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envelopes of the non-analytic kind
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bachus



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PostPosted: Wed May 16, 2007 6:40 pm    Post subject: envelopes of the non-analytic kind Reply with quote  Mark this post and the followings unread

I'm rather late coming to the party but envelopes are the subject of my current focus of interest:
Posted Image, might have been reduced in size. Click Image to view fullscreen.
I cant' help but note that at each vertical line in the above drawing the function is non-analytic: only piecewise continuous i.e. the first derivative is undefined. Such conditions do not occur in nature. Is this an issue for anyone besides me? Has anyone considered that an issue worth addressing?

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PostPosted: Wed May 16, 2007 7:04 pm    Post subject: Re: envelopes of the non-analytic kind Reply with quote  Mark this post and the followings unread

bachus wrote:
Posted Image, might have been reduced in size. Click Image to view fullscreen.Has anyone considered that an issue worth addressing?


I'm not a mathematician. Often I mix the output from multiple envelope generators. Note that on the Aries Modular, which utilizes ADSR EGs, the VCAS' responses are continuously variable between linear and exponential.

To me, one of the major issues is that initial attack. For some attacks, the slope is ok however the peak occurs later than I want. If I create a steeper slope, then the note sounds when I want it to but with too percussive an attack. The solution is to mix the output of a second EG which has a fast attack. The result (I wish I know how to graph it here) is a slope that is "instant" up to about 50% then rises a little slower up to max.

I don't know if this answers your questions. I've gotten pretty "spoiled" with, first with the Casio eight-stage EGs, and now the Kurzweil eight-stage EGs.

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bachus



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PostPosted: Thu May 17, 2007 4:57 am    Post subject: Reply with quote  Mark this post and the followings unread

The issue that concerns me are those points where the rate of chance becomes infinite such as that illustrated by A. In the natural world (at scales where Newtonian mechanics applies) the situation illustrated by A never occurs, rather the actual situation would be as shown in B


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PostPosted: Thu May 17, 2007 7:15 am    Post subject: Reply with quote  Mark this post and the followings unread

I think that for an analog synth situation B would occur as well, being a physical system.

Don't know about the synth "calculators" though, maybe they smooth, maybe not. I've never experienced any clicks caused by discontinuities in the derivative. What does give clicks is fast rise and fall times when they do not occur at or near the zero crossing of the signal being enveloped.

Theoretically the sharp bend should add some harmonics to the signal for an infinite small amount of time I guess (??), maybe that's why it wouldn't be audible - unless you would actually take the derivative of the processed signal, I never did that ... Very Happy

Ok, that was for amplitude modulation, we can modulate more things of course with envelopes ...

When the envelope is used for FM there would be sudden changes in the speed of the frequency change, I think the ear is not able to follow those. Phase modulation would be the same thing I guess, what more do you have ...

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PostPosted: Thu May 17, 2007 10:32 am    Post subject: Reply with quote  Mark this post and the followings unread

Ah, ok...

The Aries has a lag circuit that could be utilized to turn those peaks into curves. I'll give it a try. Must admit, I have never thought about it.

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PostPosted: Thu May 17, 2007 3:59 pm    Post subject: Reply with quote  Mark this post and the followings unread

The blue envelopes are the kind of thing I'm thinking about. The question I mean to ask is if there is an aesthetic dimension here worth exploring or is it irrelevant. The the more concrete issue that drew my attention was the true suckyness of the vast majority of legatos with glissandos not achieved by real time human input of some kind. Could a solution lie here.


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PostPosted: Thu May 17, 2007 4:02 pm    Post subject: Reply with quote  Mark this post and the followings unread

Blue Hell wrote:
I think that for an analog synth situation B would occur as well, being a physical system. .


That is no doubt true. But the scales (i.e. the lengths of the radii that could be used to model the curves) would be very different between electronic systems and mechanical systems the size of musical instruments; I would think.

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PostPosted: Thu May 17, 2007 4:18 pm    Post subject: Reply with quote  Mark this post and the followings unread

More as to portamentos, it's clear that the effect has to begin before what is felt as the beginning of the next note occurs. Kevin must be the possible person to ask about this. Is that so?
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PostPosted: Thu May 17, 2007 4:31 pm    Post subject: Reply with quote  Mark this post and the followings unread

In fact it seems to me the look-ahead data would have to include the pitch of the next note. A job for Sonar's CAL Cool I'm planing to write the look-ahead data as channel data.
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PostPosted: Thu May 17, 2007 7:44 pm    Post subject: Reply with quote  Mark this post and the followings unread

You have touched upon one of the many problems with quantization.

Normally, if a note has a slow attack, the musician will play a little ahead of the beat. For most keyboard players, this kind of thing becomes pretty subconscious.

Interestingly, Wendy Carlos' solution is to combine a patch with slow envelope with another patch that has a percussive attack -- like a little "pling" or "chiff" at the start of the note.

