difference between linear and exponential applications

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jimmyedgar
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difference between linear and exponential applications

Post by jimmyedgar » Tue Feb 07, 2012 1:36 pm

hi there,

i know the definition of the terms, but searching the forum i didn't find any clear definitions. especially with FM.

i realize exponential is a sharper and fast curve while log and linear are longer and straight.

how does this also apply to CV/VCAs? one is more appropriate for CV and the other for audio. How does this also play into FM?

thnx

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Post by vasculator » Tue Feb 07, 2012 1:45 pm

Valhalla DSP explains it very well here: http://www.kvraudio.com/forum/viewtopic.php?p=4419694

In short, linear will not typically sound as extreme/deep as exponential but you have the capability to allow the modulated sound to track pitch properly on a scale.

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Post by jimmyedgar » Tue Feb 07, 2012 1:51 pm

from the link:

"Why does linear, Chowning FM sound better than octave/note based FM?

Most synthesizers use linear FM, in other words the modulator changes the frequency by the same number above and below the the operator level, for example 440hz +/- 200hz.

it would seem like it makes more sense to modulate the operator by the same amount of notes above and below its set frequency, for example 440 +440/-220(+12 notes/-12 notes)

both versions have stable side bands, except exponential frequency sounds like the octave timber climbs exponentially -too high and too fast- even though the notes stay on tune.

As far as I understand, if you see a linear FM wave in an oscilloscope, the waveform changes slowly on each note, so logically it should not scale well across the keyboard, but if you use exponential, then the waveform stays the same all the way across the keyboard, just getting faster and faster, so why does it not sound better?

It would make sense to me that linear FM would be less stable because the amount of frequency modulation relative to the ratio of the notes does not follow the scale of the octave. In other words, at the low notes 200hz is the same as one octave, and on the high notes it's the same as one semi-tone.

Maybe I didn't understand it right-if you use a ratio of 1/2, that means that the modulator is always one octave different to the operator.

I have been told that the human ear interprets higher sounds as being louder than the ones, and that is related to balancing FM."
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"Many analog synthesizers used exponential FM: Minimoog, Prophet-5, Octave Cat, ARP Odyssey, most modular synths. The main problem with exponential FM is, as you increase the FM index, the perceived fundamental of the pitch shifts. Bernie Hutchins wrote a good explanation of why this happens in Electronotes, but I forget what it is. So, if you set up a simple 2-oscillator carrier/modulator pair with exponential FM oscillators, the pitch of the note would change as the index varies. It's a cool sound, but it doesn't get you that classic FM sound.

For a monosynth, exponential FM can be fun, assuming you have enough time to tweak the patch to your liking. Changing the waveshape of the modulator will change the perceived fundamental pitch. The Minimoog used the modulation wheel to control FM, so any jostling of this would change the pitch. As far as poly synths, the slight differences between the VCAs used for oscillator levels for FM would result in pitch differences between voices. On my (long since departed) Prophet-5, it was near impossible to create a patch with high FM indices and be able to play a chord that was in tune.

As far as your question about the ratio between carrier and oscillator in linear FM, it is usually represented as a pitch ratio. So, if you have a 2:1 ratio between modulator and carrier, the modulator will always be 1 octave above the carrier. This is how you get stable pitches for different notes. "

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Post by jimmyedgar » Tue Feb 07, 2012 1:54 pm

ok, that makes a bit more sense... but could someone explain to me setting up a patch with linear and exponential FM?

where in the patch does this differentiate? obviously i would assume from the 1v/o CV. or is this somehow related to attenuation of the FM (or thats index right?)

is it the difference between tracking your FM carrier or not? linear being stable pitch and exponential being 1v/oct?

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Post by vasculator » Tue Feb 07, 2012 1:56 pm

yup. kind of necessary for pitched FM. also helps to have linear VCAs so you can control the amount of modulation in a linear fm patch in a linear fashion.

