19 - [Outdoor Sound Propagation](outdoor-propagation.md) — atmospheric absorption α(f) (ISO 9613-1) and the ISO 9613-2 general method: divergence, atmospheric absorption, ground effect and barrier screening (occupational exposure ISO 9612 lives in [Levels](levels.md))

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docs/hearing-threshold.md

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··· 1 1 + ← [Documentation index](README.md) 2 2 + 3 3 + # Hearing threshold (age and reference zero) 4 4 + 5 5 + Two standards describe where the hearing threshold sits. **ISO 7029:2017** 6 6 + gives the **statistical distribution of the hearing threshold with age** for an 7 7 + otologically normal population — the slow, high-frequency-first loss known as 8 8 + presbycusis. **ISO 389-7:2006** fixes the **reference threshold of hearing**, 9 9 + the audiometric zero (0 dB HL) expressed as a sound pressure level under 10 10 + free-field and diffuse-field listening. Both are defined over the audiometric 11 11 + frequencies from 125 Hz to 8000 Hz. 12 12 + 13 13 + <picture><source media="(prefers-color-scheme: dark)" srcset="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold_dark.svg"><img src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold.svg" alt="The hearing-threshold model: age, sex and a population fractile feed the ISO 7029 chain — the median deviation from age 18 (a times (age minus 18) to the power b, from Table 1 by sex), the upper and lower spreads su and sl (degree-5 polynomials in age minus 18, Tables 2 to 5), and the fractile threshold (median plus the standard-normal quantile z of the fractile times the spread), giving the expected hearing threshold level in dB HL, which is referenced to the audiometric zero, the ISO 389-7 free-field or diffuse-field reference threshold" width="82%"></picture> 14 14 + 15 15 + ## 1. Age-related threshold (ISO 7029) 16 16 + 17 17 + For a person older than 18, the **median** hearing threshold deviation from the 18 18 + value at age 18 grows as a power law of age (ISO 7029 clause 4.2, Table 1): 19 19 + 20 20 + $$ 21 21 + \Delta H_{md} = a\,(Y - 18)^{b}, 22 22 + $$ 23 23 + 24 24 + with coefficients $a$, $b$ per frequency and sex. The spread around the median 25 25 + is modelled by two half-Gaussians whose standard deviations $s_u$ (worse than 26 26 + the median) and $s_l$ (better) are fifth-degree polynomials in $(Y - 18)$ 27 27 + (clause 4.3, Tables 2–5). Any **population fractile** $Q$ follows from the 28 28 + standard-normal quantile $z(Q)$ (clause 4.4): $\Delta H_Q = \Delta H_{md} + 29 29 + z(Q)\,s$, using $s_u$ when $z \ge 0$ and $s_l$ otherwise. 30 30 + 31 31 + ```python 32 32 + import phonometry as ph 33 33 + 34 34 + # Median threshold shift of a 65-year-old man, all audiometric frequencies. 35 35 + result = ph.age_threshold(65, "male", fractile=0.5) 36 36 + 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] 37 37 + print(result.median[8].round(1)) # 26.2 dB at 4000 Hz 38 38 + 39 39 + # The worst-hearing decile (90th percentile) at 4000 Hz: 40 40 + print(ph.age_threshold(65, "male", fractile=0.9).threshold[8].round(1)) # 50.3 41 41 + ``` 42 42 + 43 43 + The loss is largest at the high frequencies and grows with age — the classic 44 44 + downward-sloping presbycusis audiogram. Men and women follow different 45 45 + coefficients (the `sex` argument), and a subset of the audiometric frequencies 46 46 + can be requested with `frequencies=`. 47 47 + 48 48 + ## 2. Reference threshold of hearing (ISO 389-7) 49 49 + 50 50 + The audiometric zero is not a fixed sound pressure level: it depends on how the 51 51 + sound reaches the listener. ISO 389-7:2006 Table 1 gives the reference 52 52 + threshold for **free-field** (frontal incidence) and **diffuse-field** 53 53 + listening. 54 54 + 55 55 + ```python 56 56 + import phonometry as ph 57 57 + 58 58 + print(ph.reference_threshold("free-field")) 59 59 + # [22.1 11.4 4.4 2.4 2.4 2.4 -1.3 -5.8 -5.4 4.3 12.6] 60 60 + print(ph.reference_threshold("diffuse-field")[4]) # 0.8 dB at 1000 Hz 61 61 + ``` 62 62 + 63 63 + The two fields agree at low frequencies and diverge above about 1 kHz, where 64 64 + the ear-canal resonance and head diffraction make the frontal free field the 65 65 + more sensitive condition (a lower threshold) around 3–4 kHz. 66 66 + 67 67 + <picture><source media="(prefers-color-scheme: dark)" srcset="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold_dark.png"><img src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold.png" alt="Two panels. Left: the ISO 7029 median hearing-threshold deviation for men at ages 20, 40, 60 and 80, plotted on an inverted (audiogram) axis so worse hearing falls lower, with the 10 to 90 percent fractile band shaded around the 70-year curve; the loss deepens toward the high frequencies and with age. Right: the ISO 389-7 reference threshold of hearing for free-field and diffuse-field listening, which coincide below 1 kHz and diverge above it, dipping to a minimum near 3 to 4 kHz" width="96%"></picture> 68 68 + 69 69 + <details> 70 70 + <summary>Show the code for this figure</summary> 71 71 + 72 72 + ```python 73 73 + import matplotlib.pyplot as plt 74 74 + import phonometry as ph 75 75 + from phonometry.hearing import AUDIOMETRIC_FREQUENCIES as f 76 76 + 77 77 + # One line for the age distribution: 78 78 + ph.age_threshold(70, "male", 0.5).plot() 79 79 + plt.show() 80 80 + 81 81 + # By hand, both panels: 82 82 + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5)) 83 83 + for age in (20, 40, 60, 80): 84 84 + r = ph.age_threshold(age, "male", 0.5) 85 85 + ax1.plot(f, r.median, "o-", label=f"{age} yr") 86 86 + ax1.set_xscale("log"); ax1.invert_yaxis(); ax1.legend() 87 87 + 88 88 + ax2.plot(f, ph.reference_threshold("free-field"), "o-", label="Free-field") 89 89 + ax2.plot(f, ph.reference_threshold("diffuse-field"), "s--", label="Diffuse-field") 90 90 + ax2.set_xscale("log"); ax2.legend() 91 91 + plt.show() 92 92 + ``` 93 93 + 94 94 + </details> 95 95 + 96 96 + The `AgeThresholdResult` carries the `median`, the `spread_upper` and 97 97 + `spread_lower`, and the `threshold` at the requested fractile, and its 98 98 + `.plot()` draws the median with the 10–90 % band. The noise-induced permanent 99 99 + threshold shift of ISO 1999 — which adds a noise component on top of this age 100 100 + component — is a separate topic. 101 101 + 102 102 + --- 103 103 + 104 104 + **Standards.** ISO 7029:2017, *Statistical distribution of hearing thresholds 105 105 + related to age and gender* — the median (clause 4.2, Table 1), the spread 106 106 + around the median (clause 4.3, Tables 2–5) and its application (clause 4.4). 107 107 + ISO 389-7:2006, *Reference zero for the calibration of audiometric equipment — 108 108 + Reference threshold of hearing under free-field and diffuse-field listening 109 109 + conditions* (Table 1).

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scripts/conformance_report.py

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··· 1379 1379 return numeric(ref.RN_RC35_LMF, ph.room_criterion(ph.rc_curve(35.0)).lmf, 1e-9, places=3) 1380 1380 1381 1381 1382 1382 + _HEAR = "Hearing threshold (ISO 7029 / ISO 389-7)" 1383 1383 + 1384 1384 + 1385 1385 + @register(_HEAR, "ISO 7029:2017 Table 1", "Median threshold, male age 60 at 4 kHz") 1386 1386 + def _chk_hearing_median() -> Outcome: 1387 1387 + value = float(ph.age_threshold(60, "male", 0.5).median[8]) 1388 1388 + return numeric(ref.HEARING_MEDIAN_MALE_60_4KHZ, value, 1e-3, unit="dB", places=3) 1389 1389 + 1390 1390 + 1391 1391 + @register(_HEAR, "ISO 7029:2017 Table 2", "Upper spread su, male age 60 at 1 kHz") 1392 1392 + def _chk_hearing_spread() -> Outcome: 1393 1393 + value = float(ph.age_threshold(60, "male", 0.5).spread_upper[4]) 1394 1394 + return numeric(ref.HEARING_SU_MALE_60_1KHZ, value, 1e-3, unit="dB", places=3) 1395 1395 + 1396 1396 + 1397 1397 + @register(_HEAR, "ISO 389-7:2006 Table 1", "Free-field reference threshold at 1 kHz") 1398 1398 + def _chk_hearing_reference() -> Outcome: 1399 1399 + value = float(ph.reference_threshold("free-field")[4]) 1400 1400 + return numeric(ref.HEARING_REF_FREE_1KHZ, value, 1e-9, unit="dB", places=3) 1401 1401 + 1402 1402 + 1382 1403 # =========================================================================== 1383 1404 # Markdown rendering 1384 1405 # ===========================================================================

