Do you really need expensive stuff?

[dgatwood]

As you might see, there is confusion in nomenclature amongst musicians and engineers. This is because in engineering, "first order" is (usually) in reference to the fundamental, thus "second order" is 2x the fundamental frequency, etc. This corresponds to what a musician understands as the first harmonic, the octave.

To make things more confusing, your definition of "even order" differs from the mathematical definition. I hope you're just being sloppy. If not, then the engineering definitions are on crack.

Octaves are power-of-two harmonics, not even harmonics. Non-power-of-two even numbered harmonics are decidedly not octaves.

2^0 (1x) fundamental
2^1 (2x) octave up
3x octave and a fifth
2^2 (4x) two octaves up
5x two octaves and a third
6x two octaves and a fifth *
7x two octaves and a minor 7th
2^3 (8x) three octaves up
9x three octaves and a major second
10x three octaves and a major third *
11x three octaves and an augmented fourth (tritone)
12x three octaves and a fifth *

* indicates even numbered harmonic that is not an octave.

and so on.

Thirds and fifths are very close to being correct. It's the other intervals that are horrible. The even numbered harmonics get closer together the higher up the harmonic series you go. It should be noted that beyond 3x, the odd harmonics are way out of tune, which is one reason that they sound harsh. We're not talking a little bit like the fifths. The 5x harmonic is just a little flat, the 7x harmonic is very way flat, the 9x is just a hair sharp, the 11x is way flat (by almost a quarter step).

Another neat thing about the harmonics is that the error from ideal (in cents) for non-prime harmonics can be calculated by finding their prime factors and summing the errors of those harmonics. For example, the 3x harmonic is 2 cents sharp, the 5x harmonic is 14 cents flat, so the 15x harmonic is 12 cents flat.

 

[Harvey Gerst]

Thirds and fifths are very close to being correct. It should be noted that beyond 3x, the odd harmonics are way out of tune, which is one reason that they sound harsh.

The 3x distortion frequency of a C note (starting with c6 being 1046.50 Hz) is 3139.5 Hz, a little above a tempered g7 (which is 3115.96 Hz).

The 5x distortion frequency of that c6 is 5214.5 Hz (which is close to a tempered e8 at 5232.4 Hz).

Close, but no cigar.

If you play a C Major chord on the guitar with 3 C's, a couple of E's, and a G, the distortion of any odd harmonics of the C note are gonna be off to the tempered G's and E's in your original C chord.

It's annoying as hell to listen to.

 

[mshilarious]

To make things more confusing, your definition of "even order" differs from the mathematical definition. I hope you're just being sloppy. If not, then the engineering definitions are on crack.

Well I'm always sloppy but I think I just said second-order was an octave

 

[mshilarious]

It's annoying as hell to listen to.

It's a big factor in playing even moderately complex chords with a distorted guitar. Beyond looking for a source of distortion that lacks IM, it's also good to try to tune your guitar in (somewhat) perfect intervals for the key you will be playing in, such that at least the major thirds of the I IV V are closer to the harmonics generated by the overdrive.

I thought about that as I ponder the fact that I happen to have a product that generates (cough!) 1% second order distortion at 94dBSPL actually the distortion can be cleverly controlled with cathode bias, and can go much higher than that, perhaps coming soon to an effects pedal near you . . .

More fun with harmonic distortion! I've sketched out a podcast that illustrates creative use of harmonic distortion. In DAW-land, a pitch shift plug tastefully used can be used to do all kinds of special effects that take advantage of these principles. Want to sing opposite-sex harmony parts with yourself (not that there's anything wrong with that)? Don't have an oboe, but you have a flute? Don't own a 12-string guitar? All this can be yours, without MIDI or modelers . . .

 

[dgatwood]

The 5x distortion frequency of that c6 is 5214.5 Hz (which is close to a tempered e8 at 5232.4 Hz).

Close, but no cigar.

I did say close. The fifths are very close. I guess I shouldn't have said "very" for the thirds. They're not what I'd call awful, though. Most of the error is due to temperament raising where the pitch should be compared with the pure major chord.

For the purposes of computation, I'm going to use the frequencies from indiana.edu. They differ a little from yours, but I needed a complete table of frequencies for illustration purposes.

C6 is 1046.502, E8 is 5274.042, and 5xC6 = 5232.51. That's an error of 41.53200. However, Eb8 is 4978.032, so the difference between that ane E8 is 296.01. Divide 41.5/296 and you find that it is about 14 cents flat. Yup. That's just what Wikipedia said it should be based on an equal temperament.

