Speed knob scaling formula?

Reid115

https://vi-control.net/community/threads/what-is-the-formula-for-this.3978/

https://www.native-instruments.com/forum/threads/calling-nicki-marinic-or-other-scripters-good-at-math.37073/#post-233780

These are the only real discussions I could find on this topic, and they're from 2006. Basically I need the percent value (0-800%) that's set with the speed knob in TM2 mode. I need this value because I need to determine how long it takes for a part of my sample to play. Approximations won't work for my needs -- even a few milliseconds of error could be a problem. What is the current best solution for this? Has anyone ever figured out the formula(s)? If not, is the lookup table given in that forum post the furthest anyone has gotten? I figured I could have my speed knob snap to whole percent values and then look up the 0-1000k value to send to the real speed knob. The lookup table in those threads starts jumping by 10 at 150.

https://pastebin.com/raw/MSXs19gm

EvilDragon

If you use SublimeKSP, you can use these two conversion functions, for engine par to real-world value, and vice versa:

   define int(x) := real_to_int(x)
   define real(x) := int_to_real(x)

   function math.log2(value) -> return
       return := log(value) / log(2.0)
   end function

   function math.cbrt(value) -> return
       return := pow(value, 1.0 / 3.0)
   end function

   {
       USAGE
       E2V -> Engine Parameter to Real-World
       V2E -> Real-World to Engine Parameter

       ARGS
       x - input number for equation.

       INFO
       Fundamental equation: speed = 2^[K * (X^3 + 1) + A, K = 2.807354922, A = 7.380821784
       E2V output and V2E input: 0.0% to 800.0% (scaled by 10)
       Accepts and returns only integers!
   }
   define E2V.SPEED_BASE(ep) := int(round(pow(2.0, 2.807354922 * (pow(((float(ep) - 500000.0) / 500000.0), 3.0) + 1.0) + 7.380821784) - 166.666666))
   define V2E.SIGN(ep) := ((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0) / abs(((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0))
   define V2E.SPEED_BASE(ep) := int(math.cbrt(abs((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0)) * (V2E.SIGN(ep) * 500000.0) + 500000.0)

   function E2V.speed(x) -> return
       return := E2V.SPEED_BASE(x)
   end function

   function V2E.speed(x) -> return
       return := V2E.SPEED_BASE(x)
   end function

Wolinger

@Matt @ NI knows anyone can help this guy? I never seen this before and i don't know how to help him.

Matt_NI

This is way beyond my level of expertise 😅

It's something for @EvilDragon perhaps.

EvilDragon

If you use SublimeKSP, you can use these two conversion functions, for engine par to real-world value, and vice versa:

   define int(x) := real_to_int(x)
   define real(x) := int_to_real(x)

   function math.log2(value) -> return
       return := log(value) / log(2.0)
   end function

   function math.cbrt(value) -> return
       return := pow(value, 1.0 / 3.0)
   end function

   {
       USAGE
       E2V -> Engine Parameter to Real-World
       V2E -> Real-World to Engine Parameter

       ARGS
       x - input number for equation.

       INFO
       Fundamental equation: speed = 2^[K * (X^3 + 1) + A, K = 2.807354922, A = 7.380821784
       E2V output and V2E input: 0.0% to 800.0% (scaled by 10)
       Accepts and returns only integers!
   }
   define E2V.SPEED_BASE(ep) := int(round(pow(2.0, 2.807354922 * (pow(((float(ep) - 500000.0) / 500000.0), 3.0) + 1.0) + 7.380821784) - 166.666666))
   define V2E.SIGN(ep) := ((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0) / abs(((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0))
   define V2E.SPEED_BASE(ep) := int(math.cbrt(abs((math.log2(float(ep) + 166.66666) - 7.380821784) / 2.807354922 - 1.0)) * (V2E.SIGN(ep) * 500000.0) + 500000.0)

   function E2V.speed(x) -> return
       return := E2V.SPEED_BASE(x)
   end function

   function V2E.speed(x) -> return
       return := V2E.SPEED_BASE(x)
   end function

Reid115

Awesome, thanks ED.