Dancing Drops and De Broglie’s Pilot Wave

Just watched a Youtube video from Veritasium showing silicone oil droplets dancing on a vibrating surface of the same liquid.

Analogies are made between droplets guided by standing waves and quantum mechanics.  Much of this is universal to any wave phenomenon.  QM involves waves, depends crucially on the idea of waves, so it’s no surprise there are matches to be found between quantum phenomena and acoustics, mechanics, etc.   The match-up seems especially strong when de Broglie’s idea of Pilot Waves, or his earlier more comprehensive Theory of the Double Solution, is considered.

Pilot wave, or de Broglie’s original Theory of the Double Solution from which PW descended, is a no-go for me. I was fascinated with this idea long ago, in grad school. But it didn’t survive.

For one, it does a poor job dealing with multiple identical particles. Two electrons need two pilot waves. Just what is it that’s doing the waving? In the demo with the dancing drops, it’s the surface of the water or oil, a single “universal” shared entity filling space, with one wavefunction – height above the average surface. Attempts to make Pilot Wave quantum mechanics work like that fail. It’s inherent in the math of QM that each particle needs its own wave.

Then there’s metaphysical garbage to be collected. Suppose an electron goes flying along then whack! Right into a piece of metal. There’s be a circular pilot wave escorting it along until the electron stops – does the pilot wave suddenly stop? All at once? Does the part of it near the electron suddenly stop along with the electron while the outer parts continue? Is there an outward ring of sudden-slowing of the PW, expanding at the speed of light? Are there 10^hundreds of ’empty’ pilot waves fluttering through every point of space from all the electrons which suddenly changed motion or were cancelled out of existence by positrons?

Real QM doesn’t have an answer to such questions because we just throw away the wavefunction, and write a new one for the electron in its new home. This is unsatisfying to Human minds, but it’s what works. Reality is weird.

Finally, pilot wave theory is deterministics, and “realistic” in the sense of EPR paradoxes and Bell Theorem. PW will obey Bell’s inequalities. Reality, as measured by experiments since the 1990s, does not. Entanglement is real, and is described by Hilbert space mathematics of the sort that lets you fly past Bell’s limitations. PW just can’t do that.

So goodbye Pilot Wave, and I won’t waste time on meaningless fluff like Many Worlds. Interpretations based on subtleties of statistics don’t generalize or explain Delayed Choice experiments, and other interpretations… I could write a book. Copenhagen is empty, philosophically unsatisfying, but truly nothing better has come along. Copenhagen works for the practical everyday physicist or electronics engineer.

Hmm, I wasn’t expecting to write a short philosophy of physics essay on YT today, but there you go.

Improving Acoustics in a Church’s Multipurpose Room

This is a slightly polished-up version of a quick report I wrote for a local church, recommending ways to improve the noisy acoustics of a room used for post-service conversation and snacks.  It’s not meant to be slick or a masterpiece of writing. This is just a text dump, formatting ignored.


Improvement to Acoustics in a Multipurpose Room at a Local Church United
Daren Scot Wilson, B.S. Physics


PROBLEM SUMMARY after the 2nd service, when the crowd filtered out of the sanctuary and headed for coffee and conversation, the room with the round tables, known as Fellowship Hall, became quite noisy. At a table of three, one fine fellow said that it was hard to hear the other person and myself only 3 feet away. I have heard similar comments during past Sundays. There is plenty of reverb. A cacophony of conversation arises during peak snack time. I imagine the acoustics of that room could be a problem anytime the room is used for any purpose except pantomime classes (were the church to do such a thing.)

Main observations on the problem:
* Mostly human voice frequencies
* Bass frequencies are not much of a problem
* The room’s N wall, and the S side consisting mostly of closed closet doors, are a parallel pair of flat hard surfaces. Parallel walls are a common cause of “slap echo” which interferes with conversation.
* The W and N walls are fairly hard, reflecting more sound than desired.
* The ceiling slopes join at close to 45 degrees, making a partial corner reflector. Anyone sitting anywhere but the centerline of the room will hear, more clearly than usual, sounds originating from certain other parts of the room, typically people not involved in the same conversation.
This is work for a Physicist! Or at least for a physicist to make some initial observations and recommendations to consider and inspire owners and leaders to ask an experienced building acoustics professional.

