Soundscape Analysis (ISO/TS 12913)

A sound level tells how much sound arrives at a place. It does not tell whether the people there find it pleasant, busy, calming or annoying, and two squares at the same $L_{\mathrm{Aeq}}$ can be heard as opposite places. A soundscape is the acoustic environment as a person perceives it, in context (ISO 12913-1), and its study “relies primarily upon human perception and only then turns to physical measurement” (ISO/TS 12913-2).

That makes this the first page of the library whose input is not a signal but a questionnaire: the boxes people ticked on a soundwalk. ISO/TS 12913-2 prints the questionnaires and says what a study has to report; ISO/TS 12913-3 turns the ticks into numbers, places each site on a two-dimensional model of how pleasant and how eventful it sounds, correlates the answers with the acoustic measurements, and says how a binaural recording made at the same place is analysed.

This page implements the 2019 edition of ISO/TS 12913-3. ISO has published a 2025 edition that revises Annex A, where the pleasantness and eventfulness formulas are; it has not been read for this implementation, so a study that cites the 2025 edition should check those formulas against it.

Eleven London sites of the International Soundscape Database on the model of Figure A.1 (left), and the rank correlation of their pleasantness with their level (right), both drawn by the results’ own .plot(), with the two rank axes named for what was ranked.

Method A of ISO/TS 12913-2 (clause C.3.1) is a questionnaire in four parts, every one on five boxes: which sources are heard and how much (Figure C.2, or the three-source Figure C.3), how the place is perceived on eight attributes (Figure C.4), how good the sound environment is overall (Figure C.5) and how appropriate it is to the place (Figure C.6). The library publishes all of it, every question, item and response category as printed, with the scale values ISO/TS 12913-3 Table A.1 assigns:

from phonometry import environment

part2 = environment.METHOD_A_SCALES[2]
print(part2.figure, part2.categories[0], part2.scale_values)  # C.4 Strongly agree (5, 4, 3, 2, 1)
print(environment.method_a_scale_values([1, 2, 5], part=2))  # [5. 4. 1.]
print(environment.method_a_scale_values([1, 2, 5], part=4))  # [1. 2. 5.]

The orientation is the thing to get right. Parts 1 and 4 run 1 to 5 from the left-hand box, so “not at all” is 1; parts 2 and 3 run 5 to 1, so “strongly agree” and “very good” are 5. method_a_scale_values converts the position of a ticked box, counted from the left, into the value of its part; everything after it takes scale values, never box positions.

The tables keep the text as printed, including two slips of the page: the questions of Figures C.2 to C.4 read “to what extend” and their instructions “reponse alternative”. A study that prints its questionnaire from them should correct both; the errata register has the entry.

Every Method A scale is ordinal, so ISO/TS 12913-3 A.2 reports the median of each item per site as its central tendency and the range as its dispersion. A blank answer is left out of both:

answers = {"pleasant": [5, 4, 4, 2, 5], "annoying": [1, 2, 1, 4, 1]}
summary = environment.method_a_summary(
    answers, part=2, sites=["park", "park", "park", "road", "road"]
)
print(summary.sites)              # ('park', 'road')
print(summary.medians.tolist())   # [[4.0, 1.0], [3.5, 2.5]]
print(summary.ranges.tolist())    # [[1.0, 1.0], [3.0, 3.0]]

A 2-D array (responses, items) is read in the order of the part’s figure, and summary.plot() draws each item’s median with its range as a bar, site beside site.

