Source: https://jmrplens.github.io/phonometry/guides/tone-prominence/ # Prominent Discrete Tones (ECMA-418-1) Tonal components in machinery noise are far more annoying than their level suggests. ECMA-418-1:2024 (referenced by ECMA-74 Annex D) gives two FFT-based methods to decide whether a discrete tone is *prominent*: `tone_to_noise_ratio()` compares the tone level with the masking noise in its critical band (clause 11), and `prominence_ratio()` compares the critical band centred on the tone with the two contiguous bands (clause 12). Both return a structured verdict against the frequency-dependent prominence criteria. ## 1. Tone-to-noise ratio and prominence ratio ```python import numpy as np from phonometry import psychoacoustics fs = 48000 rng = np.random.default_rng(0) t = np.arange(fs) / fs x = np.sin(2 * np.pi * 1000 * t) + 0.05 * rng.standard_normal(fs) # 1 kHz tone in noise tnr = psychoacoustics.tone_to_noise_ratio(x, fs) # highest peak, or tone_freq=... pr = psychoacoustics.prominence_ratio(x, fs, tone_freq=1000.0) print(tnr.ratio_db, tnr.criterion_db, tnr.prominent) tnr.plot() # the tone against its prominence criterion (needs matplotlib) ``` The methods hinge on the **critical band**, the ear's analysis bandwidth, $\Delta f_c = 25 + 75\ [1 + 1.4(f/1000)^2]^{0.69}$ Hz (162 Hz at 1 kHz): a tone is masked only by the noise *inside* its critical band, so both methods focus on that band rather than the whole spectrum, but they use it differently. The tone-to-noise ratio works within the band, separating its spectral lines into tone and noise and subtracting their levels (clause 11, Formulae 9–11); the prominence ratio instead compares the *whole* band centred on the tone with the mean of its two contiguous critical bands (clause 12, Formula 23): $$ \mathrm{TNR} = L_t - L_n, \qquad \mathrm{PR} = 10\,\lg\!\frac{W_M}{\tfrac{1}{2}(W_L + W_U)}\ \text{dB}, $$ where $L_t$ is the tone level (the energy sum of the tonal lines above the band-edge baseline, Formula 9), $L_n$ the level of the masking noise that remains in the critical band, rescaled to the full critical bandwidth (Formulae 10–11), and $W_M$, $W_L$, $W_U$ the powers in the middle, lower and upper critical bands (below $f_t = 171.4$ Hz the truncated lower band is rescaled to a 100 Hz bandwidth, Formula 24).

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```python import numpy as np import matplotlib.pyplot as plt from scipy.signal import welch from phonometry import psychoacoustics fs = 48000 rng = np.random.default_rng(21) t = np.arange(30 * fs) / fs x = (np.sqrt(2) * 0.1 * np.sin(2 * np.pi * 1000 * t) + 0.05 * rng.standard_normal(t.size)) res = psychoacoustics.tone_to_noise_ratio(x, fs) # Averaged 1 Hz Hann spectrum (the clause 11.1 front end) and the # critical band about the detected tone (edges approximated as +/- dfc/2): f, p = welch(x, fs, window="hann", nperseg=fs, scaling="spectrum") dfc = 25 + 75 * (1 + 1.4 * (res.frequency / 1000) ** 2) ** 0.69 sel = (f > 700) & (f < 1400) plt.plot(f[sel], 10 * np.log10(p[sel])) plt.axvspan(res.frequency - dfc / 2, res.frequency + dfc / 2, alpha=0.15) plt.title(f"TNR = {res.ratio_db:.1f} dB (criterion {res.criterion_db:.1f} dB)") plt.xlabel("Frequency [Hz]"); plt.ylabel("Bin power [dB]") plt.show() ```

A TNR at or above $8 + 8.33\log_{10}(1000/f_t)$ dB below 1 kHz (a flat 8 dB for $f_t \ge 1$ kHz) classifies the tone as *prominent*; the PR criterion is $9 + 10\log_{10}(1000/f_t)$ dB below 1 kHz and 9 dB from there up, likewise applied with $\ge$. Low frequencies get higher thresholds because wider relative bands mask more. `ToneAssessment.plot()` puts the verdict in its context: it draws the criterion of the producing method over the whole 89.1 Hz to 11.2 kHz range of interest and marks the assessed tone at its own frequency, so the margin that decides the verdict is visible rather than implied.

