Zimtohrli Audio Similarity Metric

• Zimtohrli is a full-reference audio similarity metric that uses a 128‐bin gammatone filterbank and psychoacoustically grounded processing to assess quality.
• It employs a modified Dynamic Time Warping and NSIM method to align perceptual spectrograms, producing a score that correlates strongly with human ratings.
• The metric offers efficient runtime and lower memory usage, making it suitable for codec evaluation, VoIP monitoring, and Music Source Restoration.

Zimtohrli is a full-band, full-reference audio similarity metric designed for efficient and perceptually accurate quality assessment. It compares a processed or degraded signal to a clean reference and outputs a perceptually meaningful score through a psychoacoustically grounded pipeline that combines a 128-bin gammatone filterbank front-end, a non-linear resonator model, modified Dynamic Time Warping (DTW), and a modified Neurogram Similarity Index Measure (NSIM) (Alakuijala et al., 30 Sep 2025). In the inaugural Music Source Restoration (MSR) Challenge, Zimtohrli was used as one of three objective metrics, alongside Multi-Mel-SNR and FAD-CLAP, to evaluate the recovery of original, unprocessed instrument stems from professionally mixed and degraded audio (Zang et al., 7 Jan 2026).

1. Definition and conceptual position

Zimtohrli is presented as an interpretable, psychoacoustically grounded, and efficient metric intended to fill a gap between proprietary standards such as POLQA, transparent but sometimes underpowered signal-processing approaches such as ViSQOL, and computationally heavy learned metrics (Alakuijala et al., 30 Sep 2025). It is explicitly described as a full-reference metric: evaluation requires a content-matched clean reference and a processed or degraded counterpart.

The metric is designed for applications in codec evaluation, VoIP and telephony quality monitoring, audio enhancement benchmarking, and the assessment of generative audio systems where temporal alignment and perceptual invariances are essential. It is also described as operating at full band and at 48 kHz, rather than switching between speech and audio modes.

In the MSR setting, Zimtohrli serves a distinct role relative to the other objective metrics. Multi-Mel-SNR is used for spectro-temporal reconstruction fidelity, and FAD-CLAP is used for semantic instrument identity. Zimtohrli is included to provide a perceptual similarity measure grounded in psychoacoustics, with the stated purpose of assessing how restored stems sound to human listeners beyond purely numerical signal reconstruction (Zang et al., 7 Jan 2026).

A common misconception is that Zimtohrli is a direct mean-opinion-score predictor. The available description does not support that interpretation. The metric reports its own score directly, and no proprietary MOS mapping is required; if desired, users can fit a monotonic mapping to their own MOS scale via logistic or isotonic regression (Alakuijala et al., 30 Sep 2025).

2. Psychoacoustic front-end and signal representation

The Zimtohrli pipeline begins with pre-processing. Both signals are resampled to 48 kHz, and a single channel is selected for comparison; for stereo, tools can calculate channel-wise distances and aggregate via L2 if needed. The metric also applies partial level normalization: the maxima of the two perceptual spectrograms are brought 82% closer, reducing pure gain differences while preserving loudness cues that affect perceived quality (Alakuijala et al., 30 Sep 2025).

Its cochlear analysis uses 128 complex gammatone filters of order $n = 3$, with center frequencies $f_k$ spaced uniformly on the ERB scale across the full band. A commonly used gammatone impulse response is

$$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$

or in complex form,

$$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$

The bandwidth is set from the Equivalent Rectangular Bandwidth of the center frequency:

$$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$

The ERB-rate scale is given by

$E(f) = 21.4 \log_{10}(4.37\, f/\mathrm{kHz} + 1),$

with inverse

$f(E) = 1000 \, (10^{E/21.4} - 1)/4.37.$

The adaptive bandwidth controls an integration coefficient through the empirical relation

$$C \approx 0.9996^{(\mathrm{BW}_{\mathrm{Hz}} \times 0.7323)}.$$

Zimtohrli also includes a parallel “eardrum resonator” path. The input is first passed through a 32-bin time-based linear filter and then through a resonator that performs complex spectral energy shifting, intended to mimic transient response and damping observed in mass-spring systems. The paper does not publish exact governing equations for this component, but it describes the pathway as introducing controlled nonlinearity inspired by the tympanic membrane’s mechanical behavior (Alakuijala et al., 30 Sep 2025).

