Watermelon In Easter Hay: ride-ghost reproduction

0. The matched-control attack test, and it is the first positive result

Design. From each on-beat plain ride at t0 with a log-linear decay fitted over t0+30 ms to t0+250 ms, score the three notated offbeat slots at t0 + 271.1, 542.2 and 813.3 ms against off-lattice controls at t0 + 135.6, 406.7 and 677.8 ms, halfway between them, where the score notates nothing. One detector scores both and it never receives ghost status: sparse log-compressed subband novelty, k=8, 1,322 peaks at 2.42/s, 30 ms tolerance. Controls are matched to slots by nearest predicted decay level, median absolute log-level gap 0.0085, so decay depth is held fixed.

The asymmetry is the finding. Notated positions sit 16.8 points above their rotation null while decay-matched off-lattice points sit 10.0 points below theirs, a 26.8-point separation between two sets scored by one detector under one null model. For the controls, 99.8 percent of null draws matched as well or better.

Across 563 decay-matched pairs: notated 171 of 563 = 30.4%, control 31 of 563 = 5.5%, difference 24.9 points, paired permutation over the label with 5,000 draws one-sided p = 0.0002.

The ratio does not fall as the preceding strike decays, which is the opposite of what residual decay predicts. Five of eleven sections favour the notated position at Benjamini-Hochberg q < 0.05, strongest section 3 at 55.1% against 4.3% with 35 of 35 discordant pairs favouring the notated position.

1. The definition census

GPIF deduplicates <Note> definitions, so a ghost flag lives on a definition and one element can produce many notated occurrences. Reading the definition table directly:

The confound that does survive is metric position

Ride plain on the beat, ride ghosted on the three offbeat sixteenths. Two events out of 1,724 break the rule. Only 2 ghosted ride notes sit on a beat, so a metric-position control is impossible in this tab.

2. The sweep mechanism, established structurally

3. Ghost census, reconciled by track and scope

Three figures circulate. All three are correct at different scopes.

1,333 = 1,317 + 16. The sweep removed the drum-track flags and left the guitar flags untouched.

4. The 1,724 against 596 question, closed

The snare lane changes MIDI number and drops from 193 to 11. Closed hat goes from 0 to 125. Kick rises from 107 to 475. The bar grid more than doubles. Removing AntiAccent preserves note instances and cannot do any of that. Two independent transcriptions of two different renderings. Deletion, rebar and flag stripping are all excluded.

5. Detector specification, stated completely

The match rule is presence, and it is neither a local maximum nor a separately identified onset. Consecutive frames from one excursion can support a match, and one broad excursion can serve more than one window. The correct description of a positive is "matched the flux criterion".

6. The detector, reconciled

The 3.51× threshold gap was an operator difference. The band in the written spec was correct.

7. Alignment, locked and exposed

The scoring clock is piecewise-linear through the accepted snare anchors. The global line seeds anchor matching and supplies the pruning residual. No ride event is scored against the global line.

Alignment error against anchor gap, 5,469 held-out tests

"Anchor gap" means distance to the nearer bracketing anchor. Withholding every third anchor from a dense set never creates a large gap, so error at 10 to 20 s needs deliberate thinning.

Degradation is gradual. No band keeps its 90th percentile inside the 45 ms detector half-window, so alignment error contributes misses everywhere. The distance filter stays exploratory and a 10 s cutoff does not establish reliable performance across the region it keeps.

8. The coincidence result under the correct detector

9. Block-preserving nulls

Contiguous runs displaced together with within-block spacing preserved, alongside the per-note procedure. All under the reconciled detector at threshold 4.41.

The measured association is stable across the tested per-note and block-preserving randomisations. That is a narrow statement about the procedures tested, and it is not a claim of independence from every possible dependence structure.

10. Double counting ruled out

Under the reconciled detector, supra-threshold excursions run median 6 ms, 90th percentile 17 ms, max 81 ms, and none exceeds 181 ms, so none can span two windows spaced 271 ms apart.

Crossing operator against null, so the cause is shown

Two candidates could produce the 1.47×: the collision structure of the per-note null, or the operator whose long excursions let one run serve several notes. Crossing both settles it.

11. Spectral identity of disputed positions

Reference exemplars are plain ride positions that matched the flux criterion with the nearest anchor inside 3 s, giving 171. The disputed set is ghost positions at the same anchor quality, giving 770. Features measured on the mono MP3 from 30 ms before to 180 ms after each position.

Section-matched over 12 equal sections, 9 of which carry at least 5 of each: transient peak lower at ghost positions in 9 of 9 sections, attack-to-floor lower in 9 of 9, decay ratio higher in 7 of 9.

11b. Positive control, under the reconciled detector

An offset sweep from -200 to +200 ms. The snare control uses the snare stem with the same band-sum operator over 200 to 4000 Hz at its own 80th percentile.

The control recovers real temporal structure, so the method works. Both ride sets peak at 0 ms, which the first version of this page did not show because it used the wrong operator. The ghost set has the shallowest peak-to-floor contrast of the three, consistent with sitting inside a continuously active cymbal texture.

11c. The decay-prediction test

The sharpest question this data can be asked: does a disputed ghost slot carry energy beyond the predicted tail of the preceding verified plain ride strike?

For each strong plain on-beat exemplar at time T, a log-linear decay is fitted to the smoothed envelope over T+30 ms to T+250 ms. That window is clean, because the next notated ride sits at T+271 ms and nothing else is notated inside it. The fit is extrapolated to the notated ghost slot at T+271 ms and to an off-grid control at T+135 ms where the score notates nothing at all.