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```python import numpy as np import matplotlib.pyplot as plt from phonometry import psychoacoustics # A 250 Hz fan tone recorded in broadband machinery noise, 10 s at 48 kHz. fs = 48000 rng = np.random.default_rng(4) t = np.arange(10 * fs) / fs x = (np.sqrt(2) * 0.011 * np.sin(2 * np.pi * 250.0 * t) + 0.03 * rng.standard_normal(t.size)) res = psychoacoustics.tone_to_noise_ratio(x, fs) print(round(res.ratio_db, 1), round(res.criterion_db, 1), res.prominent) # 15.1 13.0 True # One line: the tone against the criterion curve of its own method. res.plot() plt.show() # By hand, mirroring what ToneAssessment.plot() draws: f = np.logspace(np.log10(89.1), np.log10(11200.0), 400) criterion = np.where(f < 1000.0, 8.0 + 8.33 * np.log10(1000.0 / f), 8.0) fig, ax = plt.subplots() ax.semilogx(f, criterion, color="#d62728", label="prominence criterion") ax.plot([res.frequency], [res.ratio_db], "o", label="assessed tone") ax.plot([res.frequency] * 2, [res.criterion_db, res.ratio_db], ":", color="0.6") ax.set_xlabel("Frequency [Hz]") ax.set_ylabel("Tone-to-noise ratio TNR [dB]") ax.legend() plt.show() ```

**When the two ratios disagree.** Near the criteria the verdicts can differ, because each ratio is fragile in a different situation. TNR has to *split* the critical band into tonal and noise lines first, so it degrades when that separation is ambiguous: a tone riding a steep noise slope, or closely spaced components whose skirts overlap. PR needs no separation, which makes it the robust, automatable choice when **several tones share the critical band** (they all land in $W_M$); in exchange it reads low when a *neighbouring* band also carries a tone (the flanking bands are then not noise) and is biased on sharply sloping spectra, where the two flanking bands no longer estimate the masking at the tone. In practice: prefer TNR for a clean, isolated tone, prefer PR for multi-tone complexes sharing a band, and report both when they straddle their criteria. ## 2. Where to measure (ECMA-74) and practice ECMA-74 (which delegates its tone assessments to ECMA-418-1) also fixes where to measure around a device (context only): phonometry implements the ECMA-418-1 assessments, not the ECMA-74 Annex D measurement procedure: Proximate secondary tones in the same critical band are combined per clause 11.6; for harmonic complexes assess each component (`tone_freq=`). Both methods work on Hann-windowed, RMS-averaged spectra and need no absolute calibration (the ratios are level differences). ### `tone_to_noise_ratio()` / `prominence_ratio()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `x` | 1D array | any (uncalibrated OK) | ≥ `fs/resolution_hz` samples | Ratios are level differences: calibration cancels out | | `fs` | int | Hz | > 0 | | | `tone_freq` | float, optional | Hz | 89.1–11 200; default `None` | `None` assesses the highest peak in the range of interest | | `resolution_hz` | float | Hz | > 0; default `1.0` | Tone band must stay within 15 % of the critical band (clause 11.2) | Both return a `ToneAssessment(frequency, ratio_db, criterion_db, prominent)`. ## 3. Which tonality metric, and when The library implements four tonality assessments, and they are not interchangeable: each belongs to a different standard with its own purpose, input and output. | | TNR / PR | Tone audibility `ΔL` | Psychoacoustic tonality `T` | Wind-turbine tonal audibility | | :--- | :--- | :--- | :--- | :--- | | Standard | ECMA-418-1:2024, clauses 11 and 12 | ISO/PAS 20065:2016, adopted by ISO 1996-2:2017 Annex J | ECMA-418-2:2025, clause 6 | IEC 61400-11:2012, clause 9.5 | | Question answered | Is this discrete tone prominent in the emission of a device? | Is the tone audible above the noise that masks it, and by how much? | How tonal does the sound feel? | Is a turbine tone audible at the reference position, wind bin by wind bin? | | Input | One FFT spectrum, no calibration needed | Narrow-band spectra with the line spacing declared | The calibrated pressure signal, through the Sottek hearing model | Narrow-band spectra per wind-speed bin, with the reference distance | | Output | A ratio in dB against a frequency-dependent criterion, plus a prominent / not prominent verdict | An audibility in