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scripts/generate_diagrams.py

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··· 69 69 "H siseo: una banda ≥ 1000 Hz supera RC en > 3 dB", 70 70 "N neutral: within both tolerances": 71 71 "N neutro: dentro de ambas tolerancias", 72 72 + # Hearing threshold (ISO 7029 / ISO 389-7) 73 73 + "Hearing-threshold model (ISO 7029 age distribution, ISO 389-7 zero)": 74 74 + "Modelo del umbral de audición (ISO 7029 por edad, cero ISO 389-7)", 75 75 + "Age Y, sex, population fractile Q": 76 76 + "Edad Y, sexo, fractil poblacional Q", 77 77 + "audiometric frequencies 125 Hz – 8000 Hz": 78 78 + "frecuencias audiométricas 125 Hz – 8000 Hz", 79 79 + "Median deviation from age 18 (ISO 7029, 4.2)": 80 80 + "Desviación mediana respecto a los 18 años (ISO 7029, 4.2)", 81 81 + "dHmd = a · (Y − 18) ^ b (Table 1, by sex)": 82 82 + "dHmd = a · (Y − 18) ^ b (Tabla 1, por sexo)", 83 83 + "Spread su / sl (ISO 7029, 4.3)": 84 84 + "Dispersión su / sl (ISO 7029, 4.3)", 85 85 + "degree-5 polynomials in (Y − 18) (Tables 2–5)": 86 86 + "polinomios de grado 5 en (Y − 18) (Tablas 2–5)", 87 87 + "Fractile threshold (ISO 7029, 4.4)": 88 88 + "Umbral del fractil (ISO 7029, 4.4)", 89 89 + "dHQ = dHmd + z(Q) * s (su if Q >= 0.5, else sl)": 90 90 + "dHQ = dHmd + z(Q) * s (su si Q >= 0.5, si no sl)", 91 91 + "Expected hearing threshold level (dB HL)": 92 92 + "Nivel del umbral de audición esperado (dB HL)", 93 93 + "referenced to the audiometric zero": 94 94 + "referido al cero audiométrico", 95 95 + "Audiometric zero = ISO 389-7 reference threshold": 96 96 + "Cero audiométrico = umbral de referencia ISO 389-7", 97 97 + "free-field / diffuse-field (Table 1) — the dB HL / dB SPL zero": 98 98 + "campo libre / campo difuso (Tabla 1) — el cero dB HL / dB SPL", 72 99 "Speech Ei'": "Habla Ei'", 73 100 "Noise Ni'": "Ruido Ni'", 74 101 "Threshold Ti'": "Umbral Ti'", ··· 2200 2227 s.text(rxc, 525, "RC-NN(A)", 23, th.fg, "middle", bold=True) 2201 2228 2202 2229 2230 2230 + def _d_hearing_threshold(s: SVG, th: Theme) -> None: 2231 2231 + """Hearing-threshold model: ISO 7029 age distribution + ISO 389-7 zero.""" 2232 2232 + cx = 450.0 2233 2233 + # --- Inputs -------------------------------------------------------------- 2234 2234 + iw, ih = 540.0, 62.0 2235 2235 + s.rect(cx - iw / 2, 56, iw, ih, th.panel, th.fg, rx=10, sw=2) 2236 2236 + s.text(cx, 84, "Age Y, sex, population fractile Q", 20, th.fg, 2237 2237 + "middle", bold=True) 2238 2238 + s.text(cx, 106, "audiometric frequencies 125 Hz – 8000 Hz", 15, th.muted, 2239 2239 + "middle") 2240 2240 + s.arrow(cx, 118, cx, 152, th.fg, 1.8) 2241 2241 + 2242 2242 + bw, bh = 620.0, 60.0 2243 2243 + x0 = cx - bw / 2 2244 2244 + 2245 2245 + def _step(y: float, l1: str, l2: str, color: str) -> None: 2246 2246 + s.rect(x0, y, bw, bh, th.panel, color, rx=10, sw=2) 2247 2247 + s.text(cx, y + 26, l1, 18, th.fg, "middle", bold=True) 2248 2248 + s.text(cx, y + 47, l2, 14, th.muted, "middle") 2249 2249 + 2250 2250 + # --- ISO 7029 chain ------------------------------------------------------ 2251 2251 + _step(152, "Median deviation from age 18 (ISO 7029, 4.2)", 2252 2252 + "dHmd = a · (Y − 18) ^ b (Table 1, by sex)", th.primary) 2253 2253 + _step(244, "Spread su / sl (ISO 7029, 4.3)", 2254 2254 + "degree-5 polynomials in (Y − 18) (Tables 2–5)", th.fg) 2255 2255 + _step(336, "Fractile threshold (ISO 7029, 4.4)", 2256 2256 + "dHQ = dHmd + z(Q) * s (su if Q >= 0.5, else sl)", th.fg) 2257 2257 + s.arrow(cx, 212, cx, 244, th.fg, 1.8) 2258 2258 + s.arrow(cx, 304, cx, 336, th.fg, 1.8) 2259 2259 + s.arrow(cx, 396, cx, 430, th.fg, 1.8) 2260 2260 + 2261 2261 + # --- Output + ISO 389-7 reference --------------------------------------- 2262 2262 + s.rect(x0, 430, bw, 58, "none", th.primary, rx=10, sw=2.4) 2263 2263 + s.text(cx, 456, "Expected hearing threshold level (dB HL)", 19, th.fg, 2264 2264 + "middle", bold=True) 2265 2265 + s.text(cx, 476, "referenced to the audiometric zero", 14, th.primary, 2266 2266 + "middle") 2267 2267 + s.rect(x0, 506, bw, 52, th.panel, th.secondary, rx=10, sw=2) 2268 2268 + s.text(cx, 530, "Audiometric zero = ISO 389-7 reference threshold", 2269 2269 + 17, th.fg, "middle", bold=True) 2270 2270 + s.text(cx, 549, "free-field / diffuse-field (Table 1) — the dB HL / dB SPL zero", 2271 2271 + 14, th.muted, "middle") 2272 2272 + 2273 2273 + 2203 2274 DIAGRAMS = { 2204 2275 "diagram_calibration_setup": (_d1, "Calibration chain — from calibrator to physical units", 560), 2205 2276 "diagram_env_measurement": (_d2, "Environmental noise measurement positions (ISO 1996-2)", 560), ··· 2258 2329 "diagram_room_noise": ( 2259 2330 _d_room_noise, 2260 2331 "Room-noise rating methods (ANSI/ASA S12.2-2019): NC and RC Mark II", 580), 2332 2332 + "diagram_hearing_threshold": ( 2333 2333 + _d_hearing_threshold, 2334 2334 + "Hearing-threshold model (ISO 7029 age distribution, ISO 389-7 zero)", 600), 2261 2335 } 2262 2336 2263 2337

