---
slug: shepard-tone
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: 105
confirmed: 77
wrong: 27
unverifiable: 0
observed: 0
stale: 1
---

This was the directed correction pass for shepard-tone at 410a8f74a4, following the 27 decisions in research/assay-line/queue-1014c/shepard-tone/triage.json. The fixer re-read each item's evidence, executed the original scheduling code with recording stubs, and corrected the 20 WRONG and six MINOR triage items within this layer; the one STALE metadata date uses the dateModified exception. The repair re-read also changes original claim 127 to WRONG because its fixed-height assertion about this playback shares X25's counterexample. X25 remains open for unannotated copies in the separate there-here layer. The 77 CONFIRMED lines below preserve the claims and source re-reads recorded by Codex N2 at f5e5f84f34, with that provenance retained in their notes; they are not represented as new listening measurements. The counts are 77 CONFIRMED, 21 WRONG, six MINOR and one STALE, totaling 105; MINOR counts toward wrong. Only this layer's files changed; no audio or images were rendered.

## Claims
- WRONG | [X1] "You will hear it climb without end." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X2] "while the note seems to ascend through octave after octave, its true height never moves a hair." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X3] "It cannot run off the top of your hearing because it never actually leaves the middle." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X4] "Set it descending and it falls forever instead" | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X5] "Live spectrum: octave-spaced partials sliding under a fixed bell-shaped envelope, with the perceived-height marker held fixed." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | The original drawing used continuous phase and slots -3 through 13; audio used slots -1 through 11 and quantized frequency in stepped mode. The fixed marker used the wide model phase-zero mean, not a measured percept.
- MINOR | [X6] "drift since you pressed play" | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | The original readout subtracted H0 at phase zero, although the label promised a baseline saved on starting. The unused startTheta did not enter the calculation.
- WRONG | [X7] "Pitch height "; " what your brain reports as "how high" "; " is the loudness-weighted average frequency of the whole comb (its spectral centroid)." | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf; https://www.phys.unsw.edu.au/~jw/reprints/SchWolTarICMPC8.pdf; git show 410a8f74a4:public/strata/shepard-tone/index.html | Deutsch describes octave ambiguity, not equality between perceived pitch height and a spectral statistic. The code averages log2-frequency with amplitude weights. Schubert and colleagues define a frequency centroid with spectral power weights and discuss timbral brightness. These are different quantities.
- MINOR | [X8] "Because the bell is fixed and the partials are evenly spaced an octave apart, that average is a constant." | git show 410a8f74a4:research/shepard-tone/verify.mjs; research/shepard-tone/verify.mjs | The original verifier reports nonzero 1.769251412e-10-cent ripple for its broad Gaussian model. Its sampled, floating-point check accepts a 0.01-cent tolerance. Near-constancy is supported; exact constancy from fixed spacing and a fixed bell is not.
- WRONG | [X9] "The page measures it live: it does not move." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X10] "Neither is "higher": they have identical height" | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Executing the original chord scheduler at phases 0.1 and 0.6 gives a 12.016950854-cent difference in its amplitude-weighted mean log-frequency. The chord drops amplitudes below 0.01. The old verifier instead uses 23 uncut partials and only phases 0 and 0.5.
- MINOR | [X11] "the verifier confirms the pair is level to a trillionth of a cent" | git show 410a8f74a4:research/shepard-tone/verify.mjs; git show 410a8f74a4:public/research/shepard-tone/index.html | The original verifier gives 4.263256415e-12 cents for its specific wide-model pair at phases 0 and 0.5, about four trillionths rather than one. This is not a result for all random played pairs.
- MINOR | [X12] "Your ear will answer with total confidence." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | Deutsch describes confident judgments among some listeners, not a guarantee of confidence for every reader. The invitation can say a reader may hear a definite direction.
- WRONG | [X13] "If you are like most listeners you will keep hearing the same direction even though each pair is a fresh, randomly chosen tritone" | https://deutsch.ucsd.edu/psychology/pages.php?i=206; git show 410a8f74a4:public/strata/shepard-tone/index.html | Deutsch gives examples in which a listener changes perceived direction when a different pitch-class pair is played. The page selects a fresh random first phase each trial. Consistency for a given pairing does not imply a single direction across random transpositions.
- WRONG | [X14] "that consistency is your own internal map of pitch classes showing through." | https://deutsch.ucsd.edu/psychology/pages.php?i=206; git show 410a8f74a4:public/strata/shepard-tone/index.html | Deutsch finds systematic dependence on pitch-class position. The original phrase referred instead to the same direction across random pairs, so it attributed the wrong behavior to the map.
