That Wikipedia reading is going straight into the new Boards of Canada song

"We dont just listen to arrangements of pure sine waves" Laughs in Fourier

I'm a guitar player and just wanna thank you for this, especially the vibrato/tremolo bit! I thought I was the only one bothered by this.

lmao, my man called out 99% of guitarists just like that xD

I too come from a Live Audio background, something I’ve been doing for 30 years now, but I really began it all at University with a music degree and a specialty in Electro Acoustic composition. As a kid who always had audio engineering in my head, along with drum machines, sequencers, and a 4 track recorder through my teens, I had a moment when I applied to a renowned Recording Engineering school the same year I applied to music school. As much as I made abstract and very non traditional music I still saw myself more an engineer than a musician. Lo and behold I was rejected from engineering school and accepted to a music program. In my second year I signed up for this electronic composition program, and no, it wasn’t hip hop or dance music we learned about. What we had was access to a ‘studio’, which was an 8 track 1/2” recording machine, a couple of 2 track tape machines, a very very early sampler, a couple of ARP 2600’s and similar bit and bobs from the 70’s and 80’s. Our ‘engineering’ class? Exactly 2 hours (here’s a patch bay, here’s how you feed tape into the machine, here’s how you splice the tape, etc), then it was GO. Mess stuff up, make art, if you dare. I spent three years like that, making 50’ tape loops that stretched around the room, just because why not. But what I primarily learned from my professor was how to listen to sounds a certain way. Density, dynamics, harmony, dissonance, cohesion, in very abstract terms how to MIX. Eventually I moved to live audio, toured the world, and for a long time faked all the technique stuff while quietly learning and absorbing the ‘correct’ way to do things. I applied this to the studio when I could get into one, and to my live tours. At some point I could (almost) talk about correct techniques. But I’ll never forget going to do a session at the famous BBC Maida Vale studio, and watched in awe when the engineer pulled together an album ready mix of the band I’d done 150 shows with in about 20 min. That was a moment of clarity for me. There IS value in true understanding of audio engineering as a technical craft. Since then I’ve strived to top up what I cobbled together till then and really understand what is going on. Suffice to say, Dan I certainly relate to your past as a self-taught live engineer, but more than anything your way of filling in the gaps for me have been nothing short of incredible. Thanks for the videos and keep up the great work!

"Like trying to weigh something using a tape measure." If this wasn't in a Douglas Adams book, it should have been.

The intro segment is just too true. Too many so called "youtube producers" speak with full confidence about different subjects with clickbait titles ("The trick that No mAsTeRIng eNGineEr wIlL tEll yOu") when in reality it's not very accurate, or not true at all. Thank you for this. You're among the few I trust.

Dan, I wish you were my teacher when I started audio engineering man. Grateful for doing this and for having this channel.

My introduction to the notion of linearity in electronic circuits came in the 70s at college and then in training to be a production/repair technician. I was already a guitarist turned bassist by this time and it was very interesting to learn how my amplifiers worked. They showed us the way that amplifier circuits vary their in/out ratio at different levels and at different frequencies. Whether solid state or valve based, there would always be a reactive element to the responses of amplification stages. A particular highlight of these lessons outlined the difficulties involve with getting a linear response out of Valve based hi-fi. Winding output transformers, and coupling transformers, with their coils and inductances to give linearity was/is a major headache and the largest part of the cost of making them. Finding the straightest part of the response 'Curve' is the goal. Then we musicians do our damndest to lose that 'fidelity' for the most part in one way or another.

The toughest thing about learning sound engineering today is getting bombarded by 20 different ways to do a thing and everyone screaming at you that they're right and everyone else has no idea what they're talking about. Oh, that and finding a job in anything other than bland disposable electronic music

You totally had me when expaining "vibrato" and "tremolo", with that little kick at Leo Fender (the "trem bar") - I hope you do get in some sense what a well of good and interessting information you are! Happens to be one of the best decisions I made, when I subscribed to your channel!

