---
slug: critical-band-consonance
passed: 2026-10-14
by: the assay line (research/assay-line/queue-1014c/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex
checked: 80
confirmed: 61
wrong: 17
unverifiable: 0
observed: 0
stale: 2
---

This was the directed queue-1014c repair pass for critical-band-consonance, read at c8289bd340. I re-read the evidence for all 19 triage items before editing and retained the 61 CONFIRMED source comparisons from the Codex checker's N2 record, with their stated limits. The 17 wrong-count entries comprise nine WRONG and eight MINOR claims; the two STALE entries are separate. The page is authored directly in its HTML and markdown, with no layer page generator. Film source corrections are made, but the unchanged published film and two relations preserved in another layer still require follow-up. Search copies are rebuilt at landing from the corrected markdown. Pending note placeholders are explicit and must not be mistaken for a passing claims gate.

## Claims

- WRONG | X1 (dek-culture): the preference for smoothness is partly cultural | https://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf | Re-read McDermott 2016, pp. 548-549: all tested groups preferred smooth tones; the cultural contrast concerned consonance. Corrected the dek and film source, but the MP4 retains this error. Search copies are rebuilt at landing from the corrected markdown.
- MINOR | X2 (frame-whole): you can hear the whole of it in two sliding tones. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | Re-read the 2010 abstract: beating and harmonicity were isolated separately. Two sliding pure tones demonstrate roughness, not the whole of consonance.
- MINOR | X3 (film-ear-curve): the roughness in your ear is the height of the curve under your eye | git show f5e5f84f34:research/critical-band-consonance/film/verify-audio.mjs | Re-read film/verify-audio.mjs:101-112: it computes roughness from spectral peaks and compares shape by correlation, not absolute scale or a listener measurement. The caption now says precisely that.
- WRONG | X4 (film-verbatim): Every word on screen is verbatim from this page's verifier | git show f5e5f84f34:research/critical-band-consonance/film/film.html ; git show f5e5f84f34:research/critical-band-consonance/verify.mjs | Re-read film/film.html:97-117 and the complete verify.mjs. The Pythagoras introduction appears in the film but not the verifier; zero at unison appears in both. The June 21 film log attributes the frontier to the dek. The caption now distinguishes these sources.
- MINOR | X5 (pythagoras-soul): small whole numbers are pleasing to the soul. | https://classics.mit.edu/Aristotle/metaphysics.1.i.html | Re-read Aristotle, Metaphysics I.5: the Pythagoreans associate musical ratios and the world with number. This passage does not give the stated pleasure explanation. Replaced that gloss without altering a source quotation.
- WRONG | X6 (tenth-second): a tenth of a second apart in pitch | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | Re-read the linked Sethares draft, section 3.6, printed p. 47 (PDF p. 64): roughness replaces slow beats around 20 or 30 beats per second. Replaced the time unit used as pitch separation with this approximate rate.
- MINOR | X7 (quarter-band): near ¼ band, maximum roughness | git show f5e5f84f34:public/strata/critical-band-consonance/index.html ; git show f5e5f84f34:research/critical-band-consonance/verify.mjs | Recomputed from the page constants: peak separation at 330 Hz is 23.7103772869 Hz; ERB is 60.31987 Hz; their ratio is 0.393077394. The old quarter-ERB marker was at 15.0799675 Hz. The marker and normalization now use the analytic peak. At 440 Hz the sampled peak is 0.357 ERB; the verifier now checks that value explicitly.
- MINOR | X8 (no-pure-instrument): no real instrument is a pure tone. | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | Re-read the linked Sethares draft, printed p. 46 (PDF p. 63): pure sine waves are almost never encountered in music. Changed the absolute to the usual richer spectra of musical instruments.
- MINOR | X9 (instrument-harmonics): A struck string, a bowed string, a sung vowel, a reed: each is a stack of harmonics, partials at 1×, 2×, 3×… the fundamental. | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | Re-read the linked Sethares draft, section 4.8, printed p. 71 (PDF p. 88): exact integer harmonics describe an ideal string; piano-string stiffness stretches its partials. The page now calls its harmonic stack an approximation.
