How Do You Know You Are Right?

A drum detective story, with all the wrong turns left in.

1The song, and what we were arguing about

Sheet music is a set of instructions. We were arguing about what one instruction means.

Sheet music tells a musician what to play. For drums, each line and space on the page means a different drum or cymbal. A mark high up might mean the hi-hat. A mark low down might mean the kick drum you hit with your foot.

The drummer on this song is Vinnie Colaiuta. Our sheet music for his part has 2,091 drum hits written across 105 bars of music.

Here is the argument. 1,316 of those hits have little brackets around them, like this: (note). Brackets mean play this one quietly. Drummers call a quiet hit a ghost note, because you barely hear it.

All 1,316 of those bracketed marks sit on the ride cymbal line. Somebody said that was a mistake, because ghost notes are a drum thing and not a cymbal thing. So a plan was made to delete all 1,316 of them.

2Mistake one: we looked it up in the wrong book

Imagine trying to fix your bike using a cookbook.

To settle Question A, we needed a rule book. We used one called the Essential Dictionary of Music Notation by Gerou and Lusk. We quoted it three separate times.

Then we did something obvious that nobody had done. We searched the whole book for the words we were arguing about. A computer read all 82 scanned pages out loud, so to speak, and counted.

The right book said the opposite thing

There is a proper rule book for drum sheet music. It was written by Norman Weinberg in 1994 and it is the standard drummers use. Here is the sentence that settles it:

It is recommended that parenthetical note heads be used to indicate ghost strokes. Ghost strokes written as parenthetical notes allow the use of this performance technique on any type of instrument (drums, cymbals, cowbells, etc.). Norman Weinberg, Guidelines for Drumset Notation, Percussive Notes, June 1994, printed page 20. Verified in ~/.claude/skills/notation-evidence-gate/refs/Weinberg-PercussiveNotes-1994-Drumset-Notation.pdf, PDF page 6 of 13, the page headed "PERCUSSIVE NOTES · JUNE 1994 20" and carrying "Ex. 11. Parenthetical Notes for Ghost Strokes".

Read that carefully. Any type of instrument, and it lists cymbals by name. So a quiet mark on a cymbal line is spelled perfectly correctly. The 1,316 marks are fine.

3The big idea: compare everything to luck

This one idea catches more bad answers than anything else on this page.

Say you flip a coin and guess heads or tails. Guessing at random, you will be right about 50% of the time. That 50% is your luck score.

Now say your friend guesses and gets 52% right. Nobody would call that friend psychic, because 52% is basically 50%. You would have to see something like 90% before it means anything.

Every measurement needs its luck score written right next to it. A number on its own tells you nothing.

Here is where that bit us. There was a second repair planned, adding about 172 foot hi-hat hits to the sheet music. The evidence for it looked like this:

35% found
26% by pure luck
--------------------
1.35 times luck

A tiny number that fooled us

One test spat out a number written p = 2.75e-06. That is science-speak for "there is less than a 3 in a million chance this happened randomly", and it looks like a slam dunk.

That number appeared right beside the 1.35 times luck score above, and both came from the same data. The tiny number was measuring the wrong thing. The math behind it assumes every drum hit is separate from every other one, and drum hits in a song are nothing like separate. A drummer plays patterns.

A very impressive-looking number sitting beside a boring ratio is the exact shape of a finding that means very little.

4The best trick we learned: test yourself with a wrong answer

If your metal detector beeps at rocks, it is not finding gold.

We built a tool to line up the sheet music with the actual recording, so we could check whether the written notes matched the sounds. It reported that it matched things very well.

Then we tried something sneaky. We fed it a completely different song, another Zappa track called Joe's Garage, which this sheet music has nothing to do with. If the tool is any good it should fail badly.

Then it got worse, and that was useful

We built a better tool and ran the same trick. This time we scored it two ways. Coverage counts how many notes it matched up. Wobble measures how much those matches disagree with each other.

Look at the top row. The wrong song got a better coverage score than the right song. Coverage pointed us in the wrong direction while looking like it was working.

One result nobody was aiming for

5The bug that would have wrecked the file

One rubber stamp, 855 pages.

Sheet music files save space by sharing. If the same drum beat happens 855 times, the file stores it once and then points at it 855 times. Like one rubber stamp used on 855 pages.

This means that if you change the stamp, all 855 pages change with it.