Not only the gain stage of ProQ is linear. Actually, all the static EQ curves are too. Mathematically what we call a linear process (more formally linear time invariant system, or LTI system) is a process that can be reversed by running the inverse of the process on the already processed signal to get you back to the unmodified signal. In other words linear processes are non-destructive! So in the case of ProQ (and any other ordinary digital EQ) you can boost 1kHz by x dB, place a second instance right after that cuts the same frequency by the same amount. Since this type of filtering is built on LTI code, the resulting signal is identical to what you fed the first instance, bar eventual _very_ low level differences introduced if the algorithm were to use some kind of (non-linear) approximation to save CPU power (or sloppy coding). Now, try the same thing with for example Mwaveshaper by Melda, which is a classic transfer curve shaper. Bend the transfer curve in a convex manner so that medium intensity signals get amplified by factor 1.5, for example. Place another instance of Mwaveshaper behind it that attenuates medium intensity signals by multiplying with 0.666... If Mwaveshaper was linear we would expect to get us back to square one, but the resulting signal is anything but identical to the one you had from the start. What causes this is non-linear expressions such as exponentials in the code. They are inherently non-linear. The problem becomes even more unsolvable if you introduce attack and release times such as in a common compressor - in such case the transfer function isn't even time invariant (in other words, the process parameters change depending on time and what signal came before the signal you are currently processing).

THANK YOU -- the fact that guitarists (and guitar amp manufacturers) refer to distorting/overdriving amplifiers as "high gain" has always vexed me. It's really "failed gain." Now, failed gain can sound AWESOME, but it's not "high gain."

3:20 "i need to get that off my chest". Wonderfull. Thanks for the always interesting and never banal topics.

The mighty myths: gain = distortion, tremolo = vibrato & linear = whatever the last "plugin" flogger suggests. Informative and the odd clever dig to make it amusing. Thanks.

This was great, Dan. Loved the track, too - put me in mind of moments of 'Ok Computer`. Cheers.

The vibrato/tremolo dig was fantastic, thank you.

Amazing like aways! I am happy there are a few good teachers out there explaining things correctly. Where would we be without you. Thanks again ✌️😊

Informative as always. Was really digging that music too

The GOTO for clear smart thoughtful audio info. Thank you.

my brain is drooling over how well articulated this is thank you so much for pumping out these kind of videos

Gold. Pure gold. And thx for bringing up the Fender trem/vibrato point. 🎊

Whenever you feel the need to speak up, I'm listening. Thank you!

The extra harmonics on the analyzer blew my mind. It adds so much!

Thank you for describing the Hammerstein measuring system! What a great tool.

Really digging the track in this one. Appreciate everything you do, Dan!

Profoundly educative, as always, Dan! I love how you educate the guitarists as well ;). Being an engineer AND a guitarist you got it of my chest as well :) Excellent video, thank you.

Bomber tune Dan!

incredible as always, Dan. when you write a book and/or narrate an audiobook I'll be preordering it.

I love the way you produce your videos. The music behind this one, as with many others of yours, really kept the momentum going and held interest while you were explaining the topic. Also, I appreciated the video distortion on the closing title. Nice touch :)

Actually, linearities include invariance by both multiplication (aka, change in volume) and addition, which is to say, in a linear plugin, if you run the sum of two signals, you should expect the same output as if you ran both signals to the plugin separately, then added them. This is the reason we often use reverbs in bus tracks. Since reverbs are linear, this achieves the same as if I had one instance of the reverb in each track.

Dan, you make the best and most understandable mixing related content on all of KZfaq and maybe anywhere. Thank you so much

This is the best video that I've ever seen in my entire life on any subject. Thank you!

Got to love Dan's directness ;-) excellent video as always!

Brilliant commentary on this topic, I quite enjoyed it!

Hey Dan, myself and for sure many other people would appreciate an indepth series about PD and its correct usage and interpretation of its curves. Demonstrated by actual real usage case scenarios. In fact there is hardly anything useful to find on YT about it. This would be a great help imo. Any plans? Thank you.

Excellent presentation on a very complex topic The style and content is ideal for my interests and limited attention span. I often listen to instructional videos at 1.25 speed, but Dan’s presentations are so fast and concise that I watch at 1.0 to keep up with the rapid flow of info. This vid packs a lot into a short presentation so I enjoyed watching it twice.

Great composition, Dan - this is great.

Brilliant demonstration, as usual.

I actually use broken tube on a square wave with 8 voices. It sounds really nice for a bit of ear candy in any genre honestly

Bravo Dan. Excellent video as always

Your background track is ace, I love the warbles

So well explained! Thank you!

Thank you for all your content, really learling a lot here!!