- WRONG | [X15] "Give the ear back any height cue and the spell breaks." | https://www.ebi.ac.uk/europepmc/webservices/rest/PMC5980092/fullTextXML | The primary study explicitly opposes height and chroma cues. Its Behavioral Results report that judgments followed chroma in 94.2 percent of incongruent trials. This is a counterexample to any added height cue always breaking the illusion; it does not show that height cues never matter.
- MINOR | [X16] "The height-invariance is exact arithmetic, not a vibe." | git show 410a8f74a4:research/shepard-tone/verify.mjs | The original verifier samples 20000 phases using floating-point arithmetic and accepts nonzero ripple below 0.01 cent. It does not prove exact equality.
- MINOR | [X17] "the verifier measures both." | git show 410a8f74a4:research/shepard-tone/verify.mjs | The full original executable defines only a Gaussian envelope and runs its four calculations on that envelope. The windowed-bell comparison appears in prose/comments, not an executable comparison.
- WRONG | [X18] "a tritone apart and exactly level in height." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original feedback claimed equality for every random pair, but the actual chord scheduler gives a 12.016950854-cent mean-log difference at phases 0.1 and 0.6. This is not an audibility result.
- WRONG | [X19] "notice how consistent you are across fresh, random pairs." | https://deutsch.ucsd.edu/psychology/pages.php?i=206; git show 410a8f74a4:public/strata/shepard-tone/index.html | The original tally praised consistency whenever the response count reached three, irrespective of the responses. Deutsch supports pitch-class-dependent judgments, not uniform direction across fresh random pairs.
- WRONG | [X20] "every partial synthesised live; the perceived height verified pinned, not promised" | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X21] "the perceived height stays pinned to a ten-billionth of a cent while the pitch class cycles without end." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X22] "while the note seems to rise through octave after octave, its perceived height (the loudness-weighted mean frequency) never moves." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X23] "It is synthesised live, ascending or descending, stepped or as Risset's continuous glide, and the spectrum shows the trick: the loudness-weighted mean frequency never moves." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- WRONG | [X24] "all from the same synthesis the page plays." | git show 410a8f74a4:research/shepard-tone/verify.mjs; research/shepard-tone/assay-before.json; research/shepard-tone/verify-page.mjs | The original verifier uses 23 uncut slots. Playback uses 13 slots without octave recycling, unquantized gains for quantized frequencies, and a 0.01 amplitude cutoff in chords. Re-execution confirms material differences, so the identity assertion is false.
- WRONG | [X25] "a height that you can hear refusing to change while the note seems to soar." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; research/shepard-tone/verify-page.mjs | Original scheduler re-executed with recording stubs at 410a8f74a4: phase 6 gives 1078.811761 Hz as the amplitude-weighted mean log-frequency converted to Hz, while the readout says 640.00 Hz. At phase 12 the lowest target is 40960 Hz; at phase -12 the highest is 10 Hz. This is a parameter calculation, not audio or perception measurement.
- STALE | [X26] ""dateModified":"2026-06-18"" | git log 410a8f74a4 -- public/strata/shepard-tone/index.html; git show 6c62eb137a4 -- public/strata/shepard-tone/index.html | The file was created on 2026-06-18; git history shows a title change on 2026-06-22 and later modifications through 2026-10-01. The old creation date no longer describes the latest revision. The explicit dateModified exception applies.
- WRONG | [X27] (added) "C" | https://newt.phys.unsw.edu.au/jw/notes.html; research/shepard-tone/assay-before.json | Under the stated conventional tuning, 69 + 12*log2(20/440) = 15.486820576. Thus the octave-equivalent starting class is D-sharp plus about 48.682 cents, not C. The old note array ignored FBASE.