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scripts/generate_graphs.py

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··· 4 4 from typing import Any 5 5 6 6 import matplotlib.pyplot as plt 7 7 + import matplotlib.ticker as mticker 7 8 import numpy as np 8 9 from scipy import signal as scipy_signal 9 10 ··· 205 206 "Nivel de presi\u00f3n sonora por banda de octava [dB]", 206 207 "Rumble tol. (+5 dB)": "Tol. retumbo (+5 dB)", 207 208 "Hiss tol. (+3 dB)": "Tol. siseo (+3 dB)", 209 209 + "ISO 7029 — age-related threshold (male)": 210 210 + "ISO 7029 — umbral por edad (hombres)", 211 211 + "ISO 389-7 — reference threshold of hearing": 212 212 + "ISO 389-7 — umbral de referencia de la audición", 213 213 + "Audiometric frequency [Hz]": "Frecuencia audiométrica [Hz]", 214 214 + "Median threshold deviation from age 18 [dB]": 215 215 + "Desviación mediana del umbral respecto a los 18 años [dB]", 216 216 + "Reference threshold [dB]": "Umbral de referencia [dB]", 217 217 + "Free-field (frontal)": "Campo libre (frontal)", 218 218 + "Diffuse-field": "Campo difuso", 208 219 "Sound Intensity with a p-p Probe (IEC 61043)": 209 220 "Intensidad sonora con sonda p-p (IEC 61043)", 210 221 "Plane wave: Lp \u2248 LI": "Onda plana: Lp \u2248 LI", ··· 431 442 r"Criterios de sala Mark II RC-\1"), 432 443 (r"^Tangent @ (.+) Hz$", r"Tangente @ \1 Hz"), 433 444 (r"^Reference RC-(.+)$", r"Referencia RC-\1"), 445 445 + (r"^(\d+) yr$", r"\1 años"), 446 446 + (r"^10-90 % band \((\d+) yr\)$", r"banda 10-90 % (\1 años)"), 434 447 ] 435 448 436 449 ··· 3473 3486 plt.close() 3474 3487 3475 3488 3489 3489 + def generate_hearing_threshold(output_dir: str) -> None: 3490 3490 + """ISO 7029 age-related threshold and ISO 389-7 reference threshold.""" 3491 3491 + print("Generating hearing_threshold.png...") 3492 3492 + from phonometry import age_threshold, reference_threshold 3493 3493 + from phonometry.hearing import AUDIOMETRIC_FREQUENCIES 3494 3494 + 3495 3495 + freqs = AUDIOMETRIC_FREQUENCIES 3496 3496 + fig, (ax_age, ax_ref) = plt.subplots(1, 2, figsize=(12.5, 5.6)) 3497 3497 + 3498 3498 + # --- Left: ISO 7029 median threshold by age (male) + 10-90 % band @70. --- 3499 3499 + ages = [(20, COLOR_GRID), (40, "#7f7f7f"), (60, COLOR_PRIMARY), 3500 3500 + (80, COLOR_SECONDARY)] 3501 3501 + for age, color in ages: 3502 3502 + r = age_threshold(age, "male", 0.5) 3503 3503 + ax_age.plot(freqs, r.median, "o-", color=color, label=f"{age} yr") 3504 3504 + r70 = age_threshold(70, "male", 0.5) 3505 3505 + z90 = 1.2816 3506 3506 + ax_age.fill_between(freqs, r70.median - z90 * r70.spread_lower, 3507 3507 + r70.median + z90 * r70.spread_upper, 3508 3508 + color=COLOR_PRIMARY, alpha=0.12, 3509 3509 + label="10-90 % band (70 yr)") 3510 3510 + ax_age.set_xscale("log") 3511 3511 + ax_age.set_xticks(list(freqs)) 3512 3512 + ax_age.set_xticklabels([f"{f:g}" for f in freqs], rotation=45, ha="right") 3513 3513 + ax_age.xaxis.set_minor_formatter(mticker.NullFormatter()) 3514 3514 + ax_age.invert_yaxis() 3515 3515 + ax_age.set_xlabel("Audiometric frequency [Hz]") 3516 3516 + ax_age.set_ylabel("Median threshold deviation from age 18 [dB]") 3517 3517 + ax_age.set_title("ISO 7029 — age-related threshold (male)", 3518 3518 + fontweight="bold", pad=10) 3519 3519 + ax_age.grid(which="both", color=COLOR_GRID, linestyle="-", alpha=0.4) 3520 3520 + ax_age.set_axisbelow(True) 3521 3521 + ax_age.legend(loc="lower left") 3522 3522 + 3523 3523 + # --- Right: ISO 389-7 reference threshold, free vs diffuse field. --- 3524 3524 + ax_ref.plot(freqs, reference_threshold("free-field"), "o-", 3525 3525 + color=COLOR_PRIMARY, label="Free-field (frontal)") 3526 3526 + ax_ref.plot(freqs, reference_threshold("diffuse-field"), "s--", 3527 3527 + color=COLOR_SECONDARY, label="Diffuse-field") 3528 3528 + ax_ref.set_xscale("log") 3529 3529 + ax_ref.set_xticks(list(freqs)) 3530 3530 + ax_ref.set_xticklabels([f"{f:g}" for f in freqs], rotation=45, ha="right") 3531 3531 + ax_ref.xaxis.set_minor_formatter(mticker.NullFormatter()) 3532 3532 + ax_ref.set_xlabel("Audiometric frequency [Hz]") 3533 3533 + ax_ref.set_ylabel("Reference threshold [dB]") 3534 3534 + ax_ref.set_title("ISO 389-7 — reference threshold of hearing", 3535 3535 + fontweight="bold", pad=10) 3536 3536 + ax_ref.grid(which="both", color=COLOR_GRID, linestyle="-", alpha=0.4) 3537 3537 + ax_ref.set_axisbelow(True) 3538 3538 + ax_ref.legend(loc="upper left") 3539 3539 + 3540 3540 + plt.tight_layout() 3541 3541 + plt.savefig(themed_path(output_dir, "hearing_threshold.png")) 3542 3542 + plt.close() 3543 3543 + 3544 3544 + 3476 3545 def generate_all(img_dir: str) -> None: 3477 3546 """Generate every documentation figure for the currently active theme.""" 3478 3547 generate_filter_type_comparison(img_dir) ··· 3550 3619 3551 3620 # Room-noise criteria (ANSI S12.2-2019): NC tangency and RC Mark II. 3552 3621 generate_room_noise_criteria(img_dir) 3622 3622 + 3623 3623 + # Hearing threshold (ISO 7029 age-related, ISO 389-7 reference). 3624 3624 + generate_hearing_threshold(img_dir) 3553 3625 3554 3626 # Psychoacoustics / open-plan plots (sharpness weighting, spatial decay) 3555 3627 generate_sharpness_weighting(img_dir)

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site/astro.config.mjs

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··· 291 291 { 292 292 label: 'Perception & speech', 293 293 translations: { es: 'Percepción e inteligibilidad' }, 294 294 - items: ['guides/psychoacoustics', 'guides/speech-intelligibility'], 294 294 + items: ['guides/psychoacoustics', 'guides/speech-intelligibility', 'guides/hearing-threshold'], 295 295 }, 296 296 { 297 297 label: 'Sound power & intensity',

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site/src/content/docs/es/guides/hearing-threshold.md