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Post by vasculator » Tue Feb 07, 2012 1:58 pm

jimmyedgar wrote:ok, that makes a bit more sense... but could someone explain to me setting up a patch with linear and exponential FM?

where in the patch does this differentiate? obviously i would assume from the 1v/o CV. or is this somehow related to attenuation of the FM (or thats index right?)

is it the difference between tracking your FM carrier or not? linear being stable pitch and exponential being 1v/oct?
exactly it allows the FM carrier to track. linear maintains the stable pitch. basically 1v/oct multed into the carrier and modulator. waveform output (typically sine/tri) of the modulator into the carrier's linear FM input. you can then make that entire tone actually track depending on how many octaves the oscillator itself will track.

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Post by jimmyedgar » Tue Feb 07, 2012 2:00 pm

ok after reading i get it a bit more...

if i was to use maths to attenuate my 1v/o signal, would that be the equivalent to linear fm? or would i have to use a module thats simply adds a specific number to the cv signal.. I'm not sure if maths channel 2-3 would do that, or if its scaled

what sort of utility module would allow me to choose what type of fm i am utilizing?

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Post by vasculator » Tue Feb 07, 2012 2:04 pm

jimmyedgar wrote:ok after reading i get it a bit more...

if i was to use maths to attenuate my 1v/o signal, would that be the equivalent to linear fm? or would i have to use a module thats simply adds a specific number to the cv signal.. I'm not sure if maths channel 2-3 would do that, or if its scaled

what sort of utility module would allow me to choose what type of fm i am utilizing?
you can only do it if your osc has a linear fm input. all osc i've seen seem to have exponential ins but some like the z3k, antiosc and vcob have both. you don't necessarily need to attenuate your 1v/oct signal. it all depends. but yeah any quantized 1v/oct source can be attenuated to hit different areas of the "keyboard" basically. if you are using a midi to cv converter you definitely don't want to attenuate the output if you are looking for a 1:1 hit C on your keyboard/computer and get C on an osc. i'm actually not sure if maths 2/3 are linear/exponential or otherwise. some vcas that use the THAT corp chip are kind of linear and expontential. that's one of the reasons i sold my hexvca. i needed more linear vcas and got the uvca instead. but any linear attenuator will let you kind of dial in the amount of that 1v/oct without screwing up the initial source pitches in theory.

this also opens up the rabbit hole of how well your oscillators are calibrated and how many octaves they will track. z3000 tracks the best in my system. i need to calibrate my vcob it's way out of tune.

getting the free gtune vst helped me a lot.
Last edited by vasculator on Tue Feb 07, 2012 2:07 pm, edited 1 time in total.

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Post by jimmyedgar » Tue Feb 07, 2012 2:06 pm

so a linear via would basically allow you to route your FM and the attenuation from the linear VCA would be the "pitch" of your linear FM?

otherwise, the 1v/oct multi going through the maths scale knob would be the "pitch" of the exponential FM?

is this correct?

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Post by jimmyedgar » Tue Feb 07, 2012 2:07 pm

vasculator wrote:
jimmyedgar wrote:ok after reading i get it a bit more...

if i was to use maths to attenuate my 1v/o signal, would that be the equivalent to linear fm? or would i have to use a module thats simply adds a specific number to the cv signal.. I'm not sure if maths channel 2-3 would do that, or if its scaled

what sort of utility module would allow me to choose what type of fm i am utilizing?
you can only do it if your osc has a linear fm input. all osc i've seen seem to have exponential ins but some like the z3k, antiosc and vcob have both. you don't necessarily need to attenuate your 1v/oct signal. it all depends. but yeah any quantized 1v/oct source can be attenuated to hit different areas of the "keyboard" basically. if you are using a midi to cv converter you definitely don't want to attenuate the output if you are looking for a 1:1 hit C on your keyboard/computer and get C on an osc. i'm actually not sure if maths 2/3 are linear/exponential or otherwise. some vcas that use the THAT corp chip are kind of linear and expontential. that's one of the reasons i sold my hexvca. i needed more linear vcas and got the uvca instead. but any linear attenuator will let you kind of dial in the amount of that 1v/oct without screwing up the initial source pitches in theory.

