I recently worked out the formula for ACE's multiples, to figure out how to do more complicated things with them, and I thought I'd post it here in case anyone else runs into the need for it.
When the multiple has a mod source connected, the output of the multiple is:
(1-F)A + FAM + (1-G)B + GB(1-M)
where
F is the level control for inputs 1 and 2
A is the sum of inputs 1 and 2
G is the level control for inputs 3 and 4
B is the sum of inputs 3 and 4
M is the mod source
Here I'm treating F as ranging from 0 to 1, whereas it is actually labelled 0 to 100 in ACE; ditto for G. I.e., it is labeled as percentage but the formula above treats it as a fraction.
If you attach a bipolar signal (-1 to 1) to mod, then to use that signal to "select" between two input signals, the manual suggests you attach the one of the signals to both inputs 1 and 2, and the other signal to input 3, and turn F to 50 (0.5) and G to 100 (1.0). If X and Y are the two input signals being selected, then the formula above gives:
0.5*2*X + 0.5*2*X*M + (1-1)B + 1*Y*(1-M) = X*(1 + M) + Y*(1 - M)
When M = -1, this equals 2Y, and when M = 1, it equals 2X. So really you're selecting between X and Y and doubling the amplitude.
(Urs, does this look right?)
-Luddy
equations for ACE multiples
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- KVRAF
- 2628 posts since 30 Mar, 2007 from In and Out Burger
what...the f**k
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- KVRist
- 420 posts since 29 May, 2005 from Central Ohio, USA
Do you write owners manuals for Cycling74 products (Max in particular)?
Fig Newton: The force required to accelerate a fig 39.37 inches per sec.
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- KVRer
- Topic Starter
- 15 posts since 29 Jul, 2009
haha, c'mon you guys, be nice.JackD wrote:Do you write owners manuals for Cycling74 products (Max in particular)?
If you don't care what the multiples actually do, in detail, then this stuff doesn't matter.
Here's the thing: the multiple was really designed for a unipolar mod signal, like the ramp or an envelope or a controller. But ACE's LFOs (and audio signals) are bipolar. So the question is, what does the multiple do when you feed bipolar signals into the mod input? The manual describes one case -- crossfading between two signals with a bipolar mod input -- but it just gives the answer and doesn't explain why it works or how to do other stuff with a bipolar mod signals. The only way to work this out is to understand the actual signal processing algorithm carried out by the multiple, so that's what I've written down (so far as I've been able to make it out).
Even with this formula in hand, it is a little mind-bending to figure out how it's going to behave with bipolar inputs.
One hint for anyone trying to read the equations: audio signals are assumed to range from -1 to 1 in the forumla.
-Luddy
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- KVRian
- 787 posts since 15 Nov, 2005 from sweden
I am trying very hard to get my head around what you are explaining here Luddy. PLEASE try one more time to lay this out for us. I am getting lost in the way you are wording your method. I REALLY would like to understand what you are getting at. Perhaps take it in segments.
I get the part about the inputs and the different polarity of signals (and how they look on a graph), but I do not know first off why You use 1 and 0 to represent these values and furthermore I do not understand how you arrived at that first equation to represent the behaviour of the multiple in the first place. How/Where did you get that out of the signal from the multiple? If you tell us where you've been, perhaps it will help us understand better where you are going with your nice explanation here. I think we are OK smart guys here but what you have is a case of you being immersed in this subject for some days and a lot of us have not put a thought to it until just now. I think a lot of us were using our ears and basic multiple knowledge before. I think given the ability to understand what you are talking about however we could improve upon existing designs and better predict the multiples' signals.. Thanks in advance, seriously. I am extremely curious!
I get the part about the inputs and the different polarity of signals (and how they look on a graph), but I do not know first off why You use 1 and 0 to represent these values and furthermore I do not understand how you arrived at that first equation to represent the behaviour of the multiple in the first place. How/Where did you get that out of the signal from the multiple? If you tell us where you've been, perhaps it will help us understand better where you are going with your nice explanation here. I think we are OK smart guys here but what you have is a case of you being immersed in this subject for some days and a lot of us have not put a thought to it until just now. I think a lot of us were using our ears and basic multiple knowledge before. I think given the ability to understand what you are talking about however we could improve upon existing designs and better predict the multiples' signals.. Thanks in advance, seriously. I am extremely curious!
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- KVRer
- Topic Starter
- 15 posts since 29 Jul, 2009
Hi,
OK, I'll be glad to try to explain more.
First, you might want to read the relevant section of the manual concerning the multiples, because they actually have some equations, for ring modulation and amplitude modulation. The important bit is this:
So far so good?
Now, the mod signal in the middle of the multiply is like an automated fader. In other words, the mod signal acts as if it it turning the fader up and down as fast as the mod signal is moving. This means that the mod signal is simply being multiplied by the input signal, just as the fader would be. If the mod signal is moving at audio rates, i.e., it is a bona fide audio signal, then the result is ring modulation, multiplying the mod signal by the input signal. That's what the manual says about the left inputs and the mod signal. The right inputs behave a little differently, because the mod signal is "inverted", i.e., it is as if turning the mod signal down turns the fader up and vice versa.
OK, so that's all fine as far as it goes. But when the mod signal is bipolar, i.e., swinging from -1 to+1, then "inverting" it by subtracting it from 1 doesn't really invert it at all. After all, 1 - -1 = 2. So, something more complicated is going on in that case. The equations I wrote down try to give the actual arithmetic of the whole multiplier, so that it's easier to see what's going on in the general case, i.e., in the case where the mod signal is bipolar.
Let me know if that makes sense. I can explain more if the original equations still don't make sense.
hth,
-Luddy
OK, I'll be glad to try to explain more.