188 usable exemplars from 224 candidates. Median fitted decay time constant 304 ms.

Sign test on the paired difference: 106 of 188 positive, one-sided p = 0.047, two-sided p = 0.093. Both slots exceed the fitted tail, because real cymbal decay is not a single exponential. The notated slot exceeds it only marginally more than the off-grid control does.

11z. The notation-evidence gate overrules every rate on this page

/notation-evidence-gate and its verdict_gate.py were run before any done-claim. Both are the authority here, and they reject the rates on density grounds rather than on the cross-window finding.

The prescribed repair, run

FMP 6.1.2, a sparser onset representation: log compression Y = log(1 + 100|X|), positive first difference per subband across 2-4, 4-6, 6-9 and 9-12 kHz, summed, local average over 300 ms subtracted, peak-picked with a 50 ms refractory gap.

11k. Both tracks reconstructed

Numerator: five alignments built without the 97-anchor map

Chart tempo, global fit, kick-anchored and crash-anchored maps, across 240 configurations of source stem, band, operator, window and threshold percentile.

Denominator: eight nulls, detector and population frozen

The historical 49.0 percent is reproduced to 0.1 points by a displacement measured in time, with an unambiguous signature: sixteenth-phase preservation falls from 100 percent to 2.8 percent. Every phase-preserving procedure lands between 62.2 and 63.7 percent. Seed spread 0.38 points across three seeds, so it is stable rather than tuned.

The two do not share a window

11j. The ledger, and three corrections to my own earlier claims

The 1.45× enrichment is not treated as recovered. Numerator and denominator are tracked as separate forensic problems, because they may come from two separate implementation choices.

11g. The discrepancy is the NULL, and its cause is measured

Anchors: 123 reachable by local-window refinement, and DTW failed

DTW was tried first. Over a sparse impulse reference the cost is near zero wherever both signals are quiet, so the warp slides: unconstrained it disagreed with the validated map by a median of 7.7 s, and inside a ±4 s Sakoe-Chiba band still by 2.1 s. The map was right and the method was wrong.

Local-window onset refinement works. Keeping the validated map and resetting each notated snare inside a ±120 to 150 ms window reaches 123 anchors from 97. All 122 local slopes fall inside 0.918 to 1.103, median residual against the global line is -9 ms, and it agrees with the 97-anchor map at a median difference of 0.0 ms.

Better alignment moves observed and null together

Raising anchor density lifted the observed rate 0.7 points and the null 1.0 point. Alignment quality cannot produce the reported ratio, because it moves both terms.

A grid-breaking displacement reproduces the depressed null

The score alternates 4/4 bars of 4,286 ms and 5/4 bars of 5,357 ms, and the ride sits on a 268 ms sixteenth grid. A displacement preserving position within the bar keeps destinations on that grid. A displacement measured in time cannot, since no fixed interval is a whole number of bars in both meters.

11h. The observed-rate gap is the WINDOW, and the deviations do not compound

Detector frozen at 2000-12000 Hz, sum before differencing, threshold 4.407, 123-anchor map. Only the rule turning a mapped position into a scored sample varies, applied identically to observed and null.

Crossing the two deviations

11i. The 1.19× against 1.45× gap, reconciled

The reported pair is 71.3 percent observed and 49.0 percent null. The observed figure needs a 65 ms half-window, so the question is what null reaches 49.0 percent at that same window. At 65 ms the observed ghost rate is 69.9 percent, so 1.45× requires a null of 48.2 percent.

11d. The eye overrules the detector

Read from Watermelon-In-Easter-Hay_p1.jpg as a native-resolution crop of a 595×842 scan, upscaled only for viewing. BartoRomeo, drumnet.ru, "Watermelon In a Easter Hay", From Joe's Garage Act III Record, for Solo Guitar & Drums, section marker (1:20) A.

11e. Published notation authority

Norman Weinberg, "Guidelines for Drumset Notation", Percussive Notes, June 1994, page 20, section Ghost Strokes, plate Ex. 11 "Parenthetical Notes for Ghost Strokes". Read at 400 DPI from the image-only scan, which carries no text layer.

11f. Ghost against staccato, one predicate on both sides

The Montana repair converted ghosts into staccato dots, a substitution a count check cannot see. Tested here with the same predicate applied to both flags in all three files.

No dot substitution happened on s35881. The sweep deleted flags cleanly, so the restore is a flag restoration plus the definition split, with no dots to remove.

12. Withdrawn, and historical

Historical, and not reproducible

Kept separate because no script on disk regenerates them: 137 anchors split 91 fit and 46 withheld, where the reconstruction reaches 97 and saturates near 116 even at a 250 ms acceptance window; band medians 18.1, 16.9 and 70.4 ms, where 1,337 thinning tests give 29.8 ms for the 10 to 20 s band; max withheld error 107.7 ms across 46 anchors, where the reconstruction gives 32 withheld points with a 55.6 ms max; and 1,626 scored with 98 outside the span, where all 1,724 map inside 59.33 to 506.08 stem seconds.

13. Inputs and scripts

Earlier drafts printed 48 of the 64 hex characters. These are the complete digests. Scripts live at ~/Projects/_outputs/zappa-watermelon-ride-analysis/tools/: gpif_events.py, definition_census.py, onsets.py, align.py, anchor_sensitivity.py, threshold_sweep.py, scramble_variants.py, excursion_taxonomy.py, corrected_null.py, final_measures.py.

What this supports