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Comparison of fundamental frequency estimators with subharmonic voice signals

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read FCN-F0, a deep-learning pitch tracker, is most accurate on subharmonic voice signals.

desk verdict A solid empirical comparison of pitch estimators on subharmonic voices, but the headline accuracy gaps lack cluster-aware statistics and should be read as trends, not a settled ranking. read the letter →

arxiv 2501.04789 v1 pith:DNDT56XR submitted 2025-01-08 eess.AS cs.SD

Takeshi Ikuma , Melda Kunduk , Andrew J. McWhorter This is my paper · ORCID
classification eess.AScs.SD
keywords fundamentalfrequencyestimationsubharmonicsvoicedisorderspitchdetectiondeeplearningCREPEFCN-F0subharmonics-to-harmonicsratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks which fundamental-frequency estimators can correctly identify the speaking pitch of pathological voices that contain subharmonic vibrations, a condition that makes the true pitch ambiguous because the signal repeats over several glottal cycles. Using 15,941 manually annotated 50-ms intervals from 703 recordings of sustained /a/ vowels, the authors compared five estimators plus a baseline against a quality-of-estimate classification that separates subharmonic errors (estimates at $f_o^*/M$) from other errors. The paper claims that FCN-F0, a fully convolutional deep network, is the most accurate overall (96% correct estimates) and reduces subharmonic errors by a third relative to CREPE, with CREPE and Harvest close behind at 95%. It also claims that no estimator reliably handles strong subharmonics (SHR above $-3$ dB), a reliability limit that matters because clinical acoustic parameters such as jitter and shimmer depend on the speaking fundamental frequency and mishandling subharmonics can cause false negatives.

What carries the argument

The study's key machinery is a quality-of-estimate classification built on the harmonic power profile $P(f_o)=\sum_{k=1}^{K(f_o)}|S_{xx}(k f_o)|^2$, where $S_{xx}$ is the periodogram of the 50-ms Hamming-windowed signal and $K(f_o)=\lfloor f_s/(2f_o)\rfloor$. For each annotated truth $f_o^*$, the profile's local minima define intervals around $f_o^*/M$; an estimate landing in the $M=1$ interval is correct, in an $M>1$ interval is a subharmonic error, and elsewhere is another error. Subharmonic strength is measured by the subharmonics-to-harmonics ratio (SHR), computed from the autocorrelation baseline's estimates, which quantifies the power of subharmonic tones relative to harmonic tones. These tools separate incidental autocorrelation errors (the main SHR peak near $-25$ dB) from true subharmonic intervals (secondary peak near $-10$ dB) and attribute each estimator's failures.

What would settle it

Re-run the comparison on the same recordings with ground-truth f0 established by glottal inverse filtering or simultaneous high-speed videoendoscopy or electroglottography, and check whether FCN-F0's 96% accuracy and its 34% subharmonic-error reduction over CREPE persist; a second check would be testing the ranking on running speech with subharmonics, since the paper attributes its disagreement with [27] to the difference between sustained vowels and connected speech.

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Extended reading notes

Core claim

The central discovery is that FCN-F0, a deep-learning model, performs the best both in overall accuracy and in correctly resolving subharmonic signals: it achieved 96% correct estimates versus 95% for CREPE and Harvest, 88% for Praat and YAAPT, and 62% for the autocorrelation baseline. FCN-F0 reduced subharmonic errors by 34% compared with CREPE, and its error profile was the most balanced between subharmonic and other mistakes. The paper further establishes a reliability boundary: among the 755 intervals with subharmonics-to-harmonics ratio above $-10$ dB, FCN-F0 correctly estimated only 63.7%, and none of the estimators could reliably handle strong subharmonics with SHR above $-3$ dB.

Load-bearing premise

The manual annotation of the true speaking fundamental frequency is itself uncertain for strong subharmonics, where a female voice with strong subharmonics could be mistaken for a normal male voice; all accuracy numbers rest on this ground truth.

