Re: gain-mapping - was Re: OSC next

1260 is doable that´s no problem. Problematic it get´s when floating point
needs to be done but that is the problem with all micro controllers.



2016-05-14 14:40 GMT+02:00 Robin Gareus <[email protected]>:

> On 05/13/2016 08:53 PM, Len Ovens wrote:
> > On Fri, 13 May 2016, Melanie Bernkopf wrote:
> >
> >> yes I can only give a full ack to this it is just mimic of the
> >> position and not about gain or DB.
>
> At first thought, I think this is not a good idea.
>
> It would limit the control surface to the same fader-deflection which
> Ardour chose and does not expose any actual relevant numerics.
>
> But the lack of a well defined "no gain" 0dB point is the most obvious
> flaw.
>
>
>
> Internally Ardour uses a floating point gain-factor (coefficient) for
> both: state and processing. Resetting a fader sets it exactly to 1.f and
> the control has a detent (in the GUI) because it is impossible to
> otherwise reach this point (With integer ratios 41 bits of precision are
> required for the power law to result in exactly 1.f).
>
> > Yes and no. With either gain or dB I can remotely say I want x amount of
> > gain. It is easy to put a button in that zeros a fader with either dB
> > (send 0) or gain (send 1.0). It is impossible to do that with 1023 INT.
> > 800 comes closest at 0.006990539841353893 dB. (Using two surfaces one
> > with int1024 and the other with dB, setting position to 799, 800 or 801
> > and seeing what Ardour sends to the other surface)
>
> +1 for testing the whole system. That's very good practice and pretty
> much the simplest way to find out how rounding (and float
> parsing/precision) behaves.
>

> Here's the math for completeness:
>
> With fader position 0 <= p <= 1.0, Ardour calculates the gain as follows:
>
>   $g = 2^{\frac{1}{6}(-192 + 198 \sqrt[8]{p})}$ [1]
>
> The inverse of which is
>
>   $p = (\frac{1}{198} (6 \log_2(g) + 192))^8$ [2]
>
>
> At unity gain, [2] evaluates to (192/198)^8 = (32/33)^8
>
> You'll need to add a factor much much larger factor than 1024 to
> represent unity gain with an exact integer.
>
> <details>
> As you can read in the source [3], the gain/fader-position relation is
> derived from measuring a console fader. The intended range is 0..2
> (-inf, +6. dB) which is reflected in the base of the logarithm, but the
> actual range is configurable(!).
>
> The initial polynomial fit (old gain math) had a problem that inverse
> function had a large error and  f(f^{-1}(x)) was off by a few dB for
> smaller values of x. The power-function is a close approximation of it
> though.
>
> $ gnuplot
> set key horizontal top left
> set ylabel "dB"
> set xlabel "% fader"
> set samples 250
> plot[0:100][-200:6] 20 * log10 (2**((198 * (x / 100)**(.125) - 192) /
> 6)) t "Ardour fader"
>
>
> Also note that granularity of the fader position p is not fixed in
> Ardour. Fader length scales with the GUI, and the fine-grained mode is
> constrained by a gtk adjustment. Default GUI granularity is  250 *
> ui_scale (rounded to px),  hence "set samples 250" in the plot, With
> "Keyboard::GainExtraFineScaleModifier" Ardour increases granularity by
> a factor of 200 to a total of 50K steps with default GUI scaling.
> </details>
>
>
> > So with dB, I can on
> > the surface enter as text an exact gain in dB. Also, the text value on
> > the surface shows the value in dB which is much more useful to the user
> > than some number from 0 to 1023.
>
> exactly.
>
>
> However, are there any OSC controllers out there that can provide a
> power-law fader?
>
> As far as I know the answer is no. Furthermore neither log-scale (dB)
> nor linear (coefficient) are appropriate for a fader.
>
>
> One way would be to add a *new* interface specifically for OSC with the
> following properties:
>
>  - power-scale - similar to Ardour's Fader
>  - 0dB can be represented by an integer fraction with small denominator.
>  - the range is independent of Ardour's max_gain configuration
>  - relatively simple relation to dB.
>
> One candidate that fulfills these criteria is
>
>  $g = (1.26 p)^3 ; 0 \leq p \leq 126; p \in \mathbb{Z}_{\geq 0}$
>
> with x = 100 / 126 this results in a gain = 0dB
> and x = 126/126; gain ~= +6dB
>
> This could also be mapped to MIDI 0..127 with a small overshoot (1.26 *
> 127 / 126)^3 = 6.23 dB  and OSC could use 0 .. 1260  with unity at 1000.
>
>
> This interface would be available in *addition* to a dB interface (two
> in total).
>
> ciao,
> robin
>
>
>
> The equations in text (non LaTeX) are:
>
> [1] g = 2 ^ ((198 * p ^ (1/8) - 192) / 6)
>
> [2] p = ((6 * log(g) / log(2) + 192) / 198) ^ 8
>
> [3]
> https://github.com/Ardour/ardour/blob/master/libs/ardour/ardour/utils.h
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>

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