“Architectural acoustics did not exist on a scientific basis until a young professor of physics at Harvard University in 1895 corrected the abominable acoustics of the newly constructed Fogg Lecture Hall.” [small edit for grammar] – Ar. Mukunda K.S, Dean of School of Architecture, some school in Bangalore


* Absorbers: complex objects, holes, cloth, foam, fiber, bass trap. These reduce the overall sound power filling the room.
* Diffusers: complex objects, beams, columns, boxes, panels. These scatter the sound, breaking up hard echoes, defocusing sound from each specific source.
* Reflectors: at crazy angles, to escort unwanted sound out of the room or into holes or absorbers. Likely not useful for this situation, but may play some role.

I should also mention blocking – thick walls, steel plates and such – but this is a special case of absorbing and reflecting. Walls are of architectural nature, and not really practical for fixing the acoustics of an existing room. Also, great distances will make any noise quiet, but not relevant for solving a problem within a room.
Fellowship Hall needs mostly absorption. My best guess is that a mere -5dB reduction of all noise received at any typical point, from an average source anywhere else in the room, would help greatly. People *do* converse, and mostly *do* understand each other, most of the time, but often it’s right at the edge of becoming unclear. There’s only about 5dB difference in SNR between the best of difficult conversation muddled by echos, and acceptable quality conversation. Another 5dB or more will allow easy clear conversation.

We should aim for -4dB to -8dB reduction in total power received anywhere in the room from all sources, in the frequency range 200 to 3500 Hz. We don’t need more than that. A little more, okay. Too much reduction will make the room “dead” or “flat” which, ironically, also makes conversation less pleasant. Absorbers are best, but some scatterers will help reduce impulse slap, to “de-color” the reverb.

Note that this report is about sound generated and reverberating within one room. Not relevant are other acoustics problems such as outside noises (from elsewhere in the building or from outdoors) intruding into a quiet room, and preventing loud noises within the room from escaping to annoy surrounding areas.


PROPOSED EASY SOLUTIONS – Inexpensive and Good Enough
1. Foam/fibery panels or thick objects on walls. Cover 1/3 or more of total wall area of W, N walls, with object at least 6 inches thick, and ideally of irregular shapes. If rectangular, aim for different sizes and varying spacings between them.
2 Drapes for windows. Can be effective even when open, if not bunched up real tight.
3. Hang some new lighting fixtures, and/or some sort of banner/flag/sign from ceiling.
4. If some large object or two could be placed in the corner, or somewhere, not interfering with traffic or vital coffee supply operations, even if acoustically reflective, would help scatter the sound, softening any sources “seen” through corner reflectors or large flat walls.
5. We do use tablecloths on all the tables, don’t we? Cheap and easy, except someone has to put them through laundry regularly. It’s not the softness of cloth compared to the hard table tops that matters, but the overhang of soft cloth from tabletop to near the floor. Low frequency “boominess” will be reduced slightly.

* Decorative fully 3D objects on ceiling, wall. Candle-holders, large thick cross, sculptures…
– Intricate elements, irregular patterns.
– Any material, but better with absorbers = fibery material, glass wool
– Thick, though even an ordinary painting against the wall will help a little.
* Cloth hangings, curtains/drapes, towels on hooks… anything soft anywhere in sufficient amounts
* Foam, slabs of glass fiber, or “egg-carton” boards on wall.
– Rockwool is popular brand.
– 1/2″ thick will do for us. Is not a recording studio.
– make several pieces 1ft square to 2x3ft or so. arrange artistically on wall.
– standoffs about 2″ or so help reduce frequencies not directly snuffed by panel.
– foam fins in strategic places, corners, foam “stairs”
– for a room intended for kids, painted literal egg cartons are cheap and effective.
* Latticework room dividers or against wall a few inches away. Dividers can interfere with traffic, however.
* Add shelves with random objects, with gaps between vases/books
* Remodeling to avoid parallel surfaces.
– Remove last 2 of the 3 closets, or the first of the three.
– Add decorative semi-columns to N, W walls.
– Fill in corners w diagonal surface, about 3ft across
– probably the most expensive way to fix acoustics
* Chandelier or pendant lighting fixtures
* Rectangles of cloth, or boards of wood or plastic, hanging from the ceiling. Qualcomm does this to scatter, block and reduce talking noise in their open cubicle farms.
* Fuzzier carpet (but much is hidden under tables, has little effect)
* Tablecloths act as bass traps.
– not much needed in this situation. Bass is not the problem.
* Look for existing flat surfaces of brick, linoleum, glass, thick wood. Obscure them.

