Exactly, that's what I did. I would not do this for sound reinforcement where drivers run at the edge of capability, but for home HiFi this is not an issue.
Are you implying that odd orders are more audible than even ones? Do you have any evidence of that, because I never found it to be true.
@gedlee
What do you mean with more audible?
I don't know about pure audibly, but in general we prefer and find 2nd order over odd order.
As far as I am aware that's because 2nd order is masked much easier.
Source: well ehm some of those books about psycho-acoustics.
I really don't mean that on a silly way, but it's by now under the umbrella that I really have to dive into the literature again to be more specific, sorry. Aka it has been a while, assumed it was common knowledge by know.
If you really want to, I can dig again, but that's gonna take a while.
As for a reply to your personal addition.
In listening as well as playing music, I also find even order harmonics much more difficult to hear vs odd order.
Which seems to be in line with music theory, the further a harmonic (note) is away from the fundamental, the "spicier" it gets to our ears. Aka, the closer it gets, the bigger the masking effect is.
On the same way that even harmonics, make the sound thicker, while odd harmonics makes it a bit more "harsh".
But fair enough, that doesn't show any quantitative data.
What do you mean with more audible?
I don't know about pure audibly, but in general we prefer and find 2nd order over odd order.
As far as I am aware that's because 2nd order is masked much easier.
Source: well ehm some of those books about psycho-acoustics.
I really don't mean that on a silly way, but it's by now under the umbrella that I really have to dive into the literature again to be more specific, sorry. Aka it has been a while, assumed it was common knowledge by know.
If you really want to, I can dig again, but that's gonna take a while.
As for a reply to your personal addition.
In listening as well as playing music, I also find even order harmonics much more difficult to hear vs odd order.
Which seems to be in line with music theory, the further a harmonic (note) is away from the fundamental, the "spicier" it gets to our ears. Aka, the closer it gets, the bigger the masking effect is.
On the same way that even harmonics, make the sound thicker, while odd harmonics makes it a bit more "harsh".
But fair enough, that doesn't show any quantitative data.
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I know of no data to support that position.
Harmonics of tones (like in music) are not the same as distortion (due to nonlinearities) of tones. Don't get them confused. There is no reason to believe that liking even order harmonics from musical instruments (which is certainly believable) means that you will prefer even order nonlinearities.
Like I said, it has been a while, after reading so much literature, I am not always gonna double check over and over again what was exactly written
I mean that with no-offence btw, that is just the nature of those kind of things.
I understand the objective nature of your second part, but logically speaking I am not really following it.
There are plenty of reasons to believe that it would work the same for distortion or harmonics of musical instruments.
That being said, and the part I agree with you, is that doesn't mean it is necessarily true of-course. ☝️
We could return the question, by asking ourselves why it wouldn't be true?
Or what (other) elements will there be in distortion that it won't work the same as the harmonics of tones?
Even distortion is still correlated to the signal, which is even complex music instead of one single instrument.
So by deductive reasoning, I have a tendency to believe it will be even harder to hear (aka masking effect is bigger).
About instruments and distortion... in aggressive style guitarist often look for tube amplifier distortion ( not from the preamp but the power stage distortion) because it 'brings' something.
From my experience it is in no way even order harmonics. Much more 3rd and fifth which are liked. 🤘
From my experience it is in no way even order harmonics. Much more 3rd and fifth which are liked. 🤘
@gedlee
Little side note (also for the reader).
Something you obviously know hence the Gm metric
It's very similar, but it's very easy to confuse the "liking" of certain harmonics with spectral masking.
So I guess this also can lead to confusion.
Because of spectral masking, 2nd order distortion will always be masked more than 3rd order distortion.
Or in other words, we can have more of 2nd order distortion because of the masking effect.
Under roughly 200-400Hz this masking effect even goes up more.
Little side note (also for the reader).
Something you obviously know hence the Gm metric
It's very similar, but it's very easy to confuse the "liking" of certain harmonics with spectral masking.
