Jack Endino Newsletter 2.0 (9/1997)

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OK gang, welcome to Newsletter #2. I'm going to get a bit technical, so I hope this isn't over anyone's head. To understand this it will help if you know a teeny bit about music and the science of sound.

I'd like to discuss digital vs. analog. Can't lose with this subject, can I? OK, why do people complain about digital sound? They say it's cold, clinical, sterile, etc. You've all heard it. I said many of the same things at first, still do sometimes. It's as though it's doing something bad to the sound.

Surprise. It's not. It's what its NOT doing to the sound that we hear.

I was pretty skeptical for a long time. It took me a number of jobs on various digital formats (starting in 1990 on a Mitsubishi X-850 32-track, and now ADAT's...) before I was able to make a record I didn't hate. Even now I still don't quite have it down yet, but I'm starting to get the hang of it.

One of my personal failings is that I like to dig into the science of things when possible, I want to know the why of things. After hours, the recording studio can be a pretty good laboratory, and I've done many a science experiment there. After all, you've got a room full of audio measuring and processing gear. Add to it a frequency generator, a frequency counter, a graphic spectrum analyzer or "RTA", and a bunch of calibration tapes and some logarithmic graph paper and there are many experiments you can do... but I get ahead of myself...

I figured out at some point that digital, when functioning as intended, is basically a mirror. What goes in, comes out, or DAMN close. Don't rave to me about analog sounding better, I didn't say it didn't... but nonetheless digital is the closest thing to a mirror, soundwise, that there is. I had to acknowledge this, so the next question is what is the analog recording process adding to the signal that we MISS when it is absent?

You hear about "tape compression" all the time. This means when really loud peaks hit the tape, there's some loss of level, as though a gentle compressor or peak limiter was being applied to the music. Imagine a compressor with attack time of zero and release time of zero, and variable ratio so that the harder you hit it, the higher the compression ratio. The effect is subtle but still very much there, though it is hard to measure. I have noticed in the studio magazines a number of popular 8-channer limiters being offered specifically for the 8-track digital multitracks, so people know about this effect and want to try to duplicate it. I suspected there was more than this involved. What's left? Other kinds of distortion.

You know how when you record too loud on a cassette it sounds fuzzy and distorted? Well, this happens in all analog recording, it's only a question of degree. The louder the signal on the tape, the more distortion. Those high-level peaks hitting the tape are not only getting compressed a tiny bit, they are also becoming slightly distorted for their brief duration, though you can't really recognize it as such. Get the levels hot enough and the rest of the music starts to sound audibly distorted, not just the peaks... but the point is, varying amounts of distortion are there no matter how loud or soft you record on the tape, it's never zero.

I decided to find out what kind of distortion. I fed a 1000 Hz tone into a half-inch tape machine, and cranked the input level way up. Then I looked at the signal coming back from the tape on my spectrum analyzer. What I got was a big peak at 1000 Hz; the original signal. As the level on the tape got hotter, though, other peaks appeared on the display as they became loud enough for my machine to measure: one at 3000 Hz, another lower one at 5000 hz, and a faint one, barely there, at 7000 Hz. (With more sensitive gear I'm sure I would have found more, going up the frequency spectrum.) These are called ODD HARMONICS, and I'll explain what they mean in a minute.

Then on a hunch I took a tube-powered microphone preamp, an expensive Summit Audio model, and tried the same experiment. I fed it a 1000 Hz signal and cranked the input level up until there was some distortion, then looked at it on the analyzer. I got my original signal at 1000 Hz, and then... a peak at 2000 Hz, the next smaller at 4000 Hz, and a faint one at 6000 Hz. These are called EVEN HARMONICS and they are a totally different kettle of fish!

To explain why these two types of distortion sound completely different, I'm gonna have to resort to some music theory 101, sorry about that. OK, given that the unfortunately-named "octave" actually has 12 notes in it (the twelfth fret on the guitar being the octave point, don't forget) lets talk about frequencies for a minute. Most of us as musicians don't need to know what frequency corresponds to which note on the piano or guitar, though we've probably heard somewhere that 440 Hz is an "A". But you've probably heard that an octave represents a doubling of the frequency. If "A 440" is in the middle of the piano keyboard, the next "A" note up will be 880 Hz, the next one down will be 220 Hz, and so on. Take this fact, and a scientific calculator, and much can be deduced...if you have one more crucial bit of information:

In the common western "equal-tempered" musical scale all the notes are equally far apart; for example, all the notes in an octave between say, A440 and A880 (or any other octave at all) are evenly spaced apart. Each note (called "half-steps" for some inane reason) has a frequency that is a tiny fraction higher than the note below it; the next note is an equal fraction higher still, and so on for the whole musical scale. So, take any note's frequency, multiply it by this "magic fraction" exactly TWELVE times, and what you'll get is finally a number twice the frequency you started with; in other words one octave above where you started.

This number (think about it) is the 12th root of two, and it's... 1.059463!

Another way to think about it is that each note's frequency is 5.9463 % higher than the note just below it. (Its like investing at 5.9463%; after 12 years you'd double your money...) I think of it as 6% to make it easier. Speed tape up 6%, and a song goes up a half-step in key. Got me so far?