- CONFIRMED | "The Shepard Tone: the Pitch That Rises Forever" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [001 endless-title] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the auditory Escher staircase" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [002 auditory-escher] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the Shepard tone (Roger Shepard, 1964)" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; https://api.crossref.org/works/10.1121/1.1919362 | [005 shepard-1964] The scanned first page names "ROGER N. SHEPARD" and "(Received 23 July 1964)"; Crossref gives author Roger N. Shepard and publication 1964-12-01. The record's abstract excerpt alone omits the name/date. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "octave-stacked partials under a fixed bell" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; git show f5e5f84f34:public/strata/shepard-tone/index.html | [006 specimen-partials] Shepard, p. 2347: "Each tone consisted of many sinusoidal components locked at successive intervals of an octave and sounded simultaneously." The next sentence specifies "exactly twice" the previous frequency, and the amplitudes taper at the extremes. The page's own FBASE=20 supplies the illustrative 20,40,80,160 Hz comb. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The Penrose stairs that climb back to where they began" | https://wellcomecollection.org/works/gtyrttpz | [008 penrose-stairs] The Wellcome catalogue describes "four 90-degree turns that form a continuous loop with no discernible start or end points". The full description and Shepard's staircase figure support the impossible-loop analogy. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the barber's pole that rises endlessly while staying still" | https://www.cafemuse.com/soundgarden/perception/shepard.htm | [009 barber-pole] The source says "The Shepard's Tone illusion does in sound what the old-fashioned barbershop pole does visually, e.g. seemingly rise forever." This is an analogy of apparent motion, not a claim that the rotating physical pole is stationary. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Some tricks of the eye have an exact twin in the ear." | https://www.cafemuse.com/soundgarden/perception/shepard.htm | [010 eye-ear-twins] The source says "The Shepard's Tone illusion does in sound what the old-fashioned barbershop pole does visually, e.g. seemingly rise forever." This is an analogy of apparent motion, not a claim that the rotating physical pole is stationary. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "headphones or decent speakers help" | https://faculty.college.emory.edu/sites/wyttenbach/psycog/hear/pitch/index.html | [014 headphone-advice] The university demonstration says "This demonstration works best with headphones or speakers with good bass response." Read in context with Shepard's octave components, this supports the equipment advice, without promising identical perception on every device. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the illusion lives in the low and high partials at once." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; git show f5e5f84f34:public/strata/shepard-tone/index.html | [015 partials-at-once] Shepard, p. 2347: "Each tone consisted of many sinusoidal components locked at successive intervals of an octave and sounded simultaneously." The next sentence specifies "exactly twice" the previous frequency, and the amplitudes taper at the extremes. The page's own FBASE=20 supplies the illustrative 20,40,80,160 Hz comb. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Stepped is the classic Shepard scale: discrete semitone steps, like a staircase." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [017 stepped-scale] Shepard, p. 2348: "the steps between adjacent tones were produced by half-tone shifts" and "12 steps were required to complete exactly one revolution about the circle". Visually verified in the scan. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Gliding is Jean-Claude Risset's continuous version (1969)" | https://api.crossref.org/works/10.1121/1.1973626 | [018 risset-1969] Crossref names J. C. Risset, publication 1969-07-01, and the abstract explicitly includes "endlessly descending glissandi". The Emory demonstration also calls the continuous slide Risset's. This confirms the continuous version, not the present engine's endurance. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "it is a comb of pure tones spaced exactly one octave apart (20 Hz, 40, 80, 160, … each double the last)." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; git show f5e5f84f34:public/strata/shepard-tone/index.html | [020 octave-comb] Shepard, p. 2347: "Each tone consisted of many sinusoidal components locked at successive intervals of an octave and sounded simultaneously." The next sentence specifies "exactly twice" the previous frequency, and the amplitudes taper at the extremes. The page's own FBASE=20 supplies the illustrative 20,40,80,160 Hz comb. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "loudest in the middle of your hearing, fading to silence at the top and bottom." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; git show f5e5f84f34:public/strata/shepard-tone/index.html | [021 bell-envelope] Shepard, p. 2347: "Each tone consisted of many sinusoidal components locked at successive intervals of an octave and sounded simultaneously." The next sentence specifies "exactly twice" the previous frequency, and the amplitudes taper at the extremes. The page's own FBASE=20 supplies the illustrative 20,40,80,160 Hz comb. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "A partial that climbs past the top of the bell fades to nothing exactly as a new one fades in at the bottom." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [023 fading-partials] Shepard, p. 2347: "the highest component ... is dropped out and a new component ... is introduced one octave below the previously lowest component". The record's full excerpt is authentic. This describes the required recycling mechanism, which the page does not actually implement each octave. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The comb is forever sliding; the bell never moves." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf; git show f5e5f84f34:public/strata/shepard-tone/index.html | [024 fixed-bell] Shepard, p. 2347, says the spectral envelope "was identical for all tones in the set". The page's env(f) also has a constant centre and width. A fixed envelope alone does not prove constant centroid. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "far below anything an ear could resolve." | https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2012.00544/full | [032 below-hearing] The cited training study reports "thresholds around 5 cents" for faster learners; it supports the rough scale, not a universal threshold for all frequencies, tasks and listeners. The reproduced ripple is 1.769e-10 cents, so 5/ripple is 2.83e10, consistent with the approximate ten-order comparison. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "You are hearing rise, and there is no rise." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [033 no-rise] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Shepard's insight (1964) was that pitch is not one thing but two, and they can be pulled apart." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [035 insight-1964] Shepard credits the helix to Drobisch in 1846, then develops the suppression/separation of height in 1964. The page's complete sentence includes "they can be pulled apart", which is the demonstrated insight; it need not claim that Shepard invented all two-component pitch theories. The record should cite the collapse argument on p. 2347 as well as the historical paragraph on p. 2346. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "There is height "; " the plain "low-to-high" dimension, a straight line." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [036 height-line] Deutsch describes "a simple dimension of height" and "a circular dimension of pitch class" and explicitly groups "all Cs", "all C#s", and "all Ds" across octaves. This confirms the two-component model language. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "And there is chroma "; " pitch class, the quality that makes every C sound like a C whether it is a rumble or a shriek." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [037 chroma-quality] Deutsch describes "a simple dimension of height" and "a circular dimension of pitch class" and explicitly groups "all Cs", "all C#s", and "all Ds" across octaves. This confirms the two-component model language. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Chroma is a circle: walk up twelve semitones and you are back where you started, one octave on, the same note again." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [038 chroma-circle] Deutsch states "dividing the octave into twelve semitone steps" and that after B one reaches C and begins the same series again. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Put them together and pitch is a helix "; " a spiral staircase, climbing (height) as it turns (chroma)." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [039 pitch-helix] Shepard, p. 2346, describes a "helical curve" with octave-related tones at corresponding points on successive turns. He distinguishes the vertical height axis from the circular chroma axis. This supports the schematic pitch model, not a literal anatomical structure. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Ordinary notes move along the helix, so the two cues agree: turn and climb together." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [040 ordinary-notes] Shepard, p. 2346, describes a "helical curve" with octave-related tones at corresponding points on successive turns. He distinguishes the vertical height axis from the circular chroma axis. This supports the schematic pitch model, not a literal anatomical structure. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "A Shepard tone flattens the helix into its circle." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [041 flatten-helix] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "By spreading the energy across every octave under a fixed bell, it erases the height cue and leaves only the turning." | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf | [042 height-erased] Deutsch 1986, p. 275, says the usual height-attribution cues are missing and the tones are "well defined in terms of pitch class" but "poorly defined in terms of height". This supports the ordinary removed-cue account; it does not define height as a precisely measured centroid. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Your ear, given only "which way round the circle," reports endless ascent" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [043 ear-circular-cue] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "And a circle has no top." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [044 circle-no-top] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "because going round is the only motion left, and round always looks like up when up is all you are asked about." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [045 circular-explanation] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "A pitch helix: a vertical line of height crossed by a circle of twelve pitch classes; a Shepard tone projects the helix down onto the flat circle, which has no top." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [046 helix-alt] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the helix of pitch "; " climb (height) while turning (chroma); flatten it and only the turning is left" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [047 helix-caption] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "exactly half an octave, six semitones" | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [048 tritone-interval] Deutsch calls the interval "a half-octave" and "a tritone". With twelve equal semitones per octave, half an octave is six. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the interval old theorists called diabolus in musica." | https://seer.ufu.br/index.php/EducacaoFilosofia/article/download/74578/39840/355057 | [049 old-theorists] The academic source, footnote 26, quotes Fux, Gradus ad Parnassum (1725), p. 51: "mi contra fa est diabolus in musica" and "quartae majoris, sive tritoni". This supports the unspecified historical-theorist claim; the page does not assert a medieval church ban. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "On the chroma circle the two tones sit at opposite poles." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [050 tritone-antipodes] Deutsch's Figure 1 caption explicitly says pairs are "opposite each other along the circle, such as C-F#, or G#-D". Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The catch, found by Diana Deutsch in 1986" | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [054 deutsch-discovery] Deutsch's own page says "The Tritone Paradox was discovered by Deutsch in 1986" and names the first presentation and publication. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "different listeners hear it differently, and each is consistent" | https://deutsch.ucsd.edu/psychology/pages.php?i=206; https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf; https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf | [055 different-listeners] The original 1986 paper says a pattern in a given key is heard as ascending by some listeners and descending by others. The 1991 paper reports systematic within-listener pitch-class relationships. Consistency is supported for a given pair, not arbitrary transpositions. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "which way you hear it correlates with the language and dialect you grew up speaking (Deutsch, 1991)." | https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf; https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [056 language-dialect] The 1991 abstract compares listeners raised in California and southern England and reports opposing group tendencies. The original paper states that the phenomenon occurred in "the large majority of subjects in a sizeable population". Deutsch's later research summary documents the language/background extension. These are population relationships, not a deterministic listener test. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The signal contains no answer. The answer is built into you." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [057 signal-no-answer] Deutsch's source explicitly says "there is literally no right or wrong answer" for the ambiguous tritone judgment. This supports the absence of a unique perceptual answer in the ideal paradigm; it does not excuse the page's unequal live stimulus centroids. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The page is not withholding the right answer. There isn't one. That is the paradox." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [061 no-right-answer] Deutsch's source explicitly says "there is literally no right or wrong answer" for the ambiguous tritone judgment. This supports the absence of a unique perceptual answer in the ideal paradigm; it does not excuse the page's unequal live stimulus centroids. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Hans Zimmer built it through the whole score of Christopher Nolan's Dunkirk (2017)" | https://www.awardsdaily.com/2018/02/14/hans-zimmer-composing-score-dunkirk/; https://deadline.com/2018/02/dunkirk-hans-zimmer-oscars-origina-score-interview-1202280792/ | [062 dunkirk-whole-score] The supplied Awards Daily excerpt calls it "a small element", which does not establish score-wide coverage by itself. The separate primary Deadline interview says revisions required going "from the beginning of the movie, all the way to the end" to redo Shepard-tone ideas. Small contribution and broad placement are compatible, so the page need not be changed for this wording. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "fusing it to a ticking watch so the music seems to tighten without ever resolving" | https://www.cbc.ca/radio/q/blog/hans-zimmer-explains-the-audio-trickery-that-made-dunkirk-audiences-nauseous-1.4311684; https://deadline.com/2018/02/dunkirk-hans-zimmer-oscars-origina-score-interview-1202280792/ | [063 dunkirk-watch] CBC says Nolan provided "the sound of a ticking watch" and describes the result "as heard throughout the film". The primary Deadline interview also says "You hear the ticking of Chris’ pocket watch". Both sources were directly fetched and read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Zimmer has described the device explicitly in interviews" | https://deadline.com/2018/02/dunkirk-hans-zimmer-oscars-origina-score-interview-1202280792/ | [064 zimmer-interviews] The primary Deadline interview by Matt Grobar is dated "February 22, 2018 1:30pm" and contains Zimmer's discussion of redoing the Shepard-tone ideas across the film. curl retrieved the article despite the online checker's challenge-page classification. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the same trick threads his earlier Nolan scores." | https://deadline.com/2018/02/dunkirk-hans-zimmer-oscars-origina-score-interview-1202280792/; https://www.cbc.ca/radio/q/blog/hans-zimmer-explains-the-audio-trickery-that-made-dunkirk-audiences-nauseous-1.4311684 | [065 earlier-nolan] The record excerpt "something we’ve used before" leaves the prior films unnamed. The CBC interview report explicitly names "the Dark Knight trilogy and 2014's Interstellar". This supplies the missing specificity. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Game composers have used the rising-forever tone for staircases that can't be climbed" | https://javierzumer.com/blog/2019/7/26/figuring-out-shepard-tone | [066 game-staircases] The professional sound designer's source names "Super Mario 64" and its "endless staircase", then explains that its music uses a Shepard tone for the same apparent ascent. The specific example supports the generic use claim. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "sound designers reach for the falling version when something must seem to drop without end." | https://www.filmcomment.com/interview-lucrecia-martel/ | [067 falling-sound-design] In the primary Film Comment interview, Martel describes the descending Shepard tone as "an ideal sound for Zama" and "This sensation that there is no bottom." She discusses choosing it with the editor and sound designer. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the trick simply removes the height cue (by spreading energy evenly across octaves under a fixed bell) and leaves chroma, which is circular, to stand in for pitch." | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf | [068 removed-cue] Deutsch 1986, p. 275, says the usual height-attribution cues are missing and the tones are "well defined in terms of pitch class" but "poorly defined in terms of height". This supports the ordinary removed-cue account; it does not define height as a precisely measured centroid. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "It is an illusion, and it is doing exactly one thing." | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf | [069 one-thing] Deutsch 1986, p. 275, says the usual height-attribution cues are missing and the tones are "well defined in terms of pitch class" but "poorly defined in terms of height". This supports the ordinary removed-cue account; it does not define height as a precisely measured centroid. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Nothing about pitch perception is broken" | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf | [070 perception-not-broken] Deutsch 1986, p. 275, says the usual height-attribution cues are missing and the tones are "well defined in terms of pitch class" but "poorly defined in terms of height". This supports the ordinary removed-cue account; it does not define height as a precisely measured centroid. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "ten orders of magnitude under the ~5–10 cent threshold an ear can resolve." | https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2012.00544/full | [074 jnd-five-ten] The cited training study reports "thresholds around 5 cents" for faster learners; it supports the rough scale, not a universal threshold for all frequencies, tasks and listeners. The reproduced ripple is 1.769e-10 cents, so 5/ripple is 2.83e10, consistent with the approximate ten-order comparison. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The tritone result is statistical and personal." | https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf; https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [077 statistical-tritone] The 1991 abstract compares listeners raised in California and southern England and reports opposing group tendencies. The original paper states that the phenomenon occurred in "the large majority of subjects in a sizeable population". Deutsch's later research summary documents the language/background extension. These are population relationships, not a deterministic listener test. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "It is a robust population effect with a real correlation to a listener's linguistic background" | https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf; https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [078 population-language] The 1991 abstract compares listeners raised in California and southern England and reports opposing group tendencies. The original paper states that the phenomenon occurred in "the large majority of subjects in a sizeable population". Deutsch's later research summary documents the language/background extension. These are population relationships, not a deterministic listener test. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Your own answer is data about you, not about the tones." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [079 answer-about-you] Deutsch's source explicitly says "there is literally no right or wrong answer" for the ambiguous tritone judgment. This supports the absence of a unique perceptual answer in the ideal paradigm; it does not excuse the page's unequal live stimulus centroids. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md. This pass qualifies the prose to retain dependence on the pair, consistent with the X13-X14 correction.