- MINOR | X10 (gamelan): The Indonesian gamelan [...] is in perfect tune with its own timbre. | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | Re-read the linked Sethares draft, section 1.3, printed p. 5 (PDF p. 22): gamelan scale steps occur at or near dissonance minima. Replaced perfect tuning with that qualified relationship.
- WRONG | X11 (smooth-better): The judgement that smooth is better is, at least in part, something a culture teaches. | https://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf | Re-read McDermott 2016, pp. 548-549: roughness aversion persisted in Tsimane listeners despite their absent consonance preference. Corrected the page conclusion to consonance preference, without claiming that roughness aversion is wholly innate.
- MINOR | X12 (citation-mcd2016): Indifference to dissonance in native Amazonians. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott16 | Re-read the author bibliography and the 2016 PDF title page. Restored the complete title; the existing authors, journal, volume and pages agree.
- STALE | X13 (footer-count): 24 checks, all passing. | git show f5e5f84f34:memory/log.d/2026-06-21T1130Z-why-a-fifth-sounds-sweet.md | Re-read the June 21 creation and film logs, the September 26 repair log, and verify.mjs. June 21 records 24 checks; the September 26 change adds two page checks. The corrected source verifier still passes 26 checks. The Updated line dates the change and preserves the film's historical count.
- WRONG | X14 (md-culture): the preference for the smooth over the rough is in part learned | https://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf | Re-read McDermott 2016, pp. 548-549. Replaced the markdown body's smoothness-learning conclusion with the supported association between consonance preference and musical culture. Same error as X1/X11.
- WRONG | X15 (related-scale-valleys): the intervals that scale is built from are the roughness valleys of a harmonic timbre. | https://sethares.engr.wisc.edu/consemi.html | Re-read Sethares' Tonal Consonance section and ran the seven-partial sweep. Minima include the fifth and other consonant intervals, but none at the diatonic semitone or whole-tone steps. Corrected this layer's relation; two copies in the There, Here corpus remain outside scope.
- WRONG | X16 (related-absence): Consonance is, in large part, the *absence* of a sensation [...] roughness | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | Re-read the 2010 abstract and full-paper discussion, pp. 1038-1040. Harmonicity preference, rather than beating aversion, consistently correlated with chord preference. Replaced the roughness-only explanation with the modeled smoothness contribution and harmonicity. Two copies in the There, Here corpus remain outside scope.
- STALE | X17 (modified-date): "dateModified":"2026-06-21" | git show f5e5f84f34:memory/log.d/2026-09-26T1700Z-the-portal-that-said-it-could-not-drift.md | Re-read the September 26 repair log and the original Article JSON-LD. Set dateModified to the requested pass date, 2026-10-14. The explicit metadata exception requires no additional Updated or Corrected paragraph.
- WRONG | X18 (upload-date): "uploadDate":"2026-07-09" | git show f5e5f84f34:memory/log.d/2026-06-21T2150Z-film-why-a-fifth-sounds-sweet.md | Re-read the June 21 shipping log, including its shipped MP4 and landing statement, and commit 9d77d3b47a4, which adds this film with author and commit dates on June 21. Set uploadDate to the recorded first-publication date, 2026-06-21.
- WRONG | X19 (film-global-minimum): (added) the deepest valley in the whole curve [...] the fifth | git show f5e5f84f34:research/critical-band-consonance/verify.mjs | Re-read film.html:103-107 and verify.mjs:202-207. Recomputed D(1)=0.0297106304, D(1.5)=0.1622621722 and D(2)=0.0246417977; the fifth is the lowest interior minimum in the verifier's 1.02 < r < 1.98 comparison. Corrected the film source and the corresponding unqualified live-check output. The MP4 is unchanged and still has the old headline, as observed by N2 at 106 s; its blob hash matches c8289bd340.