In our file, one single beat was pointed at 855 times, and one single note was pointed at 1,316 times. That one note is all the ghost ride notes at once.

we meant to add:        459 notes
what came out:       66,727 notes

The fix is to make your own copy of a stamp before you change it. Then the other 854 pages keep the original.

We then checked the rest of the file. All nine instrument tracks share stamps this way. We checked our other tools too and found one more with the same bug waiting to happen. In that one, changing a single guitar finger position would have quietly rewritten up to 30 other places.

6The eight rules

Each one exists because we broke it first.

These are now a program that reads what we write and stops us before we publish a claim that breaks one. A STOP rule halts the work, and a CAREFUL rule asks us to think harder.

Run against the two documents that started all this, the checker found 16 STOP problems and 10 CAREFUL problems across 26 sentences, and blocked the work.

7So what is the answer?

Three things settled, one thing honestly unknown.

hi-hat track     1 of 4 moments
cymbals track    4 of 4 moments   <- all four
snare track      2 of 4 moments
kick track       1 of 4 moments
toms track       0 of 4 moments

8The evidence, for grown-ups

The exact numbers, kept so anyone can check the work above.

What is written in the file

105 bars, 53x 4/4 + 52x 5/4, one tempo automation at 56 BPM, 472 quarter units

midi  name              count  ghosted
  36  Bass Drum 1         107        0
  40  Electric Snare      193        0
  44  Pedal Hi-Hat          6        0
  45  Low Tom               4        0
  46  Open Hi-Hat           1        0
  48  Hi-Mid Tom            2        0
  49  Crash Cymbal 1       53        1
  51  Ride Cymbal 1      1724     1316
  57  Crash Cymbal 2        1        0
TOTAL                    2091     1317

The listening test on the four moments

Target times 181.93, 183.03, 184.10 and 185.19 seconds. Signed distance to the nearest detected sound, same detector settings on every track.

A separate hi-hat track from different separation software scored 2 of 4 at -48.1 and -33.5 ms. Two separations of the same recording disagreeing that hard means the result is about the software and is not a finding about the recording.

Loudness at those four moments

Energy in a 60 ms window either side of each moment, divided by that track's own typical loudness.

track       181.93    183.03    184.10    185.19
hi-hat       0.15x     0.25x     0.34x     4.84x
cymbals      5.20x     3.03x     2.80x     3.30x
snare      210.66x     9.04x   192.81x    13.11x
kick         3.62x   974.11x     0.74x     0.26x
toms         1.04x     1.51x     0.76x     0.35x

This rules one thing out. Three of the four moments are quieter than the hi-hat track's own average, so no setting recovers them from that track. The idea that the sound is there and the detector simply missed it is dead.

Lining up the music with the sound

Wobble is residual MAD in seconds. Lower is better. The control is a recording the sheet music does not describe.

Row two overturned a standing rule. Using the snare alone as the anchor was supposed to be the reliable method. Matching 193 sparse written hits into 1,901 dense detected sounds lets the stretch wander anywhere, so it scored exactly at luck. A sparse written side is only safe against an isolated track, where the sound side is sparse too.

The printed chart, read for the first time

Five pages of a published Drumnet chart for this song were on the same computer and had never been opened. They are ~/Projects/_outputs/zappa-drum-sources/06-drumnet/Watermelon-In-Easter-Hay_p1.jpg through _p5.jpg. Page one confirms the tempo at 55.47 and drums entering at 1:20, matching the score file bar for bar. The scans are small, so the drum systems were cropped and enlarged 5 times to read them.

Not one X notehead appears in the space below the staff, which is where a foot hi-hat would go. Sampled across bars 5 to 10, 17 to 22, 39 to 46, 61 to 68 and 83 to 88, counted on those five chart images and cross-checked against the bar numbering in the score file s35881-Watermelon-In-Easter-Hay/ORIGINAL-Frank Zappa-Watermelon In Easter Hay-07-04-2026.gp, which holds 105 bars. The chart does use a circled X above the line at bars 61 and 83. So this transcriber knew the hi-hat symbols and chose not to write a foot part.

Where each open problem belongs

Six methods here were hand-rolled and each has a proper published chapter behind it.

Corrections found while checking this

• Three file paths described as verified present on this computer do not exist here, including the folder of separated tracks. Only the source recording is present.
• One folder reported as missing entirely does exist, nested several levels deeper than expected. It holds no relevant files, and the claim was still wrong as written.
• A first version of the listening test was written up as 4 out of 4. Run properly against an isolated track it is 2 out of 4.