psychoacoustics.loudness.moore_glasberg

Stationary loudness per ISO 532-2:2017 (Moore-Glasberg method).

Clean-room implementation of the spectral loudness model of ISO 532-2:2017, the third calculation method of the ISO 532 series (distinct from the Zwicker method of ISO 532-1 and the Sottek model of ECMA-418-2). The procedure of Clause 7 (Figure 1) transforms a stationary sound spectrum into a loudness value through five stages:

• the fixed outer-ear and middle-ear transfer functions that map the recorded spectrum to the spectrum at the cochlea (clauses 7.2, 7.3, Table 1);
• the level-dependent rounded-exponential (roex) auditory filter bank that turns that spectrum into an excitation pattern along the ERB-number scale (clause 7.4, Formulae 1-6), sampled at ERB-number i from 1.8 Cam to 38.9 Cam in 0.1 Cam steps;
• the compressive transformation of excitation into specific loudness N'(i) in sone/Cam (clause 7.5, Formulae 7-9, Tables 2-4);
• the binaural inhibition model that combines the two ears (clause 8.1, Formulae 10-13); and
• the integration of specific loudness over the ERB-number scale to the total loudness N in sone, with the loudness level L_N in phon obtained by inverting the loudness/loudness-level relationship of Table 5 (clause 8.2).

The specific-loudness calibration constant C of Formula (7) is the value tabulated by the standard (0.0617 sone/Cam); a 1 kHz tone at 40 dB SPL presented binaurally in a free field yields 1.000 sone by definition of the sone (clause 3.17), which this implementation reproduces without tuning.

The stationary method is spectrum-based. loudness_moore_glasberg_from_spectrum takes the exact sinusoidal-component representation of clauses 5.2/5.4, loudness_moore_glasberg_from_third_octave takes the 29 one-third-octave band levels of clause 5.5, and loudness_moore_glasberg forms the narrowband (FFT) line spectrum of a calibrated pressure signal and feeds it to the exact sinusoidal-component method.

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loudness_moore_glasberg(
    x: Signal | list[float] | np.ndarray,
    fs: float | None = None,
    *,
    field: Literal['free', 'diffuse', 'eardrum'] = 'free',
    presentation: Literal['binaural', 'diotic', 'monaural'] = 'binaural',
) -> MooreGlasbergLoudness

Moore-Glasberg loudness of a calibrated stationary pressure signal.

Convenience wrapper around loudness_moore_glasberg_from_spectrum: the signal’s narrowband (FFT) line spectrum is formed and each bin is passed to the exact sinusoidal-component method of ISO 532-2:2017 (clauses 5.2/5.4). Because the model computes the excitation pattern per spectral component (Formula 5), a pure tone enters as a single line - so a calibrated 1 kHz tone at 40 dB SPL yields 1.000 sone / 40 phon (the definitional anchor), matching loudness_moore_glasberg_from_spectrum. The signal must be calibrated so that x is the instantaneous sound pressure in pascals.

Parameters

Returns: A MooreGlasbergLoudness.

loudness_moore_glasberg_from_spectrum(
    components: Sequence[tuple[float, float]] | np.ndarray,
    *,
    field: Literal['free', 'diffuse', 'eardrum'] = 'free',
    presentation: Literal['binaural', 'diotic', 'monaural'] = 'binaural',
) -> MooreGlasbergLoudness

Moore-Glasberg loudness from a sinusoidal-component spectrum.

Implements the exact spectral input of ISO 532-2:2017 clauses 5.2/5.4: the sound is specified as a set of discrete sinusoidal components, each a (frequency_Hz, level_dB_SPL) pair (levels re 20 uPa in the stated sound field). Bands of noise can be represented by the equivalent set of closely spaced components of clause 5.3.

Parameters

Returns: A MooreGlasbergLoudness.

A 1 kHz tone at 40 dB SPL in a free field presented binaurally yields 1.000 sone / 40 phon by definition of the sone.

loudness_moore_glasberg_from_third_octave(
    band_levels: Sequence[float] | np.ndarray,
    *,
    field: Literal['free', 'diffuse', 'eardrum'] = 'free',
    presentation: Literal['binaural', 'diotic', 'monaural'] = 'binaural',
) -> MooreGlasbergLoudness

Moore-Glasberg loudness from 29 one-third-octave band levels.

Implements the practical spectral input of ISO 532-2:2017 clause 5.5: the sound is specified by the sound pressure levels in the 29 adjacent one-third-octave bands with nominal centre frequencies 25 Hz to 16 kHz (IEC 61260-1). Each band is expanded into the equivalent set of sinusoidal components and the exact method is applied.

Parameters

Returns: A MooreGlasbergLoudness.

MooreGlasbergLoudness(
    loudness: float,
    loudness_level: float,
    specific: np.ndarray,
    erb_number: np.ndarray,
    centre_frequencies: np.ndarray,
    field: str,
    presentation: str,
)

Result of an ISO 532-2:2017 Moore-Glasberg loudness calculation.

loudness is the total loudness N in sone; loudness_level is the loudness level L_N in phon (obtained by inverting the loudness/loudness- level relationship of Table 5). specific holds the specific loudness N’(i) in sone/Cam sampled at the ERB-number grid erb_number (Cam), i.e. i from 1.8 Cam to 38.9 Cam in 0.1 Cam steps (372 values), and centre_frequencies the corresponding auditory-filter centre frequencies in Hz. For a binaural (diotic) result the specific-loudness pattern is that of a single ear before binaural inhibition; the total loudness already includes the binaural summation. field and presentation echo the listening conditions.

MooreGlasbergLoudness.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the specific loudness N’(i) over the ERB-number scale.

Requires matplotlib (pip install phonometry[plot]); returns the Axes. See phonometry._plot.psychoacoustics.