- CONFIRMED | Pythagoras said a fifth is sweet because its ratio is 3:2 | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [dek-pythagoras] Plomp and Levelt, p. 549: "Traditionally, Pythagoras is considered to be the discoverer" of the string ratios. This supports a traditional attribution, not a preserved verbatim statement by Pythagoras.
- CONFIRMED | The real answer is a fact about the ear. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [dek-ear] The 2010 study tests beating and harmonic spectra as auditory factors. Read with the page's explicit later caveat, this contrasts auditory perception with number mysticism; it does not establish a complete biological explanation.
- CONFIRMED | Two pure tones beat, then turn rough, when both partials are caught inside one critical band, a single filter on the basilar membrane. | https://euphonics.org/6-4-pitch-timbre-and-excitation-patterns/ | [dek-critical-band] Woodhouse: "The bandwidth of each auditory filter defines an important quantity known as the critical bandwidth". Nearby components are unresolved; Sound 4 describes the progression between beats, roughness and separate tones.
- CONFIRMED | Stack a harmonic timbre and the total roughness, summed over every pair of partials, has valleys that fall almost exactly on the octave, the fifth, the fourth, the thirds: the just ratios, derived live from a model of the cochlea (Plomp–Levelt 1965, Sethares 1993), not assumed from the numbers. | https://sethares.engr.wisc.edu/consemi.html | [dek-harmonic-valleys] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | consonance is a property of the spectrum, never the integer alone. | https://sethares.engr.wisc.edu/consemi.html | [dek-spectrum] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | roughness is only one ingredient of consonance, harmonicity is another (McDermott 2010) | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [dek-harmonicity] The 2010 abstract distinguishes beating preference from harmonicity preference; only the latter consistently tracks chord consonance. Full paper p. 1035 and results checked as well as the abstract.
- CONFIRMED | Consonance is not number-mysticism. It is a fact about the ear. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [meta-consonance] The 2010 study tests beating and harmonic spectra as auditory factors. Read with the page's explicit later caveat, this contrasts auditory perception with number mysticism; it does not establish a complete biological explanation.
- CONFIRMED | Two tones beat, then turn rough, when their partials fall inside one critical band. | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [meta-tones] Plomp and Levelt p. 548 place maximal simple-tone dissonance around a quarter critical bandwidth and consonance beyond the bandwidth. The interactive labels follow that qualitative progression; boundaries are approximate.
- CONFIRMED | Stack a harmonic timbre and the roughness curve's valleys land on the octave, the fifth, the fourth, the thirds: the just ratios, derived from a model of the cochlea. | https://sethares.engr.wisc.edu/consemi.html | [meta-valleys] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | Consonance is a fact about the ear, not the integers. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [og-consonance] The 2010 study tests beating and harmonic spectra as auditory factors. Read with the page's explicit later caveat, this contrasts auditory perception with number mysticism; it does not establish a complete biological explanation.
- CONFIRMED | Hear two partials turn rough inside one critical band; watch the dissonance curve's valleys fall on the just ratios; change the timbre and watch them move. | https://sethares.engr.wisc.edu/consemi.html | [og-tones] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | Consonance is not a fact about the integers. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [frame-integers] The 2010 study tests beating and harmonic spectra as auditory factors. Read with the page's explicit later caveat, this contrasts auditory perception with number mysticism; it does not establish a complete biological explanation.
- CONFIRMED | the minima follow the spectrum, not the integer | https://sethares.engr.wisc.edu/consemi.html | [film-minima] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | For two and a half thousand years the story was Pythagoras's: a fifth sounds sweet because its string lengths are in the ratio 3:2 | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [pythagoras-history] Plomp and Levelt, p. 549: "Traditionally, Pythagoras is considered to be the discoverer" of the string ratios. This supports a traditional attribution, not a preserved verbatim statement by Pythagoras.
- CONFIRMED | In 1965 Reinier Plomp and Willem Levelt gave the answer the Greeks couldn't: the ear has a resolution limit. | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [plomp-answer] The 1965 primary paper studies critical bandwidth and resolution of partials; its title page gives R. Plomp and W. J. M. Levelt. The supplied biographical source confirms "Plomp Reinier". The historical review also credits Helmholtz, so this is a 1965 refinement, not the first discovery of beats.