After filtering, the metric constructs a perceptual spectrogram, or “neurogram.” Gammatone outputs are subsampled to an 85 Hz frame rate. A sigmoid-based spread across adjacent frequency channels emulates overlapping auditory nerve excitation. The resulting representation is then converted with LoudnessDb, which adds a small noise-floor bias and applies logarithmic compression with frequency-dependent weighting:

$L_k(t) = w_k \log(E'_k(t) + \epsilon).$

This combination is described as stabilizing low-energy regions, compressing dynamic range, and modeling equal-loudness effects.

3. Temporal alignment, NSIM, and score formation

Zimtohrli aligns perceptual spectrograms with Dynamic Time Warping applied in the perceptual domain rather than on raw waveform spectrograms. A simple per-column distance may be

$$c(i,j) = \|L^{\mathrm{ref}}(:,i) - L^{\mathrm{deg}}(:,j)\|_2,$$

although the description also allows an $f_k$0 or cosine distance. The standard DTW recurrence is

$f_k$1

with appropriate initialization at the boundaries (Alakuijala et al., 30 Sep 2025).

Zimtohrli modifies this recurrence by applying a non-linear penalty to local deltas:

$f_k$2

where $f_k$3. This sub-linear weighting is described as softly discouraging excessive warping while maintaining robustness to moderate temporal drift such as codec jitter or small time-scale modifications.

After alignment, similarity is computed with a modified NSIM over local patches of the neurogram. The classical NSIM form is

$f_k$4

Here $f_k$5 and $f_k$6 are local means, $f_k$7 and $f_k$8 are local variances, $f_k$9 is the local covariance, and $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$0, $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$1 are stabilizers tied to the dynamic range. Zimtohrli introduces non-linearities inside NSIM to improve alignment with perceptual judgments, although those details are not disclosed.

Final score formation consists of partial level normalization, modified DTW alignment, NSIM on aligned spectrograms, and pooling of local similarity scores across time and frequency. Pooling can be a mean, trimmed mean, or Minkowski pooling with exponent $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$2; the available description does not mandate a single aggregation rule. The final output is a single score that is compared directly to subjective ratings, without proprietary calibration (Alakuijala et al., 30 Sep 2025).

4. Empirical performance and computational properties

The empirical evaluation reported for Zimtohrli covers speech and music with diverse impairments. The datasets include NISQA TEST FOR and P501, EARS-EMO-OpenACE, and the SQAM-POP-MUSIC subset. Reported impairments include codec artifacts, background noise, packet loss, clipping, live platform conditions such as Zoom and WhatsApp, modern codecs including Opus, EVS, LC3, and LC3Plus, and music encoded by Opus at 128 kbps and a neural Descript Audio Codec at 8 kbps (Alakuijala et al., 30 Sep 2025).

Across these datasets, all reported correlations to human ratings have $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$3. On NISQA_TEST_FOR $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$4, Zimtohrli attains $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$5, $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$6, and $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$7. On NISQA_TEST_P501 $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$8, it attains $$g(t; f_0, b, n, \phi) = t^{n-1} e^{-2\pi b t} \cos(2\pi f_0 t + \phi), \quad t \ge 0,$$9, $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$0, and $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$1. On EARS-EMO-OpenACE $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$2, it attains $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$3, $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$4, and $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$5. On SQAM-POP-MUSIC $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$6, it attains $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$7, $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$8, and $$g_c(t; f_0, b, n) = t^{n-1} e^{-2\pi b t} e^{j 2\pi f_0 t}.$$9. The average PLCC across datasets is reported as 0.68 for Zimtohrli, compared to 0.73 for POLQA, 0.60 for ViSQOL speech, and 0.48 for ViSQOL audio. The relative performance drop versus POLQA is stated as about 7% for Zimtohrli, compared to approximately 18% for ViSQOL speech and approximately 34% for ViSQOL audio (Alakuijala et al., 30 Sep 2025).

The reported runtime and memory characteristics are central to the metric’s positioning. On a 10 s audio sample, Zimtohrli runs in $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$0 and uses approximately $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$1, whereas ViSQOL audio mode at 48 kHz runs in $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$2 and uses approximately $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$3. The paper characterizes this as a greater than 5× speedup with a lower memory footprint. DTW complexity is given as $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$4, with a 10 s clip yielding approximately 850 frames at 85 Hz.

Parameter tuning is also documented. The reported optimization used alternating stochastic optimization with perturbations drawn from a Beta$$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$5 distribution with amplitude scaling and the downhill simplex method, consuming approximately 200,000 CPU hours. The objective maximized Spearman rank correlation to human ratings across ten corpora, including CORESVNET, ODAQ, PerceptualAudio, PEASS_DB, SEBASS-DB, TCD-VoIP, and two internal datasets (Alakuijala et al., 30 Sep 2025).