Using a just temperament, however, the pitch for the E8 would be 1.2500 * C8. C8 is 4186.009, so I get 5232.51125 as the equivalent pitch. Based on that, the 5x pitch is dead on. Thus, thirds should sound quite acceptable in a chord. Of course, 14 cents is enough to sound bad if another instrument/string/key is playing the equal-tempered pitch that matches.

The fifths are only about two cents off from either temperament.

The point was that thirds and fifths are at least within the realm of possibility. They aren't torture to listen to. The 11th harmonic... now that is torture. It's 49 cents off---approximatley midway between two notes.

 

[dgatwood]

Well I'm always sloppy but I think I just said second-order was an octave

I've never seen "order" used to refer to the base of an exponent. It usually refers to the exponent itself.

For x^y, the order of magnitude is y, while in this usage, it's being used to refer to x---that is, even order is being defined as 2^n for all values of n, while in my mind, even order should mean n^2k for all values of k.

 

[kojdogg]

... just trying to deepen the level of detail of this discussion.
It's always best to be an educated consumer...

okay-- in the span of a page, this discussion has now completely gone over my head

 

[Harvey Gerst]

okay-- in the span of a page, this discussion has now completely gone over my head

kojdogg, you're the one that brought up the points about negative feedback in amplifiers (to reduce distortion), and we kinda took a hard left from there.

Okay, lemme try to make it a little more understandable:

We're talking not just about distortion hear, but how things distort. Let's take a pure sine wave of 1,000 Hz. It should stay a pure sine wave whether you play it loud or soft. No overtones. That doesn't happen in the real world, when you start pushing that signal through a bunch of electronics.

If you overdrive an amplifier with a sine wave, for example, extra notes are generated (that aren't in the original signal). They're exact multiples of the original 1,000 Hz signal. So, in addition to the original 1000 Hz signal, you can get various levels of added notes at 2000, 3,000, 4,000, 5000, 6,000, 7000, etc. The even multiples are called "even harmonics", and the odd multiples are called "odd harmonics".

The even harmonics of 2000 Hz, 4000 Hz, and 8000 Hz are fine; they're perfect octaves of the original note and can add fatness and warmth to the sound. Tube are great for distortion because they naturally generate more of these even harmonics when over driven.

The odd harmonics (generated by a lot of transistor stuff) is where the problem lies. Those 3,000 Hz and 5000 Hz harmonic distortion notes actually clash musically with normal notes found in musical scales.

Most music we hear uses a "tempered scale". The pitch of some of the notes is adjusted to make all the notes sound pleasing to our Western ears. So, when we play a "C" chord, the "G" and "E" notes have been pitch adjusted to sound good with the basic "C" root note.

But, harmonic distortion doesn't give a shit about a "tempered scale". It's gonna put out perfect 3 and 5 time multiples of the original note, and that's gonna clash with some of the real notes we're playing.

The way things distort can be very important and that's what we're talking about here. Tubes tend to favor the octaves when they distort and the distortion is usually very gradual. Transistors favor the odd multiples of distortion and can come on fast and hard when you reach their limit.

These distortions are present in almost everything we use in a studio, from mics to speakers; they will all distort if pushed beyond their limits. But often, it's important to understand how they distort, so you can use that to your advantage.

In a thread here about a cover song recently, I actually suggested running the main vocal through a distortion box to add a little grit to the song; everybody agreed that the distorted vocal sounded better than the clean vocal - for that song.

So, does all this make a little more sense now?

 

[Harvey Gerst]

The rest of the argument is about semantics. What to call each harmonic overtone. We all agree on the values; but the names can be confusing.

The first harmonic is technically the octave; 2 times the original signal.

The second harmonic is 3 times the original signal. And so on, and that's where the confusion sets in.

1st harmonic = 1st overtone = fundamental times 2
2nd harmonic= 2nd overtone = fundamental times 3
3rd harmonic = 3rd overtone = fundamental times 4
4th harmonic = 4th overtone = fundamental times 5, etc.

I try to avoid that whole discussion as much as I can.

If we could all agree to call the fundamental note the "First Harmonic" (or the "Prime Harmonic") as well, everything else would fall into line and we'd never have this discussion again. This whole "what to call it" shit has been going on for decades.

 

[isfahani]

Wow. Thanks very much. It all seems so simple now. I am going to save this for posterity.

Nice one, Mr Gerst, and at this hour of the morning, too...