So I guess this also can lead to confusion.
Because of spectral masking, 2nd order distortion will always be masked more than 3rd order distortion.
Or in other words, we can have more of 2nd order distortion because of the masking effect.
Under roughly 200-400Hz this masking effect even goes up more.
In a nutshell, this is where you are wrong. The output of a nonlinear system will be correlated to input only for a sine wave (with harmonics.) But, with a complex signal this is not the case as there are intermodulations taking effect which decorrelates the I->O.
A guitar or a flute is most definitely a complex signal, and the effect does correlate with those at least.
To some extend obviously.
So there is more than just a sine wave, but there seems to be a limit somewhere as well.
How does the inter-modulation actually looks for just pure 2nd order harmonics?
Does that not always result in more even orders?
btw, again we at least can say that higher order will also be more of a problem here, since it will decorrelate things even more.
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btw, there are Harmonic Overdrive Plugins like these (I have seen others as well), so you can start playing at bit;
https://www.voxengo.com/product/shinechilla/
https://www.voxengo.com/product/shinechilla/
edit:
There is also this one, (I forgot about it);
https://distortaudio.org/pkharmonic.html
https://www.audiosciencereview.com/...ing-beta-test-of-pkharmonic-vst-plugin.19063/
I wonder how well it works, because if I max out all odd vs even, the even is MUCH more audible?
There is also this one, (I forgot about it);
https://distortaudio.org/pkharmonic.html
https://www.audiosciencereview.com/...ing-beta-test-of-pkharmonic-vst-plugin.19063/
I wonder how well it works, because if I max out all odd vs even, the even is MUCH more audible?
I did a quick Google Search and a lot comes up, although not much that I would consider "hard data" that is convincing. It seems to almost fall into the "Common Knowledge" realm.
Nelson Pass has an H2 Generator here in our very own DIYaudio store that adds H2, but interestingly no H3 or H5 generator. Here is a related article, and again it pretty much starts from the premise that some H2 can be beneficial, supporting the Common Knowledge argument. Granted that the levels of distortion in an amplifier and a speaker may be an order of magnitude apart, this still supports b_force's statement.
(edit: the H2 generator may just be harmonics vs distortion, as addressed in some of the posts above, but some of the descriptions I read did say distortion, but they may have been confusing the two also.)
Yeah it's tricky, although I couldn't help to also dive a bit deeper in it again (as you do, nerds lol), because Earl definitely has a point.
It's kinda interesting, I came across papers from even B&K (way back) stating this.
But no references.
I have been playing very briefly with PKHarmonic, and I can't say I share the point about 2nd order sounds better anymore.
But that could be as well a problem in the plugin. I have to do some loopback measurements to verify.
It seems a very different story when a more realistic spectrum is being made, especially with the higher order harmonics in it.
@gedlee
Getting late here, but Psycho-Acoustics facts and models by Hugo Fastl and Eberhard Zwicker, seems to at least tell us a little on the theoretical side, Chapter 14, page 277 - 281.
Which is about our ear's own distortion, they describe the method of cancellation as a measure of different types of distortion (even vs odd).
Although this is about the distortion of our own ears, it could be a start to understand how we also perceive distortion as well.
Or at least tells us something about certain thresholds.
Aka, if distortion from our hearing is higher anyway, there is no way we can even detect lower amounts of distortion (or at least down to a certain order of magnitude)
Getting late here, but Psycho-Acoustics facts and models by Hugo Fastl and Eberhard Zwicker, seems to at least tell us a little on the theoretical side, Chapter 14, page 277 - 281.
Which is about our ear's own distortion, they describe the method of cancellation as a measure of different types of distortion (even vs odd).
Although this is about the distortion of our own ears, it could be a start to understand how we also perceive distortion as well.
Or at least tells us something about certain thresholds.