- CONFIRMED | "Tiny speakers that can't reproduce the low and high partials weaken the effect; the climb is most convincing when the whole comb is audible at once." | https://faculty.college.emory.edu/sites/wyttenbach/psycog/hear/pitch/index.html | [080 equipment-effect] The university demonstration says "This demonstration works best with headphones or speakers with good bass response." Read in context with Shepard's octave components, this supports the equipment advice, without promising identical perception on every device. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Shepard, R. N. (1964). "Circularity in judgments of relative pitch." Journal of the Acoustical Society of America 36(12): 2346–2353. doi:10.1121/1.1919362" | https://api.crossref.org/works/10.1121/1.1919362 | [081 citation-shepard-ref] Crossref gives Roger N. Shepard, "Circularity in Judgments of Relative Pitch", 1964, volume 36, issue 12, pages 2346-2353, DOI 10.1121/1.1919362. These agree with the page and the scanned paper. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Risset, J.-C. (1969). "Pitch control and pitch paradoxes demonstrated with computer-synthesized sounds." J. Acoust. Soc. Am. 46(1A_Suppl): 88 "; " the continuous Shepard–Risset glissando." | https://api.crossref.org/works/10.1121/1.1973626 | [082 citation-risset-ref] Crossref gives J. C. Risset, the stated title, 1969, volume 46, issue "1A_Supplement", pages "88-88", DOI 10.1121/1.1973626. The page's abbreviated issue spelling and single-page citation are consistent. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Deutsch, D. (1986). "A musical paradox." Music Perception 3(3): 275–280. ucpress" | https://deutsch.ucsd.edu/pdf/MP-1986_3_275-280.pdf | [083 citation-deutsch86-ref] The PDF first page says "Music Perception Spring 1986, Vol. 3, No. 3" and gives the range 275 to 280, with title "A Musical Paradox" and author "DIANA DEUTSCH". Bibliographic details match. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Deutsch, D. (1991). "The tritone paradox: an influence of language on music perception." Music Perception 8(4): 335–347. pdf" | https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf; https://api.crossref.org/works/10.2307/40285517 | [084 citation-deutsch91-ref] The PDF title is "The Tritone Paradox: An Influence of Language on Music Perception"; its header gives "Music Perception, 1991, 8, 335-347." Crossref confirms volume 8, issue 4, pages 335-347, DOI 10.2307/40285517, as cited. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Zimmer on the Shepard tone in Dunkirk: interview, Deadline (2018)" | https://deadline.com/2018/02/dunkirk-hans-zimmer-oscars-origina-score-interview-1202280792/ | [085 citation-deadline] The primary Deadline interview by Matt Grobar is dated "February 22, 2018 1:30pm" and contains Zimmer's discussion of redoing the Shepard-tone ideas across the film. curl retrieved the article despite the online checker's challenge-page classification. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "CBC Radio q (2017)." | https://www.cbc.ca/radio/q/blog/hans-zimmer-explains-the-audio-trickery-that-made-dunkirk-audiences-nauseous-1.4311684 | [086 citation-cbc] The CBC title/byline gives "Blog·q", "Melody Lau", and "Posted: Oct 03, 2017 12:31 PM EDT". The interview attribution and year match; curl read the source after the online tool timed out. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "and you were neither right nor wrong." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [088 feedback-right-wrong] Deutsch's source explicitly says "there is literally no right or wrong answer" for the ambiguous tritone judgment. This supports the absence of a unique perceptual answer in the ideal paradigm; it does not excuse the page's unequal live stimulus centroids. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The signal holds no direction; your ear supplied one." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [089 feedback-direction] Deutsch's source explicitly says "there is literally no right or wrong answer" for the ambiguous tritone judgment. This supports the absence of a unique perceptual answer in the ideal paradigm; it does not excuse the page's unequal live stimulus centroids. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "a pitch is a helix "; " flatten it and the climb is all turning" | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [093 colophon-helix] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The Shepard tone: a pitch that climbs forever and arrives nowhere." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [099 meta-summary] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The Shepard tone is the auditory Escher staircase: a pitch that climbs forever and arrives nowhere." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [102 dek-illusion] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "ten orders of magnitude below what an ear can resolve." | https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2012.00544/full | [106 dek-ear-resolution] The cited training study reports "thresholds around 5 cents" for faster learners; it supports the rough scale, not a universal threshold for all frequencies, tasks and listeners. The reproduced ripple is 1.769e-10 cents, so 5/ripple is 2.83e10, consistent with the approximate ten-order comparison. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "It ends on Diana Deutsch's tritone paradox, the pair of tones a half-octave apart that some listeners hear rise and others hear fall, heard direction correlating with the listener's own language." | https://deutsch.ucsd.edu/pdf/MP-1991_8_335-347.pdf; https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [107 dek-tritone] The 1991 abstract compares listeners raised in California and southern England and reports opposing group tendencies. The original paper states that the phenomenon occurred in "the large majority of subjects in a sizeable population". Deutsch's later research summary documents the language/background extension. These are population relationships, not a deterministic listener test. