# Acoustic Desk

> Past the critical distance, gain cannot help. Direct sound falls 6 dB per doubling of
> distance and the reverberant field is, near enough, the same level everywhere in the
> room — so the ratio between them falls with distance and then flattens, and the distance
> where they are equal is `Dc = DF × 0.057 × √(Q × V / RT60)`. An ordinary painted meeting
> room of 72.9 m³ has 5.5 m² sabins of absorption, reverberates for 2.12 s and has a critical
> distance of 33 cm, so a table microphone at 1.8 m records −14.6 dB of room over
> talker. **Turning the gain up changes that by nothing**: it raises both sides equally.
> Replacing the whole ceiling takes the room to 0.41 s and the critical distance to only 76 cm,
> because Dc goes as one over the SQUARE ROOT of RT60. A shotgun on a talker takes it to 2.68 m for nothing.

## The one thing to know

**PAST THE CRITICAL DISTANCE, GAIN CANNOT HELP.**

```text
A     = sum of area x coefficient        metric sabins
RT60  = 0.161 x V / A                    Sabine
Dc    = DF x 0.057 x sqrt(Q x V / RT60)  DF = the mic's distance factor
D/R   = 20 x log10(Dc / d)               0 dB at d = Dc
gain  = +x dB on BOTH sides              so D/R does not move at all
```

Gain is applied after the microphone, to a signal that already contains both the direct
sound and the reverberant field, and it raises them by the same number of decibels. It is a
common-mode change. This is the most common thing done in response to a reverberant
recording and it is the one thing that provably cannot work.

Three things do move the ratio, in order of effect per pound spent:

1. **Move the microphone closer.** Distance appears on one side of the ratio and not the
   other. It is free. In the demo room 33 cm breaks even and 17 cm sits 6 dB clear.
2. **Change the pattern, or the source directivity.** A distance factor multiplies Dc
   DIRECTLY, so a shotgun's 2.5× is worth 6.25× the absorption. Also free, if the
   microphone is already in the bag.
3. **Add absorption.** The expensive one, and the one everybody starts with.

**Absorption has a fixed, poor exchange rate.** RT60 is inversely proportional to
absorption, so halving it means doubling the absorption — every time, in absolute terms.
Dc goes as one over the square root of RT60, so that doubling buys a factor of 1.41×:
**double the absorption, gain 41% more working distance.** The fourth doubling costs eight
times what the first did and still delivers 41%.

Two consequences worth stating plainly. A room treated to a broadcast target can still
have a critical distance well short of where the microphone has to be — check that before
the order, not after. And a lavalier at 20 cm in an untreated room is +4.5 dB, better than
the fully treated room with the microphone at 1.8 m at −7.5 dB.

## Why gain does nothing

| Gain change | Direct at the mic | Reverberant field | Direct-to-reverberant |
| --- | --- | --- | --- |
| as found | reference | reference | **−14.6 dB** |
| +6 dB | +6 dB | +6 dB | **−14.6 dB** |
| +12 dB | +12 dB | +12 dB | **−14.6 dB** |
| +20 dB | +20 dB | +20 dB | **−14.6 dB** |
| +40 dB | +40 dB | +40 dB | **−14.6 dB** |

**The last column is the same in every row, and that is not a simplification.** Gain is applied after the microphone, to a signal that already contains both the direct sound and the reverberant field. It raises them by the same number of decibels. IT IS A COMMON-MODE CHANGE.

There are exactly three things that do move that column:

1. **Move the microphone.** Direct sound falls 6 dB per doubling of distance and the reverberant field does not move at all, so distance is the only term on one side of the ratio and not the other. In this room the microphone is at 1.8 m and 33 cm would break even.
2. **Change the pattern or the source directivity.** A distance factor multiplies the critical distance directly — see the pattern table.
3. **Add absorption.** The most expensive of the three, because the critical distance goes as one over the square root of the reverberation time.

Nothing else on a mixing desk is in this argument.