The eight attributes of part 2 are not eight independent judgements. When people describe how an environment feels, their answers fall on two dimensions: how pleasant it is, and how eventful, how busy with human and other activity. Rotating those two axes by 45 degrees gives the other two pairs of attributes: vibrant is pleasant and eventful, chaotic eventful and annoying, monotonous annoying and uneventful, calm uneventful and pleasant. Formulas (A.1) and (A.2) project the eight answers onto the two main axes, with $\cos 45^{\circ }$ weighting the diagonal ones:

with $p$ pleasant, $a$ annoying, $ca$ calm, $ch$ chaotic, $v$ vibrant, $m$ monotonous, $e$ eventful and $u$ uneventful, each a scale value from 1 to 5. Every term is a difference, so a respondent who gives every attribute the same answer sits at the origin, and the extremes are $\pm (4+\sqrt{32})=\pm 9.66$: 4 from the main axis and $8\cos 45^{\circ }$ from the two diagonals. Dividing by $4+\sqrt{32}$ maps the coordinates to $\pm 1$.

The eleven London sites of the International Soundscape Database were surveyed almost entirely with the English questionnaire of Method A; ten answers, at four of the sites, were given on the Spanish version of the database’s survey and are counted too. Here are the site medians of their answers and the median $L_{\mathrm{Aeq}}$ of their recordings:

sites = ["Camden Town", "Euston Tap", "Marchmont Garden", "Pancras Lock",
         "Regent's Park Fields", "Regent's Park Japan", "Russell Square",
         "St Paul's Cross", "St Paul's Row", "Tate Modern", "Torrington Square"]
# Site medians of the eight attributes, in the order of Figure C.4:
# pleasant, chaotic, vibrant, uneventful, calm, annoying, eventful, monotonous.
medians = [
    [3, 4, 4, 2, 2, 3, 4, 3], [2, 4, 3, 3, 2, 3, 3, 3], [4, 2, 3, 3, 4, 2, 3, 2],
    [4, 3, 3, 2, 4, 2, 3, 2], [5, 2, 3, 3, 4, 1, 3, 2], [5, 1, 4, 3, 5, 1, 3, 2],
    [4, 2, 4, 2, 4, 1, 3, 2], [4, 2.5, 4, 2, 4, 2, 3, 2], [4, 3, 4, 2, 3, 2, 3, 3],
    [4, 3, 4, 2, 4, 2, 4, 2], [3, 4, 4, 3, 2, 3, 3, 2],
]
laeq_db = [69.96, 69.45, 55.14, 59.02, 53.12, 59.74, 66.12, 61.83, 63.34, 63.00, 63.51]

pe = environment.pleasantness_eventfulness(medians, sites=sites)
print(round(pe.normalized_pleasantness[5], 2), round(pe.normalized_eventfulness[5], 2))  # 0.85 -0.15
print(round(pe.normalized_pleasantness[0], 2), round(pe.normalized_eventfulness[0], 2))  # -0.07 0.43
print(round(environment.PLEASANTNESS_EVENTFULNESS_RANGE, 2))  # 9.66

Regent’s Park Japanese Garden (index 5) comes out the most pleasant and slightly uneventful, in the calm quadrant; Camden Town (index 0) is the most eventful and a little on the annoying side. pe.plot() draws the model of Figure A.1 with every site on it, the left panel of the figure at the top.

Given the answers of each respondent rather than site medians, pleasantness_eventfulness returns both: every respondent’s own coordinates (respondent_pleasantness, respondent_eventfulness) and the site’s. The site point is the formulas applied to the site median of each attribute, since A.2 makes the median the central tendency of the scale; central_tendency="mean" uses the mean instead. When every respondent answered all eight attributes, that mean point is also the mean of the respondents’ coordinates, the formulas being linear; a blank answer breaks the equality, because each attribute mean then runs over the respondents who answered that attribute. pe.plot(respondents=True) adds every respondent as a faint point in the colour of their site.

Clause A.3 introduces the formulas as processing “the results from part 3”. The attributes they read are part 2, as Table A.1, the rest of Annex A and ISO/TS 12913-2 Figure C.4 all say; part 3 is the single overall rating of Figure C.5. The library applies them to part 2, and the errata register has the entry.

