# Downmix Desk

> A downmix is a sum, and a sum can clip. Lo = L + clev x C + slev x Ls, and with the
> standard -3 dB coefficients that is a gain of 2.416 - so three channels at -6 dBFS fold to
> +1.66 dBFS while every source meter reads comfortably under zero.

https://downmix-desk.skillsafe.ai/

## What it is

Five lanes over one multichannel mix - a level per channel and the coefficient sets it will
be folded through - plus a **free browser-side engine** that sums every fold. The engine costs
nothing and needs no account. Writing the report costs credits.

## The arithmetic

    the fold          Lo = L + clev*C + slev*Ls
    fold gain         1 + 10^(clev/20) + 10^(slev/20)
    coherent sum      the arithmetic sum of the contributions   <- worst case
    independent sum   their root-sum-square                     <- average case
    cancellation      1 - 10^(slev/20)                          <- an inverted surround
    centre power sum  10*log10(2 * 10^(clev/10))                <- zero only at clev = -3

## Figures that are exact, and surprising

- The default coefficients apply a gain of **2.416, which is +7.66 dB**, to the sum of L, C
  and Ls. Three channels at **-6 dBFS fold to +1.66 dBFS** and clip.
- **Six of the nine standard coefficient sets clip that bed.** The only survivors are the
  three that drop the surrounds entirely - and nobody chooses which set a television uses.
- **The channel that breaks it is not the loudest one.** L arrives at unity; C and Ls each
  arrive 3 dB down. It is the two attenuated ones together that take a -6 dB front over.
- **The centre is copied into both outputs, not routed.** At clev -3 it reads -3.00 dB on
  each meter, its power sum is 0.01 dB and its coherent sum is +3.02 dB. Three different
  numbers about one channel, and quoting the wrong one starts the argument. (The exactly
  power-preserving coefficient is -3.0103 dB; the standard -3 is its rounding, which is why
  the power sum is 0.01 rather than 0.)
- **Only -3 dB preserves that power.** At -6 dB the split loses 2.99 dB, so the dialogue
  genuinely is quieter in that fold and nothing upstream shows it.
- **Phase decides whether the surrounds arrive at all.** Correlated they add **4.65 dB**;
  inverted they leave **-10.69 dB** of themselves. On a -6 dBFS bed the coherent and inverted
  sums are **15.28 dB apart** - +1.66 against -13.62 - with identical meter readings.
- **Coherent and independent are 4.65 dB apart** on three channels: +1.66 against -2.98. That
  is the whole range of uncertainty about what a given mix will actually do.
- **The LFE is absent from the fold, not attenuated.** The default coefficient is minus
  infinity, and playback convention gives that channel +10 dB, so what is in it was never
  quiet - it simply does not reach a stereo listener.

## The sheet

    MIX
    name        | the trailer bed
    L           | -6              peak level in dBFS
    R           | -6
    C           | -6
    Ls          | -6
    Rs          | -6
    LFE         | -4
    correlation | 1               1 identical, 0 independent, -1 inverted

    FOLDS
    f1 | -3 | -3  | the default decoder
    f2 | -3 | -6  | a conservative set
    f3 | -6 | off | surrounds dropped entirely

A fold row is `id | clev | slev | description`. `off` in either position drops that channel
from the fold. Any channel may be omitted, and an omitted channel contributes nothing rather
than contributing silence at some assumed level.

**Without `correlation` the page assumes 1** - the worst case and the honest default - and
says that it assumed. A coefficient outside what a decoder ships is **refused rather than
used**, because no fold-down amplifies a channel on its way down.

## Lanes

- `plan` - decide what the fold has to survive, before the mix is signed off
- `check` - what every fold actually sums to (primary)
- `sum` - where the headroom went, channel by channel
- `phase` - whether the surrounds arrive at all
- `deliver` - as it is, fix in the fold, or reopen the mix

## What it cannot do

It is peak arithmetic on stated levels and it **has not heard the mix**. Peak level is not
loudness: two mixes with identical peaks can be ten units apart in loudness, and nothing here
models that. The correlation is one number standing in for a relationship that varies with
frequency and with time - real material is coherent in some bands and independent in others,
and a mix whose surrounds hold both a decorrelated reverb and a copied effect cannot be
described by a single figure. The coherent sum assumes the peaks coincide, which is what
makes it the worst case rather than the expected one. And nothing here knows what a particular
decoder does: the sets modelled are the standard ones, and a device may use its own, apply a
limiter afterwards, or turn the whole thing down instead of clipping it.

## Links

- App: https://downmix-desk.skillsafe.ai/
- API: https://downmix-desk.skillsafe.ai/api.html
- Source skill: https://github.com/heygen-com/hyperframes (not affiliated or endorsed)