## What distance does

| Microphone at | Direct level | Reverberant level | Direct-to-reverberant | Verdict |
| --- | --- | --- | --- | --- |
| 15 cm | 0 dB relative to 15 cm | unchanged | **+7 dB** | direct wins |
| 30 cm | −6 dB relative to 15 cm | unchanged | **+0.9 dB** | direct wins |
| 33 cm — **the critical distance** | −7 dB relative to 15 cm | unchanged | **0 dB** | break even |
| 60 cm | −12 dB relative to 15 cm | unchanged | **−5.1 dB** | the room wins |
| 1.2 m | −18.1 dB relative to 15 cm | unchanged | **−11.1 dB** | the room wins |
| 1.8 m | −21.6 dB relative to 15 cm | unchanged | **−14.6 dB** | the room wins |
| 3.6 m | −27.6 dB relative to 15 cm | unchanged | **−20.6 dB** | the room wins |

The third column is the interesting one: **the reverberant level is the same at every distance in the room.** That is what makes the critical distance a real boundary rather than a rule of thumb — inside it the recording is the source, outside it the recording is the room, and the transition is at a computable place.

In this room (72.9 m³, RT60 2.12 s, omni on a point source) that place is 33 cm. Doubling the distance from there costs 6 dB and doubling it again costs another 6.

## What each pattern is worth

| Pattern | Distance factor | Critical distance | Direct-to-reverberant at 1.8 m | Equivalent absorption |
| --- | --- | --- | --- | --- |
| omnidirectional | 1× | 33 cm | −14.6 dB | 1× the absorption |
| sub-cardioid | 1.29× | 43 cm | −12.4 dB | 1.66× the absorption |
| cardioid | 1.73× | 58 cm | −9.9 dB | 2.99× the absorption |
| supercardioid | 1.93× | 65 cm | −8.9 dB | 3.72× the absorption |
| hypercardioid | 2× | 67 cm | −8.6 dB | 4× the absorption |
| figure-of-eight | 1.73× | 58 cm | −9.9 dB | 2.99× the absorption |
| shotgun (short interference tube) | 2.5× | 84 cm | −6.7 dB | 6.25× the absorption |

**Read the last two columns together.** A distance factor multiplies the critical distance directly, and absorption only reaches it under a square root — so matching a shotgun's 2.5× by treatment alone needs 6.25× the absorption in the room.

In 72.9 m³ with 110.7 m² of surface, 6.25× of 5.5 m² sabins is 34.6 m² sabins — which means taking the room's AVERAGE coefficient from 0.05 to 0.31 across every one of those square metres.

**The pattern change costs nothing and can be tried this afternoon.** It is the first thing to do and it is usually the last thing tried.

## What each halving costs

| Reverberation time | Absorption needed | Added since the last row | Critical distance | Gain in distance |
| --- | --- | --- | --- | --- |
| 2.12 s | 5.5 m² sabins | — | 33 cm | — |
| 1.06 s | 11.1 m² sabins | **+5.5 m² sabins** | 47 cm | 1.41× |
| 0.53 s | 22.1 m² sabins | **+11.1 m² sabins** | 67 cm | 1.41× |
| 0.27 s | 44.3 m² sabins | **+22.1 m² sabins** | 95 cm | 1.41× |
| 0.13 s | 88.6 m² sabins | **+44.3 m² sabins** | 1.34 m | 1.41× |

**Read the third column against the fifth.** Every halving costs MORE absorption than the one before it and buys the SAME 41% of working distance. Reverberation time is inversely proportional to absorption, so each halving requires doubling the absorption — the absolute amount added grows every time. And the critical distance goes as one over the square root, so each halving buys a factor of 1.41× and no more.

That is the whole economics of room treatment. The first panels are worth having. The fourth doubling costs eight times what the first did and moves the working distance by a further 41%, and there is no configuration in which it catches up with a change of microphone pattern.