5. Use in Music Source Restoration

In Music Source Restoration, the task is not merely source separation; it is the recovery of original, unprocessed instrument stems from audio that has been professionally mixed and then further degraded, for example by codecs or analog artifacts. The inaugural MSR Challenge used Zimtohrli as one of three objective metrics on studio-produced mixtures with available ground truth. Its role was to complement Multi-Mel-SNR, which emphasizes reconstruction, and FAD-CLAP, which emphasizes semantic instrument identity, by contributing a psychoacoustic measure of perceptual similarity (Zang et al., 7 Jan 2026).

The challenge reports Zimtohrli as a scalar distance with lower values indicating better perceptual similarity. In the results table, the column label is “Zimtohrli ($$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$6).” Objective metrics, including Zimtohrli, were computed on the non-blind test set comprising 1,000 clips. The validation set, MSRBench, consists of 2,000 professionally mixed 10-second clips at 48 kHz stereo with parallel unprocessed and processed stems under 13 conditions, namely mastered audio plus 12 degradation types.

Team	Zimtohrli
xlancelab	0.014
CUPAudioGroup	0.016
AC_DC	0.018
Hachimi	0.018
cp-jku	0.019

The top-ranked system, xlancelab, achieved the best Zimtohrli score, 0.014, and also ranked first in Multi-Mel-SNR at 4.46 dB and FAD-CLAP at 0.199. The paper states that objective and subjective rankings show strong agreement overall, with Spearman correlation $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$7, and the same system also ranked first in subjective MOS-Overall at 3.47. The challenge does not provide a correlation specific to Zimtohrli, nor does it provide a per-stem Zimtohrli analysis. Per-stem analysis is reported only for Multi-Mel-SNR, where bass averages 4.59 dB across all teams and percussion averages 0.29 dB (Zang et al., 7 Jan 2026).

This use in MSR clarifies the metric’s operational niche. A plausible implication is that Zimtohrli is particularly valuable when waveform-level mismatch is not sufficient to characterize restoration quality, because production effects and degradations alter spectral-temporal signatures in ways that may remain perceptually salient even when exact phase or sample-level correspondence differs.

6. Reproducibility, limitations, and open directions

Zimtohrli is available as an open-source implementation at https://github.com/google/zimtohrli and as a Python package at https://pypi.org/project/zimtohrli/. Reported defaults include 48 kHz processing, a 128-bin gammatone filterbank, an 85 Hz frame rate, ERB spacing, adaptive bandwidth via $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$8, sigmoid spread, LoudnessDb with frequency weighting, modified DTW with $$\operatorname{ERB}(f) = 24.7 \, (4.37\, f/\mathrm{kHz} + 1).$$9, modified NSIM, and pooling to a single score (Alakuijala et al., 30 Sep 2025).

Several limitations are explicit. Exact internal parameters of the resonator and the NSIM non-linearities are not published. Emotional speech remains challenging for all metrics in the reported comparison. Zimtohrli is not calibrated to an absolute MOS scale out of the box. In addition, severe time-stretch or content mismatch can degrade interpretability even though DTW improves robustness to alignment drift (Alakuijala et al., 30 Sep 2025).

The MSR Challenge paper adds a second layer of incompleteness from the standpoint of task-specific reproducibility. It states only that Zimtohrli “models perceptual similarity using psychoacoustic principles including gammatone filterbank analysis and temporal masking.” It does not provide the exact signal representation or preprocessing steps for the challenge implementation, does not publish a formula for the metric in that context, and does not specify whether the reported overall score is computed per stem, per track, and then averaged, or through another aggregation procedure. It also does not explicitly confirm that Zimtohrli code or the exact evaluation script is hosted on the challenge site, although it does state that the dataset, evaluation protocols, and baselines are available at https://msrchallenge.com/ (Zang et al., 7 Jan 2026).

Future work named in the Zimtohrli paper includes a fully differentiable pipeline for use as a perceptual loss in training generative audio systems, richer non-linear middle-ear modeling, improved coupling to cochlear mechanics, multi-resolution alignment through hierarchical DTW or coarse-to-fine strategies, domain adaptation for specific content domains such as emotional speech and music subgenres, and hybrid learned calibration layers or priors over NSIM pooling that retain interpretability (Alakuijala et al., 30 Sep 2025). Taken together, these directions suggest continued emphasis on the metric’s defining combination of psychoacoustic transparency, temporal alignment robustness, and computational efficiency.