Quantcast
2. order and 3. order harmonic distortion? - Gearspace.com
The No.1 Website for Pro Audio
2. order and 3. order harmonic distortion?
Old 4th June 2012
  #1
Gear Head
 
1 Review written
🎧 5 years
2. order and 3. order harmonic distortion?

Hi slutz!

What is the difference between 1., 2., 3., order harmonic distortion?
How do I hear the difference between them, and what kind of equipment produce them?

I've heard something about transistors producing 2. order, and tubes producing 3. order distortion, is this right?

Thx in advance
Old 4th June 2012
  #2
Deleted User
Guest
Quote:
Originally Posted by Rubstubs ➡️
Hi slutz!

What is the difference between 1., 2., 3., order harmonic distortion?
How do I hear the difference between them, and what kind of equipment produce them?

I've heard something about transistors producing 2. order, and tubes producing 3. order distortion, is this right?

Thx in advance
Second order harmonics are considered even harmonics, being even integer multiples of the fundamental frequency with the second multiple being the most prominent. Third order harmonics are considered odd harmonics, being odd integer multiples of the fundamental frequency with the third multiple being the most prominent. For audio purposes, the first harmonic is considered the fundamental frequency. This can be confusing, because in the RF world, the first harmonic is considered what musicians refer to as the second harmonic, or the first actual multiple of the fundamental frequency.

Even harmonics (i.e., second order harmonics) are considered to sound fat and warm, although they can be muddy and soft sounding as well. Odd harmonics (i.e., third order harmonics) are considered harsher and edgier sounding. A pure square wave gives only odd harmonics. A pure sawtooth wave gives both even and odd harmonics. A pure sine wave has no harmonics other than the fundamental.

Transistors and tubes produce both even and odd harmonics. There is a popular misconception that transistors produce odd harmonics and that tubes produce even harmonics. This simply is not true because both devices produce both types of harmonics. Transistors differ from tubes in the ratio of even to odd harmonics they produce, so it is true that tubes sound harmonically different than transistors.

The primary determinant of the prominence of even harmonic vs odd harmonics in both tube and transistor gear is the topology of the circuit. Single ended (i.e., SE) circuits without mitigating feedback produce an abundance of even harmonics, and produce odd harmonics as well. Push Pull (i.e., PP) circuits, on the other hand, naturally suppress even harmonics and leave the odd harmonics intact. Therefore, PP circuits, including differential amplifiers, tend to sound a harsher than SE circuits, assuming of course no use of feedback (FB). Once FB is introduced into the circuit, both even and odd harmonics are reduced under both PP and SE topologies.

An interesting musical fact is that the third harmonic is an Ionian Major Scale Fifth above the second harmonic, and playing in fifths is a technique commonly used my rock musicians. This factoid tells you that the best sounding guitar amp distortion subjectively needs both even and odd harmonics to sound good if you want the sound to emphasize fifths, meaning that the old idea that only even harmonics sound euphonic is purely a matter of taste when dealing with guitar amplifiers. In the case of recording preamps, even harmomics are preferred to odd harmonics, but most people would consider no harmonic distortion to be better yet, hence the extensive use of feedback within preamp circuits to remove both even and odd harmonic distortion.
Old 4th June 2012
  #3
Lives for gear
 
Jazz Noise's Avatar
 
🎧 5 years
First harmonic is the fundamental, so 1st harmonic is no distortion.

2nd harmonic is an even harmonic and produces a very octavey sound, something like an Octavia does this.

3rd harmonic is part of the odd harmonic series and these tend to sound squarey.

The idea of a triode producing JUST even or odd (I've heard claims of both) is poop. Any circuit produces various levels of even and odd harmonic distortion. Push pull, class B or any other symmetrical units which distort generaly mostly have odd order as the even harmonics cancel, single ended amplifiers tend to have both. Greater signal asymmetry leads to stronger even order harmonics so a broken Class B amp where only one side of the waveform is amplified will suffer from very high even order distortion.

While tubes have their own sound and they do tend to emphasise the lower harmonics the odd/even nature is hugely affected by amplifier topology.
Old 4th June 2012
  #4
Gear Head
 
1 Review written
🎧 5 years
This explains a lot, thanks all!

I have not tried a real hammond ever before, but PT has a hammond instrument I will be playing with
Old 7th June 2012 | Show parent
  #5
Moderator
 
Tim Farrant's Avatar
 
🎧 15 years
Quote:
Originally Posted by Jim Williams ➡️
Ever play with a Hammond organ?

It's a great harmonic teaching tool. The white drawbars pull out even harmonics. The black bars pull out odd harmonics. Listen to them and learn the differences.
Cripes, I never knew this!