## The materials

| Material | Coefficient | 27 m² of it | Takes the demo room to |
| --- | --- | --- | --- |
| `plasterboard` painted plasterboard | 0.05 | 1.4 m² sabins | 2.12 s |
| `brick` bare brick or block | 0.03 | 0.8 m² sabins | 2.35 s |
| `concrete` sealed concrete | 0.02 | 0.5 m² sabins | 2.48 s |
| `glazing` glazing | 0.03 | 0.8 m² sabins | 2.35 s |
| `wood-floor` wooden floor | 0.07 | 1.9 m² sabins | 1.93 s |
| `carpet` carpet on a hard floor | 0.25 | 6.8 m² sabins | 1.07 s |
| `heavy-carpet` heavy carpet with underlay | 0.40 | 10.8 m² sabins | 0.78 s |
| `ceiling-tile` mineral-fibre ceiling tile | 0.65 | 17.6 m² sabins | 0.54 s |
| `curtain` heavy curtain, gathered | 0.50 | 13.5 m² sabins | 0.66 s |
| `upholstery` upholstered seating | 0.60 | 16.2 m² sabins | 0.58 s |
| `panel` 50 mm broadband absorber | 0.90 | 24.3 m² sabins | 0.41 s |
| `thin-panel` 25 mm foam panel | 0.60 | 16.2 m² sabins | 0.58 s |
| `bass-trap` corner bass trap | 0.80 | 21.6 m² sabins | 0.46 s |
| `people` an audience, per person | 0.45 | 12.2 m² sabins | 0.72 s |
| `open-window` open window or doorway | 1.00 | 27 m² sabins | 0.38 s |

The fourth column is the demo room with that material on the ceiling and painted plasterboard everywhere else. **All of these are MID-BAND figures**, around 500 Hz to 1 kHz, where speech intelligibility lives. Almost every one of them does far less below 250 Hz, so a room can compute as treated on this page and still sound boomy — and the low end is what makes a small room sound small.

They are also indicative rather than measured: a real material varies with the supplier, the mounting and the air gap behind it, and an absorber on battens with a 50 mm gap behaves quite differently from the same absorber glued flat.

## Thresholds

| Threshold | Value | What it separates |
| --- | --- | --- |
| the Sabine constant | 0.161 | RT60 = 0.161 × volume ÷ absorption, in metric units. |
| the critical-distance constant | 0.057 | Dc = distance factor × 0.057 × √(Q × volume ÷ RT60), in metric units. |
| over the target, by | 1.15× | below it, treatment is fine-tuning rather than a project. |
| surfaces should account for | ±5% of the room | anything unlisted is treated as absorbing nothing, which flatters a hard room. |
| a coefficient must be | ≤ 1 | above it is a typo, not a material: it is the fraction of energy NOT returned. |
| treatment is costed at | α 0.90 | a decent 50 mm broadband absorber at mid-band. |

Defaults when the sheet is silent: a target of 0.4 s, a source Q of 1, an omni microphone, and a distance of 1.8 m. **The distance and the pattern are reported as WARNINGS when assumed**, because the verdict turns on them; the target and the source directivity are notes, because they change what gets recommended rather than what the room does.

## Sheet grammar

Two blocks. `ROOM` is `key | value`, one per line. `SURFACES` is a table.

```
ROOM
name     | what this room is
size     | 6 x 4.5 x 2.7     metres; or give length, width and height separately
target   | 0.4               the RT60 you want, in seconds (or `400 ms`)
source   | talker            directivity Q: a number, or omni / talker / loudspeaker
pattern  | cardioid          the mic: omni, cardioid, hypercardioid, shotgun...
distance | 1.8               how far the mic is from the source, in metres

SURFACES
s1 | the ceiling | 27   | ceiling-tile |
s2 | the floor   | 27   | carpet       | why this one is like this
s3 | the walls   | 56.7 | plasterboard |
```

A SURFACES row is `id | what it is | area | absorption | why`.