Aka, if distortion from our hearing is higher anyway, there is no way we can even detect lower amounts of distortion (or at least down to a certain order of magnitude)
I was personal friends with Prof. Zwicker, he stayed at my home once, so I am very familiar with his work. And yes the ear itself has a lot of internal nonlinearity to it. And likely that will mask system nonlinearity to some extent, but that's not the issue.
While it is certainly true that a 2nd order nonlinearity would be less audible/objectionable than 3rd order, one cannot conclude from this that "even orders sound better than odd orders." It's number of the order that matters not whether it is even or odd.
As to correlation of I/O, whenever there is system nonlinearity the coherence will fall, and hence the correlation must also be lower. That's simply spectrum analysis theory. Obscuring this fact however is that system noise also lowers coherence/correlation which makes sorting out the two difficult.
While it is certainly true that a 2nd order nonlinearity would be less audible/objectionable than 3rd order, one cannot conclude from this that "even orders sound better than odd orders." It's number of the order that matters not whether it is even or odd.
As to correlation of I/O, whenever there is system nonlinearity the coherence will fall, and hence the correlation must also be lower. That's simply spectrum analysis theory. Obscuring this fact however is that system noise also lowers coherence/correlation which makes sorting out the two difficult.
I mean....
The 5" coaxial tweeter is 2
The 4, 5" mid woofers, is 3
The front 15" 4
The side 15"s is 5
The coaxial tweeter thing and the 4 5" mids will appear as a single acoustical source
The 15" is the lower midbass but its crossed so low that should be nearing 1/4wl spacing
The side woofer is sub bass.
That's what I see at least....
As fate should have it.... this loudspeaker can run cardioid in the same configuration I mentally entertained but came to the conclusion that it's effectiveness wasn't real, being ~200hz and lower for the range and cardioid woofers placed at the floor boundary. I sometimes question my VituixCad sims. I only used thr inverted phase response of the front woofer as it were to the mic placed 1m in front. If I use the measurement from microphone placed in front of the side woofers, might the results have been more effective... which brings up the question. How effective is enough. How much cancellation is enough. I guess the polar map should tell us but I the above polar... is this cardioid mode or mono pole?
The 5" coaxial tweeter is 2
The 4, 5" mid woofers, is 3
The front 15" 4
The side 15"s is 5
The coaxial tweeter thing and the 4 5" mids will appear as a single acoustical source
The 15" is the lower midbass but its crossed so low that should be nearing 1/4wl spacing
The side woofer is sub bass.
That's what I see at least....
As fate should have it.... this loudspeaker can run cardioid in the same configuration I mentally entertained but came to the conclusion that it's effectiveness wasn't real, being ~200hz and lower for the range and cardioid woofers placed at the floor boundary. I sometimes question my VituixCad sims. I only used thr inverted phase response of the front woofer as it were to the mic placed 1m in front. If I use the measurement from microphone placed in front of the side woofers, might the results have been more effective... which brings up the question. How effective is enough. How much cancellation is enough. I guess the polar map should tell us but I the above polar... is this cardioid mode or mono pole?
The reason why I was mentioning it, was purely to maybe already either cross out things or maybe find some starting point from that perspective.
Or in other words, it might already give us a clue what direction we have to look for.
At this point I am wondering what happens with the masked sounds, are those simply perceived as the audio being louder?
I also did some preliminary simple experimentation with the plugins mentioned before. I get the sense that it's really frequency range dependent.
So 2nd order seems to work well for lower frequencies, but at midrange it because an horrible mess.
What do you mean with the last sentence about the number of order? I think I am misreading of misunderstanding it, but I am not totally following it?
BTW, these days it won't be to difficult to setup an online listening experiment. But just randomly adding harmonics to a piece of music is not really saying that much and not very objective or scientific.
In a nonlinear system the I/O curve is defined by a polynomial. The number of the order is the power of the independent variable. X^1 is the linear term, x^2 the 2nd and x^3 the third, ... The higher the order the more audible it is. Hence 2nd is the least.