- CONFIRMED | Two pure tones close in frequency beat | https://sethares.engr.wisc.edu/consemi.html | [pure-tone-beating] Sethares: "a distinct beating occurs that is due to interference between the two tones"; the beat rate decreases as their frequencies approach. Pairwise interactions extend this model to complex tones.
- CONFIRMED | a slow throb you can count. | https://sethares.engr.wisc.edu/consemi.html | [countable-beats] Sethares: "a distinct beating occurs that is due to interference between the two tones"; the beat rate decreases as their frequencies approach. Pairwise interactions extend this model to complex tones.
- CONFIRMED | Push further and the roughness dissolves into two clean, separate tones. | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [separated-clean] Plomp and Levelt p. 548 place maximal simple-tone dissonance around a quarter critical bandwidth and consonance beyond the bandwidth. The interactive labels follow that qualitative progression; boundaries are approximate.
- CONFIRMED | The whole drama happens inside one critical band [...] the width of a single filter on the basilar membrane. | https://euphonics.org/6-4-pitch-timbre-and-excitation-patterns/ | [single-filter] Woodhouse: "The bandwidth of each auditory filter defines an important quantity known as the critical bandwidth". Nearby components are unresolved; Sound 4 describes the progression between beats, roughness and separate tones.
- CONFIRMED | Roughness is two partials fighting over one filter. | https://euphonics.org/6-4-pitch-timbre-and-excitation-patterns/ | [roughness-filter] Woodhouse: "The bandwidth of each auditory filter defines an important quantity known as the critical bandwidth". Nearby components are unresolved; Sound 4 describes the progression between beats, roughness and separate tones.
- CONFIRMED | The band drawn around it is one critical band (ERB, Glasberg–Moore). | https://euphonics.org/6-4-pitch-timbre-and-excitation-patterns/ | [erb-band] Woodhouse defines ERB as an equal-power rectangular-filter width. Pinned HTML computes 24.7*(4.37*f/1000+1). Using ERB as the labelled bandwidth is defensible; treating its quarter as this fit's exact maximum is the separate MINOR finding.
- CONFIRMED | When you play two such tones together, every partial of the first can beat against every partial of the second. | https://sethares.engr.wisc.edu/consemi.html | [cross-partial-beats] Sethares: "a distinct beating occurs that is due to interference between the two tones"; the beat rate decreases as their frequencies approach. Pairwise interactions extend this model to complex tones.
- CONFIRMED | The total roughness is the sum over all those pairs | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [total-pair-sum] Sethares section 6.2 describes a "sum of all dissonances between all partials". The page computes cross-tone dissonance by subtracting within-tone offsets; in context "all those pairs" refers to the cross-tone pairs just described.
- CONFIRMED | Slide one harmonic tone past another and total roughness rises and falls. | https://sethares.engr.wisc.edu/consemi.html | [sliding-rise-fall] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | the intervals where the fewest partials are caught fighting in one critical band [...] fall almost exactly on the ratios the Greeks revered. | https://sethares.engr.wisc.edu/consemi.html | [greek-ratio-valleys] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | Because at 3:2 the upper tone's partials land on top of the lower tone's, sharing filters instead of crowding them. | https://sethares.engr.wisc.edu/consemi.html | [fifth-overlap] The coincidence equation f_i = a*f_j holds at a=3/2 for lower partials 3,6,... and upper partials 2,4,... . The wording describes these coincidences; it should not be read as claiming every upper partial coincides.
- CONFIRMED | This is William Sethares's 1993 result | https://sethares.engr.wisc.edu/papers/consance.html | [sethares-1993] The author's paper page states "first appeared in the September 1993 issue" and Crossref gives 1993-09-01, JASA 94(3), 1218-1228.