A study then asks whether what people say goes with what was measured. For ordinal data A.4 prescribes Spearman’s rank correlation: without ties Formula (A.3),

with $d_i$ the difference of the ranks of pair $i$, and with ties in either variable Formula (A.4), which corrects the rank variances by the tie sums $T={\sum }_j(t_j^3-t_j)/12$ and $U$ of the two variables and is Pearson’s coefficient of the average ranks. The site medians above have ties, so:

rho = environment.spearman_rank_correlation(pe.pleasantness, laeq_db)
print(rho.formula, round(rho.coefficient, 3), round(rho.p_value, 3))  # (A.4) -0.638 0.035

r = environment.pearson_correlation(pe.pleasantness, laeq_db)
print(r.formula, round(r.coefficient, 3), round(r.p_value, 3))  # (B.1) -0.66 0.027

Across these eleven sites the louder places are the less pleasant ones, and significantly so. Over all 26 locations of the database the rank correlation is about $-0.51$ ($p<0.01$). A.4 and B.3 ask for the probability value without naming a test; both functions use the Student statistic $r\sqrt{(n-2)/(1-r^2)}$ with $n-2$ degrees of freedom, exact for Pearson’s coefficient of bivariate normal data and the usual approximation for Spearman’s. alternative="greater" or "less" gives the one-sided value.

Three details of the page are worth knowing. Formula (A.3) is printed as $1-1\frac{6\sum d_i^2}{n(n^2-1)}$, with a stray factor 1 that the library reads as the typesetting remnant it is. The where-list under Formula (A.4) defines $t_j$ as “the number of in $t_j$ tied ranks” and $k(x)$ as “the numbers of tied ranks”; the library reads them as the size of each group of tied values and the number of those groups, the usual tie correction. And Formula (B.2), Pearson’s covariance for interval data, divides by $n$; the standard deviations of (B.1) are then taken with $n$ as well, which is what makes $r$ the usual coefficient. The first two, and a stray capital in the where-list of (B.2), are in the errata register. rho.plot() draws the ranked pairs, the right panel of the figure at the top.

Method B (ISO/TS 12913-2 C.3.2) is the soundwalk data collection: at each stop the participants mark continuous scales, list the sources they noticed from the most noticeable down, and write down what went through their mind. A mark may fall anywhere along a scale; its value runs from 1 at the left-hand tick to 5 at the right-hand one and is taken to one decimal (ISO/TS 12913-3 B.2). The level of measurement is interval, so B.2 reports the mean, the standard deviation and the 95 % confidence interval per site:

print(environment.method_b_scale_values([0.0, 0.37, 1.0]))  # [1.  2.5 5. ]

ratings = {"How loud is it here?": [3.9, 4.2, 3.1, 4.4, 3.6, 4.0]}
b = environment.method_b_summary(ratings)
print(round(b.means[0, 0], 2), round(b.standard_deviations[0, 0], 2))       # 3.87 0.46
print(round(b.confidence_lower[0, 0], 2), round(b.confidence_upper[0, 0], 2))  # 3.38 4.35

ranking = environment.method_b_source_ranking(
    [["traffic", "voices", "birds"], ["traffic", "birds"], ["voices", "traffic"], ["traffic"]]
)
print(ranking.sources, ranking.median_ranks[0].tolist())  # ('traffic', 'voices', 'birds') [1.0, 1.5, 2.5]

The interval is the Student one about the mean with the sample standard deviation; the median is reported beside it, as the “statistics for an ordinal scale level” B.2 allows. The source ranking is ordinal too: the median rank of each source and its range, over the participants who listed it.

The text of C.3.2.3 describes three scales labelled from “not at all” to “extremely”; Figure C.7 prints four, the fourth (“How often would you like to visit this place again?”) labelled from “never” to “very often”. METHOD_B_SCALES holds the four as printed and method_b_summary takes a table of three or four of them; the contradiction is in the errata register.

