KINSPIRATIONSoftware for the K2700Waitlist
KOACH · FUNs · Level 5 · Hidden LFOs · Lesson 10 of 14

ay+b

recursions= y = a × y + b, every 20 ms

A recursive generator: the last output times a, plus b. Like the other y-equations it can cycle like an LFO or turn chaotic, depending on the inputs.

SEE IT MOVE

SCOPE · LAST 2 S
THE WAVE · LAST 8 S
a0.00
b0.00
OUTPUT0.00

Computed in your browser with KINSPIRATION's FUN engine, step by step: this FUN keeps a state, so its output depends on what came before.

WHAT TO KNOW

INPUTS

a: the feedback (ON for a ramp, 0.5..0.95 for a smooth approach); b: the step or target.

OUTPUT RANGE

−1..+1, wrapping round from +1 to −1

USE IT FOR

With a = ON a staircase sawtooth at 25 × b Hz (b 0.04: 1 Hz); with a below 1 an exponential approach to b / (1 - a), slower as a nears 1 (a 0.9, b 0.1 creeps toward 1); a negative a overshoots and settles.

WATCH OUT

Below a = 1 it settles at b / (1 − a); if that lies beyond ±1 it wraps round instead of settling.

IN THE FACTORY PROGRAMS

No factory program uses it: one of the K2700's hidden tools.

HOW TO ON YOUR K2700 · 2046 Editor Template

The factory does not route ay+b to a sound on its own: set one up on 2046 Editor Template and hear it on the pitch.

  1. In Program mode choose 2046 Editor Template, a plain one-layer program to build on (KEYPAD, 2046, ENTER).

    Program mode with 2046 Editor Template

  2. Press EDIT, then MORE and DSP MOD. On the Pitch row set Source 1 to FUN2 and its Depth to 1200 ct: FUN2's result, −1 to +1, now bends the pitch up to an octave either way.

    The DSP MOD page of 2046 Editor Template, layer 1, the cursor on Depth (1200 ct)

  3. MORE, then LFO+. On the FUN2 row set Input a to ON and Input b to 0.04.

    The LFO+ page of 2046 Editor Template, layer 1, the cursor on Input b (0.04)

  4. Move to Function and turn the Alpha Wheel to ay+b.

    The LFO+ page of 2046 Editor Template, layer 1, the cursor on Function (ay+b)

  5. Hold a note: every 20 ms y grows by 0.04 and wraps round past +1: a stepped sawtooth at 1 Hz, 25 × 0.04.

  6. Press EXIT and answer NO to leave the factory program as it was, or SAVE to keep your version on a USER ID.