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KOACH · FUNs · Level 5 · Hidden LFOs · Lesson 9 of 14

a(y+b)

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

A recursive generator: the last output plus b, times a. 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); b: the step.

OUTPUT RANGE

−1..+1, wrapping round from +1 to −1

USE IT FOR

With a = ON a rising sawtooth at 25 × b Hz in 20 ms steps (b 0.2: 5 Hz); with a below 1 it settles at a × b / (1 - a) (a 0.5, b 0.5: 0.5).

WATCH OUT

Past +1 it wraps round to −1 rather than stopping: that wrap is what makes a ramp of it.

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 a(y+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 0.95 and Input b to 0.06.

    The LFO+ page of 2046 Editor Template, layer 1, the cursor on Input b (0.06)

  4. Move to Function and turn the Alpha Wheel to a(y+b).

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

  5. Hold a note: each 20 ms step adds a little less as y grows, a ramp that bends over near the top, then wraps round to the bottom and climbs again.

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