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REVIEW 3 major objections 6 minor 77 references

Evolving music theory for emerging musical languages

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that pitch is a listener-dependent perceptual construct, not an objective property of a tone, and shows that two standard assumptions about pitch transmission contradict each other.

desk verdict A clean logical reframing of pitch perception that overreaches from its evidence: the S5/S9 conflict is real and worth articulating, but the step to 'pitch is not objective' rides entirely on under-review data. read the letter →

arxiv 2506.14504 v2 pith:GMGPEL5L submitted 2025-06-17 cs.SD

Emmanuel Deruty This is my paper
classification cs.SD
keywords pitchperceptiontonalfusionfissioncontemporarypopularmusicelectronicproductionmultistabletuningsystemsinformationretrieval
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 argues that pitch—usually treated as a fixed, measurable property of a musical tone—is better understood as a perceptual construct that changes with the listener and the listening context. It focuses on contemporary popular music made with electronic instruments, where synthetic tones can be built so that a single tone suggests several pitches at once. The paper's central logical move is to show that two inherited assumptions, one tone conveys one pitch and two tones convey two pitches, contradict each other when applied to harmonic complex tones. If the argument holds, standard pitch-tracking and music-theoretic analysis will misrepresent much electronic music, and tuning and scale should be seen as things that can emerge from a tone's internal spectral structure rather than as fixed grids imposed before the music is made.

What carries the argument

The key machinery is the pair of assumptions labeled Specification 5 (one quasi-harmonic tone conveys one pitch) and Specification 9 (pitch is intensive, so two tones convey two pitches), together with the worked example that makes them collide. The example uses the harmonic tone model of Mauch and Dixon (2010) with $k=0.8$: a 98 Hz tone and a 196 Hz tone sum to a single harmonic complex tone at 98 Hz, so S5 and S9 give different answers for the same signal. That contradiction is resolved by two perceptual mechanisms: tonal fusion, in which simultaneous consonant tones are heard as a single fused sound, and tonal fission, in which one tone yields multiple pitches. Both mechanisms make the perceived pitch depend on the listener, which is the paper's main lever for replacing an objective-pitch model with a perception-centered one.

What would settle it

A direct test would take a set of electronic-music tones, including the octave-sum example with $f_0=98$ Hz, and collect pitch reports from a large, diverse listener panel across repeated sessions; the claim predicts scattered multi-pitch reports that vary across listeners, so the claim is falsified if all listeners converge on one pitch per tone or if a single $f_0$-based predictor matches every listener in every condition.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that pitch is not an ontologically objective property of a tone. The proof-shaped argument is a contradiction: Specification 5 says a quasi-harmonic tone conveys exactly one pitch, while Specification 9 says pitch is intensive, so two tones convey two pitches. Add a harmonic tone with $f_0=98$ Hz and one with $f_0=196$ Hz; the sum is itself a harmonic complex tone with $f_0=98$ Hz. Specification 5 applied to the sum yields one pitch, but Specification 9 applied to the two sources yields two. Since the signal is the same and the percept cannot be both, the number of pitches is not fixed by the signal. The paper then connects this to tonal fusion (two tones heard as one) and tonal fission (one tone heard as many), and to listening tests showing that perceived pitches vary across listeners and can even shift for one listener over time.

Load-bearing premise

The load-bearing premise is that the listening-test results showing different listeners hearing different pitches from the same quasi-harmonic tones generalize beyond the specific tones and listeners tested, and those results are still under review.

Editorial extensions

If this is right

  • Pitch-tracking algorithms that assume one fundamental per harmonic tone will misreport electronic music tones designed to produce several pitches, because the perceived pitches can differ from the fundamental.
  • For some electronic music, searching for a fixed tuning system is the wrong question; tuning and scale can arise from the tone's partial structure rather than from a pre-existing grid.
  • Perceptual ambiguity can be an intentional compositional resource, and multistable tones may help keep heavily repetitive music interesting across repeated listening.
  • Tonal fusion is not a marginal laboratory curiosity: its avoidance is a plausible historical driver of Western counterpoint rules, so a listener-dependent account of pitch has roots in the classical tradition itself.

Reading between the lines

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

  • Inference: if pitch is listener-dependent, then inter-listener disagreement bounds the accuracy any single pitch-tracking system can achieve on those tones; a system cannot agree with every listener better than listeners agree with each other.
  • Inference: a distribution-based representation of pitch—analogous to reporting coastline length at several ruler scales—may be a more honest target for music analysis than a single ground-truth pitch label.
  • Inference: for generative music systems, the active-tone, resultant-pitch view suggests melody could be controlled by designing partial spectra directly, bypassing note-level pitch specification.
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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 / 6 minor

Summary. The chapter argues that pitch is not an ontologically objective property of a tone but a perceptual construct shaped by listeners and conditions, using phenomenological and inductive methods. It sets out nine 'specifications' of the Western classical framework for pitch transmission, focuses on Specification 5 (one tone conveys one pitch) and Specification 9 (two tones convey two pitches), and claims that these two specifications are mutually incompatible in the general case, using the example of an octave dyad. Drawing on tonal fusion and fission, listening tests from the author's own prior papers (several under review), and an analogy with the coastline paradox, the chapter concludes that pitch is listener-dependent, that multistable pitch percepts can occur, and that tuning systems may emerge from the internal structure of synthetic tones.