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··· 1 1 + --- 2 2 + title: "Umbral de audición (edad y cero de referencia)" 3 3 + description: "La distribución del umbral de audición por edad de ISO 7029:2017 (mediana, dispersión y fractiles poblacionales por edad y sexo) y el umbral de referencia de la audición en campo libre y campo difuso de ISO 389-7:2006, sobre las frecuencias audiométricas de 125 Hz a 8000 Hz." 4 4 + --- 5 5 + 6 6 + Dos normas describen dónde se sitúa el umbral de audición. **ISO 7029:2017** da 7 7 + la **distribución estadística del umbral de audición con la edad** para una 8 8 + población otológicamente normal — la pérdida lenta y primero en altas 9 9 + frecuencias conocida como presbiacusia. **ISO 389-7:2006** fija el **umbral de 10 10 + referencia de la audición**, el cero audiométrico (0 dB HL) expresado como nivel 11 11 + de presión sonora en escucha de campo libre y campo difuso. Ambas se definen 12 12 + sobre las frecuencias audiométricas de 125 Hz a 8000 Hz. 13 13 + 14 14 + <img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold_es.svg" alt="El modelo del umbral de audición: la edad, el sexo y un fractil poblacional alimentan la cadena de ISO 7029 — la desviación mediana respecto a los 18 años, las dispersiones superior e inferior su y sl, y el umbral del fractil — dando el nivel del umbral de audición esperado en dB HL, referido al cero audiométrico de campo libre o campo difuso de ISO 389-7" style="width:82%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold_es_dark.svg" alt="El modelo del umbral de audición: la edad, el sexo y un fractil poblacional alimentan la cadena de ISO 7029 — la desviación mediana respecto a los 18 años, las dispersiones superior e inferior su y sl, y el umbral del fractil — dando el nivel del umbral de audición esperado en dB HL, referido al cero audiométrico de campo libre o campo difuso de ISO 389-7" style="width:82%"> 15 15 + 16 16 + ## 1. Umbral por edad (ISO 7029) 17 17 + 18 18 + Para una persona mayor de 18 años, la desviación **mediana** del umbral de 19 19 + audición respecto al valor a los 18 años crece como una ley de potencias de la 20 20 + edad (ISO 7029, cláusula 4.2, Tabla 1): 21 21 + 22 22 + $$ 23 23 + \Delta H_{md} = a\,(Y - 18)^{b}, 24 24 + $$ 25 25 + 26 26 + con coeficientes $a$, $b$ por frecuencia y sexo. La dispersión en torno a la 27 27 + mediana se modela con dos semi-gaussianas cuyas desviaciones típicas $s_u$ (peor 28 28 + que la mediana) y $s_l$ (mejor) son polinomios de grado cinco en $(Y - 18)$ 29 29 + (cláusula 4.3, Tablas 2–5). Cualquier **fractil poblacional** $Q$ se obtiene del 30 30 + cuantil normal estándar $z(Q)$ (cláusula 4.4): $\Delta H_Q = \Delta H_{md} + 31 31 + z(Q)\,s$, usando $s_u$ cuando $z \ge 0$ y $s_l$ en caso contrario. 32 32 + 33 33 + ```python 34 34 + import phonometry as ph 35 35 + 36 36 + # Median threshold shift of a 65-year-old man, all audiometric frequencies. 37 37 + result = ph.age_threshold(65, "male", fractile=0.5) 38 38 + 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] 39 39 + print(result.median[8].round(1)) # 26.2 dB at 4000 Hz 40 40 + 41 41 + # The worst-hearing decile (90th percentile) at 4000 Hz: 42 42 + print(ph.age_threshold(65, "male", fractile=0.9).threshold[8].round(1)) # 50.3 43 43 + ``` 44 44 + 45 45 + La pérdida es mayor en las altas frecuencias y crece con la edad — el 46 46 + audiograma descendente clásico de la presbiacusia. Hombres y mujeres siguen 47 47 + coeficientes distintos (el argumento `sex`), y puede pedirse un subconjunto de 48 48 + las frecuencias audiométricas con `frequencies=`. 49 49 + 50 50 + ## 2. Umbral de referencia de la audición (ISO 389-7) 51 51 + 52 52 + El cero audiométrico no es un nivel de presión sonora fijo: depende de cómo 53 53 + llega el sonido al oyente. La Tabla 1 de ISO 389-7:2006 da el umbral de 54 54 + referencia para escucha de **campo libre** (incidencia frontal) y **campo 55 55 + difuso**. 56 56 + 57 57 + ```python 58 58 + import phonometry as ph 59 59 + 60 60 + print(ph.reference_threshold("free-field")) 61 61 + # [22.1 11.4 4.4 2.4 2.4 2.4 -1.3 -5.8 -5.4 4.3 12.6] 62 62 + print(ph.reference_threshold("diffuse-field")[4]) # 0.8 dB at 1000 Hz 63 63 + ``` 64 64 + 65 65 + Ambos campos coinciden en baja frecuencia y divergen por encima de 1 kHz 66 66 + aproximadamente, donde la resonancia del canal auditivo y la difracción de la 67 67 + cabeza hacen del campo libre frontal la condición más sensible (un umbral más 68 68 + bajo) en torno a 3–4 kHz. 69 69 + 70 70 + <img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold_es.png" alt="Dos paneles. Izquierda: la desviación mediana del umbral de audición de ISO 7029 para hombres a los 20, 40, 60 y 80 años en un eje de audiograma invertido, con la banda del 10 al 90 por ciento en torno a la curva de 70 años; la pérdida se acentúa hacia las altas frecuencias y con la edad. Derecha: el umbral de referencia de campo libre y campo difuso de ISO 389-7, que coinciden por debajo de 1 kHz y divergen por encima, con un mínimo cerca de 3 a 4 kHz" style="width:96%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold_es_dark.png" alt="Dos paneles. Izquierda: la desviación mediana del umbral de audición de ISO 7029 para hombres a los 20, 40, 60 y 80 años en un eje de audiograma invertido, con la banda del 10 al 90 por ciento en torno a la curva de 70 años; la pérdida se acentúa hacia las altas frecuencias y con la edad. Derecha: el umbral de referencia de campo libre y campo difuso de ISO 389-7, que coinciden por debajo de 1 kHz y divergen por encima, con un mínimo cerca de 3 a 4 kHz" style="width:96%"> 71 71 + 72 72 + <details> 73 73 + <summary>Mostrar el código de esta figura</summary> 74 74 + 75 75 + ```python 76 76 + import matplotlib.pyplot as plt 77 77 + import phonometry as ph 78 78 + from phonometry.hearing import AUDIOMETRIC_FREQUENCIES as f 79 79 + 80 80 + # One line for the age distribution: 81 81 + ph.age_threshold(70, "male", 0.5).plot() 82 82 + plt.show() 83 83 + 84 84 + # By hand, both panels: 85 85 + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5)) 86 86 + for age in (20, 40, 60, 80): 87 87 + r = ph.age_threshold(age, "male", 0.5) 88 88 + ax1.plot(f, r.median, "o-", label=f"{age} yr") 89 89 + ax1.set_xscale("log"); ax1.invert_yaxis(); ax1.legend() 90 90 + 91 91 + ax2.plot(f, ph.reference_threshold("free-field"), "o-", label="Free-field") 92 92 + ax2.plot(f, ph.reference_threshold("diffuse-field"), "s--", label="Diffuse-field") 93 93 + ax2.set_xscale("log"); ax2.legend() 94 94 + plt.show() 95 95 + ``` 96 96 + 97 97 + </details> 98 98 + 99 99 + El `AgeThresholdResult` lleva la `median`, las dispersiones `spread_upper` y 100 100 + `spread_lower`, y el `threshold` en el fractil pedido, y su `.plot()` dibuja la 101 101 + mediana con la banda del 10–90 %. El desplazamiento permanente del umbral 102 102 + inducido por ruido de ISO 1999 — que añade una componente de ruido sobre esta 103 103 + componente de edad — es un tema aparte. 104 104 + 105 105 + --- 106 106 + 107 107 + **Normas.** ISO 7029:2017, *Statistical distribution of hearing thresholds 108 108 + related to age and gender* — la mediana (cláusula 4.2, Tabla 1), la dispersión 109 109 + en torno a la mediana (cláusula 4.3, Tablas 2–5) y su aplicación (cláusula 4.4). 110 110 + ISO 389-7:2006, *Reference zero for the calibration of audiometric equipment — 111 111 + Reference threshold of hearing under free-field and diffuse-field listening 112 112 + conditions* (Tabla 1).

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site/src/content/docs/guides/hearing-threshold.md