this also opens up the rabbit hole of how well your oscillators are calibrated and how many octaves they will track. z3000 tracks the best in my system. i need to calibrate my vcob it's way out of tune.

getting the free gtune vst helped me a lot.
thnx a lot, this is great information .. more reason why i need an afg and z3000

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Post by vasculator » Tue Feb 07, 2012 2:09 pm

jimmyedgar wrote:so a linear via would basically allow you to route your FM and the attenuation from the linear VCA would be the "pitch" of your linear FM?

otherwise, the 1v/oct multi going through the maths scale knob would be the "pitch" of the exponential FM?

is this correct?
the linear vca just gets you dynamic FM or amount over the amount of FM. some oscillators don't have an attenuator on their linear FM input so it's always 100% "wet". you don't even need a vca just an attenuator to control the amount. the linear vca is fun when you start to modulate the wet/dry of the FM signal. (think sync'd lfo into the linear vca cv input so your FM wet/dry amount is changing but everything stays in pitch).

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Post by vasculator » Tue Feb 07, 2012 2:11 pm

jimmyedgar wrote: thnx a lot, this is great information .. more reason why i need an afg and z3000
no problem. it was one of those 'a ha!' moments for me when i started getting into modulars. opens up a different kind of patching/pitching. all of a sudden i needed more linear vcas and vcos.

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Post by jimmyedgar » Tue Feb 07, 2012 2:17 pm

i guess a fundamental difference, which is important is knowing whether your VCA is adding/subtracting and even amount, or scaling your signal...

i image adding or subtracting would be the best in both audio and cv cases...

here is an image i made... hopefully its accurate analogy
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Post by qu.one » Tue Feb 07, 2012 2:26 pm

cwejman VCO-6 also has both types of FM inputs.
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Post by numan7 » Tue Feb 07, 2012 2:29 pm

Another "application" besides audio-rate FM is.... It's very nice using linear VCA to mix Control Voltages!

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Post by cv slime 800 » Tue Feb 07, 2012 3:00 pm

qu.one wrote:cwejman VCO-6 also has both types of FM inputs.
And the Bubblesound uLFO allows you to switch between the 2 FM modes which is helpful for hearing the difference.

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Post by daverj » Tue Feb 07, 2012 3:03 pm

jimmyedgar wrote:i guess a fundamental difference, which is important is knowing whether your VCA is adding/subtracting and even amount, or scaling your signal...

i image adding or subtracting would be the best in both audio and cv cases...

here is an image i made... hopefully its accurate analogy
What you are calling linear attenuation isn't attenuation. It is biasing. Attenuation adjusts the scale of a signal. Biasing adds or subtracts a fixed DC amount.

At a static setting you can't tell the difference between linear and exponential attenuation. You can only tell by comparing the levels at various settings, or in the case of a VCA, as a sweep of gain settings.

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Post by jimmyedgar » Tue Feb 07, 2012 4:23 pm

daverj wrote:
jimmyedgar wrote:i guess a fundamental difference, which is important is knowing whether your VCA is adding/subtracting and even amount, or scaling your signal...

i image adding or subtracting would be the best in both audio and cv cases...

here is an image i made... hopefully its accurate analogy
What you are calling linear attenuation isn't attenuation. It is biasing. Attenuation adjusts the scale of a signal. Biasing adds or subtracts a fixed DC amount.

At a static setting you can't tell the difference between linear and exponential attenuation. You can only tell by comparing the levels at various settings, or in the case of a VCA, as a sweep of gain settings.
yes you are correct, ok you cleared it up for me. thats what i was missing

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Post by Navs » Wed Feb 08, 2012 3:19 pm

I posted the attached file in another thread a while back. It shows three types of audio FM IIRC: lin, thru-zero lin & exponential. Linear is what you want for tonal, or playable, dynamic depth FM.