– Cost.
– Cleaning. We don’t want high-efficiency dust-catchers.
– Fire safety.
– Installation effort, skill, materials, disruption to normal activities.

* Do not overdamp. Room will feel “dead”
* Do something to reduce/control high frequencies, do something else for mid-range, and do something for bass. Unlikely one treatment will fix all of the problem at once.
* Ignore articles aimed at home/amateur music studios, audiophile setups, auditoriums, concert halls. We’re not putting on pricey concerts with the finest opera singers during coffee & fellowship time, are we?


FACTOIDS from various source, not necessarily consistent or verified
* 1 KHz = 1 foot wavelength. 200Hz = 5 ft.
* Human voice power is mostly in frequency range 300 to 3500 Hz.
* Fundamental of Human voice is within 90 to 250 Hz. Male 85-180, fem 165-255. For practical easy math use 100 – 300 Hz. But most of our phoneme-distinguishing ability depends more on presence and variations of higher harmonics than on the fundamental.
* Architectural elements and furniture/object details on a scale of around 5 inches, up to 10ft, are important to human voice acoustics. Actually, there’s no upper limit, but that’s the longest wavelength we need to be concerned with.
* Indoors, in a typical room: only about 1/10th to 1/1000th of what you hear is directly from the source. The rest is bounced off wall, ceiling, and objects.

in no particular order

Church Acoustics Articles Aimed at churches! This is right on topic for us, but the physics applies just as well to conference rooms or homes. Well-written, educational, does not require existing engineering knowledge. Acoustic Sciences Corp. in Eugene – did work for St Thomas Episcopal (somewhere in Oregon).

Layman’s Introduction to Room Acoustics. Aimed at audiophiles, but physics is the same for everyone. http://www.6moons.com/audioreviews/theroom/3.html

“How to Remove Echo From a Tall Ceiling”
– more oriented for interior decoration, large rooms in fancy houses

also has advice on audio mixing, PA systems, live music


http://www.auralex.com/ custom room analysis, kits, sells all kinds of absorbers, diffusors, and serious sound isolation.

– “Roominator” kits for small rooms up to 400 sqft or larger

http://realtraps.com/ aimed at home theater, recording studio, sells $$ fixes.
but has solutions for other places such as churches and bars.
educational videos:
Diffusors: http://realtraps.com/video_diffusors.htm or https://youtu.be/vb30CICG68c

Kirei USA

23 Decorative Acoustic Panel Ideas

– see about 1/3 way down: “5. Get Sticky with It and Lower Sound in Style”
– sticky foam pieces attached to wall could be ½ our solution!
– See also plenty of other ideas of ceiling and wall tiles, hanging absorbers.

Church Leaders article – Intro to Acoustics in Churches

Church Acoustics 101

Kinetics Noise Control, Inc.
products for noise control in all kinds of indoor places. Outdoors, too.

This link goes straight to a PDF paper on noise reduction and acoustics for schools, which have much in common with churches. It’s from the United Kingdom, so if you find yourself in conversation with one of the authors, be sure to say “decibel” with a British accent. http://www.ioa.org.uk/sites/default/files/Acoustics%20of%20Schools%20-%20a%20design%20guide%20November%202015_1.pdf Covers construction methods, floors, absorbers, “Speech Transmission Index” for quantifying clarity of conversation hampered by noise and echo.

A More Thorough Education on Acoustics (online slideshow)
Have spare time and desire to educate yourself on architectural acoustics? Not scared of “decibels” and wavelengths? Try this slide show:

by Ar. Mukunda K.S, Dean School of Architecture, Dayanand Sagar Acadamy of Technology & Management Bangalore

BOOK: Sound Studio Audio techniques for Radio, Television, Film and Recording, 7th Edition
by Alec Nisbett https://www.amazon.com/Sound-Studio-techniques-Television-Recording/dp/0240519116
For reducing external noise, a good article is: http://www.today.com/home/neighbors-too-loud-indoor-noise-solutions-t81876


I, Daren Scot Wilson, am not a professional architectural acoustics expert, just a physicist with some knowledge of waves and sound, and modest experience in music recording. No one should start sawing load-bearing beams in half or permanently gluing stuff to walls due to anything I said here. Consult a proper professional architect or engineer with a PE license, or at least find a better quality self-appointed expert.
UNRELATED but interesting reading for those with too much leisure time

* http://twistedphysics.typepad.com/cocktail_party_physics/acoustics/

* Acoustic tricks for reduction of toilet flush noise

One-Tilde: A New Symbol for Wavy Math

For years I’ve been using a symbol in any math involving waves.  Normally, in physics we use radians for angles, and for describing the phase of a wave along time or space.  A typical equation involving vibrations or waves will contain bits like this:

e ^ {i \omega t}

and this:

e ^ { i k x}

Omega is the angular frequency in radians per second. Angular frequency is great for differential equations, and summing infinite series for numerical computations.