Significance. If the empirical listener-variability results in the author's companion papers replicate, the chapter offers a valuable challenge to pitch-as-objective assumptions in MIR and psychoacoustics, with implications for pitch-tracking algorithms, music-theoretic models, and production practice. The S5/S9 incompatibility argument is a compact and pedagogically useful logical observation, and the chapter is honest about its limitations, explicitly stating in §3.5 that it presents no new quantitative data. The speculative sections (§5, §6) are framed as hypotheses and analogies rather than established results. However, the central empirical premise is not contained in this manuscript; it depends on under-review self-citations, which limits the current evidential weight of the strongest conclusion.

major comments (3)
  1. [§3.3] The reductio of Specifications 5 and 9 demonstrates only that applying S5 to the summed octave dyad and S9 to its two components yields conflicting predictions; it does not establish which specification is false, nor that pitch is listener-dependent. A consistent alternative, acknowledged implicitly in §3.2, is that tonal fusion is an exception to S9 for consonant intervals while S5 remains true of individual harmonic tones. The step from 'the traditional framework is inconsistent' to 'pitch is not an ontologically objective property' therefore rests entirely on the listener-variability data of Deruty et al. (2025c), which is under review and not reported here. Please either provide direct evidence against the exception-reading, or weaken the conclusion to a conditional statement.
  2. [§3.4, §3.5, Figure 3] The central empirical evidence for tonal fission consists of a figure 'adapted from Deruty et al. (2025c)' showing pitch transcriptions by seven expert listeners of one Vitalic bass line, plus assertions about guitar power chords and TR-808 kicks. The chapter states in §3.5 that it 'does not aim to present new quantitative data,' making the dependence on under-review work explicit. For a journal publication, a load-bearing claim of this kind needs either the full methodology and results in an appendix or supplementary material, or a clear reframing of the conclusion as conditional on the outcome of those studies. The current presentation does not allow the reader to assess the reliability, generality, or statistical strength of the listener data.
  3. [§6] The coastline paradox is explicitly an analogy, not evidence. The mapping between ruler length and listener characteristics is informal: no account is given of what the analogue of 'measurement scale' is in pitch perception, or why variation across listeners should be treated like variation across measurement resolutions. The analogy can remain as a rhetorical device, but the Conclusion's phrase 'These findings call for a reevaluation of pitch models' overstates the evidential weight, since the chapter's own sections repeatedly rely on unpublished data and analogical argument.
minor comments (6)
  1. [§3.3] The phrase 'two harmonic tones distant from one octave' is unclear; it should read 'two harmonic tones separated by one octave'.
  2. [Figure 2] The caption lists Fourier transforms but does not specify the partial amplitudes, the value of k in the Mauch-Dixon model, or the axis labels; please add these details so the example is reproducible.
  3. [Figure 3] The legend explains that dot area reflects certainty, but there is no scale or quantitative mapping; please add a legend or a table of certainty values.
  4. [References] The reference 'Acoustical Society of American Standards' appears to be a typo for 'Acoustical Society of America Standards'.
  5. [Abstract] The term 'tonal fission' is used in the abstract before it is defined in §3.4; consider a brief parenthetical definition at first use.
  6. [Conclusion] The statement that quantities once assumed to belong to N 'may be more accurately described as belonging to R' is imprecise, because the number of perceived pitches is integer-valued; what is real-valued is the distribution of pitch judgments across listeners or time.

Circularity Check

2 steps flagged · score 4.0 of 10

Central claim of listener-dependent pitch rests on under-review self-cited listening data; the S5/S9 conflict itself is not circular.

  1. self citation load bearing [Section 3.1 (Specification 5); see also Section 3.4]
    "However, if perceived pitch can vary across listeners and listening conditions – as demonstrated by Deruty et al. (2025c) in the case of synthetic quasi-harmonic tones – then the assumption of objectivity no longer holds."

    The chapter's central conclusion — pitch is a listener-dependent construct rather than an ontologically objective property — is carried by listening-test results in Deruty et al. (2025c), an under-review preprint by the same author team. The chapter itself states in Section 3.5 that it 'does not aim to present new quantitative data on tonal fusion', so it adds no independent empirical evidence. The cited preprint is neither machine-checked nor reproduced here, and its under-review status means it cannot serve as an independently established external fact. Thus the step from 'the S5/S9 framework is inconsistent' to 'pitch is not objective' effectively re-states the content of the author's own prior submission rather than deriving it from the present chapter's argument.