I tried Bernie Hutchins' workaround for dynamic exponential FM in December:

http://navsmodularlab.blogspot.com/2011 ... patch.html

The audio players are not working, so here are the direct links:

(bernie 1) https://www.sugarsync.com/pf/D6215934_0627191_16554
(bernie 2) https://www.sugarsync.com/pf/D6215934_0627191_16552

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Post by Dr. Sketch-n-Etch » Wed Feb 08, 2012 10:25 pm

jimmyedgar wrote:i guess a fundamental difference, which is important is knowing whether your VCA is adding/subtracting and even amount, or scaling your signal...

i image adding or subtracting would be the best in both audio and cv cases...

here is an image i made... hopefully its accurate analogy
This isn't right. What you've shown here for linear attenuation is just dc level shifting. What you've shown for exponential attenuation is attenuation but with a constant lower dc voltage (which isn't what you get with attenuation).

I'll draw something up and post it here a bit later to demonstrate the two.

Linear FM and Expo FM are different things again.
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Post by smcumber » Wed Jun 18, 2014 9:21 am

Topping this thread because I am considering purchasing a few Pittsburgh Modular Dual VCA's, which are linear.

For those of you with experience in Linear vs. Exponential, would you say for practical purposes there is a huge difference to the ear?

I find it interesting that Pittsburgh Modular does not offer exponential VCA's at all, and their pre-built systems are all Linear VCA's (thus you would use them for the audio path). There has to be some people that are fine with using Linear for audio.

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Post by daverj » Wed Jun 18, 2014 2:35 pm

There are many ways of using VCAs, both for audio and for CV. Remember that the "curve" is a combination of the type of control the VCA expects and the type of CV that you send to it. So a linear VCA, when sent a CV that is exponentially changing, acts about the same as an exponential VCA sent a linear control voltage.

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Post by smcumber » Wed Jun 18, 2014 2:42 pm

That makes sense. There seems to be a lot of hullabaloo around using exponential VCAs for audio and linear VCAs for CV but I do get the impression like you say that there are creative ways around these things.

Also, is the guy who started this thread Jimmy Edgar, like the electronic artist? If so, mad props dude!!!!!!!!

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Post by Epignosis567 » Tue Feb 03, 2015 10:00 am

I also am looking at Pittsburgh modulars dual vca and I'm surprised that they are only offered as a linear VCA. Can someone explain whether or not this would be compatible with the tip top z4000 envelope generator? I understand that whether or not the VCA is linear or exponential is just as important as whether or not the signal you're sending to it is linear or exponential. I would be using the VCA for audio by the way. So isn't the real question whether or not the envelope is sending a linear or exponential signal? Someone really needs to put together a beginners guide for this stuff. All I am trying to figure out is whether or not the Pittsburgh dual VCA is appropriate for my applications...

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Post by Mort Rouge » Tue Feb 03, 2015 10:07 am

Epignosis567 wrote:I also am looking at Pittsburgh modulars dual vca and I'm surprised that they are only offered as a linear VCA. Can someone explain whether or not this would be compatible with the tip top z4000 envelope generator? I understand that whether or not the VCA is linear or exponential is just as important as whether or not the signal you're sending to it is linear or exponential. I would be using the VCA for audio by the way. So isn't the real question whether or not the envelope is sending a linear or exponential signal? Someone really needs to put together a beginners guide for this stuff. All I am trying to figure out is whether or not the Pittsburgh dual VCA is appropriate for my applications...
Nope. Sending an exponential envelope into a linear VCA is often sufficient. It has been a fashion to have exponential VCAs for audio, since the effect will be more "organic" (ha ... ha...) when you send linear CV to it (e.g. a triangle wave). However, sending an exponential CV into an exponential VCA will further make the curve steep. Using a sine wave as a CV source will not be very even, thus.

Of course, it's a matter of taste. Some use exponential VCAs and exponential envelopes to create extremely plucky sounds. But a good rule is:

When in doubt, use linear VCA.
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