Metrics › Fluctuation strength

Fluctuation strength from the Sottek Hearing Model (ECMA-418-2)

Unit: vacil_HMS · Also known as ECMA-418-2 fluctuation strength, vacil_HMS, Sottek fluctuation strength

Fluctuation strength from the Sottek Hearing Model, new in the 4th edition of ECMA-418-2 (June 2025, Clause 9). It uses high-resolution spectral analysis for modulation rates of about 0.25 to 20 Hz.

Editions and who implements them

Project map

The project map, with only the lines for Sottek Hearing Model fluctuation strength between the projects listed for it.

• results checked against
• same contributor
• SQAT SQAT, MoSQITo, and sottek-hearing-model

Implementations

Projects in bold and other established projects come first, then newly released, developing and legacy ones. Validation is what each project says about its own testing. The details are below, and the kinds of evidence are explained on the About page.

See also: Fluctuation strength, Osses et al. model and Fastl & Zwicker formula, Loudness from the Sottek Hearing Model (ECMA-418-2).

How they were validated

As reported by each project; LISQM has not run the code. Two implementations that agree can still share the same error. Kinds of evidence.

sottek-hearing-model · ECMA-418-2:2025 (4th ed.)

compared with refmap-psychoacoustics (its source) and ArtemiS SUITE (HEAD acoustics)

Ported or adapted from refmap-psychoacoustics (the author's own code). It was compared with the code it was ported from, which checks the port only.

• A draft report (18 September 2026) compares it with acousticSHMFluctuation.m, the MATLAB code it was translated from: equal to floating-point precision on the synthetic signals and on one channel of each recording, with a small difference in a short time window on the other channel.
• Against HEAD acoustics ArtemiS SUITE v17: 0.994 against 1.003 vacil_HMS for the calibration signal (the standard's target is 1.0), −8 % to +12 % for the overall values of three binaural recordings, and correlations of 0.91 to 0.998 for the time-dependent values.

Checked by the maintainer of LISQM: In personal use, Zhenxian LI found its results in very good agreement with those of HEAD acoustics ArtemiS SUITE. This is a personal check, not a published comparison.

ecma418-torch new · ECMA-418-2:2025 (4th ed.)

compared with sottek-hearing-model and ArtemiS SUITE (HEAD acoustics)

• The 1 kHz tone amplitude-modulated at 4 Hz (60 dB SPL) gives 0.99579 vacil for 10 s (the test allows 1e-2 around 1), and the average specific fluctuation strength in band 17 is 0.38876, against 0.395 from ArtemiS v17 as quoted in the tests of sottek-hearing-model.
• Against sottek-hearing-model run as an oracle on two signals: with that package's three choices, the time-dependent values differ by at most 6.3e-5 vacil and the single values by at most 6.3e-5; with the defaults, which follow the printed text, the single values differ by 0.2 % and 0.5 %.

phonometry new · ECMA-418-2:2025 (4th ed.)

standard or paper data (calibration signal only)

• Checked at the calibration signal only (0.993 vacil_HMS).

Not stated by SQAT.

Before you compare numbers

Implementations of the same metric can give different numbers without either being wrong. Check these choices first.

• Overall value. The single value is a 90th percentile of the time-dependent values after the filters have settled. NumPy (sottek-hearing-model) and MATLAB's prctile interpolate differently, by at most 0.0005 vacil_HMS on sottek-hearing-model's test signals.
• Interpretation. Implementers report misprints and open questions in Clause 9 of the 2025 edition (phonometry's errata, sottek-hearing-model's documented departures), so implementations can differ until they are resolved.

What the projects state:

sottek-hearing-model

• Input at other sample rates is resampled to 48 kHz.
• Overall roughness and fluctuation strength are 90th percentiles computed with NumPy (linear interpolation, Hyndman–Fan type 7). The MATLAB code it was translated from uses prctile, which interpolates differently, so single values can differ slightly from RefMap and SQAT.

ecma418-torch new

• Input at other sample rates is resampled to 48 kHz (band-limited, by the Fourier method).
• The single value is the 90th percentile from torch.quantile (linear interpolation) of the time-dependent values, after the first 16 (roughness) or 36 (fluctuation strength) values at 50 Hz are left out.
• The outer and middle ear filter uses the coefficients as printed in Table 1 of the standard, where sottek-hearing-model uses unrounded ones.
• By default it follows the printed text in three places where sottek-hearing-model decides otherwise: the step limit of Formula (152) (2e-4 Hz, against 0.2), no fundamental required for an assumed order in Section 9.1.8, and machine epsilon for ε0 (against 1e-12). The options newton_cap and require_fundamental give sottek-hearing-model's choices.
• Formula (127) is computed with π instead of the printed 2π in the phase term, and Formula (144) without the printed "− 1", which the code says would shift every rate down one bin.

References

1. ECMA-418-2:2025 (4th ed.). Psychoacoustic metrics for ITT equipment — Part 2 (methods for describing human perception based on the Sottek Hearing Model). https://ecma-international.org/wp-content/uploads/ECMA-418-2_4th_edition_june_2025.pdf