Editorial extensions

If this is right

  • Clinical acoustic analysis of sustained vowels should prefer FCN-F0, with CREPE and Harvest as strong alternatives, to reduce false negatives caused by subharmonic voicing.
  • For intervals with SHR above $-3$ dB, no current estimator should be trusted; acoustic parameters computed there should be flagged as unreliable.
  • Praat's Viterbi postprocessing fixes incidental autocorrelation errors but not true subharmonic intervals, so its subharmonic error rate of about 9.3% is a lower bound for the fraction of subharmonic intervals in the dataset.
  • Retraining deep-learning models with subharmonic voice samples, as the paper suggests, may improve accuracy for the high-SHR cases that currently defeat all estimators.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the deep-learning models' advantage may come from using features beyond raw periodicity (such as harmonic amplitudes and phases), which would predict that they generalize less well to languages or recording conditions absent from their training corpora.
  • The 8-kHz resampling used in the study could limit estimates for very high-pitched voices; a testable extension is whether a higher sampling rate changes the ranking among the top three estimators.
  • The SHR-based classification could be turned into a practical clinical flag: intervals with ACF subharmonic errors and high SHR are likely true subharmonics, so a confidence mask accompanying F0 estimates could improve downstream diagnostics.
  • Because FCN-F0's training data are non-pathological English and French speech, a broader pathological corpus spanning more voice types and languages is a natural next test of whether its 96% accuracy is robust.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper compares six fundamental-frequency estimators—an autocorrelation (ACF) baseline, Praat, YAAPT, Harvest, CREPE, and FCN-F0—on 50-ms intervals of sustained /a/ vowels from the KayPENTAX Disordered Voice Database. The authors manually annotate a speaking fundamental frequency f_o^* for each interval, classify each estimate as correct, subharmonic error, or other error using intervals of the harmonic power profile P(f_o), and compute a subharmonics-to-harmonics ratio (SHR) from ACF-based subharmonic candidates. The reported headline result is that FCN-F0 has the highest per-interval accuracy (96% vs. 95% for CREPE and Harvest, 88% for Praat and YAAPT, 62% for ACF), reduces subharmonic errors by 34% relative to CREPE, and no estimator reliably handles strong subharmonics (SHR > -3 dB).

Significance. If the accuracy ranking were established, the paper would be a useful clinical benchmark: it evaluates per-frame behavior rather than per-recording averages, uses publicly available estimator implementations, and stratifies by subharmonic strength. The SHR-conditional analyses and the contingency tables against the ACF baseline are informative and go beyond simple overall accuracy. The central ranking, however, is currently supported only by pooled per-interval rates without uncertainty quantification or cluster-aware inference, and the manual ground truth is acknowledged to be uncertain precisely in the subharmonic cases that matter. These issues are fixable with additional analysis, and the clinical application is potentially valuable for voice assessment.

major comments (3)
  1. [Section III, Figs. 4-6] The central claim that FCN-F0 'performed the best' rests on pooled per-interval percentages computed over 15,941 intervals from only 703 recordings, with no confidence intervals, paired tests, or adjustment for within-recording correlation. Sustained-vowel intervals from the same recording are strongly non-independent; a small number of pathological recordings with sustained strong subharmonics can contribute large blocks of correlated errors. The 96%-vs-95% accuracy gap between FCN-F0 and CREPE/Harvest corresponds to roughly 160 intervals, and the claimed 34% subharmonic-error reduction is about a one-percentage-point absolute difference—both are within the range that a few recordings could plausibly account for. I request cluster-robust inference (e.g., bootstrap by recording or a mixed-effects logistic regression with a recording random effect), with 95% confidence intervals reported for all accuracy and subharmonic-error differences. Without this, the headline ranking is not established at the precision implied by the text.
  2. [Section II, 'fo Annotation' and the Limitations paragraph] The accuracy numbers depend entirely on the manually annotated f_o^*, which the authors acknowledge is uncertain for sustained strong subharmonics (e.g., a female voice with strong subharmonics could be mistaken for a normal male voice). Because the top three estimators differ by only about one percentage point, even a small number of annotation errors could reorder CREPE, Harvest, and FCN-F0. Please add a sensitivity analysis: exclude or relabel the intervals flagged as uncertain, quantify annotator agreement (e.g., a second annotation pass or test-retest reliability), or use an objective reference on a subset. The current statement that errors 'could slightly change' the accuracies is not sufficient to support the precision of the claimed ranking.
  3. [Section II, Quality-of-Estimate Classification] The rule that labels an estimate correct or as a subharmonic error based on whether it falls in an interval bounded by local minima of P(f_o) is novel and central to all error rates in Figs. 4-6, but no validation of this classification is provided. If the interval boundaries are sensitive to the periodogram's 0.5-Hz resolution, the Hamming window, or the choice of local-minimum search, the error counts could shift. I ask for at least a robustness check on a subset of intervals (e.g., comparison with a perceptual or manual classification) so that the reader can see that the quality labels are not driving the ranking.
minor comments (5)
  1. [Section III, Fig. 4] The percentages in the bar chart would be easier to interpret alongside a table reporting exact counts, percentages, and confidence intervals for every estimator and error category.
  2. [Section III, paragraph beginning 'The types of the estimation errors...'] The sentence 'reduces the subharmonic errors (34% less than CREPE)' is ambiguous without the absolute rates; please state both rates explicitly (e.g., CREPE 3.0% vs. FCN-F0 2.0%).
  3. [Section II, Acoustic Data] The decision to resample all signals to 8 kHz is stated, but the rationale is not; since CREPE is then run at 16 kHz, please explain whether the 8-kHz lowpass filtering has any effect on the upper range of f_o or on the harmonic/subharmonic analysis.
  4. [Section III, 'There is also a notable discrepancy...'] The comparison with Vaysse et al. is interesting but would be more useful with a direct statement of which recording types and annotation conventions differ, since the reader cannot evaluate the claim from the cited abstract alone.
  5. [General] The paper would benefit from a data/code availability statement, including access to the custom spectrogram annotation program and the scripts used for the estimators, to support reproducibility of the 15,941-interval annotations and the contingency-table analyses.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the study is an empirical comparison with manually annotated ground truth, and the central ranking is not forced by construction or by the authors' prior work.