**A bare number is METRES for a length and SQUARE METRES for an area.** `cm`, `mm` and `ft` are accepted on a length; `m2` is accepted on an area and ignored.

**The absorption column takes three things**: a coefficient between 0 and 1, a percentage (`25%`), or a material name. A coefficient above 1 is reported as an error — it is the fraction of energy NOT returned, so it cannot exceed 1.

**The areas should add up to the room's own surface area**, which for a rectangular room is `2(LW + LH + WH)`. Anything unlisted is treated as absorbing nothing at all, which flatters a hard room and is the commonest way this arithmetic goes wrong; the page reports the shortfall rather than filling it in.

`distance` and `pattern` are the two entries the verdict actually turns on, so both are reported as warnings when they have to be assumed. `target` and `source` change what gets recommended rather than what the room does, and are notes.

## Lanes

- **`plan`** — Choose the microphone position before the treatment budget. A room gets treated and then somebody discovers the microphone is still too far away. This works the other way: start from where the microphone has to be, work out the critical distance that position demands, and only then ask what pattern and what absorption deliver it — because the pattern is free and the absorption is not.
  Sections: Summary, The Sheet, The Setting, Reasoning, Next Step.
- **`check`** (primary) — Whether a recording made in this room is usable. The paid read of what the free panel computes. What the room reverberates for, where its critical distance falls, whether the microphone is inside it, what the direct-to-reverberant ratio actually is at that position — and, when it is bad, the flat statement that no gain setting changes it.
  Sections: Summary, Verdict, Findings, Corrected Sheet, Next Step.
- **`distance`** — The distance question: where the microphone can be. Direct sound falls 6 dB per doubling of distance and the reverberant field is the same level everywhere, so distance is the only thing on either side of the ratio that moves. This reads the position: what it gives, what the room would allow, and why the gain control is not in the argument at all.
  Sections: Summary, Where The Microphone Is, What The Room Allows, Why Gain Does Nothing, Next Step.
- **`treatment`** — The treatment question: what absorption actually buys. Absorption is the denominator, so reverberation time halves only when absorption doubles, and the critical distance improves by the square root of that. This reads every surface, says which one treatment should go on, and puts a number on the working distance a doubled budget delivers.
  Sections: Summary, Every Surface, What The Target Costs, Diminishing Returns, Next Step.
- **`deliver`** — Decide what changes: the microphone, the pattern, or the room. Sorts every finding into what moving the microphone fixes, what only absorption fixes, and what nothing fixes. Turning the gain up appears in none of those buckets, which is the point — it raises both sides of the ratio equally and moves nothing at all.
  Sections: Summary, Moving The Microphone Fixes, Only Absorption Fixes, Nothing Fixes, Next Step.

## Findings

All 30 are computed in the browser and cost nothing.