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··· 1 1 + --- 2 2 + title: "Hearing threshold (age and reference zero)" 3 3 + description: "The age-related hearing threshold distribution of ISO 7029:2017 (median, spread and population fractiles by age and sex) and the ISO 389-7:2006 free-field and diffuse-field reference threshold of hearing, over the audiometric frequencies from 125 Hz to 8000 Hz." 4 4 + --- 5 5 + 6 6 + Two standards describe where the hearing threshold sits. **ISO 7029:2017** 7 7 + gives the **statistical distribution of the hearing threshold with age** for an 8 8 + otologically normal population — the slow, high-frequency-first loss known as 9 9 + presbycusis. **ISO 389-7:2006** fixes the **reference threshold of hearing**, 10 10 + the audiometric zero (0 dB HL) expressed as a sound pressure level under 11 11 + free-field and diffuse-field listening. Both are defined over the audiometric 12 12 + frequencies from 125 Hz to 8000 Hz. 13 13 + 14 14 + <img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold.svg" alt="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" style="width:82%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/diagram_hearing_threshold_dark.svg" alt="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" style="width:82%"> 15 15 + 16 16 + ## 1. Age-related threshold (ISO 7029) 17 17 + 18 18 + For a person older than 18, the **median** hearing threshold deviation from the 19 19 + value at age 18 grows as a power law of age (ISO 7029 clause 4.2, Table 1): 20 20 + 21 21 + $$ 22 22 + \Delta H_{md} = a\,(Y - 18)^{b}, 23 23 + $$ 24 24 + 25 25 + with coefficients $a$, $b$ per frequency and sex. The spread around the median 26 26 + is modelled by two half-Gaussians whose standard deviations $s_u$ (worse than 27 27 + the median) and $s_l$ (better) are fifth-degree polynomials in $(Y - 18)$ 28 28 + (clause 4.3, Tables 2–5). Any **population fractile** $Q$ follows from the 29 29 + standard-normal quantile $z(Q)$ (clause 4.4): $\Delta H_Q = \Delta H_{md} + 30 30 + z(Q)\,s$, using $s_u$ when $z \ge 0$ and $s_l$ otherwise. 31 31 + 32 32 + ```python 33 33 + import phonometry as ph 34 34 + 35 35 + # Median threshold shift of a 65-year-old man, all audiometric frequencies. 36 36 + result = ph.age_threshold(65, "male", fractile=0.5) 37 37 + 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] 38 38 + print(result.median[8].round(1)) # 26.2 dB at 4000 Hz 39 39 + 40 40 + # The worst-hearing decile (90th percentile) at 4000 Hz: 41 41 + print(ph.age_threshold(65, "male", fractile=0.9).threshold[8].round(1)) # 50.3 42 42 + ``` 43 43 + 44 44 + The loss is largest at the high frequencies and grows with age — the classic 45 45 + downward-sloping presbycusis audiogram. Men and women follow different 46 46 + coefficients (the `sex` argument), and a subset of the audiometric frequencies 47 47 + can be requested with `frequencies=`. 48 48 + 49 49 + ## 2. Reference threshold of hearing (ISO 389-7) 50 50 + 51 51 + The audiometric zero is not a fixed sound pressure level: it depends on how the 52 52 + sound reaches the listener. ISO 389-7:2006 Table 1 gives the reference 53 53 + threshold for **free-field** (frontal incidence) and **diffuse-field** 54 54 + listening. 55 55 + 56 56 + ```python 57 57 + import phonometry as ph 58 58 + 59 59 + print(ph.reference_threshold("free-field")) 60 60 + # [22.1 11.4 4.4 2.4 2.4 2.4 -1.3 -5.8 -5.4 4.3 12.6] 61 61 + print(ph.reference_threshold("diffuse-field")[4]) # 0.8 dB at 1000 Hz 62 62 + ``` 63 63 + 64 64 + The two fields agree at low frequencies and diverge above about 1 kHz, where 65 65 + the ear-canal resonance and head diffraction make the frontal free field the 66 66 + more sensitive condition (a lower threshold) around 3–4 kHz. 67 67 + 68 68 + <img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold.png" alt="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" style="width:96%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/hearing_threshold_dark.png" alt="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" style="width:96%"> 69 69 + 70 70 + <details> 71 71 + <summary>Show the code for this figure</summary> 72 72 + 73 73 + ```python 74 74 + import matplotlib.pyplot as plt 75 75 + import phonometry as ph 76 76 + from phonometry.hearing import AUDIOMETRIC_FREQUENCIES as f 77 77 + 78 78 + # One line for the age distribution: 79 79 + ph.age_threshold(70, "male", 0.5).plot() 80 80 + plt.show() 81 81 + 82 82 + # By hand, both panels: 83 83 + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5)) 84 84 + for age in (20, 40, 60, 80): 85 85 + r = ph.age_threshold(age, "male", 0.5) 86 86 + ax1.plot(f, r.median, "o-", label=f"{age} yr") 87 87 + ax1.set_xscale("log"); ax1.invert_yaxis(); ax1.legend() 88 88 + 89 89 + ax2.plot(f, ph.reference_threshold("free-field"), "o-", label="Free-field") 90 90 + ax2.plot(f, ph.reference_threshold("diffuse-field"), "s--", label="Diffuse-field") 91 91 + ax2.set_xscale("log"); ax2.legend() 92 92 + plt.show() 93 93 + ``` 94 94 + 95 95 + </details> 96 96 + 97 97 + The `AgeThresholdResult` carries the `median`, the `spread_upper` and 98 98 + `spread_lower`, and the `threshold` at the requested fractile, and its 99 99 + `.plot()` draws the median with the 10–90 % band. The noise-induced permanent 100 100 + threshold shift of ISO 1999 — which adds a noise component on top of this age 101 101 + component — is a separate topic. 102 102 + 103 103 + --- 104 104 + 105 105 + **Standards.** ISO 7029:2017, *Statistical distribution of hearing thresholds 106 106 + related to age and gender* — the median (clause 4.2, Table 1), the spread 107 107 + around the median (clause 4.3, Tables 2–5) and its application (clause 4.4). 108 108 + ISO 389-7:2006, *Reference zero for the calibration of audiometric equipment — 109 109 + Reference threshold of hearing under free-field and diffuse-field listening 110 110 + conditions* (Table 1).

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src/phonometry/__init__.py

Reviewed

··· 38 38 ) 39 39 from .loudness_contours import equal_loudness_contour, hearing_threshold, loudness_level 40 40 from .sharpness import sharpness_din, sharpness_din_from_specific 41 41 + from .hearing import ( 42 42 + AgeThresholdResult, 43 43 + age_threshold, 44 44 + reference_threshold, 45 45 + ) 41 46 from .room_noise import ( 42 47 NCResult, 43 48 RCResult, ··· 402 407 "rc_curve", 403 408 "NCResult", 404 409 "RCResult", 410 410 + "age_threshold", 411 411 + "reference_threshold", 412 412 + "AgeThresholdResult", 405 413 "sweep_signal", 406 414 "inverse_filter", 407 415 "impulse_response",

+44

src/phonometry/_plotting.py

Reviewed

··· 37 37 from .loudness_moore_glasberg_time import MooreGlasbergTimeVaryingLoudness 38 38 from .room_acoustics import DecayCurve, RoomAcousticsResult 39 39 from .room_ir import ImpulseResponseResult 40 40 + from .hearing import AgeThresholdResult 40 41 from .room_noise import NCResult, RCResult 41 42 from .tonality_ecma import EcmaTonality 42 43 from .roughness_ecma import EcmaRoughness ··· 80 81 81 82 def _freq_axis(ax: Axes, freqs: np.ndarray) -> None: 82 83 """Configure a logarithmic frequency x-axis labelled with band centres.""" 84 84 + import matplotlib.ticker as mticker 85 85 + 83 86 ax.set_xscale("log") 84 87 ax.set_xticks(list(freqs)) 85 88 ax.set_xticklabels([_format_freq(f) for f in freqs], rotation=45, ha="right") 89 89 + # Suppress the log-scale minor-tick labels (2x10^2, 3x10^2, ...) that would 90 90 + # otherwise collide with off-decade band centres such as 750 or 1500 Hz. 91 91 + ax.xaxis.set_minor_formatter(mticker.NullFormatter()) 86 92 ax.set_xlabel("Frequency [Hz]") 87 93 88 94 ··· 1431 1437 ax.legend(loc=_LEGEND_UPPER_RIGHT, fontsize="small") 1432 1438 ax.grid(True, which="both", alpha=0.3) 1433 1439 return ax 1440 1440 + 1441 1441 + 1442 1442 + # --------------------------------------------------------------------------- 1443 1443 + # Age-related hearing threshold (ISO 7029) 1444 1444 + # --------------------------------------------------------------------------- 1445 1445 + 1446 1446 + 1447 1447 + def plot_age_threshold( 1448 1448 + result: "AgeThresholdResult", ax: Axes | None = None, **kwargs: Any 1449 1449 + ) -> Axes: 1450 1450 + """Median age-related hearing threshold with the 10-90 % fractile band. 1451 1451 + 1452 1452 + :param result: An :class:`~phonometry.hearing.AgeThresholdResult`. 1453 1453 + :param ax: Existing axes, or ``None`` to create a figure. 1454 1454 + :param kwargs: Forwarded to the median line ``plot``. 1455 1455 + :return: The axes. 1456 1456 + """ 1457 1457 + ax = ax if ax is not None else _new_axes() 1458 1458 + freqs = np.asarray(result.frequencies, dtype=np.float64) 1459 1459 + median = np.asarray(result.median, dtype=np.float64) 1460 1460 + su = np.asarray(result.spread_upper, dtype=np.float64) 1461 1461 + sl = np.asarray(result.spread_lower, dtype=np.float64) 1462 1462 + z90 = 1.2816 # standard-normal quantile of 0.9 1463 1463 + 1464 1464 + ax.fill_between(freqs, median - z90 * sl, median + z90 * su, 1465 1465 + color="#aec7e8", alpha=0.5, label="10-90 % fractile band") 1466 1466 + kwargs.setdefault("color", "#1f77b4") 1467 1467 + ax.plot(freqs, median, "o-", label="Median", **kwargs) 1468 1468 + if abs(result.fractile - 0.5) > 1e-9: 1469 1469 + ax.plot(freqs, np.asarray(result.threshold, dtype=np.float64), "s--", 1470 1470 + color="#d62728", label=f"Fractile {result.fractile:g}") 1471 1471 + _freq_axis(ax, freqs) 1472 1472 + ax.set_ylabel("Threshold deviation from age 18 [dB]") 1473 1473 + ax.invert_yaxis() # audiogram convention: worse hearing downward 1474 1474 + ax.set_title(f"ISO 7029 hearing threshold — {result.sex}, age {result.age:g}") 1475 1475 + ax.legend(loc=_LEGEND_UPPER_RIGHT, fontsize="small") 1476 1476 + ax.grid(True, which="both", alpha=0.3) 1477 1477 + return ax