Here's something to read...

http://www.geofex.com/effxfaq/distn101.htm
Old 7th June 2012 | Show parent
  #6
Lives for gear
 
Jazz Noise's Avatar
 
🎧 5 years
Quote:
Originally Posted by Tim Farrant ➡️
Cripes, I never knew this!

Here's something to read...

http://www.geofex.com/effxfaq/distn101.htm
All of the Geofex articles are amazing. He's pretty intense - and I mean that in an intellectual sense, of course. Still, one has to ask how come so many great engineers love making really old looking websites?

CSound is a great way to try out harmonics, too, however the sort of complex harmonic and Intermodulation stuff happening in intentional overdrive is more complicated.
Old 26th November 2014
  #7
Lives for gear
 
1 Review written
🎧 5 years
any free 3rd order harmonics vst or rtas plugs? besides tape sims.
Old 26th November 2014
  #8
Lives for gear
 
🎧 15 years
I was going to say about this, but since Jim Williams deleted his post. I'll leave a lot of it as a mystery for you guys.

but there is balance between 2nds and 3rds that makes the audio seem more realistic.
Old 27th November 2014 | Show parent
  #9
Lives for gear
 
stinkyfingers's Avatar
 
🎧 10 years
Quote:
Originally Posted by tamiya ➡️
any free 3rd order harmonics vst or rtas plugs? besides tape sims.
a waveshaper
Old 9th October 2016
  #10
Lives for gear
 
realtrance's Avatar
 
🎧 10 years
I think Frank Case gets this backwards, above. It's always been my understanding, since the days I used to enjoy reading Stereophile Magazine (in paper, even!), where regular reviews of $30,000 2-watt SET (Single End Triode) tube amps were awaited breathlessly by its readers, that third-order harmonics, i.e. the distortion produced at a higher level by tube-based amplification, were the desirable distortion harmonics.

It's true that odd-order harmonics are heard most clearly in a simple square wave, but in musical terms, such distortion is consonant with musical frequencies, whereas even-order harmonics are intrinsically dissonant, aka "harsher." This is why a pulse-width modulated square wave at low frequencies has more "oomph" and a saw wave at similar frequencies has more "buzz" or "growl."

What's true in the above is that nothing, either digital component or tube, produces purely even or odd order harmonics, always a mixture of the two.

Getting away from the mythologies of the '80's and early '90's that home theater snake oil salesmen retired to their own private islands from, it's since become apparent that that mixture has more to do with the overall design of a circuit, and is as easily produced using transistors (or ICs) as it is using tubes. Tube design just more easily lends itself to a predominance of third-order distortion, hence the reputation for "warmth." But in terms of engineering, there's nothing specific to the actual componentry that restrics non-tube circuit designs from producing similar balances of distortion for musical purposes.
Old 9th October 2016 | Show parent
  #11
Tokyo Dawn Labs
 
FabienTDR's Avatar
 
🎧 5 years
Quote:
Originally Posted by realtrance ➡️
What's true in the above is that nothing, either digital component or tube, produces purely even or odd order harmonics, always a mixture of the two.
Hey, plot this:

y = x + ( x * x )

or if you really just want a "pure" second harmonic, do this:

y = x * x


In short: Of course it's possible in digital. This is called a polynomial waveshaper. It's just that analogue is straight incapable of doing a clean, non-constant multiplication.


Quote:
Originally Posted by realtrance ➡️
Getting away from the mythologies of the '80's and early '90's that home theater snake oil salesmen retired to their own private islands from, it's since become apparent that that mixture has more to do with the overall design of a circuit, and is as easily produced using transistors (or ICs) as it is using tubes. Tube design just more easily lends itself to a predominance of third-order distortion, hence the reputation for "warmth." But in terms of engineering, there's nothing specific to the actual componentry that restrics non-tube circuit designs from producing similar balances of distortion for musical purposes.
Indeed. But it's important to point out that the measurement of distortion is rocket science. THD plots are extremely rough snapshots of certain aspects of a nonlinear system. They are in no way complete, especially for audio signals and applications.

Also, it's important to realize that in music signals, harmonic distortion never comes alone. It's directly paired with IMD (inter modulation distortion), a very non harmonic distortion. Systems producing strong even order components will always produce much more IMD than purely symmetrical types of saturation. This doesn't get mentioned much. First, it's complicated, second, it directly questions the traditional esoterica PR of these companies.

Another less well known fact is that symmetric saturation can very well produce even ordered harmonics, by simply feeding in asymmetric input (which is the standard case with guitar recordings).
Old 9th October 2016 | Show parent
  #12
Lives for gear
 
realtrance's Avatar
 
🎧 10 years
Question

Quote:
Originally Posted by FabienTDR ➡️
Hey, plot this:

y = x + ( x * x )

or if you really just want a "pure" second harmonic, do this:

y = x * x


In short: Of course it's possible in digital. This is called a polynomial waveshaper. It's just that analogue is straight incapable of doing a clean, non-constant multiplication.




