Source: https://docs.jmrp.io/phonometry/perception/hearing/audiometry/ # Audiometric Test Methods (ISO 8253-1 and -2) An audiogram is a set of hearing threshold levels, and each of them rests on a room quiet enough not to mask the faintest tone, a rule that turns "heard" and "not heard" into one number, and an uncertainty. ISO 8253-1 sets all three out for earphones and bone vibrators, and ISO 8253-2 adds what a loudspeaker needs: a room whose sound field is known. ## Is the room quiet enough? (ISO 8253-1 Clause 11) Tables 2 and 4 give the maximum permissible ambient sound pressure level $L_{S,\mathrm{max}}$ per one-third-octave band from 31.5 Hz to 8 kHz, for air conduction with supra-aural earphones and for bone conduction, and for the lowest test frequency (125 Hz, 250 Hz or, with earphones, 500 Hz). An earphone that excludes more noise adds the difference of the attenuations of Table 3, a lowest hearing threshold level other than 0 dB is added band by band, and a threshold shift of +5 dB instead of +2 dB adds 8 dB (11.1 and the NOTEs): $$ L_{S,\mathrm{max}}' = L_{S,\mathrm{max}} + \left(A_\mathrm{earphone} - A_\mathrm{supra\text{-}aural}\right) + L_\mathrm{HT,min} + \Delta $$ ```python import numpy as np from phonometry import hearing # One-third-octave ambient levels of a single-walled booth, 31.5 Hz to 8 kHz. booth = [50, 48, 45, 43, 40, 36, 30, 24, 19, 16, 14, 12, 11, 10, 10, 10, 9, 9, 9, 8, 8, 8, 8, 8, 8] supra_aural = hearing.check_audiometric_ambient_noise(booth) print(supra_aural.passes, supra_aural.lowest_measurable_hearing_level_db) # False 3.0 insert = hearing.check_audiometric_ambient_noise(booth, earphone="ER-3A") print(insert.passes) # True bone = hearing.check_audiometric_ambient_noise( booth, presentation="bone", lowest_test_frequency_hz=250 ) print(bone.lowest_measurable_hearing_level_db) # 6.0 ``` `presentation="sound field"` judges the room against ISO 8253-2 Table 2, up to 12.5 kHz, derived from ISO 8253-1 for binaural listening (footnote a); laid side by side, its cells are ISO 8253-1 Table 4 less 3 dB. For narrow-band noise as the test signal, footnote b asks for lower limits and prints no figure, so the check applies the table as printed. A measurement that leaves bands out does not pass, and `noise_floor_db=` flags the bands within 6 dB of the meter's own floor (11.1). ## From responses to a threshold (6.2 to 7.5) - **Ascending method** (6.2.3.2, 6.2.4.2): 10 dB down after each response, 5 dB up after each miss; the threshold is the lowest level answered in more than half of the ascents, once three of at most five end at one level (two of three, shortened). The presentation sequence can be replayed, and the result gives the level to present next. - **Bracketing method** (6.2.4.3): the mean of the averaged ascent and descent levels, rounded to the nearest 5 dB step (the library sends a tie up; the clause gives no rule for it). - **Automatic recording** (6.3.5): the first reversal and both ends of excursions of 3 dB or less are ignored, and the mean of the averaged peaks and valleys is rounded **up** to the next whole decibel. - **Sweep-frequency audiometry** (7.5): the three nearest peaks and valleys on a log-frequency axis, or a running average of six reversals. ```python series = hearing.ascending_method_threshold( presentation_levels_db=[30, 20, 25, 15, 20, 25, 15, 20, 10, 15, 20, 25], responses=[1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1], familiarization_level_db=40.0, ) print(series.ascent_levels_db, series.threshold_db) # [25. 25. 20. 25.] 