+279

src/phonometry/hearing.py

Reviewed

··· 1 1 + # Copyright (c) 2026. Jose M. Requena-Plens 2 2 + """ 3 3 + Age-related hearing threshold (ISO 7029:2017) and audiometric reference zero 4 4 + (ISO 389-7:2006). 5 5 + 6 6 + Implements the statistical distribution of the hearing threshold of an 7 7 + otologically normal population as a function of age and sex (ISO 7029:2017), 8 8 + and the reference threshold of hearing under free-field and diffuse-field 9 9 + listening (ISO 389-7:2006, Table 1), over the audiometric frequencies from 10 10 + 125 Hz to 8000 Hz. 11 11 + 12 12 + ISO 7029 gives the median threshold deviation from the value at age 18 as 13 13 + ``dHmd = a * (age - 18) ** b`` (clause 4.2, Table 1) and the spread around the 14 14 + median as two half-Gaussian standard deviations ``su`` (worse than median) and 15 15 + ``sl`` (better than median), each a fifth-degree polynomial in ``age - 18`` 16 16 + (clause 4.3, Tables 2-5). A population fractile is obtained by shifting the 17 17 + median by the standard-normal quantile times the appropriate spread 18 18 + (clause 4.4 / Annex A). 19 19 + 20 20 + The noise-induced permanent threshold shift of ISO 1999 (which combines a noise 21 21 + component with this age component) is not part of this module. 22 22 + """ 23 23 + 24 24 + from __future__ import annotations 25 25 + 26 26 + from dataclasses import dataclass 27 27 + from typing import TYPE_CHECKING, Any 28 28 + 29 29 + import numpy as np 30 30 + 31 31 + if TYPE_CHECKING: 32 32 + from matplotlib.axes import Axes 33 33 + 34 34 + from numpy.typing import ArrayLike 35 35 + 36 36 + # --------------------------------------------------------------------------- 37 37 + # Normative constants. 38 38 + # --------------------------------------------------------------------------- 39 39 + 40 40 + #: Audiometric frequencies, in hertz (ISO 7029 Table 1 / ISO 389-7 Table 1). 41 41 + AUDIOMETRIC_FREQUENCIES: np.ndarray = np.array( 42 42 + [125.0, 250.0, 500.0, 750.0, 1000.0, 1500.0, 2000.0, 3000.0, 4000.0, 43 43 + 6000.0, 8000.0], 44 44 + dtype=np.float64, 45 45 + ) 46 46 + 47 47 + #: Median coefficients ``(a, b)`` of ``dHmd = a*(age-18)**b`` (ISO 7029 Table 1). 48 48 + _MEDIAN_MALE: np.ndarray = np.array( 49 49 + [[2.50e-6, 3.841], [1.39e-4, 2.832], [4.59e-4, 2.537], [5.70e-4, 2.512], 50 50 + [7.02e-4, 2.494], [1.09e-3, 2.446], [1.56e-3, 2.404], [2.54e-3, 2.350], 51 51 + [3.40e-3, 2.325], [4.53e-3, 2.315], [5.06e-3, 2.328]], 52 52 + dtype=np.float64, 53 53 + ) 54 54 + _MEDIAN_FEMALE: np.ndarray = np.array( 55 55 + [[6.16e-4, 2.451], [3.98e-4, 2.568], [2.61e-4, 2.708], [2.25e-4, 2.775], 56 56 + [2.21e-4, 2.805], [2.53e-4, 2.813], [3.12e-4, 2.792], [4.88e-4, 2.728], 57 57 + [7.37e-4, 2.660], [1.47e-3, 2.539], [2.53e-3, 2.439]], 58 58 + dtype=np.float64, 59 59 + ) 60 60 + 61 61 + #: Upper-spread ``su`` polynomial coefficients c0..c5 (ISO 7029 Table 2, male). 62 62 + _SU_MALE: np.ndarray = np.array( 63 63 + [[4.63, 0.645, -8.85e-2, 3.69e-3, -5.98e-5, 3.39e-7], 64 64 + [5.27, 0.710, -9.13e-2, 3.64e-3, -5.74e-5, 3.22e-7], 65 65 + [4.98, 0.751, -9.20e-2, 3.68e-3, -5.84e-5, 3.28e-7], 66 66 + [4.65, 0.733, -8.81e-2, 3.59e-3, -5.76e-5, 3.24e-7], 67 67 + [4.42, 0.714, -8.54e-2, 3.57e-3, -5.82e-5, 3.29e-7], 68 68 + [4.14, 0.679, -8.04e-2, 3.52e-3, -5.89e-5, 3.35e-7], 69 69 + [4.10, 0.632, -7.53e-2, 3.46e-3, -5.94e-5, 3.40e-7], 70 70 + [4.29, 0.530, -6.28e-2, 3.09e-3, -5.37e-5, 2.95e-7], 71 71 + [4.68, 0.455, -5.52e-2, 2.95e-3, -5.30e-5, 2.92e-7], 72 72 + [5.61, 0.363, -4.72e-2, 2.92e-3, -5.58e-5, 3.12e-7], 73 73 + [6.62, 0.291, -4.16e-2, 2.92e-3, -5.85e-5, 3.33e-7]], 74 74 + dtype=np.float64, 75 75 + ) 76 76 + #: Lower-spread ``sl`` polynomial coefficients c0..c5 (ISO 7029 Table 3, male). 77 77 + _SL_MALE: np.ndarray = np.array( 78 78 + [[3.34, 0.131, -2.02e-2, 1.12e-3, -2.28e-5, 1.57e-7], 79 79 + [3.32, 0.230, -2.54e-2, 1.20e-3, -2.27e-5, 1.46e-7], 80 80 + [3.43, 0.362, -4.11e-2, 1.87e-3, -3.44e-5, 2.21e-7], 81 81 + [3.60, 0.384, -4.43e-2, 1.98e-3, -3.55e-5, 2.22e-7], 82 82 + [3.77, 0.363, -4.19e-2, 1.82e-3, -3.14e-5, 1.89e-7], 83 83 + [3.93, 0.365, -4.22e-2, 1.79e-3, -2.96e-5, 1.70e-7], 84 84 + [4.01, 0.387, -4.47e-2, 1.87e-3, -3.02e-5, 1.69e-7], 85 85 + [4.11, 0.405, -4.56e-2, 1.86e-3, -2.83e-5, 1.46e-7], 86 86 + [4.09, 0.439, -4.78e-2, 1.92e-3, -2.84e-5, 1.40e-7], 87 87 + [4.01, 0.497, -4.97e-2, 1.93e-3, -2.67e-5, 1.18e-7], 88 88 + [3.90, 0.559, -5.62e-2, 2.40e-3, -3.92e-5, 2.29e-7]], 89 89 + dtype=np.float64, 90 90 + ) 91 91 + #: Upper-spread ``su`` polynomial coefficients c0..c5 (ISO 7029 Table 4, female). 92 92 + _SU_FEMALE: np.ndarray = np.array( 93 93 + [[5.05, 0.400, -4.60e-2, 1.73e-3, -2.75e-5, 1.71e-7], 94 94 + [5.01, 0.481, -4.88e-2, 1.80e-3, -2.81e-5, 1.67e-7], 95 95 + [4.68, 0.510, -5.16e-2, 1.95e-3, -3.07e-5, 1.77e-7], 96 96 + [4.45, 0.511, -5.25e-2, 2.03e-3, -3.18e-5, 1.81e-7], 97 97 + [4.34, 0.492, -5.15e-2, 2.03e-3, -3.18e-5, 1.78e-7], 98 98 + [4.23, 0.479, -5.12e-2, 2.07e-3, -3.26e-5, 1.80e-7], 99 99 + [4.26, 0.456, -4.91e-2, 2.01e-3, -3.16e-5, 1.70e-7], 100 100 + [4.36, 0.476, -5.15e-2, 2.19e-3, -3.51e-5, 1.91e-7], 101 101 + [4.61, 0.477, -5.07e-2, 2.19e-3, -3.51e-5, 1.88e-7], 102 102 + [5.22, 0.483, -4.83e-2, 2.13e-3, -3.39e-5, 1.74e-7], 103 103 + [5.84, 0.516, -4.89e-2, 2.18e-3, -3.49e-5, 1.77e-7]], 104 104 + dtype=np.float64, 105 105 + ) 106 106 + #: Lower-spread ``sl`` polynomial coefficients c0..c5 (ISO 7029 Table 5, female). 107 107 + _SL_FEMALE: np.ndarray = np.array( 108 108 + [[3.64, 0.047, 2.28e-3, -6.68e-5, -8.72e-7, 2.30e-8], 109 109 + [3.11, 0.226, -7.71e-3, 9.83e-5, -7.11e-7, 9.02e-9], 110 110 + [2.98, 0.338, -1.74e-2, 3.53e-4, -2.78e-6, 1.01e-8], 111 111 + [3.03, 0.378, -2.24e-2, 5.20e-4, -4.60e-6, 1.50e-8], 112 112 + [3.15, 0.382, -2.39e-2, 5.62e-4, -4.60e-6, 9.87e-9], 113 113 + [3.32, 0.387, -2.64e-2, 6.71e-4, -5.76e-6, 1.07e-8], 114 114 + [3.47, 0.392, -2.84e-2, 7.79e-4, -7.35e-6, 1.71e-8], 115 115 + [3.69, 0.392, -2.96e-2, 8.44e-4, -7.55e-6, 8.16e-9], 116 116 + [3.84, 0.402, -3.17e-2, 9.99e-4, -1.08e-5, 2.99e-8], 117 117 + [4.04, 0.403, -3.15e-2, 1.06e-3, -1.21e-5, 3.44e-8], 118 118 + [4.15, 0.413, -3.01e-2, 1.00e-3, -9.97e-6, 8.74e-9]], 119 119 + dtype=np.float64, 120 120 + ) 121 121 + 122 122 + _MEDIAN = {"male": _MEDIAN_MALE, "female": _MEDIAN_FEMALE} 123 123 + _SU = {"male": _SU_MALE, "female": _SU_FEMALE} 124 124 + _SL = {"male": _SL_MALE, "female": _SL_FEMALE} 125 125 + SEXES: tuple[str, ...] = ("male", "female") 126 126 + 127 127 + #: Reference threshold of hearing, in dB, free-field then diffuse-field, at 128 128 + #: :data:`AUDIOMETRIC_FREQUENCIES` (ISO 389-7:2006 Table 1). 