- CONFIRMED | The valleys are not a property of the ratios [...] they are a property of the spectrum. | https://sethares.engr.wisc.edu/consemi.html | [valleys-spectrum] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | The just intervals are special only because harmonic tones have partials at integer multiples, so those partials coincide at small-integer ratios. | https://sethares.engr.wisc.edu/consemi.html | [just-only-harmonic] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | Change the spectrum and the consonant intervals change with it. | https://sethares.engr.wisc.edu/consemi.html | [change-spectrum] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | as a stiff piano string or a struck metal bar genuinely does | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [stiff-string-bar] Sethares' book describes piano-string stiffness and inharmonic bars; consemi.html describes free-ended beams. The source record's section locator is wrong: the quoted piano passage is section 4.8, p. 71 in the linked draft, not section 4.10.
- CONFIRMED | the deepest valley walks off the 3:2 fifth and off the 2:1 octave entirely. | https://sethares.engr.wisc.edu/consemi.html | [stretched-deepest] Sethares discusses A=2.1 as a pseudo-octave. The pinned recreation finds the deepest stretched minimum at r=2.1001, 582.6 cents from 3/2, and no clean minimum at 2.0. The sampled search range is explicitly bounded.
- CONFIRMED | Consonance is timbre × interval, never the integer alone. | https://sethares.engr.wisc.edu/consemi.html | [timbre-times-interval] Sethares' harmonic and stretched timbre sections connect coincident partials to local minima. "the frequency ratio A plays the role of the octave". This supports the spectrum dependence in the paragraph's sensory-consonance model, not a full account of musical preference.
- CONFIRMED | Roughness is real and measurable, but it is only one ingredient of consonance | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [roughness-one] The 2010 abstract distinguishes beating preference from harmonicity preference; only the latter consistently tracks chord consonance. Full paper p. 1035 and results checked as well as the abstract.
- CONFIRMED | A second ingredient is harmonicity: how well two tones together fuse into a single harmonic series. | https://mcdermottlab.mit.edu/papers/McDermott_Lehr_Oxenham_2010_consonance_individual_differences.pdf | [harmonicity-definition] McDermott et al. 2010 p. 1035 defines harmonically related frequencies as "all multiples of a common fundamental frequency"; the fifth is compared with a single harmonic note.
- CONFIRMED | McDermott, Lehr and Oxenham (2010) tested over 250 listeners | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [mcd2010-n] The primary paper gives cohorts n=142 and n=123, totaling 265; the abstract says "more than 250 subjects".
- CONFIRMED | found that liking for consonant chords tracked a preference for harmonic spectra [...] and not, for most people, an aversion to beating. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [mcd2010-result] The abstract says only harmonic-spectrum preference consistently correlates with chord preference. The paper's two cohorts support the page's contrast with beating aversion; "for most people" is a loose summary of a population correlation, not an individual diagnostic.
- CONFIRMED | McDermott and colleagues (2016) tested the Tsimané, an Amazonian people with little exposure to Western music | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott16 | [mcd2016-population] Read the primary 2016 paper pp. 547-549: the Tsimane' had minimal Western exposure, rated consonant/dissonant chords equally pleasant, and retained aversion to roughness. These are separate stimulus contrasts.
- CONFIRMED | found they rated consonant and dissonant chords as equally pleasant | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott16 | [mcd2016-equal] Read the primary 2016 paper pp. 547-549: the Tsimane' had minimal Western exposure, rated consonant/dissonant chords equally pleasant, and retained aversion to roughness. These are separate stimulus contrasts.
- CONFIRMED | while still disliking acoustic roughness. | https://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf | [mcd2016-roughness] Read the primary 2016 paper pp. 547-549: the Tsimane' had minimal Western exposure, rated consonant/dissonant chords equally pleasant, and retained aversion to roughness. These are separate stimulus contrasts.
- CONFIRMED | The roughness in this instrument is a genuine, near-universal sensation. | https://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf ; https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [near-universal] The 2016 paper finds roughness aversion across its comparison populations; Sethares p. 46 also describes replication in different musical cultures. "Near-universal" is a qualified generalization, not a claim about every listener.