In electronics engineering, radio, music, signal processing, and almost all areas of applied mathematics, we like to count cycles. Hertz, which is cycles per second. Wavelengths, the size of one full cycle.  Convert according to \omega=2\pi f.  We write plenty of things like this:

e ^ {2 \pi i f t}


$latex  e ^ {2 \pi i x \lambda}$

You find 2\pi i factors all over the place.   Frequency in cycles is much easier for everyday application, for measurement, and for labeling electronic parts.

Sometimes I want to stick with cycle frequency, but prefer not to write 2\pi i over and over.   So I invented:

{\rlap {1}{\sim}} = e^{2\pi i}

Here it is, as an image in case my LaTeX markup doesn’t work right:


We all know that

e^{2\pi i} = 1

so maybe I could use just a plain one?  No, because $1^p = 1$; unity to any power doesn’t do anything interesting. The tilde over the one means that, for noninteger $p$, don’t take the principal value but the “next” value.  It works like this:

{{\rlap {1}{\sim}}}^{f t} = (e^{2\pi i})^{f t} = e^{(2\pi if t)} = e^{i\omega t}

We can write a Fourier transform like this:

S(t) = \int_{-\infty}^{\infty} A(f){\rlap {1}{\sim}}^{ft} dt

and reverse it as:

A(t) = \int_{-\infty}^\infty S(f) {{\rlap {1}{\sim}}}^{-ft} dt


I find it nice that there’s no 2\pi factors appearing anywhere.

When adding waves in the study of X-ray diffraction in crystals, or understanding image formation from radio dish arrays, or toying with harmonics in audio processing, the one-tilde keeps things neat and clean.

One-Tilde in LaTeX

This works, allows for some adjusting, but leaves out some fine points of good typography.


$\psi(t) = \onetilde^{ft}$

This is simple, but ugly since there’s no kerning for good taste:

{\rlap {1}{\sim}}


One-Tilde in Lout

I don’t know yet….

Imperfect Harmonics of String Instruments

A question appeared on Physics Stack Exchange asking why the harmonics of a piano string aren’t the exact integer multiples of the fundamental as Pythagoras and Fourier had taught.  The question asks about pianos, but this applies as well to guitars, violins, and all other string instruments.


There are several effects to consider.

  • Stiffness of a non-zero thickness wire means higher harmonics are harder to make, due to having more bends, thus a teeny bit higher in frequency, more so the higher the harmonic.  There is a fourth-order differential equation to replace the usual wave equation, from which we obtain the frequency deviations for each harmonic.
  • The ends of the wire are clamped.  Naively, these would be nodes (zero crossings) of a sine wave.  But the clamp prevents the wire from being at an angle.  In effect, the standing wave has less room to exist in that you’d think when measuring the distance between clamps.  This shifts everything up, including the fundamental. Higher harmonics with the same partial amplitude want greater angles at their nodes, thus are more affected.
  • The string is pushing against air as it vibrates.  Resistance tends to slow things down. But does that mean harmonics would be higher or lower relative to their expected naive frequency based on the fundamental?
  • The wire at rest is a straight line between two points. When vibrating, it’s longer. The higher harmonics may be thought of as fast short-scale activity riding on a curved slightly longer string.  This would lower the harmonic frequencies relative to the fundamental.  But this effect is smaller, and not yet mentioned in the answers (as of this writing.)

One fine day at a music store in Fort Collins, years ago, I saw a whimsical bass guitar, much smaller than normal, more like lute sized, and with strings of soft rubbery stuff, some kind of plastic or silicone probably.  It made an interesting bass sound.  Whereas a normal bass guitar string is under great tension, these strings were maybe under just a few pounds.  It made an interesting and different sound.  I suppose that instrument would exhibit interesting nonlinearities and off-integer harmonics in easy to measure ways.  But I had more important things to spend my money on.