129 129 + _REFERENCE_FREE: np.ndarray = np.array( 130 130 + [22.1, 11.4, 4.4, 2.4, 2.4, 2.4, -1.3, -5.8, -5.4, 4.3, 12.6], 131 131 + dtype=np.float64, 132 132 + ) 133 133 + _REFERENCE_DIFFUSE: np.ndarray = np.array( 134 134 + [22.1, 11.4, 3.8, 1.2, 0.8, 1.0, -1.5, -4.0, -3.8, 1.4, 6.8], 135 135 + dtype=np.float64, 136 136 + ) 137 137 + _REFERENCE = {"free-field": _REFERENCE_FREE, "diffuse-field": _REFERENCE_DIFFUSE} 138 138 + FIELDS: tuple[str, ...] = ("free-field", "diffuse-field") 139 139 + 140 140 + _REFERENCE_AGE = 18.0 # lower age limit of the ISO 7029 formulae. 141 141 + 142 142 + 143 143 + @dataclass(frozen=True) 144 144 + class AgeThresholdResult: 145 145 + """Age-related hearing threshold distribution (ISO 7029:2017). 146 146 + 147 147 + All arrays are in dB and aligned with :data:`AUDIOMETRIC_FREQUENCIES`. 148 148 + 149 149 + :ivar age: Listener age, in years. 150 150 + :ivar sex: ``"male"`` or ``"female"``. 151 151 + :ivar fractile: Population fractile of ``threshold`` (0-1). 152 152 + :ivar frequencies: Audiometric frequencies, in hertz. 153 153 + :ivar median: Median threshold deviation from age 18 (clause 4.2). 154 154 + :ivar spread_upper: Upper half-Gaussian standard deviation ``su``. 155 155 + :ivar spread_lower: Lower half-Gaussian standard deviation ``sl``. 156 156 + :ivar threshold: Threshold deviation at ``fractile`` (clause 4.4). 157 157 + """ 158 158 + 159 159 + age: float 160 160 + sex: str 161 161 + fractile: float 162 162 + frequencies: np.ndarray 163 163 + median: np.ndarray 164 164 + spread_upper: np.ndarray 165 165 + spread_lower: np.ndarray 166 166 + threshold: np.ndarray 167 167 + 168 168 + def plot(self, ax: "Axes | None" = None, **kwargs: Any) -> "Axes": 169 169 + """Plot the median threshold with the fractile band over frequency. 170 170 + 171 171 + Requires matplotlib (``pip install phonometry[plot]``); returns the 172 172 + :class:`~matplotlib.axes.Axes`. 173 173 + """ 174 174 + from ._plotting import plot_age_threshold 175 175 + 176 176 + return plot_age_threshold(self, ax=ax, **kwargs) 177 177 + 178 178 + 179 179 + def _select(values: np.ndarray, frequencies: ArrayLike | None) -> np.ndarray: 180 180 + """Return ``values`` for a requested frequency subset, or all of them.""" 181 181 + if frequencies is None: 182 182 + return values.copy() 183 183 + fr = np.atleast_1d(np.asarray(frequencies, dtype=np.float64)) 184 184 + idx = [] 185 185 + for f in fr: 186 186 + matches = np.isclose(AUDIOMETRIC_FREQUENCIES, f, rtol=1e-3) 187 187 + if not matches.any(): 188 188 + raise ValueError( 189 189 + f"frequency {f} Hz is not an ISO 7029 audiometric frequency " 190 190 + f"(125 Hz - 8000 Hz)." 191 191 + ) 192 192 + idx.append(int(np.argmax(matches))) 193 193 + return values[idx] 194 194 + 195 195 + 196 196 + def _spread(coeffs: np.ndarray, u: float) -> np.ndarray: 197 197 + """Evaluate the degree-5 spread polynomials (ascending powers) at ``u``.""" 198 198 + powers = u ** np.arange(coeffs.shape[1], dtype=np.float64) 199 199 + return coeffs @ powers 200 200 + 201 201 + 202 202 + def age_threshold( 203 203 + age: float, 204 204 + sex: str = "male", 205 205 + fractile: float = 0.5, 206 206 + frequencies: ArrayLike | None = None, 207 207 + ) -> AgeThresholdResult: 208 208 + """Age-related hearing threshold distribution (ISO 7029:2017). 209 209 + 210 210 + Returns, per audiometric frequency, the median threshold deviation from the 211 211 + value at age 18 (clause 4.2), the upper/lower half-Gaussian spreads 212 212 + (clause 4.3) and the threshold at the requested population ``fractile`` 213 213 + (clause 4.4): ``median + z * spread`` where ``z`` is the standard-normal 214 214 + quantile of ``fractile`` and the spread is the upper one for ``z >= 0`` 215 215 + (worse than the median) or the lower one otherwise. 216 216 + 217 217 + :param age: Listener age, in years (must be at least 18). The standard's 218 218 + formulae are established up to 80 years for frequencies at or below 219 219 + 2000 Hz and up to 70 years above; ages beyond that extrapolate. 220 220 + :param sex: ``"male"`` or ``"female"``. 221 221 + :param fractile: Population fractile in the open interval (0, 1); ``0.5`` 222 222 + gives the median. 223 223 + :param frequencies: Optional subset of the audiometric frequencies, in 224 224 + hertz; ``None`` uses all eleven (125 Hz - 8000 Hz). 225 225 + :return: An :class:`AgeThresholdResult` with the distribution and ``.plot()``. 226 226 + :raises ValueError: for an age below 18, an unknown sex, a fractile outside 227 227 + (0, 1), or an unknown frequency. 228 228 + """ 229 229 + if age < _REFERENCE_AGE: 230 230 + raise ValueError( 231 231 + f"age must be at least {_REFERENCE_AGE:.0f} years (the ISO 7029 " 232 232 + f"lower limit); got {age}." 233 233 + ) 234 234 + if sex not in _MEDIAN: 235 235 + raise ValueError(f"sex must be one of {SEXES}; got {sex!r}.") 236 236 + if not 0.0 < fractile < 1.0: 237 237 + raise ValueError(f"fractile must be in (0, 1); got {fractile}.") 238 238 + 239 239 + from scipy.special import ndtri # standard-normal quantile 240 240 + 241 241 + u = float(age) - _REFERENCE_AGE 242 242 + med_coeffs = _MEDIAN[sex] 243 243 + median = med_coeffs[:, 0] * u ** med_coeffs[:, 1] 244 244 + su = _spread(_SU[sex], u) 245 245 + sl = _spread(_SL[sex], u) 246 246 + 247 247 + z = float(ndtri(fractile)) 248 248 + threshold = median + z * (su if z >= 0.0 else sl) 249 249 + 250 250 + return AgeThresholdResult( 251 251 + age=float(age), 252 252 + sex=sex, 253 253 + fractile=float(fractile), 254 254 + frequencies=_select(AUDIOMETRIC_FREQUENCIES, frequencies), 255 255 + median=_select(median, frequencies), 256 256 + spread_upper=_select(su, frequencies), 257 257 + spread_lower=_select(sl, frequencies), 258 258 + threshold=_select(threshold, frequencies), 259 259 + ) 260 260 + 261 261 + 262 262 + def reference_threshold( 263 263 + field: str = "free-field", frequencies: ArrayLike | None = None 264 264 + ) -> np.ndarray: 265 265 + """Reference threshold of hearing (ISO 389-7:2006, Table 1). 266 266 + 267 267 + The sound pressure level, in dB, that corresponds to the audiometric zero 268 268 + (0 dB HL) under the given listening condition, at the audiometric 269 269 + frequencies. 270 270 + 271 271 + :param field: ``"free-field"`` (frontal incidence) or ``"diffuse-field"``. 272 272 + :param frequencies: Optional subset of the audiometric frequencies, in 273 273 + hertz; ``None`` uses all eleven (125 Hz - 8000 Hz). 274 274 + :return: The reference threshold, in dB, aligned with the frequencies. 275 275 + :raises ValueError: for an unknown field or frequency. 276 276 + """ 277 277 + if field not in _REFERENCE: 278 278 + raise ValueError(f"field must be one of {FIELDS}; got {field!r}.") 279 279 + return _select(_REFERENCE[field], frequencies)