full rationale

This paper performs an empirical benchmark of five fundamental-frequency estimators (plus an ACF baseline) on sustained vowels. The central claim is that FCN-F0 achieves the highest accuracy and the best subharmonic-error handling. I walked the derivation chain and found no step that reduces to its own input. The ground-truth annotation uses Praat only as an initial rough estimate that is then manually reviewed on a spectrogram with playback and refined by a time-varying harmonic model; the final truth is not defined as the output of any evaluated estimator. This is further confirmed empirically: Praat itself scores only 88% correct while the two deep-learning models score 95-96%, so the annotation procedure did not simply re-import Praat's outputs. The subharmonic-error classification is based on the annotated truth f_o* and a harmonic power profile P(fo), not on any estimator's self-derived quantity. SHR is computed from the ACF baseline and used only as an explanatory variable to stratify subharmonic strength; it is not used to 'predict' the compared estimators' outcomes in a way that is equivalent to fitting them. The authors cite several of their own previous papers, but these citations support background claims (vocal bifurcation phenomena, harmonic-model refinement, kymographic analysis) rather than the ranking result. No uniqueness theorem or ansatz is imported from those citations to force the choice of FCN-F0. The paper also candidly discusses annotation uncertainty in the Limitations paragraph, which affects precision but is not a circularity. Therefore no circular step can be quoted, and the score is 0.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central result rests on the reliability of manual ground truth and the validity of the custom error classification. No fitted parameters or invented entities are used.

assumptions (2)
  • domain assumption The manually annotated fundamental frequency f_o^* correctly represents the speaking fundamental frequency for every interval, including cases with strong subharmonics.
    All estimator accuracy scores are computed against this annotation; the paper's limitation section admits that strong subharmonics can make female voices look like male voices.
  • ad hoc to paper The quality-of-estimate classification, using intervals bounded by local minima of the harmonic power profile P(f_o), correctly labels estimates as correct or subharmonic errors.
    This classification is introduced by the authors and is not externally validated; the outcome labels drive the reported error rates.

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Cite this review

Pith. "Pith review of Comparison of fundamental frequency estimators with subharmonic voice signals." pith.science (2026). https://pith.science/paper/DNDT56XR

@misc{pith2026250104789,
  author       = {Pith},
  title        = {Pith review of: Comparison of fundamental frequency estimators with subharmonic voice signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DNDT56XR}},
  note         = {Machine review of arXiv:2501.04789}
}
read the original abstract

In clinical voice signal analysis, mishandling of subharmonic voicing may cause an acoustic parameter to signal false negatives. As such, the ability of a fundamental frequency estimator to identify speaking fundamental frequency is critical. This paper presents a sustained-vowel study, which used a quality-of-estimate classification to identify subharmonic errors and subharmonics-to-harmonics ratio (SHR) to measure the strength of subharmonic voicing. Five estimators were studied with a sustained vowel dataset: Praat, YAAPT, Harvest, CREPE, and FCN-F0. FCN-F0, a deep-learning model, performed the best both in overall accuracy and in correctly resolving subharmonic signals. CREPE and Harvest are also highly capable estimators for sustained vowel analysis.

Figures

Figures reproduced from arXiv: 2501.04789 by the authors.

Figure 1
Figure 1. Histogram of the annotated fundamental frequencies [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (color online) Illustration of harmonic power profile [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. (color online) (left column) Scatter plots of estimated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: (color online) Quality-of-estimate outcomes: Correct [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: (color online) Contingency tables of the outcomes of the ACF estimator vs. the other five [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: (color online) Conditional histogram of the SHRs of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Towards detecting the pathological subharmonic voicing with fully convolutional neural networks

    eess.AS 2025-01 conditional novelty 6.0 of 10

    Fully convolutional networks trained on synthesized subharmonic phonation classify subharmonic period M=1-4 with >98% synthetic accuracy, with qualitative only evidence on real voices.

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.