LIGO Announces 2nd Gravitation Wave Observation

This is great news for physicists!  As I started to drive home from work today, I heard this on NPR.   LIGO, the pair of mile-long L-shaped super-sensitive interferometers in Washington and Louisiana, picked up data last December looking a lot like a black hole collision.  Everyone by now has heard the announcement last February, of a signal picked up last September, indicating black holes of masses of about 29 and 36 solar masses.  Now there’s this collision, with masses about 8 and 14 solar masses.

Of course, it has been turned into audio.  The version I heard on the radio sounded very much like something watery or airy being suddenly sucked up, or  falling into a hole (of course.)   The audio at  https://www.ligo.caltech.edu/video/ligo20160211v2  uses the same data, but it doesn’t sound the same to me, but then, my car’s audio and my home computer’s audio aren’t the same.

The main news story from LIGO:  https://www.ligo.caltech.edu/news/ligo20160615

Background Sounds & Ambient Environments

Sometimes it’s too quiet to concentrate on work.  Or too quiet to sleep.  Maybe there’s too much distracting noise from down the hall or from the neighbors.   How to create background noises more conducive to a desired state of mind, such as sleeping, studying or focused intellectual work?

Cafe Sounds on Youtube

I found a long clip on Youtube of random cafe noises, with occasional bean grinder whirrrs, muddled conversation, chairs scooching and outside traffic.  Robert aka “Duff The Psych”   made it with binaural microphones, which I suppose is something like what Kevin Braheny used to record vividly realistic you-are-there sound clips in his “Secret Rooms” album.   DtP creates “ASMR” recordings.  The clip is available to play at https://www.youtube.com/watch?v=BOdLmxy06H0  But note that visually, it’s just a latte sitting there.

Beware of some cafe or library background sound clips on Youtube – they are only one or two minutes long, looped many times to fill an hour.  You’ll get tired of those quickly.  Duff’s clip is not repeated, but a true hour long recording.

The cafe clip was nice, but even at one genuine hour of material, I don’t want to play it over and over and over day after day. It would get too familiar, though it may do its job just as well, played with the volume way down to be barely perceptible.  To cover distracting sounds, though, you’d want it cranked up more.   You’ll need more variety.  So where to get a wider variety of cafe sounds, and other useful backgrounds?


The website Coffitivity provides several types of cafe. You get three free online, and three more (as of this writing) for a few bucks.  I usually run this all day long with their volume slider at “5” even if I’m running other background sound sources.  The volume slider has only multiples of five. Zero is no sound.  You may wish there was finer control at the quiet end.  You could set the site’s volume slider to higher, say 10, and turn down the volume on your speaker, but then what if you need to watch an occasional Youtube video or lecture on Coursera?   Coffitivity provides apps for Android and iOS.


What would really be nice is to have a way to play a variety of subtle background noises.  A distant train.  Ocean waves.  Wind.  Maybe all three at the same time?  Defonic  shows you a bunch of icons. Click one, adjust the slider, and you’ve got a distant train, ocean, electric fan, cricket chirping at night, thunder, traffic, even “starship bridge”.    Try running their cafe along with Coffitivity in another browser tab.   Free, and I don’t see a “donate” button.  Defonic provides a mobile app.  Also, video backgrounds.

I saw another site similar to Defonic, forgot the name, with the same icons but missing the starship and some others. Maybe it was an older version?


For some real ear candy, a wide variety of adjustable sounds can be played at MyNoise created by Dr. Ir. Stéphane Pigeon.    Free, but easier to use if you chip in five bucks.  There are oceany sounds, night sounds, droning sounds, all kinds of acoustic environments.  You will find a set of sliders like on a sound mixing board, or audio equalizer, to adjust the volume of various elements and frequency ranges in the soundscape.  Every noise generator has a few pre-designed mixes.  Pick for example “Twilight” and find mixes “Floating”, “Calming”, “Purity” and more.  Or pick the noise machine Warp Speed and choose Engine Control Room, Aboard the Enterprise, The Bridge or others, or set the sliders however you like. “Asleep in Quarters” is great for sleep, of course.  Or try Ice World with Clear Water, Magnetic Fields, Floating Particles and so on.

One great feature about MyNoise is the “animate” button, which causes the sliders to vary over time, changing the mix of elements contributing to the soundscape.  Night time crickets fade a bit a bit while the wind picks up, and later you may hear frogs dominate.  Keeps you from getting bored.


If you feel like spending time in a old-time scholarly sound environment with a few distinguished colleages quietly (but not silently) studying, try the Hufflepuff Common Room.   There are several Harry Potter sound themes at  Ambient Mixer, along with Turkish coffee house, heavy industrial machines, meditative drums, science fiction places, everyday castle sounds, humming data center full of fans… there are *plenty* of sounds I haven’t started to explore.