25.0 print(hearing.bracketing_method_threshold([30, 30, 35], [30, 35, 35]).threshold_db) # 35.0 tracing = hearing.automatic_audiometry_threshold( [38, 22, 31, 21, 32, 20, 30, 29, 31, 19, 30, 20, 31, 21] ) print(tracing.mean_db, tracing.threshold_db) # 25.75 26.0 ``` Each rule carries its clause's reliability test: a spread of more than 10 dB between the levels it combines. Three more rules judge the levels once found. `hearing.check_retest_agreement` applies Step 3 of 6.2.3.2: the repeat at 1 kHz agrees to 5 dB or less, or a change of 10 dB or more sends the test back to the further frequencies. `hearing.audiogram_cautions` flags an air-conduction level of 40 dB or more (cross-hearing, 6.2.3.2) and a bone-conduction level at the average vibrotactile threshold of 8.4, 40, 60 and 70 dB at 250 Hz, 500 Hz and 1 kHz for the mastoid and about 10 dB lower for the forehead (`hearing.VIBROTACTILE_HEARING_LEVELS_DB`). ```python print(hearing.check_retest_agreement(25.0, 35.0).retest_further_frequencies) # True cautions = hearing.audiogram_cautions( [250, 500, 1000, 2000], air_conduction_db=[20, 25, 30, 45], bone_conduction_db=[40, 20, 25, 40], ) print(cautions.cross_hearing, cautions.vibrotactile) # [False False False True] [ True False False False] ``` ## The uncertainty of a threshold (Annex A) Eight uncorrelated inputs with a sensitivity coefficient of 1: $u = \sqrt{\sum u_i^2}$ and $U = 2u$. With the typical values of A.3, air conduction below 4 kHz without masking gives the example of Table A.2: ```python budget = hearing.audiometric_uncertainty(1000.0) print(np.round(budget.components_db[:4], 1)) # [2.5 2.3 2.9 2. ] print(round(budget.combined_db, 1), round(budget.expanded_db)) # 4.9 10 ``` ## The sound field (ISO 8253-2) `hearing.check_free_sound_field` (5.2: ±1 dB at the lateral positions up to 4 kHz, ±2 dB above, the axial pair at 0.15 m within ±1 dB of the inverse distance law), `hearing.check_quasi_free_sound_field` (5.4: ±2 dB, the axial pair at 0.10 m, and a usable frequency range) and `hearing.check_diffuse_sound_field` (5.3: six positions within ±2.5 dB, the ear sides within 3 dB, and from 500 Hz a directional microphone's variation within Table 1) qualify the room band by band; the directional test is a requirement, and without it a diffuse field does not pass. The same diffuse-field check serves ISO 4869-3 on the [hearing protectors](https://docs.jmrp.io/phonometry/perception/hearing/hearing-protectors/) page. `hearing.incidence_correction` reads the off-axis increases of Annex B, which the text announces from 200 Hz and the table prints from 125 Hz (see [ERRATA](https://docs.jmrp.io/phonometry/reference/errata/)). ## References - International Organization for Standardization (2010). *Acoustics — Audiometric test methods — Part 1: Pure-tone air and bone conduction audiometry* (ISO 8253-1:2010). Clause 11 with Tables 2 to 4, the threshold rules of 6.2.4, 6.3.5 and 7.5, the repeat and the cautions of 6.2.3.2 and 8.4, and Annex A, validated against Tables 2 to 4, the levels of 8.4 and Table A.2. - International Organization for Standardization (2009). *Acoustics — Audiometric test methods — Part 2: Sound field audiometry with pure-tone and narrow-band test signals* (ISO 8253-2:2009). The sound fields of 5.2 to 5.4, the ambient limits of Table 2 and the off-axis increases of Table B.1. ## Standards ISO 8253-1:2010, which sets the maximum permissible ambient levels of an audiometric test room (Clause 11, Tables 2 to 4), the rules that turn responses into a hearing threshold level (6.2.4, 6.3.5, 7.5), the repeat at 1 kHz and the cautions that judge that level (6.2.3.2, 8.4), and its uncertainty (Annex A). ISO 8253-2:2009, which qualifies a sound field as free, quasi-free or diffuse (Clause 5), sets its ambient limits (Clause 6) and prints the off-axis increases of Annex B. ## See also - [Hearing threshold (age and reference zero)](https://docs.jmrp.io/phonometry/perception/hearing/hearing-threshold/): the audiometric zero the hearing levels are measured from. - [Hearing Protectors (ISO 4869-1, -2, -3 and -6)](https://docs.jmrp.io/phonometry/perception/hearing/hearing-protectors/): the same diffuse-field test on the site where an earmuff is screened. - API reference: [`hearing.audiometry`](https://docs.jmrp.io/phonometry/reference/api/hearing/audiometry/) and [`hearing.sound_field_audiometry`](https://docs.jmrp.io/phonometry/reference/api/hearing/sound-field-audiometry/).