Understanding SPD & MULT in LFO: Math, Proportions, and Two Useful Shortcuts

[igors48]

I decided to do some Math around the SPD and MULT parameters of the LFO to finally resolve all my questions on this topic. This might also be useful to someone else, as SPD & MULT are not the most intuitive LFO control parameters compared to other synthesizers.

I used this post as a starting point.
So, the LFO full waveform is divided into 128 parts.
The product of SPD * MULT determines how many of these parts should fit into one bar. How can this be used?

Let’s say we need the LFO to complete one full cycle per X/Y note. In this case, SPD and MULT can be calculated using a proportion.

Math#1

This brings us to the first shortcut: if you set MULT to BPM128, then SPD will be equal to the denominator of the 1/Y note. For example, to get a full LFO cycle in 1/8 note, you can set MULT to BPM128 and SPD to 8.

How to choose SPD and MULT if we need the LFO to complete a full cycle in a given time or at a given frequency?

First, we need to calculate how long one bar lasts at the given BPM.

Math#2

Full cycle at a given frequency F
In other words, we need to fit 128 parts F times into 1000 milliseconds.

Math#3

For any BPM

For 120 BPM

Here, we can see the second shortcut: if we set MULT to 256, then SPD will be equal to the frequency.

Full cycle in a given time T
In other words, we need to fit 128 parts into T milliseconds.

Math#4

For any BPM

For 120 BPM

That’s it. Hope it will be useful.

UPDATE

If you need the LFO to complete a full cycle in STEPs steps, you can set MULT to BPM32 and calculate SPD using the formula

[bibenu]

Appreciate the effort that you have put in (I do, really) but honestly, I’d prefer it if elektron did something like this across the board.

@bigdave

the LFO length in steps somewhere on the screen. Please don’t make me keep looking at a paper table of numbers.

[Phillip]

I’m too stupid to understand any of this

[igors48]

Skip the Math!
You have two shortcuts

[Humanprogram]

Hm, for rhythm-based LFOs, I just use speed at 48.00 (default) and 64 (okay, 63.99) with BPM-based mults. The mult is the note division value, so 8 x 48 = dotted 8th, 8 x 64 = 8th, 2 x 48 = dotted half, 2 x 64 = half, etc etc. (Yes, these are values for half-cycle LFOs, but it’s easy to remember.) Longer LFOs divide speed down from 1 x 64 as a whole note, so 2 bars is 1 x 32, 4 bars is 1 x 16, etc…

What I’m curious about here, though, is frequency: If we’re looking at audio-rate LFOs, do the maths above make an easy way to dial in a specific frequency?

[igors48]

@Humanprogram

What I’m curious about here, though, is frequency: If we’re looking at audio-rate LFOs, do the maths above make an easy way to dial in a specific frequency?

I think yes.

Just use this formula from Full cycle at a given frequency F with some big enough MULT.

For example, LFO @248Hz:

SPD = 256 * 248 / 1024 = 62

So MULT: 1k, SPD: 62 (or MULT: 2k, SPD: 31) should produce 248Hz LFO

You can create a Google Spreadsheet with needed formulas like I did.
For me it the easiest way to calculate any needed SPD/MULT pairs.