Katz's Corner Episode 25: Adventures in Distortion

I. The Genesis
I've been preparing to write this article for many years! In order to make this investigation, I needed to create a laboratory-grade distortion processor, which I've just completed designing and building. Let me introduce you to Bob's Blender (Fig 1). In a moment we'll discover its features and controls.1 But first a little background: The underlying topologies in analog amplifiers, preamps, and equalizers have been evolving for decades. At first there were only tubes: triodes, tetrodes and pentodes. Then, of course came solid state, the germanium bipolar transistor (which was not particularly good-sounding), then the silicon bipolar transistor, different types of FETs, discrete opamps (which can be tube or solid state), and integrated circuit opamps which often contain hybrids of bipolar and FET elements. Some people have claimed that the choice of individual components governs the sound of the circuit (e.g. tube versus transistor, FET versus bipolar, etc.) but a skilled designer can make different components perform similarly, or the same components perform differently, depending on the circuit he chooses. So the circuit and layout are just as important as the component topology. That said, the first amplifier component ever designed, the triode tube (invented in the year 1906!), has a pretty simple distortion character. For my Blender, I chose a low voltage, low gain, ultra-miniature, metal and ceramic Nuvistor tube, the 8056 (one for each channel). The Nuvistor's footprint is smaller than a dime and it's not even as tall as the first joint of my thumb! (Fig. 2) One distinction of a Nuvistor is that it has a very high bandwidth, which can extend into the low-Gigahertz range, while many of the larger glass tubes exhibit high frequency rolloff just above the audio range. My tube blender is flat, not even a tenth of a dB drop at 89 kHz, the limit of my measurement system, so I don't know where it drops off! Of course bandwidth also depends on the circuit, so one designer can make a 12AX7 extend higher in frequency than another through use of optimized impedances.


Fig. 1: Bob's Blender is a processor that adds calibrated, controllable and repeatable amounts of second harmonic distortion, as little as 0.0003% THD, as much as 1% at full peak level.


Fig. 2: The ultra-miniature Nuvistor, from Wikipedia: Photo By Jim Rees en:User:Rees11, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=10993169

Reason Number One Why Bob Is So Interested in Tubes
So why am I so interested in tubes, triodes in particular? Reason number one: The sonic nature of triode distortion and saturation. Triodes have been variously characterized as sounding "smooth", "sweet", "round", "creamy", "warm", "three-dimensional" and "present". This is largely thanks to the presence of second harmonic, the triode's dominant harmonic component.

Distortion is signal compression, so as the input level goes up, the triode softens transients by adding more second harmonic (twice the fundamental), and eventually other harmonics when levels get very high. The triode soft clips—rather than instantly turning a sine wave into a square wave. In contrast with many solid state circuits, it starts to round off the corners in a gentle way. Other devices and topologies (including tetrode and pentode tubes) are more prone to adding higher harmonics, which are known to sound harsh compared with the second harmonic that predominates in triodes. But to repeat: a good designer can create a warm-sounding solid state circuit dominant in second harmonic or with reduced upper harmonics if he wishes. Witness the warm sound quality of the Mjolnir Pure Bipolar headphone amplifier and many of the Pass products as well as the Bricasti power amp and power amplifiers from Krell, many others.

Reason Number Two Why Bob is So Interested in Tubes
Some more background: From 1950 on, many designers have been seeking ever lower harmonic distortion figures. 1950s audio gear exhibited distortion of "under 1%", sometimes as low as 0.1 or 0.2%. The earliest solid state devices exhibited similar distortion numbers, but these values quickly lowered, and by 1980 solid state audio circuits produced lower distortion than the analyzers of the day were capable of measuring. I wonder if the race for the lowest distortion figure was sponsored by the measurement equipment makers! I remember in my youth lusting over an analyzer which could measure as low as 0.01% distortion. That analyzer was soon superseded by another and yet another, each successor capable of measuring an order of magnitude lower. Some of today's amplifiers measure as low as 0.0008% (that's three zeros and an 8, 8 tenths of a thousandth of a percent). Lower is good, right? Not so fast, number crunchers!

Let's cut to the chase, it was the increasing use of negative feedback that engendered ever-lowering distortion figures. Negative feedback is a perfectly good mathematical technique that works very well. But the designer has to realize that the circuit may not sound good even if its measured THD (total harmonic distortion) is very low. If the designer pays attention solely to the THD value, he may not realize that sometimes the "good-sounding, lower harmonics" get suppressed at the expense of the "bad-sounding, higher harmonics". Research by Norman Crowhurst points out that feedback mostly reduces the level of the 2nd and 3rd harmonics, leaving the upper harmonics more or less alone, or sometimes at higher level than before feedback. It doesn't take very much level of a 5th, 7th, or 9th harmonic to make the sound "bitter", "dry", "clinical", "cold" "small" "dynamically limited" or "harsh". This is all part of the psychoacoustics of distortion and masking.

In today's investigation I aim to get a handle on how to use distortion to improve the sound quality of our playback gear. Yes, I said "improve", because we're going to redistribute the harmonic emphasis of our signal chain. Not all amplifiers with ultra-low distortion sound harsh or small: Notable among good sounding (or at least sonically neutral) low-distortion amplifiers is the Hypex Class D amplifier, invented by Bruno Putseyz. His recent model, the Hypex NCore, has near zero harmonic distortion and is audibly close to the proverbial straight wire with gain. No distortion sounds better than a little bit of bad distortion, but moderate, well-distributed distortion sounds better, too!. I believe there's a middle amount where distortion can sound deadly. Why? Because in that middle area, where the overall distortion measures somewhat low, but not close enough to zero, the presence of some higher harmonics can psychoacoustically predominate over the important lower ones. In other words, the distribution of the distortion is the key to sonic differences.