A soundscape study records the place with an artificial head at 1.6 m, for at least 3 min, sampled at 44.1 kHz or more (ISO/TS 12913-2 Annex D), and equalizes the recording to approximate a monaural measurement before it is analysed. Every metric of ISO/TS 12913-3 Table D.1 is then determined for each ear, and the higher of the two is the single representative value “indicating the overall experience”; their mean may be reported as well (D.2). binaural_indicators does that for a calibrated two-channel recording, left ear first, with the library’s own implementation of each metric. A synthetic street, eight seconds with one vehicle passing left to right:

import warnings

import numpy as np

fs = 48_000
rng = np.random.default_rng(12913)
t = np.arange(8 * fs) / fs
background = 0.02 * rng.standard_normal(t.size)
swell = np.exp(-0.5 * ((t - 4.0) / 0.9) ** 2)
vehicle = 0.08 * rng.standard_normal(t.size)
left = background + swell * vehicle
right = 0.9 * background + 10 ** (-3 / 20) * np.roll(swell, int(0.3 * fs)) * vehicle

with warnings.catch_warnings():
    # Eight seconds is short of the 3 min of ISO/TS 12913-2 D.3, which the
    # analysis would otherwise say with a SoundscapeWarning.
    warnings.simplefilter("ignore", environment.SoundscapeWarning)
    bi = environment.binaural_indicators(
        np.vstack([left, right]), fs, parameters=("sound_pressure_level", "loudness", "sharpness")
    )
laeq = bi.metrics["LAeq,T"]
print(round(laeq.left, 1), round(laeq.right, 1), round(laeq.representative, 1))  # 63.5 61.1 63.5
print(round(bi.representative("N5"), 1), round(bi.representative("N5/N95"), 2))  # 22.2 2.27
print(sorted(bi.not_implemented))  # ['S5', 'S95', 'Saverage']

Each row of the table comes from a function the library already has, and each metric says which in its method:

$N_{\mathrm{rmc}}$ is the root mean cube of the loudness over time, the cube root of the mean of $N^3$, as the formula of the NOTE under ISO/TS 12913-2 A.3 f) prints it; the text of that NOTE calls the second step “the exponent 3” where the formula applies $1/3$, and the errata register has the entry. $N_5/N_{95}$ is the variability ratio D.2 suggests. Table D.1 cites ECMA-74 for tonality; the current edition of ECMA-74 refers its psychoacoustic tonality method to ECMA-418-2 clause 6, which is what tonality_ecma implements. For roughness and fluctuation strength the table cites a textbook, and ISO/TS 12913-2 Annex B noted in 2018 that no standardized method existed; the library uses the hearing model of ECMA-418-2:2025 for both, and $R_{10}$ is the value that model reports as its roughness (the value exceeded 10 % of the time).

The sharpness row is left empty, on purpose. $S_5$, $S_{\mathrm{average}}$ and $S_{95}$ are percentiles of a sharpness that varies in time. The library’s DIN 45692 sharpness is computed from the stationary specific loudness, and its time-varying loudness does not publish the specific loudness over time a time-varying sharpness needs, so not_implemented says why instead of a stationary number appearing under a percentile’s name.

The hearing-model metrics are expensive: on a 3 min recording tonality, roughness and fluctuation strength take minutes each, tonality most of all. parameters picks the rows to compute. A recording shorter than 3 min or sampled below 44.1 kHz raises a SoundscapeWarning; the equalization, the position and the calibration are the caller’s.

Two rows of Table D.1 at both ears of the synthetic street, from bi.plot(parameter="sound_pressure_level") and bi.plot(parameter="loudness"). The left ear hears the vehicle first and louder, so it is the representative ear for every metric.