+11

tests/reference_data.py

Reviewed

··· 469 469 RN_NC40_SELF = 40.0 # NC-40 curve -> tangency rating (Table 1) 470 470 RN_RC31_63HZ = 51.0 # RC-31 curve, 63 Hz octave-band level (Table D.1) 471 471 RN_RC35_LMF = 35.0 # RC-35 curve, mid-frequency average LMF (clause D.4) 472 472 + 473 473 + # --------------------------------------------------------------------------- 474 474 + # Hearing thresholds - ISO 7029:2017 (age) and ISO 389-7:2006 (reference). 475 475 + # The median deviation follows a*(age-18)**b (Table 1); at 4 kHz for a 60-year 476 476 + # male it is 20.21 dB. The upper spread su is a degree-5 polynomial (Table 2); 477 477 + # at 1 kHz age 60 male it is 10.15 dB. The free-field reference threshold at 478 478 + # 1 kHz is 2.4 dB (ISO 389-7 Table 1). 479 479 + # --------------------------------------------------------------------------- 480 480 + HEARING_MEDIAN_MALE_60_4KHZ = 20.2085 # dB, ISO 7029 Table 1 median formula 481 481 + HEARING_SU_MALE_60_1KHZ = 10.1533 # dB, ISO 7029 Table 2 upper spread 482 482 + HEARING_REF_FREE_1KHZ = 2.4 # dB, ISO 389-7 Table 1 free-field

+114

tests/test_hearing.py

Reviewed

··· 1 1 + # Copyright (c) 2026. Jose M. Requena-Plens 2 2 + """Tests for :mod:`phonometry.hearing` (ISO 7029:2017 and ISO 389-7:2006). 3 3 + 4 4 + The age-related model is validated against the standard's own boundary 5 5 + behaviour (at age 18 the median deviation is zero and the spreads equal the 6 6 + constant polynomial terms of Tables 2-5) and its monotonic/sex trends, and the 7 7 + reference threshold against the ISO 389-7 Table 1 values. 8 8 + """ 9 9 + 10 10 + from __future__ import annotations 11 11 + 12 12 + import numpy as np 13 13 + import pytest 14 14 + 15 15 + from phonometry import hearing as h 16 16 + 17 17 + 18 18 + def test_frequency_and_table_shapes() -> None: 19 19 + assert h.AUDIOMETRIC_FREQUENCIES.size == 11 20 20 + assert h.AUDIOMETRIC_FREQUENCIES[0] == 125.0 21 21 + assert h.AUDIOMETRIC_FREQUENCIES[-1] == 8000.0 22 22 + for table in (h._SU_MALE, h._SL_MALE, h._SU_FEMALE, h._SL_FEMALE): 23 23 + assert table.shape == (11, 6) 24 24 + for table in (h._MEDIAN_MALE, h._MEDIAN_FEMALE): 25 25 + assert table.shape == (11, 2) 26 26 + 27 27 + 28 28 + @pytest.mark.parametrize("sex", ["male", "female"]) 29 29 + def test_reference_age_is_zero_median(sex: str) -> None: 30 30 + # ISO 7029 clause 4.2: at age 18 the median deviation is zero everywhere, 31 31 + # and the spreads reduce to the constant terms c0 of Tables 2-5. 32 32 + result = h.age_threshold(18, sex, 0.5) 33 33 + np.testing.assert_allclose(result.median, 0.0, atol=1e-12) 34 34 + np.testing.assert_allclose(result.threshold, 0.0, atol=1e-12) 35 35 + np.testing.assert_allclose(result.spread_upper, h._SU[sex][:, 0]) 36 36 + np.testing.assert_allclose(result.spread_lower, h._SL[sex][:, 0]) 37 37 + 38 38 + 39 39 + def test_median_matches_reference_values() -> None: 40 40 + # Reference median deviations computed from the Table 1 formula. 41 41 + male = h.age_threshold(60, "male", 0.5) 42 42 + assert male.median[4] == pytest.approx(7.8473, abs=1e-3) # 1000 Hz 43 43 + assert male.median[8] == pytest.approx(20.2085, abs=1e-3) # 4000 Hz 44 44 + female = h.age_threshold(60, "female", 0.5) 45 45 + assert female.median[8] == pytest.approx(15.3218, abs=1e-3) 46 46 + 47 47 + 48 48 + def test_median_increases_with_age() -> None: 49 49 + m = [h.age_threshold(a, "male", 0.5).median[8] for a in (18, 30, 50, 70)] 50 50 + assert all(x < y for x, y in zip(m, m[1:])) 51 51 + assert m[0] == pytest.approx(0.0, abs=1e-12) 52 52 + 53 53 + 54 54 + def test_fractiles_bracket_the_median() -> None: 55 55 + # A worse fractile (0.9) lies above the median; a better one (0.1) below. 56 56 + median = h.age_threshold(60, "male", 0.5).threshold 57 57 + worse = h.age_threshold(60, "male", 0.9).threshold 58 58 + better = h.age_threshold(60, "male", 0.1).threshold 59 59 + assert np.all(better < median) 60 60 + assert np.all(worse > median) 61 61 + 62 62 + 63 63 + def test_male_median_exceeds_female_at_high_frequency() -> None: 64 64 + male = h.age_threshold(70, "male", 0.5).median[8] # 4000 Hz 65 65 + female = h.age_threshold(70, "female", 0.5).median[8] 66 66 + assert male > female 67 67 + 68 68 + 69 69 + def test_reference_threshold_matches_iso389_7() -> None: 70 70 + free = h.reference_threshold("free-field") 71 71 + diffuse = h.reference_threshold("diffuse-field") 72 72 + # ISO 389-7:2006 Table 1 (audiometric frequencies). 73 73 + assert free[4] == pytest.approx(2.4) # 1000 Hz free-field 74 74 + assert free[10] == pytest.approx(12.6) # 8000 Hz free-field 75 75 + assert diffuse[4] == pytest.approx(0.8) # 1000 Hz diffuse-field 76 76 + # Free- and diffuse-field agree at low frequencies, diverge higher up. 77 77 + assert free[0] == diffuse[0] 78 78 + assert free[4] != diffuse[4] 79 79 + 80 80 + 81 81 + def test_subset_by_frequency() -> None: 82 82 + result = h.age_threshold(60, "male", 0.5, frequencies=[1000, 4000]) 83 83 + np.testing.assert_allclose(result.frequencies, [1000.0, 4000.0]) 84 84 + assert result.median[0] == pytest.approx(7.8473, abs=1e-3) 85 85 + ref = h.reference_threshold("free-field", frequencies=[1000, 8000]) 86 86 + np.testing.assert_allclose(ref, [2.4, 12.6]) 87 87 + 88 88 + 89 89 + def test_invalid_inputs_raise() -> None: 90 90 + with pytest.raises(ValueError, match="at least 18"): 91 91 + h.age_threshold(10, "male") 92 92 + with pytest.raises(ValueError, match="sex must be"): 93 93 + h.age_threshold(40, "other") 94 94 + with pytest.raises(ValueError, match="fractile"): 95 95 + h.age_threshold(40, "male", fractile=1.0) 96 96 + with pytest.raises(ValueError, match="audiometric frequency"): 97 97 + h.age_threshold(40, "male", frequencies=[777.0]) 98 98 + with pytest.raises(ValueError, match="field must be"): 99 99 + h.reference_threshold("random") 100 100 + 101 101 + 102 102 + def test_result_fields_and_plot() -> None: 103 103 + import matplotlib 104 104 + 105 105 + matplotlib.use("Agg") 106 106 + import matplotlib.pyplot as plt 107 107 + 108 108 + result = h.age_threshold(55, "female", 0.75) 109 109 + assert result.age == 55.0 110 110 + assert result.sex == "female" 111 111 + assert result.threshold.shape == (11,) 112 112 + ax = result.plot() 113 113 + assert isinstance(ax, plt.Axes) 114 114 + plt.close("all")