dB, whose decisive and mean values feed the tonal adjustment `Kt` | A tonality in `tu_HMS`, a perceptual magnitude with no criterion | An audibility in dB per bin, reported with the turbine's sound power | | Use it for | Declaring ITT equipment emission (ECMA-74 Annex D) | Environmental-noise rating: justifying, or refusing, a tonal penalty | Sound-quality work: comparing designs, not passing a limit | Type testing and acceptance of wind turbines | Read the table as a decision: the *purpose of the report* picks the metric, not the convenience of the input. A device emission declaration is an ECMA-418-1 prominence verdict; a complaint about a tone from an installation is an ISO 1996-2 rating, so it needs the audibility `ΔL` that maps to `Kt` ([tone audibility](https://jmrplens.github.io/phonometry/reference/api/psychoacoustics/tone-audibility/)); a product comparison where nobody is being fined is where the ECMA-418-2 tonality earns its place, because it is a magnitude rather than a threshold test ([sound quality](https://jmrplens.github.io/phonometry/guides/sound-quality/)); and a turbine is its own regime, with a measurement procedure in IEC 61400-11 that fixes the geometry and the wind bins ([wind-turbine noise](https://jmrplens.github.io/phonometry/reference/api/aeroacoustics/wind-turbine-noise/)). Two consequences worth keeping in mind. First, the numbers do not convert: a TNR of 12 dB is not an audibility of 12 dB, because the masking model, the band definition and the reference differ. Second, the metrics can disagree about the same sound, and legitimately so. A tone can be prominent by ECMA-418-1 in the near field of the machine and inaudible at the dwelling where the ISO 1996-2 assessment is made, while a hearing-model tonality stays moderate throughout because it rates the whole sound and not one spectral line. Report the metric the assessment calls for, and quote any other only as supporting evidence. ## See also - [Levels](https://jmrplens.github.io/phonometry/reference/api/levels/levels/): the ISO 1996-1 rating levels whose tonal adjustments (Table A.1) these prominence verdicts justify objectively. - [Sound Quality Metrics](https://jmrplens.github.io/phonometry/guides/sound-quality/): the ECMA-418-2 psychoacoustic tonality T in tu_HMS, the hearing-model counterpart of these FFT ratios. - [Objective audibility of tones in noise](https://jmrplens.github.io/phonometry/reference/api/psychoacoustics/tone-audibility/): the ISO/PAS 20065 audibility ΔL that the ISO 1996-2 tonal adjustment Kt is read from. - [Wind-turbine noise](https://jmrplens.github.io/phonometry/reference/api/aeroacoustics/wind-turbine-noise/): the IEC 61400-11 tonal audibility, the same question asked per wind-speed bin. - [Impulsive-sound prominence](https://jmrplens.github.io/phonometry/reference/api/environment/impulse-prominence/): the NT ACOU 112 counterpart for impulsive (rather than tonal) character. - [Theory](https://jmrplens.github.io/phonometry/reference/theory/perception/): the critical-band model and criteria derivation. - API reference: [`psychoacoustics.tonality`](https://jmrplens.github.io/phonometry/reference/api/psychoacoustics/tonality/). ## References - Ecma International. (2024). *ECMA-418-1: Psychoacoustic metrics for ITT equipment — Part 1: Prominent discrete tones* (3rd ed.). [Free PDF](https://ecma-international.org/wp-content/uploads/ECMA-418-1_3rd_edition_december_2024.pdf). The implemented standard, freely downloadable: the TNR (clause 11) and PR (clause 12) methods, the critical-band model and the prominence criteria of section 1. - Ecma International. (2025). *ECMA-74: Measurement of airborne noise emitted by information technology and telecommunications equipment* (22nd ed.). [Free PDF](https://ecma-international.org/wp-content/uploads/ECMA-74_22nd_edition_december_2025.pdf). The parent emission standard, freely downloadable: the operator/bystander measurement positions of section 2, with Annex D delegating the tone assessments to ECMA-418-1. ## Standards ECMA-418-1:2024 (3rd edition), *Psychoacoustic metrics for ITT equipment — Part 1: Prominent discrete tones* — the tone-to-noise ratio (clause 11), the prominence ratio (clause 12), the critical-band model and the frequency-dependent prominence criteria.