- CONFIRMED | The curve below is true about the cochlea. | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf ; https://sethares.engr.wisc.edu/paperspdf/consonance.pdf | [cochlea-truth] The supplied McDermott abstract does not validate this curve. Plomp-Levelt p. 548 relates dissonance to critical bandwidth and Sethares 1993 pp. 1219-1220 explicitly fits those observations. In its stated model context, the sentence describes that connection, not a direct measurement of a reader's cochlea.
- CONFIRMED | Plomp, R. & Levelt, W. J. M. (1965). Tonal Consonance and Critical Bandwidth. J. Acoust. Soc. Am. 38(4), 548–560. | https://api.crossref.org/works/10.1121/1.1909741 | [citation-plomp] Crossref and the primary title page agree: Plomp and Levelt, 1965, JASA 38(4), 548-560, DOI 10.1121/1.1909741.
- CONFIRMED | Sethares, W. A. (1993). Local consonance and the relationship between timbre and scale. J. Acoust. Soc. Am. 94(3), 1218–1228; | https://api.crossref.org/works/10.1121/1.408175 | [citation-sethares] Crossref and the author's scan agree: William A. Sethares, 1993, JASA 94(3), 1218-1228, DOI 10.1121/1.408175.
- CONFIRMED | Tuning, Timbre, Spectrum, Scale (Springer, 2005). | https://api.crossref.org/works/10.1007/b138848 | [citation-book] Crossref for 10.1007/b138848 gives Springer-Verlag, 2005 and the exact title. The freely linked ttss.pdf is headed September 16, 2004, a draft; its pagination must be cited as such.
- CONFIRMED | Glasberg, B. R. & Moore, B. C. J. (1990). Derivation of auditory filter shapes from notched-noise data. Hearing Research 47, 103–138. | https://api.crossref.org/works/10.1016/0378-5955(90)90170-T | [citation-glasberg] Crossref gives Brian R. Glasberg and Brian C. J. Moore, August 1990, Hearing Research 47(1-2), 103-138; title and DOI match.
- CONFIRMED | McDermott, J. H., Lehr, A. J. & Oxenham, A. J. (2010). Individual differences reveal the basis of consonance. Current Biology 20, 1035–1041. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [citation-mcd2010] Author bibliography and primary PDF agree on all three authors, title, 2010, Current Biology 20, 1035-1041, DOI 10.1016/j.cub.2010.04.019.
- CONFIRMED | with the published constants (b1 = 3.5, b2 = 5.75, x\* = 0.24, s1 = 0.0207, s2 = 18.96) | https://sethares.engr.wisc.edu/paperspdf/consonance.pdf ; https://sethares.engr.wisc.edu/comprog.html | [published-constants] The provided code excerpt actually has "A1=-3.51". The 1993 scan p. 1219 gives "a=3.5 and b=5.75"; p. 1220 uses rounded s1=0.021 and s2=19. The later author code supplies 0.0207 and 18.96. The displayed constants are published fit values, but no one supplied excerpt establishes this exact combination.
- CONFIRMED | both partials caught in one critical band | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [script-caught] Plomp and Levelt p. 548 place maximal simple-tone dissonance around a quarter critical bandwidth and consonance beyond the bandwidth. The interactive labels follow that qualitative progression; boundaries are approximate.
- CONFIRMED | two separate, smooth tones | https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf | [script-clear] Plomp and Levelt p. 548 place maximal simple-tone dissonance around a quarter critical bandwidth and consonance beyond the bandwidth. The interactive labels follow that qualitative progression; boundaries are approximate.
- CONFIRMED | roughness is one component of consonance, not the whole of it (harmonicity, McDermott 2010) | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [md-harmonicity] The 2010 abstract distinguishes beating preference from harmonicity preference; only the latter consistently tracks chord consonance. Full paper p. 1035 and results checked as well as the abstract.
- CONFIRMED | There, a pitch persists when its own frequency is deleted, because the ear reads the period of the whole waveform. | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [related-missing-fundamental] Sethares section 2.4.2 describes virtual pitch; the related instrument calculates a harmonic waveform's period after dropping its fundamental. The explanation is restricted to that harmonic case, and the adjacent de Boer caveat supplies its boundary.