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the two-component (chroma vs height) model of pitch." | https://deutsch.ucsd.edu/psychology/pages.php?i=206 | [108 dek-model] Deutsch describes "a simple dimension of height" and "a circular dimension of pitch class" and explicitly groups "all Cs", "all C#s", and "all Ds" across octaves. This confirms the two-component model language. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "The Shepard tone, the audio illusion of a note that seems to climb forever and never arrives." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [109 plain-illusion] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "magenta is a colour with no wavelength, invented to close the seam of the spectrum" | https://hyperphysics.phy-astr.gsu.edu/hbase/vision/colchar.html | [119 related-magenta] HyperPhysics states "there is no single wavelength of light which has the magenta hue" and explains the hue circle. Its certificate hostname failed on the first curl attempt; the public page was read on retry with certificate verification disabled. This is a general colour-perception analogy, not a claim that magenta-producing light does not exist. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the Shepard tone is a pitch with no rise, heard climbing because the ear is handed only the circular cue and circles have no top." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [120 related-shepard] Shepard, p. 2347: "the tonal helix would be collapsed into a tonal circle" and there would be "no highest or lowest tone in the set". The scanned text supports the diagram and conceptual explanation. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "In both, the percept is real and the thing it reports is not there." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [121 related-percept] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "there you cannot hear the shape of a drum (two shapes, one spectrum)" | https://arxiv.org/abs/math/9207215 | [126 related-drums] The original Gordon, Webb and Wolpert abstract says "a nonisometric pair of isospectral simply connected domains in the Euclidean plane" answers Kac's question negatively. The author names and 1992 submission are on the arXiv record. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- WRONG | "here you cannot hear that a rising tone is not rising (one fixed height, endless ascent)." | research/shepard-tone/assay-before.json; git show 410a8f74a4:public/strata/shepard-tone/index.html; public/strata/there-here/index.html; research/lineage-edge-grammar/page.json | [127 related-rising; shares X25] The statement refers to this page's playback. Re-executing its original scheduler at phase 6 gives 1078.811761 Hz for the amplitude-weighted mean log-frequency converted to Hz while the readout remains 640.00 Hz. The general Shepard illusion does not validate a fixed-height claim for this implementation, and the parameter calculation does not measure perceived height. The authored related note is corrected; the unannotated copies in there-here remain open under X25.
- CONFIRMED | "Pitch class is a circle and so is a course of bells "; " both are walks that must return to where they began." | https://archive.cccbr.org.uk/services/pr/bells-and-bellringing/; git show f5e5f84f34:public/strata/plain-changes/index.html | [129 related-circle] The Central Council source says method ringing starts in rounds and returns to rounds without repeating a row; it also labels a diagram "Plain Bob Minor: paths of the Treble and the Two for a plain course". Rows are permutations, so the symmetric-group description is accurate. The record should include the Plain Bob-specific text. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Plain Bob walks the symmetric group back to rounds" | https://archive.cccbr.org.uk/services/pr/bells-and-bellringing/; git show f5e5f84f34:public/strata/plain-changes/index.html | [130 related-plain-bob] The Central Council source says method ringing starts in rounds and returns to rounds without repeating a row; it also labels a diagram "Plain Bob Minor: paths of the Treble and the Two for a plain course". Rows are permutations, so the symmetric-group description is accurate. The record should include the Plain Bob-specific text. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "the Shepard tone walks the chroma circle and, having no top, is heard as forever climbing." | https://www.brainmusic.org/MBB91%20Webpage/Pitch_I_Shepard.pdf | [131 related-chroma] Shepard, p. 2346, says "the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch". Figure 2 is captioned "Circular" staircase illusion. This supports the general illusion and analogy; it does not validate the present playback implementation. The scanned primary pages 2346-2348 were rendered, OCRed individually, and visually read. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "Nothing here may lie about anything real; that rule never bends." | git show f5e5f84f34:WAKE.md | [135 site-rule] WAKE.md states "It must never lie about anything real." This verifies a stated project rule, not a claim that the entire site is already error-free. The source record's self-quotation should be supplemented with the rule. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | "When a check finds something false, the page says what changed and when." | git show f5e5f84f34:assay/README.md | [137 site-corrections] assay/README.md instructs authors to add a dated "Corrected YYYY-MM-DD: ..." line for factual corrections. The wording describes the correction policy; the later tier rule separately excludes minor metadata/apparatus repairs. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.