Indeed. But it's important to point out that the measurement of distortion is rocket science. THD plots are extremely rough snapshots of certain aspects of a nonlinear system. They are in no way complete, especially for audio signals and applications.

Also, it's important to realize that in music signals, harmonic distortion never comes alone. It's directly paired with IMD (inter modulation distortion), a very non harmonic distortion. Systems producing strong even order components will always produce much more IMD than purely symmetrical types of saturation. This doesn't get mentioned much. First, it's complicated, second, it directly questions the traditional esoterica PR of these companies.

Another less well known fact is that symmetric saturation can very well produce even ordered harmonics, by simply feeding in asymmetric input (which is the standard case with guitar recordings).
You're right, of course! My advanced mathematics skills shine forth yet again...... that kind of multiplier is exactly what ring modulation is, basically, on synths.

So refreshing to hear from someone who really understands this stuff; the point primarily being, I assume, that the non-linearity of such systems is impossible to capture completely with mathematics...? Or is it, and it's just a question of more ongoing research and mathematical work, like multi-layered matrices of neural networks (aka "machine learning, deep learning, whatever latest buzzword, etc."...)?
Old 9th October 2016 | Show parent
  #13
Tokyo Dawn Labs
 
FabienTDR's Avatar
 
🎧 5 years
Quote:
Originally Posted by realtrance ➡️
the point primarily being, I assume, that the non-linearity of such systems is impossible to capture completely with mathematics...? Or is it, and it's just a question of more ongoing research and mathematical work, like multi-layered matrices of neural networks (aka "machine learning, deep learning, whatever latest buzzword, etc."...)?
Both, really.

It depends on the nature of the nonlinearity.

If it's just a level dependency, the system can be completely described via simple X to Y mapping. If it contains frequency (level) dependency, it could be replicated via simple pre/post emphasis techniques and a waveshaper (or similar trickery). Dynamic convolution covers this in a more general sense, though.

Luckily, most audio distortion mechanisms are level and frequency depend. They safely cover 90% of what we hear when analyzing cool analogue audio gear.

However, there are other forms of nonlinearities. And the black box aspect of many cool sounding analogue circuits make it extremely difficult, if not even impossible to be fully understood/replicated.

simple example, let's say a creative pedal designer add a moon phase dependency into his circuit. Without detailed knowledge, you most certainly won't find it.

There are also extremely complicated, history dependent forms of nonlinearites which can't be fully measured or calculated in finite time. Examples are insanely "deep" magnetic hysteresis effects (e.g. transformers, inductors, tape), thermal effects, but even simple hysteresis effects found in dynamic processors can be extremely challenging to analyze without detailed knowledge about the nature of the nonlinearity. This is where neural networks come into play, still subject to intense research afaik.

Last edited by FabienTDR; 9th October 2016 at 09:55 PM..
Old 9th October 2016
  #14
Lives for gear
 
realtrance's Avatar
 
🎧 10 years
Cool stuff.

I remember in the days of stereophilia, Transient Intermodulation Distortion was a big thing -- you wanted to get rid of it, and it had a lot to do, supposedly, with the "air" or lack thereof in the sound of any musical notes with sharp attacks.

I wonder whether the same issue (IF I'm remembering it correctly!) is applicable to the kinds of distortion used in making pedals and synth fx? In other words, does one make an effort to design out TIM in those cases? Or is it just a factor controlled against others, since it's usually a balancing act when designing a circuit?

Last edited by realtrance; 9th October 2016 at 09:40 PM..
Old 9th October 2016 | Show parent
  #15
Lives for gear
 
GJ999x's Avatar
 
1 Review written
🎧 5 years
Quote:
Originally Posted by Tim Farrant ➡️
Cripes, I never knew this!

Here's something to read...

http://www.geofex.com/effxfaq/distn101.htm
Nice, thanks
📝 Reply
Topic:
Post Reply

Welcome to the Gearspace Pro Audio Community!

Registration benefits include:
  • The ability to reply to and create new discussions
  • Access to members-only giveaways & competitions
  • Interact with VIP industry experts in our guest Q&As
  • Access to members-only sub forum discussions
  • Access to members-only Chat Room
  • Get INSTANT ACCESS to the world's best private pro audio Classifieds for only USD $20/year
  • Promote your eBay auctions and Reverb.com listings for free
  • Remove this message!
You need an account to post a reply. Create a username and password below and an account will be created and your post entered.


 
 
Slide to join now Processing…

Forum Jump
Forum Jump