| Code | Severity | Scope | What it means |
| --- | --- | --- | --- |
| `NO-ROOM` | error | room | No room dimensions, so there is nothing to compute |
| `TARGET-ASSUMED` | note | room | The target reverberation time was assumed |
| `MIC-DISTANCE-ASSUMED` | warn | room | The microphone distance was assumed |
| `PATTERN-ASSUMED` | warn | room | The microphone pattern was assumed |
| `Q-ASSUMED` | note | room | The source directivity was assumed |
| `NO-SURFACES` | error | room | No surfaces, so there is no absorption |
| `SURFACE-AREA-SHORT` | warn | room | The surfaces do not account for the room |
| `SURFACE-AREA-OVER` | warn | room | The surfaces add up to more than the room has |
| `ALPHA-OUT-OF-RANGE` | error | surface | An absorption coefficient above 1 |
| `ALPHA-IS-A-MID-BAND-FIGURE` | note | room | Every coefficient here is a mid-band figure |
| `REVERB-TIME` | note | room | What the room reverberates for |
| `CRITICAL-DISTANCE` | note | room | Where direct and reverberant sound are equal |
| `MIC-BEYOND-CRITICAL` | error | room | The microphone is past the critical distance |
| `MIC-INSIDE-CRITICAL` | note | room | The microphone is inside the critical distance |
| `GAIN-CANNOT-HELP` | error | room | Turning the gain up will not change this |
| `DIRECT-TO-REVERBERANT` | note | room | The direct-to-reverberant ratio at this distance |
| `MOVE-THE-MIC` | note | room | Where the microphone would have to be |
| `ABSORPTION-NEEDED` | warn | room | How much absorption the target requires |
| `HALVING-COSTS-DOUBLE` | note | room | Halving the reverberation time doubles the absorption |
| `DIMINISHING-RETURNS` | note | room | What doubling the absorption buys in working distance |
| `DIRECTIVITY-IS-WORTH-MORE` | note | room | The microphone pattern is worth more than the treatment |
| `TARGET-CANNOT-REACH-THE-MIC` | warn | room | Even at the target, the microphone is still too far |
| `NO-ROOM-REACHES-THIS` | warn | room | No amount of treatment puts the microphone inside |
| `SURFACE-DOMINATES` | note | surface | What this surface contributes |
| `BIGGEST-OPPORTUNITY` | warn | room | The surface where treatment buys the most |
| `ALREADY-ABSORBENT` | note | room | This surface is already doing its share |
| `AT-TARGET` | note | room | The room is already at its target |
| `OVER-TARGET` | warn | room | The room reverberates for longer than the target |
| `SABINE-ASSUMES-DIFFUSE` | note | room | Sabine assumes a diffuse field and this room may not have one |
| `ROOM-IS-SMALL` | note | room | This room is small enough for its modes to matter |

## What this page cannot do

This page computes from the dimensions and coefficients on the sheet. It has not measured anything.

- **Sabine assumes a diffuse field**: sound equally likely to be anywhere and arriving from everywhere. A long thin room, a room with one very absorbent surface and five hard ones, or any room at low frequency does not satisfy that. Sabine OVER-predicts reverberation as a room gets dead, where Eyring is the better model.
- **Every coefficient here is a mid-band figure**, around 500 Hz to 1 kHz. Almost all materials absorb far less below 250 Hz, so a room can compute as treated and still sound boomy — and the low end is what makes a small room sound small. This page does not model frequency at all.
- **The coefficients are indicative, not measured.** A real material varies with the supplier, the mounting and the air gap; an absorber on 50 mm battens behaves quite differently from the same absorber glued flat.
- **Below about 100 cubic metres the low-frequency behaviour is a handful of discrete modes**, not a statistical field, and no model of this kind describes it.
- **The critical distance is a statistical boundary, not a wall.** Early reflections arriving within a few milliseconds of the direct sound behave differently from the late diffuse field, and a first reflection off a nearby table is not modelled here at all — it is often the thing that makes a close microphone sound wrong.
- **Distance factors assume the source is on-axis** and the diffuse field is genuinely diffuse. A shotgun aimed slightly off, or used in a small room where its interference tube does not work below a few hundred hertz, will not deliver its 2.5.
- **Nothing here models noise**, and a room can be perfectly dry and still unusable because of ventilation, traffic or a projector fan.
- Nothing here reaches the network, reads a file, or listens to anything.

## API

`POST https://api.skillsafe.ai/v1/app-api/run` with a bearer token from
https://acoustic-desk.skillsafe.ai/tokens.html. The body IS the input object — there is no
`input` wrapper and no `X-App-Slug` header. `task` is required and must be one of plan, check, distance, treatment, deliver. `POST /estimate` is free and validates the same body.
Full documentation at https://acoustic-desk.skillsafe.ai/api.html.

## Provenance

Lanes derived from the `openai-whisper` skill in https://github.com/steipete/clawdis.
The arithmetic, thresholds, sheet grammar and findings are this app's own.
Not affiliated with or endorsed by the authors of that repository.