First, you might want to read the relevant section of the manual concerning the multiples, because they actually have some equations, for ring modulation and amplitude modulation. The important bit is this:
A fader, when implemented digitally, simply multiplies the input signal by a value from 0 to 1. This makes sense right? If the fader is pulled all the way down, it is the same as multiplying the signal by 0, i.e., it turns it off completely. If the fader is pulled all the way up, it is the same as multiplying the signal by 1, i.e., it lets the full value of the signal through. (I'm talking about a fader that doesn't have a gain greater than unity, i.e., a knob that can attenuate but not amplify.)ring modulation could be written as y = a x mod, amplitude modulation is normally y = a x (1 + mod). However, amplitude modulation in ACE's multiples is defined as y = a x (1 - mod)
So far so good?
Now, the mod signal in the middle of the multiply is like an automated fader. In other words, the mod signal acts as if it it turning the fader up and down as fast as the mod signal is moving. This means that the mod signal is simply being multiplied by the input signal, just as the fader would be. If the mod signal is moving at audio rates, i.e., it is a bona fide audio signal, then the result is ring modulation, multiplying the mod signal by the input signal. That's what the manual says about the left inputs and the mod signal. The right inputs behave a little differently, because the mod signal is "inverted", i.e., it is as if turning the mod signal down turns the fader up and vice versa.
OK, so that's all fine as far as it goes. But when the mod signal is bipolar, i.e., swinging from -1 to+1, then "inverting" it by subtracting it from 1 doesn't really invert it at all. After all, 1 - -1 = 2. So, something more complicated is going on in that case. The equations I wrote down try to give the actual arithmetic of the whole multiplier, so that it's easier to see what's going on in the general case, i.e., in the case where the mod signal is bipolar.
Let me know if that makes sense. I can explain more if the original equations still don't make sense.
Well, I've spent a lot of time in Chinese night clubs this past year.If you tell us where you've been, perhaps it will help us understand better where you are going with your nice explanation here.
hth,
-Luddy
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- KVRian
- 528 posts since 2 Jan, 2007
Luddy,
Thanks for your persistence in trying to explain
as I have a much clearer idea of what is going
on with the multiples now. Any hints on what
"something more complicated" in relation to the
right inputs would sound like? :-)
Cheers,
Scott
Thanks for your persistence in trying to explain
as I have a much clearer idea of what is going
on with the multiples now. Any hints on what
"something more complicated" in relation to the
right inputs would sound like? :-)
Cheers,
Scott
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- KVRer
- Topic Starter
- 15 posts since 29 Jul, 2009
Hi,rexlapin wrote:Luddy,
Thanks for your persistence in trying to explain
as I have a much clearer idea of what is going
on with the multiples now. Any hints on what
"something more complicated" in relation to the
right inputs would sound like?
Cheers,
Scott
Honesty, there's no "sound" that you can ascribe to the multiples per se. If you use them in a simple configuration, then they either
1) cross-fade the inputs (if the mod source is a control signal -- 0 to 1 moving at low frequency)
2) ring modulate the left input
3) amplitude-modulate the right input
But if you attach an audio signal to mod and feed stuff into both left and right inputs and set the faders to interesting values, then ... I dunno what to call it. It does some razmatazz three-way modulation.
The equations aren't a substitute for just plugging stuff in and listening; that's the way to discover cool modulation possibilities. They're useful when you're trying to accomplish something specific and technical, like amplifying a signal or inverting the phase of a signal and adding it to the other signal or something like that.
-Luddy
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- KVRian
- 787 posts since 15 Nov, 2005 from sweden
Luddy,
I read you loud and clear now, but not because of your latest (and great) effort to explain your method.
You see, I read the ACE manual many times over some months ago (and find myself going back still on occasion) but the specifics on the multiples went right in and out of the brain (I blame my general dislike for Maths). I vaguely remembered that the ACE multiples were 'different' from traditional multiples found on modular synths etc. but I did not recall the important details of the difference (stated in the manual). I've become accustomed to what I hear when I feed the multiples different signals and pairs. I never thought twice about the mechanics.
At any rate, I just reread that portion on multiples in the manual and everything clicked on what you posted in the beginning. It is not really so advanced if one follows the explanation carefully after rereading about that characteristics of ACE's multiples once more beforehand. It now makes sense what you have arrived at for the output when modulated by given signals. That said, I never would have had the patience to sit and figure out the equation to the entire multiple. Bravo. I intend to sit down with this more and try various signal routing scenarios based your info. As one becomes more serious with the synth, it is definitely interesting to understand details such as these. Thanks for taking the time to make sure all is clear. Much appreciated
I read you loud and clear now, but not because of your latest (and great) effort to explain your method.
You see, I read the ACE manual many times over some months ago (and find myself going back still on occasion) but the specifics on the multiples went right in and out of the brain (I blame my general dislike for Maths). I vaguely remembered that the ACE multiples were 'different' from traditional multiples found on modular synths etc. but I did not recall the important details of the difference (stated in the manual). I've become accustomed to what I hear when I feed the multiples different signals and pairs. I never thought twice about the mechanics.
At any rate, I just reread that portion on multiples in the manual and everything clicked on what you posted in the beginning. It is not really so advanced if one follows the explanation carefully after rereading about that characteristics of ACE's multiples once more beforehand. It now makes sense what you have arrived at for the output when modulated by given signals. That said, I never would have had the patience to sit and figure out the equation to the entire multiple. Bravo. I intend to sit down with this more and try various signal routing scenarios based your info. As one becomes more serious with the synth, it is definitely interesting to understand details such as these. Thanks for taking the time to make sure all is clear. Much appreciated