Yes I had the same wonder and feeling about matters not being represented correcly at probably the same recent video 😉. Thanks for explaining and clearing it up!

It's always a good day when Dan uploads a video!

I haven't produced anything in my life but I could watch these videos all day. You can just tell from the delivery, the detailed and logical explanations and demos that this dude knows his shit at a special level. Not to mention the video audio sounds better-mixed than most of the music I listen to.

Great content as usual sir!

Very insightful matey! Well said!

Great explanation, thanks, Dan.

Thanks so much, was not able to figure out how on Earth to use that Hammerstein analysis until now, very handy!

Wonderful primer! I often tire of people citing "non-linearities" as some sort of holy grail. Thanks Dan!

Wonderful explanations and graphics, thanks.

👋Thank you Dan your videos bring so much clarity on every subject you cover. Keep up the great work 🤘😌🎶

Someone once said "talking about nonlinear systems is like talking about non-elephant zoology", which I think points out an interesting fact about nonlinearity: Almost everything is non-linear - something being linear is the very rare (but important) exception. Although in audio we often assume nonlinearity to mean 'adding harmonics' or 'saturating', this is not generally true: "Non-linear" just means what it says: something is "not linear" - but whatever else it might be, we in fact don't have a clue! A system where I put a Mozart sonata in and get a Beatles song out is also a nonlinear system, for example.

i love the quality of your videos

Excellent explanation, in Dan‘s own inimitable style.

This was a great explanation. Also the track used for this is super cool - I really enjoyed the synth bass sound having some nice saturation! Would love to hear the track by itself or even have a breakdown of it. Love your videos!

A lot of people new to math get confused about the meaning of linear. Linearity is two properties, *additivity* and *homogeneity* . suppose I take a signal x and feed it in to a filter f, giving me the output f(x). Suppose i have another signal y and likewise I can feed that in to the filter with the output f(y). Suppose further that I can scale either signals amplitude by A and B respectively. The filter is linear if and only if f(Ax + By) = Af(x) + Bf(y) Where f(Ax) = Af(x) Is the property called *homogeneity* and f(x+y) = f(x) + f(y) is the property called *additivity* To put this all in terms of a DAW, suppose you have two tracks with samples playing, 1 and 2. You put the same plugin with the same settings on each track, then increase the gain of each track by 3dB, respectively. Thats the right side of the equation. This will sound identical to sending both tracks to a single send channel with the same plugin with an input gain of +3dB (the left side of the equation) *if and only if* the plugin is linear.

“Abused disgracefully”. Wonderful wording!

THAT'S IT! From now on I'm exclusively listening to pure sine wave arrangements!

Excellent - and thank you so much for the information!

The rich deep vibes of every video is what keeps me coming back to the channel.

Fascinating! I hope this is leading to a gain structure masterclass! Track level, daw input level, plug-in strip in/out, plug in fader, daw fader, send levels, bus levels, sub groups, vca, master bus plugins, master fader. Linear/non linear. So much potential to help/harm a mix just at the gain stage/fader volume level. Wisdom and guidance please. Cheers!

WOW, first time I hear (and see) a such good explanation about this. The Hammerstein analysis is a mind blowing visualization for me!!!! How cool is that!! Now I see very clearly why some saturation are more "fat" and some others more "crisp". An even cooler way would be to visualize that with an added time axis, like a waterfall, showing how a plugin reacts harmonically over time. Since no real life sound is static, maybe it would show what does a plugin reacts to a transient, for example? Different harmonics appear differently depending on the input energy - sometimes with resonance, like from transformer hysteresis. On percussive material like drums, a kind of "sweet spot" is attained when only transients being saturated, leaving most of the body of sound untouched, making gentle saturation as a nice (and surprisingly transparent) transient control.... For now, Plugin Doctor is also buggy and lagging on my almost-new processor... It might have to do with the software....

I thoroughly enjoy your videos. Thank you sir!

Love your work!

True about information today. This is one of the few KZfaq channels I'm watching. Virgil Donati (one of the 7 drummers which auditioned for Dream Theater) said in an interview: the hardest part for him to get what he is today as a drummer was to weed out the infinite bad info floating around.

Can't wait for Dan Worrall plugins...Instant buy for sure.

Learned a lot today! Thank you.

FYI this is one of the best audio KZfaq channels folks.