OK, certain pairs of notes sound better than others, depending on how far apart they are; these "intervals" as they are known are given special names. It so happens that the intervals (note pairs) that sound the best have SIMPLE FREQUENCY RATIOS. Start with your low E on the guitar (it's 82.4 Hz, by the way). Play another note along with it; hmmm, the open A string doesn't sound bad. That one is 110 Hz. 110/82.4 equals 4/3! This ratio is called a "perfect fourth". The next best note is two frets up the A string, or a B, at 123.5 Hz. Play that with the open low E, at 82.4, and you get the most basic bare-minimum form of the rock and roll bar chord. The ratio is 123.5/82.4, or... 3/2! This ratio is called a "perfect fifth". The "next octave" E is of course 164.8/82.4, or 2/1! The most musically useful intervals correspond to the simplest fractions, frequency-ratio-wise.

The next best one is A flat, at 103.83 Hz. Play that with the E at 82.4 Hz and you get an interval called a "major third". The ratio is 1.26, or ALMOST 5/4. A "perfect" third interval would be exactly 1.25 but it doesn't exist in the western musical scale. (If you're thinking that this is why you can't get certain chords to sound exactly in tune on your guitar no matter how much you tune, you're right! But that's for another time!...)

OK, back to harmonic distortion. Harmonics of a given note (the "fundamental") are simply whole-number multiples of its frequency. Even harmonics are notes 2 times the "fundamental" frequency, 4 times, 6 times, 8 times etc ad infinitum. Odd harmonic notes are 3 times, 5 times, 7 times the frequency etc. Harmonic distortion is when "phantom notes" are generated by the distortion process that correspond to some of these harmonics. (Bet you didn't know distortion had discrete components like this! Distortion components are related mathematically to the original signal, depending on the nature of the distortion process.) As I showed above, the tube pre-amp's distortion was even harmonics, the analog tape's was odd. What does this mean to our ears?

Let's look at the tube preamp: notice that 2000 Hz is an octave above 1000 Hz. 4000 Hz is two octaves up. Musically, it's the same scale note. 6000 Hz is two octaves up plus a perfect fifth, but this component is so much lower than the first two that it barely counts. Finally, 8000 Hz, though vanishingly low in level, is three octaves up.

How about the tape? 3000 Hz, the loudest distortion component by far, is an octave up (from 1000 Hz) plus a perfect fifth... a form of that basic rock chord I mentioned! 5000 Hz is two octaves up plus a perfect third, further augmenting our phantom chord here. 7000 Hz, though, doesn't correspond to any interval, it hits right between 'em. Ugly, but very low in level compared to the first two harmonics; and 9000 Hz is even uglier but so low as to be insignificant.

In both these cases it is the first two harmonic components that are most important as they are by far the loudest. So what do we have? Even harmonic (tube) distortion as stacked octaves; odd harmonic (tape) distortion as a chord!

You may ask, how about other tube gear that I did not test? Good question. I did my homework, though. Tube mic preamps have a type of cicuit that is called a "type A" amplifier circuit. According to the RCA Radiotron Designers Handbook (1940 -- and tube designs have not changed much since then, honest!) type A tube circuits tend to have mostly 2nd harmonic distortion ("with some higher order harmonics at much lower levels", that's as specific as it gets). I haven't tested any other studio tube gear yet, but I bet I'd get similar results. There's a type of circuit called "AB push-pull" used in the power output stages of guitar amps that is known for ODD harmonic distortion, but it is far from a flat circuit (it's just loud) and is rarely used in preamps.

Note that tape distortion doesn't have ANY 2nd harmonic. Analog tape distortion/saturation is not duplicated by tube gear! I submit to you that it is mostly this odd-harmonic distortion that we miss when we listen to a digital recording. You don't realize it was ever there until it's completely gone!

Imagine every single frequency, every part of the sound in a piece of music, generating phantom frequencies depending on which kind of distortion we have. In ANY analog recording or signal processing there's a faint, low-level "cloud" of harmonic distortion components lurking under the music, blending perfectly with it. The two kinds of distortion I'm talking about sound very different, though it's hard to describe. Even harmonics are described as "nicer" distortion, almost like no distortion... If you want something you're familiar with, imagine a Vox AC30 guitar amp (type A output circuit, EVEN) vs. a cranked Marshall (type AB output circuit, mostly ODD) as an extreme example of the difference. So next time someone tells you they can "warm up" a digital recording with some tube preamps or whatever, you'll know that it's not the same thing as analog tape at all, though their intentions may be good.

There are other, lesser kinds of distortion created by the analog tape recording process: intermodulation distortion, where sum and difference frequencies are generated, and phase distortion, and self-biasing of the high frequencies, and time smear or "smudging", and probably others, none of which I have the equipment to measure... but they're all absent from digital recordings. Is this good? Is it bad? I don't know. You just have to be aware of it, and deal with it, that's all, because we're stuck with digital!

As an aside I'd like to speculate that the process of making vinyl records, being the multi-step electro-mechanical process that it is, probably adds further kinds of mild "distortion" to the music. I know of some kinds (like the fact that the inmost grooves always sound the worst) but if anyone has any idea on what other kinds are inherent in the process I'd be interested.

Hope this wasn't too dense/dull...

'Till next time,
Jack E.

P.S. I'm going to start archiving these on my site, so if you missed one you can find it there. By the way, if anyone has any trouble accessing my website, please let me know; I have no idea how my ISP is doing unless people tell me. Thanks!

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