 

[kojdogg]

kojdogg, you're the one that brought up the points about negative feedback in amplifiers (to reduce distortion), and we kinda took a hard left from there.
...
So, does all this make a little more sense now?

I was being at least a little bit facetious there Harvey.
Thank you very much for sharing your knowledge and to folks like mshilarious for contributing (not being facetious at all here).

 

[mshilarious]

koj, with respect to your comment about feedback, read this head (it's OK, this one explodes my head too):

http://recforums.prosoundweb.com/index.php/t/16557/0/

 

[Harvey Gerst]

I was being at least a little bit facetious there Harvey.

You mean I went though all that technical shit for nothing? Damn, I hate you, kojdogg!!

 

[eeb]

damn i wish i knew 10% of what you guys know.. I know how to point a mic til it sounds good.. and starting to understand some basic compression and eq theory.. other than that i tweak til things sound good. (it's mainly by chance with me right now).. all this stuff is so far beyond me right now that i have a hard time even reading it haha

 

[kojdogg]

You mean I went though all that technical shit for nothing? Damn, I hate you, kojdogg!!

The way I look at it, your writings here and in other threads have produced a steaming mound of technical shit (i.e. knowledge) that will serve and inform the efforts of aspiring recordists for years to come and that is a real contribution to humanity. It also may serve to dramatically drive up the prices of vintage MXL microphones in the year 2087.

Hope I'm out of the dogg house a little Harvey

 

[Harvey Gerst]

damn i wish i knew 10% of what you guys know.. I know how to point a mic til it sounds good.. and starting to understand some basic compression and eq theory.. other than that i tweak til things sound good. (it's mainly by chance with me right now).. all this stuff is so far beyond me right now that i have a hard time even reading it haha

Try reading the big mic thread at the top of this forum; it can answer a lot of questions - and without all the technical jargon.

 

[Harvey Gerst]

The way I look at it, your writings here and in other threads have produced a steaming mound of technical shit (i.e. knowledge) that will serve and inform the efforts of aspiring recordists for years to come and that is a real contribution to humanity. It also may serve to dramatically drive up the prices of vintage MXL microphones in the year 2087.

Hope I'm out of the dogg house a little Harvey

The way I look at it is that these discussions kinda bitch-slap my memory cells to help keep them going a little while longer.








Now, if I could just remember where I put my keys....

 

[eeb]

harvey,

I know things were much different when you first started out. But how did you do it.. were like some of us (myself included) that just messed around until you got things to sound good.. reading anything you could on the matter.. or were you trained by someone? (school.. or otherwise)

cause i must say.. I get really intimidated with you and alot of people on this forums stuff.. my stuff isn't even a fraction as good (actually it's complete garbage in comparison).. i know alot of you have been doing this for a long time.. but i gotta say sometimes i doubt myself.. there's just so much that goes into recording and i wanna learn. I just hope i can ya know

 

[Harvey Gerst]

eeb,

When I started, I was making recordings on 10" metal disc with a thin vinyl coating. You had one mic and that was it.

In the early 50's, I moved up to a Brush SoundMirror tape recorder, which recorded on paper backed magnetic tape. A few years later, mylar backed tape was introduced. You recorded everything with one mic, and you really had to know how to place that mic to get a balanced sound.

If you were lucky enough to work in a studio in the mid 50's, you had access to more mics, an 8 channel mixer, and bass and treble controls (if it was a really state of the art studio), but it still all went to one track; usually an Ampex 300 or 350 mono recorder. Again, mic placement was everything.

In the late 50's, stereo and multi-tracking hit and everything changed for engineers, but it seemed that newer engineers just miked everything and their mantra was, "we'll fix it in the mix". But the older engineers who really understood mic placement seemed to consistently wind up with superior recordings.

The older engineers weren't just tape jockeys; they had to fix and align all the equipment as well.

That's the horse and buggy background I come from, and I don't know if I could align anything these days, but some of my gray synapses are still firing, and I still remember some stuff from back then. "Plug N' Play" is great these days, but it doesn't help you with some of the basics. I live in fear of those fundamentals getting lost to future generations, so that's why I post to all these forums.

I'm just trying to pass on what I've learned over the years, before it gets forever lost in the past. That's why I advise people to take whatever they can from my posts; someday, maybe it'll all start to make sense.

 

[cusebassman]

I almost wish things were like that today... of course, if that were the case, home recording would still be an extremely limited endeavor, if it were to exist at all - and mainly because in the house you just don't have the quality of space you have in the studio... But that makes mic positioning all the more important!

Keep the history stories coming... its quite fascinating