Most sequencers allow you to shift the playback of a track forward or backward in 1ms increments. This is important -- if you sequence a track then decide to change the patch's attack speed, then you will likely need to shift the track to compensate.

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PostPosted: Fri May 18, 2007 3:04 pm    Post subject: Reply with quote  Mark this post and the followings unread

One thing is the discontinuities, another is those linear segments themselves which could be said to be slightly at odds with nature, at least a lot of the time. Using exponential segments or other forms of shaping is quite interesting, and each individual segment could use an appropriate transfer function. Of course it is not a solution for the discontinuities, but it is very interesting sound-wise. For those that use flexible software synhthesis such as Csound or Chuck, this should be easy enough to do. Modular envelopes with time modulation inputs and feedback are also fun. And one can always run the envelope through a lag generator or lowpass filter to smooth it out a bit - trying other filters too, cranking up he resonance, playing around. I have sometimes used exponential envelopes, like in the picture below.

As Jan points out, in a digital system the pointed envelope violates the sampling theorem and will result in aliasing. This lasts for such a short time tough, and is coincidental with a marked change in the sound. Thus the adverse effects of it are probably well enough masked to not bother people.

Edit: Must read more carefully - I see that Kevin has taken to his lag module already - way to go! Very Happy

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PostPosted: Fri May 18, 2007 3:53 pm    Post subject: Reply with quote  Mark this post and the followings unread

DrJustice wrote:
One thing is the discontinuities, another is those linear segments themselves which could be said to be slightly at odds with nature,...
Right, and I didn't mean to stress being "true" to nature, or to condemn such envelopes as inherently bad; only that nature exhibits an alternative to the linear and discontinuous that could provide rich aesthetic soil particularly in the context of creating compellingly phrased legatos/portamentos. I would like to stir up discussion of what generalizable parameters, solutions, instruments (VL70m etc.) cogitations, etc people have come up with in the pursuit the synthesized legato (with and without portamento).

DrJustice wrote:
For those that use flexible software synhthesis such as Csound or Chuck, this should be easy enough to do.


Yes certainly, and CSound is where I first encountered legato using lookahead. I've never done it myself, but am very interested and hope some day to define such a synth in Reaktor. But I seem to have several worlds to traverse first.

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PostPosted: Sun May 20, 2007 5:48 am    Post subject: Reply with quote  Mark this post and the followings unread

Retriggering with look-ahead allows for a preparation for the new attack as in C below where the envelope of the first attack is modified to accentuate the second. Has anyone here worked with this kind of technique, have anything to share on the problem?


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PostPosted: Sun May 20, 2007 7:14 am    Post subject: Reply with quote  Mark this post and the followings unread

kkissinger wrote:
Most sequencers allow you to shift the playback of a track forward or backward in 1ms increments. This is important -- if you sequence a track then decide to change the patch's attack speed, then you will likely need to shift the track to compensate.


Excellent point!

Trivia: I´ve heard a lot of berlin school flavoured music where absolutely no attention has been paid to this. Obviousy working with analogue step sequencers is different, but .. still..

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PostPosted: Sun May 20, 2007 9:19 am    Post subject: Reply with quote  Mark this post and the followings unread

DrJustice wrote:
... And one can always run the envelope through a lag generator or lowpass filter to smooth it out a bit -...
--


By the nature of the beast I'm dealing with I'm thinking of an analytic solution. The blue line in these graphs is the un-smoothed envelope. The green line is in the center of the region to be smoothed. Each segment of the envelope generator will begin with one of these. The mid point for internal segments would be the juncture of two segments. I'm still cogitating on the end points.

Setting duration to 0 would effectively remove it.

whayathnk?


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PostPosted: Sun May 20, 2007 9:25 am    Post subject: Reply with quote  Mark this post and the followings unread

elektro80 wrote:
kkissinger wrote:
Most sequencers allow you to shift the playback of a track forward or backward in 1ms increments. This is important -- if you sequence a track then decide to change the patch's attack speed, then you will likely need to shift the track to compensate.


Excellent point!
...


Indeed. But it does not provide a lot direction on handling cases where the attack varies dynamically. It's still a tricky problem for me.

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PostPosted: Sun May 20, 2007 12:52 pm    Post subject: Reply with quote  Mark this post and the followings unread

bachus wrote:
Indeed. But it does not provide a lot direction on handling cases where the attack varies dynamically. It's still a tricky problem for me.


Even if your attack varies dynamically, if you change the initial attack speed this change would impart a shifting effect on all the articulations. Thus, you may be able to shift the entire track, even with a dynamically varied attack.

If you change the attack speed's sensitivity -- that is, if each note isn't shifted similarly -- then you'd encounter syncing problems.

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PostPosted: Sun May 20, 2007 1:55 pm    Post subject: Reply with quote  Mark this post and the followings unread

kkissinger wrote:

If you change the attack speed's sensitivity -- that is, if each note isn't shifted similarly -- then you'd encounter syncing problems.


Yes that's one of the problems as I am interested in the expressive extremes of phrasing and articulation.