ISO/TS 12913-2 Annex A (normative) lists the minimum a soundscape study reports: who the participants were and how they were selected (A.2), the acoustic environment with the results of its measurements (A.3), and how the perception data were collected (A.4), with a copy of the questionnaire. SoundscapeReport holds the three records and refuses to be built with a required item missing, naming its clause; the seven results of A.3 f) come straight from the binaural analysis:

report = environment.SoundscapeReport(
    participants=environment.SoundscapeParticipants(
        selection="visitors approached at the entrance, one in three",
        residents_or_visitors="visitors",
        lay_or_expert="lay people",
        age_and_gender_distribution="18 to 74 years, 52 % women",
        other_relevant_information="self-reported normal hearing",
    ),
    acoustic_environment=environment.SoundscapeAcousticEnvironment(
        environment_type="real",
        sound_sources="road traffic in the background, a passing car in the foreground",
        weather_and_wind="dry, wind under 2 m/s",
        time_of_year_and_day="June, 14:00 to 16:00",
        measurement_points="kerbside, artificial head at 1.6 m facing the road",
        measurement_results=bi.reporting_results(),
        site_description="urban street, residential",
    ),
    data_collection=environment.SoundscapeDataCollection(
        methods="Method A questionnaire, parts 1 to 4",
        questions="Figures C.2 to C.6 of ISO/TS 12913-2, answers on paper",
        language="English, as printed in Annex C",
        instrument_copy="Appendix B",
        rating_scale_construction="five-category scales of Figures C.2 to C.6",
    ),
)
print(round(report.acoustic_environment.measurement_results["N5"], 1))  # 22.2

Each item is free text, because the annex says what is stated and not how. A site description is required for a field study or recordings, the recording and reproduction for a recorded or virtual environment; a record that exists meets the minimum as far as a record can tell, and whether what it says is true and sufficient stays with the author.

import matplotlib.pyplot as plt

fig, (ax_model, ax_rank) = plt.subplots(1, 2, figsize=(14.0, 6.6))
pe.plot(ax_model)    # Figure A.1 with the eleven sites
rho.plot(ax_rank)    # the ranked pairs of Formula (A.4)
ax_rank.set_xlabel(r"Rank of the site pleasantness $P$")
ax_rank.set_ylabel(r"Rank of the site $L_\mathrm{Aeq}$")
plt.tight_layout()   # room for the site legend under Figure A.1

fig, (ax_levels, ax_loudness) = plt.subplots(1, 2, figsize=(14.0, 5.8))
bi.plot(ax_levels, parameter="sound_pressure_level")
bi.plot(ax_loudness, parameter="loudness")
plt.tight_layout()
plt.show()

• Covered

  ISO/TS 12913-3:2019, the quantitative analysis: the scale values of Table A.1 with the orientation of each part, the median and range per site and item (A.2), the pleasantness and eventfulness of Formulas (A.1) and (A.2) per respondent and per site, raw and normalised, with the model of Figure A.1 as the plot; Spearman’s coefficient with Formulas (A.3) and (A.4) and Pearson’s with (B.1) and (B.2), each with its probability value; the Method B scale values, mean, standard deviation, confidence interval and source ranking of Annex B; and the binaural analysis of Annex D, every metric of Table D.1 the library implements at each ear with the representative value of D.2 and the $N_5/N_{95}$ ratio. ISO/TS 12913-2:2018: the questionnaires of Annex C as published tables, the recording checks of Annex D (3 min, 44.1 kHz), and the minimum reporting requirements of Annex A as a record.

• Not covered

  The 2025 edition of ISO/TS 12913-3, which revises Annex A, is not implemented. The time-varying sharpness $S_5$, $S_{\mathrm{average}}$ and $S_{95}$ of Table D.1 is not computed. The qualitative analyses (the Grounded Theory and content analysis of clause 6 and Annex C, the free comments of Method B, the interview guideline of Method C), the triangulation of Annex E, the laboratory studies of Annex F, the clustering and psychoacoustic mapping of D.2 and D.3, the unexplained variance of D.1 and the coefficient of variation of repeated measurements are not modelled. The equalization of the binaural recording and the binaural measurement protocol of ISO/TS 12913-2 D.7 are the caller’s.