  2. self citation load bearing [Section 3.4 (Tonal fission)]
    "Deruty et al. (2025c) report listening tests showing that (1) synthetic quasi-harmonic tones can produce multiple perceived pitches, most of them not corresponding to the f0, and (2) perceived pitches vary across listeners and listening conditions."

    This citation supplies the specific empirical premise — that the studied electronic-music tones produce listener-dependent multiple pitches — which is then used in Sections 5 and 6 to support the broader claim that pitch is a perceptual construct. The independent literature cited here (Bregman, Van Noorden) establishes the general phenomenon of fission, but not the particular result about Vitalic bass tones, guitar power chords, and TR-808 drums with seven expert listeners. That particular result comes only from the author's own under-review paper, so the chapter's empirical basis for the strongest claim reduces to a self-citation whose reliability is not independently established within this chapter.

full rationale

The logical conflict between Specification 5 and Specification 9 in Section 3.3 is a genuine, self-contained reductio: the sum of two octave-related harmonic tones is itself a harmonic tone, so S5 predicts one pitch while S9 predicts two. That part of the argument does not depend on the author's prior work. The same is true for the historical and independent evidence for tonal fusion (Stumpf; DeWitt & Crowder; Shepard; Deutsch; Bregman). However, the paper's strongest conclusion — that pitch is not an ontologically objective property but a listener-dependent construct — is not entailed by the S5/S9 conflict alone, and the paper's own Section 3.5 concedes it contributes no new quantitative data. The empirical gap is filled by repeated citation to Deruty et al. (2025a,b,c,d), several of which are under review, especially the listening tests of Deruty et al. (2025c). Because the load-bearing empirical premise is asserted through self-citation rather than demonstrated or externally verified here, a moderate circularity score is warranted. The coastline-parallel discussion is analogical and therefore not itself a circular step, but it does not add independent evidence. No constructed prediction or definitional circularity was found; the issue is specifically that the central empirical claim reduces to an unverified self-citation.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The chapter introduces no free parameters or invented entities. It relies on methodological axioms (phenomenological stance, inductive reasoning, analogy) and domain assumptions about tonal fusion and the generalizability of the author's own listening tests.

assumptions (5)
  • ad hoc to paper The phenomenological epoché, bracketing all preconceptions, is a valid method for studying pitch perception.
    Section 2 introduces this methodological choice; it is not a standard scientific method in music psychology and is not independently justified.
  • ad hoc to paper Inductive reasoning from particular observations to general principles is appropriate here, without the exhaustive enumeration that Descartes recommends.
    Section 2 acknowledges that exhaustive collection is impractical and substitutes analogy, which is a weaker form of inference.
  • domain assumption Tonal fusion as described by Stumpf and DeWitt and Crowder is a real and sufficiently characterized phenomenon.
    Section 3.2 relies on this for the argument against Specification 9, but the paper notes that quantitative measures of fusion vary across experiments.
  • domain assumption The listening tests in Deruty et al. (2025c) are valid and their results generalize beyond the tested stimuli and listeners.
    Section 3.4 uses those results to assert tonal fission across listeners, but the sample is small and the paper is under review.
  • ad hoc to paper The parallel between coastline measurement and pitch perception is a legitimate form of argument.
    Section 6 uses analogy, which is not deductive proof, to support the central claim.

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Cite this review

Pith. "Pith review of Evolving music theory for emerging musical languages." pith.science (2026). https://pith.science/paper/GMGPEL5L

@misc{pith2026250614504,
  author       = {Pith},
  title        = {Pith review of: Evolving music theory for emerging musical languages},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMGPEL5L}},
  note         = {Machine review of arXiv:2506.14504}
}
read the original abstract

This chapter reconsiders the concept of pitch in contemporary popular music (CPM), particularly in electronic contexts where traditional assumptions may fail. Drawing on phenomenological and inductive methods, it argues that pitch is not an ontologically objective property but a perceptual construct shaped by listeners and conditions. Analyses of quasi-harmonic tones reveal that a single tone can convey multiple pitches, giving rise to tonal fission. The perception of pitch may also be multistable, varying for the same listener over time. In this framework, the tuning system may emerge from a tone's internal structure. A parallel with the coastline paradox supports a model of pitch grounded in perceptual variability, challenging inherited theoretical norms.

Figures

Figures reproduced from arXiv: 2506.14504 by the authors.

Figure 1
Figure 1. Specifications related to pitch transmission in Western classical music. ‘1P’ denotes the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. (1) Fourier transform (FT) of a harmonic complex tone with [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. ‘Stamina’ (Vitalic, 2012). Pitches perceived by seven expert listeners from a sequence of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.