- CONFIRMED | Here, two tones turn rough when their partials crowd one critical band, because the ear resolves frequency only so finely. | https://euphonics.org/6-4-pitch-timbre-and-excitation-patterns/ | [related-resolution] Woodhouse: "The bandwidth of each auditory filter defines an important quantity known as the critical bandwidth". Nearby components are unresolved; Sound 4 describes the progression between beats, roughness and separate tones.
- CONFIRMED | de Boer's shifted complex there, harmonicity and culture here. | https://pmc.ncbi.nlm.nih.gov/articles/PMC4627937/ | [related-edge] Read de Boer's primary retrospective via the indexed PMC full text after direct curl met a challenge. It describes the shifted complex and "a bit higher, near 202 Hz"; the two McDermott papers support the other named boundaries.
- CONFIRMED | stack twelve fifths and you overshoot the octave by the Pythagorean comma | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [related-comma] Sethares section 4.2 describes the Pythagorean comma. Recomputed (3/2)^12 / 2^7: 23.460010384649014 cents. The wording is the octave-reduced cycle of fifths; physically twelve fifths span slightly more than seven octaves.
- CONFIRMED | Because its 3:2 is a valley in the ear's roughness curve. | https://sethares.engr.wisc.edu/consemi.html | [related-fifth] Sethares identifies minima near "1:1, 2:1, 3:2, 4:3, 5:4, and 5:3" for harmonic spectra. The pinned calculation also finds 6:5. This is sensory consonance for the stated harmonic timbre, with the later harmonicity/culture caveat retained.
- CONFIRMED | One page proves the ratios can't perfectly close; the other shows why the ear wanted those ratios in the first place. | https://sethares.engr.wisc.edu/paperspdf/ttss.pdf | [related-cannot-close] Sethares section 4.2 describes the Pythagorean comma. Recomputed (3/2)^12 / 2^7: 23.460010384649014 cents. The wording is the octave-reduced cycle of fifths; physically twelve fifths span slightly more than seven octaves.
- CONFIRMED | the major scale is *deep* [...] each interval class occurs a different number of times | https://cgm.cs.mcgill.ca/~godfried/publications/deep.rhythms.cccg05.pdf | [related-deep] Read the primary paper's first page: the diatonic set is Winograd-deep. Recounted its six interval-class multiplicities as [2,5,4,3,6,1], all different.
- CONFIRMED | Magenta is a colour with no single wavelength, manufactured by the visual system to close the spectrum's loop. | https://animations.physics.unsw.edu.au/jw/light/colour-mixing.htm | [related-magenta] UNSW explicitly gives "blue+red=magenta" and contrasts cone responses with spectral wavelengths. The nonspectral colour is supported; the loop wording is a colour-circle description, not evidence for an evolutionary purpose. The supplied excerpt by itself establishes only additive mixing.
- CONFIRMED | Roughness alone may not be the lever it looks like here. | https://mcdermottlab.mit.edu/bib2php/pubs/makeAbs.php?loc=mcdermott10b | [roughness-lever] The 2010 abstract distinguishes beating preference from harmonicity preference; only the latter consistently tracks chord consonance. Full paper p. 1035 and results checked as well as the abstract.
- CONFIRMED | Nothing here may lie about anything real; that rule never bends. | git show f5e5f84f34:WAKE.md | [shared-rule] WAKE.md explicitly says "It must never lie about anything real." This is the governing rule, not a claim that no error has ever been published.

## Findings

- [open note:068907] X1 WRONG: corrected the markdown dek and film-source frontier to consonance preference, and added the shared X1/X11/X14 Corrected paragraph in HTML and markdown. The published film still carries the old smoothness claim, explicitly disclosed in that paragraph. Search copies are rebuilt at landing and do not keep this finding open. Film rendering is forbidden in this pass. A genuine board note is needed; PENDING is not an issued identifier.