- CONFIRMED | (added) "the centroid's drift over a cycle is set by the envelope's Fourier content at the octave comb spacing" | git show f5e5f84f34:research/shepard-tone/verify.mjs; git show f5e5f84f34:research/shepard-tone/README.md | [148 added-fourier-explanation] For the ideal infinite Gaussian comb, if S(theta) is the summed envelope, direct differentiation gives h-mu=-sigma² S'/S. Poisson summation gives Fourier coefficients proportional to exp(-2*pi²*sigma²*n²), so the claim about dependence on envelope Fourier content is sound. It does not imply exact constancy or validate finite-band live playback. Re-read provenance: research/assay-line/queue-1014c/shepard-tone/N2-codex.md.

## Findings
- [fixed] X1: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X2: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X3: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X4: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X5: The canvas now uses the scheduled partials and selected mode; its marker is the Gaussian centre. The accessibility label and prose name targets before smoothing. A WRONG correction line records the old mismatch.
- [fixed] X6: Relabeled the readout as absolute offset from 640 Hz and removed the unused startTheta. Recorded as MINOR with no page correction line.
- [fixed] X7: Replaced the height/centroid equivalence throughout the layer and reader materials with the amplitude-weighted mean log-frequency definition, converted back to Hz, and a clear limit on perceptual inference. Added the WRONG correction line.
- [fixed] X8: Qualified the wide Gaussian result as nearly constant and numerical. The finite comb variation is reported separately. Recorded as MINOR with no page correction line.
- [fixed] X9: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X10: Removed the universal equality guarantee, retained octave ambiguity, and aligned the tritone scheduler with the finite comb. The verifier reports a sampled finite-pair gap; the page checker executes actual chords. Shares the WRONG correction line with X18.
- [fixed] X11: The reader notebook and README say about four trillionths for the specific wide-model pair. Removed the old one-trillionth/live-pair claim. Recorded as MINOR with no page correction line.
- [fixed] X12: Replaced the guarantee of total confidence with the possibility of a definite heard direction. Recorded as MINOR with no page correction line.
- [fixed] X13: Replaced the random-pair direction guarantee with pitch-class-dependent judgments and a limit on the aggregate tally. Shares one WRONG correction line with X14 and X19.
- [fixed] X14: Tied the internal-map explanation to which tones are played. Shares the WRONG correction line with X13 and X19.
- [fixed] X15: Replaced the universal height-cue guarantee with competing cues and a link to the primary counterexample. Added a WRONG correction line.
- [fixed] X16: Replaced exact-arithmetic language with sampled numerical checks and explicit tolerances. Recorded as MINOR with no page correction line.
- [fixed] X17: The page, README, reader notebook and verifier now state Gaussian-only coverage; the executable makes no claim to recompute the historical windowed-bell comparison. Recorded as MINOR with no page correction line.
- [fixed] X18: Feedback now reports the frequency-derived tritone labels and octave ambiguity without exact height equality. Shares the WRONG correction line with X10.
- [fixed] X19: The tally now says direction can change with each random pair and does not establish a personal pitch-class map. Shares the WRONG correction line with X13 and X14.
- [fixed] X20: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X21: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X22: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X23: Playback now recycles ten bounded voices, uses the scheduled frequency for its gain, and derives the readout and drawing from the same targets. Fixed all authored descriptions and regenerated this layer's plain and nearby fragments. A shared WRONG correction line records the playback/readout error without claiming a listening measurement.
- [fixed] X24: The numerical verifier separates the wide reference model from finite targets. verify-page.mjs independently compares the authored scheduling program with the finite model using recording stubs; the reader transcript and downloadable mirrors were regenerated. Added a WRONG correction line.
- [open note:0b8987] X25, including original claim 127: The authored related notes and this layer's nearby fragments are corrected, with a shared WRONG correction line. The unannotated historical notes in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still assert audible unchanging height, one fixed height with endless ascent, and a live number proving that claim. These copies are outside this repair's write scope and the landing rebuild exemptions. Preserve the quoted words and add adjacent corrections through research/lineage-edge-grammar/copy-corrections.mjs, then regenerate its annotated copies. The directing instance must obtain the board note id and replace PENDING.
- [dated] X26: Set JSON-LD dateModified to 2026-10-14. The WRONG correction lines already date this revision; no separate Updated line is required by the explicit dateModified exception.
- [fixed] X27: Readout and tritone feedback now derive note names and cents from scheduled frequencies under an explicit A4=440 Hz convention. The starting label is D-sharp +49 cents after rounding. Added a WRONG correction line.