Harmonic complexity

[daz]

I realize it's a perfect combination of things coming together that make this happen. But are there things that tend to cause more complexity to happen? for example, i read something about a certain cathode R value bringing out certain harmonics. Just an example and i don't know whether it's true, but are there any values or design tweeks that tend to give you more chance of pulling that sweetness out in the tone? I have my EL34 build sounding close to where i want it, but it seems like every time i get one thing more to my liking the complexity then drops. get it back then something else goes.

[Chris - CMW amps]

There ain't no "single magical part value" that will work in every circuit...

Easier sad than done: just tweak till you're happy...

[daz]

I understand that as i mentioned in my post. But i know some people have opinions on this and i just want to see what some may say.

[Chris - CMW amps]

Without seeing the schematic, voltages and transformer-types it's almost impossible to say...

[Steve Conner]

Broadly speaking, harmonic complexity is what tubes have by their nature, and transistors, JFETs, op-amps, LEDs, etc. don't have. It's hard to get it with silicon, and hard to avoid it with tubes.

Much of the sweetness of tone is in your guitar, your strings, your pick and your technique, too. Confucius say: "There is more harmonic complexity in the end of my plectrum than in a wall of AC30s"

Harmonic complexity is not to be confused with obsessive compulsive disorder, either.

[black_labb]

harmonic complexity can be confused with having less bass and more treble and mids, as the harmonics are what make up the mids and treble. harmonically complex could also be thought of as bright, as it contains more harmonics.

[BackwardsBoB]

A little theory, a soldering iron and a box of caps and resistors should get you just about as far as a soldering iron and a box of caps and resistors, but theory is just so much fun...

Let's start with a guitar that makes a nice sine wave output at constant amplitude. Now if we had a circuit that could add a signal that was three times the frequency at a low amplitude, and phase it so that the positive going zero-crossings lined up, the circuit would square up the input sine wave a bit, dropping the peaks, and raising the shoulders of the peaks. By adding similarly phased higher odd harmonics of the proper amplitude, we could generate a square wave.

Now we certainly don't want to build that circuit out of a bunch of tubes, but it's pretty easy to make something close to a square wave out of a sine wave. Just amplify it alot, and clip the tops and bottoms. What do we get? A square wave made up of lots of odd harmonics riding along with the sine wave.

Next, let's take our bizarre guitar's sine wave output, and make a circuit that adds another sine wave an octave higher (the second harmonic), phased so that the octave is at its maximum at each positive and negative peak of the sine wave. This makes the positive peaks of the input larger, and the negative peaks of the input smaller.

Again, we don't want to go synthesizing octaves of the input and summing the two waveforms with tubes, but it's easy to amplify the input with a single-tube circuit so that the gain is higher on positive input peaks than it is on negative peaks. All we need to do is run through a triode with a cathode capacitor, and stay away from saturation and cutoff. Bingo. We get even harmonics.

A picture is worth a thousand words. Pictures are left as an exercise for the reader.

We can also get both even and odd harmonics by making it all the way to saturation or cutoff in a single tube, and giving one side of the input a haircut. You get odd harmonics from the haircut, and even harmonics from the assymetry.

We can see that a single-ended output stage can have assymetric gain, and will generate even harmonics. A balanced push-pull stage is more likely to favor odd harmonics if the two halves are similarly non-linear.

But what does all this sound like? Well, even harmonics will be dominated by the 2nd and 4th harmonic, and these are one and two octaves above the input.

Long ago, when long-hairs wore wigs, Bach and his friends made a set of rules called counterpoint, that assured that multiple voices of music would sound like, well, Bach, as long as the rules were followed. The rules prohibited parallel octave motion, basically because it was boring. It sounds like a 12-string. Very pretty.

But what does the third harmonic sound like? If you get out your yardstick and a guitar, you'll find it's an octave above the 5th. Bach and friends ruled that parallel fifths were also prohibited, but they did it because it doesn't sound like Bach, especially if all the 5ths are seven half-steps apart, as in this case, creating an accidental when you play the 7th of a major scale. It's a bit edgier.

Applying all this, we can see that if we do assymetric things to a sine wave, we get octaves, and if we do symmetric things, we get 5ths and stuff, but we made a big compromise when we modelled the guitar as a sine-wave generator. In fact, when you strike a note with your pick, the output starts out atonal, and quickly settles in to a complex waveform strong in second, third, fourth and higher harmonics, as well as the fifth of the note being played, at 1.5 times the fundamental frequency. The relative amplitude of these signals will vary as the note decays. So before we even get to the amp, we have lots of even and odd harmonics.

Also, if we have a non-linearity in our amplifier, and we send in two frequencies, we will get the two frequencies out, along with some of their harmonics, but we will also get components that are the sum and difference of the two frequencies, and their harmonics. This is intermodulation (IM) distortion.

So, unlike constipation, the actual result is hard to work out with a slide rule, but we can say that non-linear amplification such as that performed by a tube in its active region without linearizing feedback will produce octave harmonics, among other things, that clipping waveforms will produce odd harmonics among other things, and that balanced tube non-linearities, such as you might find in an AC30's power section, will also provide some odd harmonics. We also know from experience that clipping waveforms or compressing peaks tends to mask the harmonic structure and dynamics of a guitar and substitute its own tonal signature, particularly to the detriment of individual notes in chords.

Also, a guitar can have a wide dynamic range, and softly played notes will be less affected by non-linearities in the amp and may avoid clipping entirely.

Power supply sag can introduce compression, which is a non-linearity, producing odd harmonics and IM ghost notes.

Guitars with a rich harmonic structure (acoustic, hollow and semi-hollow body electrics, etc.) may have little need for a musical distortion contribution from an amplifier, while a solid-body guitar is usually in a bit more need of assistance. Single note lead lines can tolerate more distortion than chords, which might turn to mud with the same treatment.

So how do we avoid the complication of harmonics in our tube amps?

1. A well regulated power supply with silicon diode rectifiers.
2. A preamp comprised of triodes with un-bypassed cathode resistors for linear operation, operated at a point that avoids saturation or cutoff.
3. A balanced, linear phase inverter.
4. A push-pull output stage linearized with un-bypassed cathode resistors or negative feedback from the output to some point earlier in the amp.

This can still sound very nice, by the way.

And how do we generate harmonics?

1. Power supply sag (tends more toward compression, which generates harmonics and ghost notes if you get carried away with it).
2. Bypassed cathodes on the preamp tubes. fixed bias or bypassed cathode bias on the output tubes.
3. A more creative phase inverter.
4. A single-ended output stage.
5. Reduction or elimination of negative feedback from the output.
6. Overdriving most any of the tubes into saturation or cutoff.

All these things can also sound great.