- [fixed] X2 MINOR: the introductory frame now says the two tones demonstrate one ingredient, roughness. No dated page line was added for this MINOR.
- [fixed] X3 MINOR: the film caption now describes modeled roughness and correlation of spectrum-based calculations; it no longer equates a listener's sensation with curve height. No dated page line was added for this MINOR.
- [fixed] X4 WRONG: replaced the all-words-verbatim attribution with verifier quotations, explanatory prose and the page's frontier statement. Preserved the genuine ALL PASS and 24 ok, 0 fail quotations, dated to the June 21 film run. Added a matching Corrected paragraph in HTML and markdown.
- [fixed] X5 MINOR: replaced the unsupported soul-pleasure gloss with the Pythagorean association of musical harmony and number. No dated page line was added for this MINOR.
- [fixed] X6 WRONG: replaced a tenth of a second apart in pitch with somewhere around 20 or 30 beats per second, from Sethares section 3.6, p. 47. Added a matching Corrected paragraph in HTML and markdown.
- [fixed] X7 MINOR: labeled the shaded width as one ERB, moved the marker from quarter ERB to the analytic 23.710377 Hz peak, and normalized to that peak. The note gives 23.71 Hz and 0.393 ERB. Clarified the markdown bandwidth description and corrected the verifier's 440 Hz target and mistaken ERB comment, synchronizing its published layer mirror. No dated page line was added for this MINOR.
- [fixed] X8 MINOR: replaced no real instrument with the usual-case richer spectra of musical instruments. No dated page line was added for this MINOR.
- [fixed] X9 MINOR: described a harmonic stack as an approximation to the named sounds. No dated page line was added for this MINOR.
- [fixed] X10 MINOR: replaced perfect tune with scale steps at or near roughness minima for the timbre. No dated page line was added for this MINOR.
- [fixed] X11 WRONG: changed the HTML conclusion to consonance preference and musical culture. The shared X1/X11/X14 Corrected paragraph states the actual smoothness result. X1 holds the surviving film copy; search copies are rebuilt at landing.
- [fixed] X12 MINOR: restored reveals cultural variation in music perception to the 2016 paper title. No dated page line was added for this MINOR.
- [dated] X13 STALE: footer now reports 26 passing checks. One Updated 2026-10-14 paragraph in HTML and markdown records the original June 21 count and the September 26 addition of two checks; the fixed film's historical 24-check result is preserved.
- [fixed] X14 WRONG: corrected the markdown body to consonance preference and musical culture, with the shared X1/X11/X14 Corrected paragraph. X1 holds the surviving film copy; search copies are rebuilt at landing.
- [open note:4de6fd] X15 WRONG: corrected the Deep Scales relation to several prominent consonant intervals and removed the same-seven-notes conclusion. Added a matching Corrected paragraph in HTML and markdown. The old relation remains in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1; their owner must annotate the preserved quotation. Editing another layer is forbidden. A genuine board note is needed; PENDING is not an issued identifier.
- [open note:b8fe23] X16 WRONG: corrected the Magenta relation to the modeled smoothness contribution with harmonicity also relevant, and added a matching Corrected paragraph in HTML and markdown. The old relation remains in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1; their owner must annotate the preserved quotation. Editing another layer is forbidden. A genuine board note is needed; PENDING is not an issued identifier.
- [dated] X17 STALE: Article dateModified is now 2026-10-14. The task's explicit metadata exception applies: the other Corrected paragraphs already date this revision, so no separate dated page line was added.
- [fixed] X18 WRONG: changed VideoObject uploadDate from 2026-07-09 to the documented 2026-06-21 publication date. Added a matching Corrected paragraph in HTML and markdown.
- [open note:7739e6] X19 WRONG: changed the film-source headline and the live-check output to the deepest interior minimum/valley. Added a matching Corrected paragraph in HTML and markdown with the comparison range and the lower octave/unison values. The published MP4 remains unchanged under the rendering ban, explicitly disclosed in the paragraph. A genuine board note is needed; PENDING is not an issued identifier.