It is great to see my major cross paths with audio engineering. Studying mechanical engineering and this semester in a experimental engineering class where the topic was doing measurements, experiments and reporting them basically with all the needed terminology. In error and measurement lesson the professor told us about linearity and the exact graph at 7:29 was used to show non-linearity. It was mentioned that in real systems, truly linear behaviour is only approximately reached, quoted exactly from the lecture slides.

I'm really glad I discovered this channel. Thank you, from a recording school student.

Brilliant..well explained and from someone who’s obviously been involved in making records for many years, unlike the video channel your referring too, I too experienced it pop up on my YT feed, only to bemused by its strange regurgitation of bitsize marketing mixed with tutorial quotes from some who has yet to make a record.

I think this could use a bit of expansion on intermodulation. A linear function follows the rule that f(a*x+b*y)=a*f(x)+b*f(y) and your change in input level only shows that f(a*x)=a*f(x). It's part of being linear, but not all of it. The other part is that a linear plugin on a bus receiving two inputs produces the same output as both inputs going through instances of the plugin and then summed. Distortion-free nonlinearities occur, when the relation above holds for x and y being levels of signal at a particular point in time, but not for x and y being the entire input function.

Thanks Dan! Finally got it. Good music too!

Thank you for your generosity, i needed this info!!!!!

Great video and explanation. Thank you. Subscribed.

It may also be useful to some to understand 2 tests for a system's linearity: the superposition and homogeneity principles. Superposition principle is: if you first add (mix) 2 signals together and then process them through the system, you'd get the same result as if you process them individually through 2 copies of that system and then add them together at the end. Homogeneity principle is: if you apply gain to a signal and then process it through the system, you'd get the same result as if you first process the signal through the system and then apply that gain. If a system is linear, both of these principles will apply. Effects like compression and distortion fail both of these tests and are thus nonlinear.

Love this channel!

One of your best so far ThankYou

Love your work as always 🙏 Would love to see that Saturn clean tube algo on the Hammerstein.

Great stuff man.

love this channel so much ty bro

The simplest definition of nonlinear would be f(a+b) not equal f(a)+f(b), where a and b are 2 signals and f is the processing applied (eg distortion). This means that whether you apply the processing to the sum of signals (eg bus group), or independently on each signal and then sum them afterward will lead different result. That will be of course the case with distortion, but also, and I wished you mentioned it, compression! That would have been a better way to explain nonlinearities, especially since I think most people will understand that applying compression to individual channels clearly lead to different results than applying compression on your final mix.

KZfaq university of Dan Worrall has been better for me than my year of music tech college... Now have a job in the industry and found learning the hard way to be much more effective than any classroom 😂

Loved it, Funny and educational at the same time.. brilliant..

This was beautiful!

it is really good video .I learnt a lot of worth things ,I got stuck about this linear and nonlinear case .Now I completely got it .Very thank you sir

@4:51 : We don't just listen to arrangement of sine waves .... OR DO WE ? Ahaha lovely video Dan !

Damn so much good reliable info !

Wow, the atmosphere of the video with this music is like you're diving into a very deep hole of secrets or conspiracy theories :) I've got so many insights from it. I always knew that Pro-Q3 is a clean EQ, but I haven't realized, HOW clean it is. So, FF Volcano 3 is also non-linear, right?

Huge thanks. Love your videos. 🙏🏾🙏🏾🙏🏾

Another fun lesson. Thanks!

Absolutely correct on the Internet being filled with audio advice, its a severe case of TMI.

lol, I've just watched this week the video you're responding to.. you're a gentleman for not pointing it out who he is, but at the same time it's important for the youtuber to acknowledge the erroneous information he posted.. and obviously take down the video as it's wrong info and will mislead people into thinking non-linearity is an effect simply regarding eq curves.

Hi, i don´t know why YT algorithm doesn´t show me this channel before lol. This is the most usefull channel about audio that i found in internet. I´m enjoying watching all your videos, new sub here and i will let my like in every video, greetings from Argentina.

Damn Dan... Back to the drawing board! Thanx a lot..KNOWN KNOWNS, KNOWN UNKNOWNS AND UNKNOWN UNKNOWNS!

Your trippy glitch music is always a real draw imo. Not to ignore the fantastic information and dry humour of course.

Best audio channel in KZfaq.