“Distant world sounds help people mediate and improve the activities of the brain which involve the sensory processing and focus ability. The slow distant sounds have a relaxing effect on the nerves, giving people a beautiful feeling of happiness, freedom and optimism.”

Soundscapes are made up of several elements. Some run continuously, and some play at random times.    Like MyNoise, you have sliders to adjust the strength of the various elements.  No frequency EQ, but with Ambient Mixer you can pan left/right, set how often random elements such as quill scribbling or coffee pouring occur.    There is also a crossfade button, and mute if you don’t want that element at all.   A pause button stops everything temporarily in case you need quiet for a minute.   The only thing lacking is a master volume control – that would be nice to have.

The great thing about Ambient Mixer is that the various elements are separate – not all stuck on loops the same length.  The random play feature keeps the acoustical journey from getting stagnant.   With the volume low, playing one of the Harry Potter themes or a cafe, and the browser window buried under stuff I’m working on, I can completely forget it’s there, as well as forget where I am.



When I am painting or drawing or doing other artwork, or doing something requiring no word-thinking, I prefer a whole different sort of noise.  While mixing colors and dabbing at a canvas, I like talk radio – to keep the verbal part of my mind out of the way.   Depending on the time of day, I play broadcast radio, or look for archived recording on websites.   Favorites are Coast to Coast AM (George Noory’s show) with its wide variety of interesting guests, or if I feel like metaphysics, Nile MacFlouer’s Ageless Wisdom radio show or whatever crazy thing is airing on BBS Radio.

Overheard at a rehearsal for 4’33”

Overheard at a rehearsal for 4’33”:

Oboist: …and over at measure 84, shall I take that full-measure rest right in line rhythmically with the previous and following measures, or do you suppose it would come off better with a bit of emphasis, maybe a bit of ritardo?

Conductor: Good question. I see… well, before that point, the score is building up energy, with soaring alternating arcs of silence, gradually going from not using the strings to the woodier instruments, but at the same time you have these absolutely soundless action punches in the support, the… er… the bass parts, and you’re kind of caught in the middle having to not play both as they come together there… and… yes, yes, I think you have a good idea. Quite perceptive! Ha ha, with all you talented musicians here, why they made me the conductor, I don’t know!

(laughter among whole group)

First Violinist: Because, Joe, you have a face made for having your back to the audience!

(more laughter)

Conductor: (tap, tap) Very funny, Maeve. Okay everyone, note what Linda suggests, we’ll go with a kind of ritardo in measure 84, just a little slow down, then resume the normal tempo. And… remember to watch me! Don’t miss that downbeat, because if we aren’t all together in doing nothing, right on the beat, the audience is going to get sore. Again.

Trombonist: Yeah, sounds great. Hey, I’ve got a smudge on my sheet music here, or.. a little tear in the page, in measure 115. I can’t tell what was written there. Is that a hushed D that I don’t play, or a D flat?

Tuba: D flat. I got the exact same part as you, but down an octave. But damn! I just realized something! I got my B flat tuba here, but I’m supposed to be playing my E flat, which is out in my van in the parking lot. Damn! DAMN!

Conductor: Chill, Harvey. Ah, that could be a problem. Could you transpose the key mentally as you go along?

Tuba: Hey, I’m a tuba player! How smart do you think I am?

(scattered laughter)

Conductor: Well, Harvey, don’t mind the instrument. This would be a serious problem with other pieces, but for this one, just finger the notes as if you had your E flat. Because…I’ll tell you a little secret… the audience isn’t going to notice!

Tuba: Okay, cool, I’ll do that. No problem.

Conductor: (tap, tap) Okay! Let’s play through the whole thing again, with all the changes discussed. And remember that quirky one-beat measure at the top of page four. I expect to hear exactly one beat of nothing there, between the restful quietude before and bold stillness following. (make big downstroke with baton, then holds still)

(faint sounds of an air conditioner, muffled outdoor traffic…)

(four and a half minutes later…)

Conductor (looking surprised, in a good way): Hey, nice! That was all right! You did great! Yes, fantastic! We’ll do fine at the concert. I suppose that’ll be all for today. Yes, let’s pack up. No more 4’33” for now. We don’t want to peak too soon. Unless anyone has any comments or suggestions?

Cowbell Specialist: Uh, yeah… so, maybe this piece could use more cowbell?