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PostPosted: Sun May 20, 2007 2:12 pm    Post subject: Reply with quote  Mark this post and the followings unread

BTW parabolic interpolation can provide useful transformations not just twiddling refinements


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PostPosted: Sun May 20, 2007 2:12 pm    Post subject: Reply with quote  Mark this post and the followings unread

Interesting stuff Bachus Smile

I was always dissapointed with the envelopes on the Nord Modular- especially the attack. Yamaha's DX range had really musical envelopes. They never really got it right after that (my AN1x never sounded as good as my DX100).

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PostPosted: Sun May 20, 2007 2:18 pm    Post subject: Reply with quote  Mark this post and the followings unread

elektro80 wrote:
kkissinger wrote:
Most sequencers allow you to shift the playback of a track forward or backward in 1ms increments. This is important -- if you sequence a track then decide to change the patch's attack speed, then you will likely need to shift the track to compensate.


Excellent point!

Trivia: I´ve heard a lot of berlin school flavoured music where absolutely no attention has been paid to this. Obviousy working with analogue step sequencers is different, but .. still..


what is needed is a master clock with a 'look ahead' trigger output (or a time machine Shocked )

we need more clock design in the DIY sections (along with cool envelopes- as I've already suggested- but Thomas Henry says he has some cool designs there. electro-music.com really needs to set up a publishing house Very Happy )

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PostPosted: Sun May 20, 2007 2:24 pm    Post subject: Reply with quote  Mark this post and the followings unread

Linearity is not one of the human ear's traits. You've certainly got my "ear" with this position.

There are a couple of practical issues. Due to fast envelope attacks, I'm curious if the ear actually percieves the difference between a linear envelope and an exponential one. Which brings up an underlying thought.

If you have designed your electronics for 1V/Oct then you're working in an exponential world. If the design of all the control inputs was true to 1V/Oct then you should have an exponential response to a linear input.

Reading this discourse, I agree that the transitions of linear envelopes should not be abrupt, however I am curious about the point of measurement. My understanding was that you could have a linear voltage go into a circuit that then interpreted the input as exponential. Maybe I'm off base. My observation is that in some designs there is a linear envelope generation which is follows an exponential interpretation.

If you are implying that the peaks are rounded, I think there is physical evidence to support it, for example a rim shot's envelope is decidedly exponential. The peak and decay should follow, assuming the model of the space you are trying to synthesize. I don't think I agree with the graphs I see, but this may be the difference between what the control voltages are doing and what the ear hears.

I remember a number of the old envelope generators could do linear or exponential responses. I also remember that different circuits could respond exponentially to a linear input. Again, my memory/interpretation could be very wrong.

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PostPosted: Sun May 20, 2007 3:58 pm    Post subject: Reply with quote  Mark this post and the followings unread

EdisonRex wrote:
... Due to fast envelope attacks, I'm curious if the ear actually percieves the difference between a linear envelope and an exponential one. ...

In my experience the difference is clearly audible, up to a certain (very short) minimum time. The exponential shapes are found in many acoustic instruments. Struck strings, drums etc. exhibit exponential decays. The onsets of many sounds also have exponential attacks. Things can get into a more "organic" sound by not using linear ramps everywhere. Then perhaps add smoothing of discontinuities and a legato-function that picks up from where you are (ref. Bachus illustrations above) and you may just arrive at a new level of expression.... After all, the (amplitude) envelopes are instrumental in controlling the dynamics which may be a very important part of a composition.

bachus wrote:
The question I mean to ask is if there is an aesthetic dimension here worth exploring or is it irrelevant.

Absolutely. It seems that synths in general have much more control and variation of timbre than of amplitude. While the evolution of synths have brought fantastic timbral possibilities, we are still being served the same old linear ADSR most of the time. Sad really, since much more advanced envelopes, including all the stuff discussed in this thread, would be a doddle to implement.

As for practical aesthetics, when I synthesize a sound, I often find myself struggling to achieve satisfying dynamics, with the amplitude attack and release portions being the trouble spots. Much of this is directly related to the segment shapes, like e.g. how a release can seem to linger for too long at too high amplitudes (in which case an exponential decay might be what you want) and how the attack can be just wrong. Some of this probably stems from the discontinuities too. In synths that have multiple segments before the sustain, I sometimes use two or three segments for just the attack portion of the sound - that can help a lot.

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PostPosted: Sun May 20, 2007 4:05 pm    Post subject: Reply with quote  Mark this post and the followings unread

DrJustice wrote:
Sad really, since much more advanced envelopes, including all the stuff discussed in this thread, would be a doddle to implement.


Hmm.. I´m convinced the "Dr. Justice Envelope Module" will sell really well.

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PostPosted: Sun May 20, 2007 7:22 pm    Post subject: Reply with quote  Mark this post and the followings unread

EdisonRex wrote:
My observation is that in some designs there is a linear envelope generation which is follows an exponential interpretation.
Yes, it is a relatively trivial problem to map one to the other, it's done all the time.
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