Distortion is additive. You, the consumer, cannot take it away, so when you add a preamplifier in series with your amplifier, you hear the distortion of both units. So you can increase the amount of distortion by putting one device in series with another. But why would anyone want to add more distortion to your audio reproduction? The answer is my reason number two: Masking. Just as noise can mask signal, distortion of a certain magnitude and frequency content can mask other distortion. I'd like to prove this in a controlled manner. My Blender allows us to test this hypothesis and perhaps for the first time, quantify the amount that is needed. This is not a commercial product, I have not put it into production. There is only one "Bob's Blender".

The Blender can add second harmonic distortion in a controlled and repeatable manner from an extremely low amount up to very high. It has balanced inputs and outputs, for use with professional gear such as my audio mastering chain. But it can be easily unbalanced with only slight loss of headroom using an XLR to RCA adapter, so we can use the Blender with our collection of consumer headphone amplifiers. In solid state mode, the Blender has very good input and output headroom, up to +28 dBu (19.5 volts), and very low noise (below -90 dBu) so it can interface with anything. Here are its simple controls:

  • Audio Power: Turns the power to the audio section on and off.
  • Solid State: This button enables or mutes the solid state section which can be mixed in any proportion with the tube section.
  • Tube: Likewise, this button enables or mutes the tube section which can be mixed in any proportion with the solid state section.
  • Mix: When engaged, the mixer is active. When disengaged, the Blender is hardware bypassed so we can instantly compare the blender against no blender.
  • Next comes the meter, to read the plate voltage of each tube for fine adjusting the bias. Typically I bias the tube for minimum distortion.
  • Next, the meter switchto meter either the left or right plate voltage.
  • Next, bias adjustment and drive potentiometers. The drive can be adjusted to produce any gain up to the maximum of the tube, or to overdrive the tube or keep it closer to its linear operation.
  • Next are two 1 dB/step potentiometers which I have hand-built from rotary switches and metal-film resistors. The solid state and tube sections can be mixed in any proportion in 1 dB steps from 0 dB down to -22 dB.

For example, at -6 solid state/-6 tube, the tube and solid state sections are mixed at exactly -6 dB attenuation, and the sum of the two is at unity gain. Since the solid state portion of my circuit has vanishingly low distortion, I can obtain any degree of triode distortion from the box I might wish. The adjustments are performed in the analog domain so there is no DSP which could cause aliasing artifacts. Moreover, the amount of distortion is calibrated and repeatable which allows us to listen, make changes, find our preferences and then measure the amount of distortion that resulted in the sound we prefer.

The tube drive levels have been adjusted to produce a not-excessive amount of saturation at full peak level. The stepped attenuator is located after the tube so that the distorted signal can be mixed with the "dry" signal. The power supplies are well-regulated. The tube cathode is grounded and the bias control adjusts the level of a regulated negative voltage imposed on the grid. An FET buffer isolates the tube and keeps it from being loaded down. The solid state portion uses highly-regarded THAT-brand chips for summing and balanced conversion. Here are some intriguing measurements, the source being the same Prism Callia DAC that I use to drive my headphone amplifiers. The Callia's balanced output feeds the Blender. The Callia's output level is -6 dBu (0.39 v) at -20 dBFS, which we call "nominal level", approximately the level of a mezzo forte musical passage.

In Fig. 3 we measure the Blender's solid state section (the tube section is muted). Solid state attenuation is set to 0 dB, with 1 kHz at -20 dBFS, -6 dBu. The distortion measures only 0.0003%. Any harmonic products are below -115 dBu (inaudible). The rise in noise at supersonic frequencies is due to the Prism noise-shaped converter I use for analysis.

SpectraPLUS-SC Sound Card Edition

Fig 3: Blender, Solid State @ 0 dB, Tube muted. 1 khz @ -20 dBFS, -6 dBu. THD 0.0003%.

In Fig. 4, we raise the level to nearly full peak level, 1 kHz at -1 dBFS, which produces +13 dBu. Blender is set again to solid state only, attenuation 0 dB. The THD has barely risen, to only 0.0005%. Although there are some visible higher harmonics, even at full peak level, the highest harmonic is only at -95 dBu, so the solid state section is probably audibly transparent or nearly so. I don't detect any audible harshness from this solid state section, but there's nothing to prevent a designer from using even more linear components than the THAT amps I chose. And regardless, when a proportion of tube is mixed in with the solid state section, the dominant second harmonic will hopefully mask any higher harmonics.

SpectraPLUS-SC Sound Card Edition

Fig. 4 Blender at nearly full peak level, 1 kHz at -1 dBFS, +13 dBu, SS @ 0 dB, tube muted.0.0005% THD

In Fig 5: We mute the solid state section, and set the tube section to 0 dB attenuation. 1 kHz @ -20 dBFS -6 dBu yields 0.1% THD. Distortion is all second harmonic, at a magnitude of -66 dBu, which I think is a sonically meaningful level. Notice that the tube noise masks all the higher order solid state distortion. The fact that the left and right distortion levels match so well is a testament to the matching of the two tubes and the precision of the bias adjustment.

SpectraPLUS-SC Sound Card Edition

Fig 5: Blender 0 dB tube. 1 kHz @ -20 dBFS -6 dBu. 0.1% THD

In Fig 6, we mix Solid State and tube at equal level, -6 dB each. 1 kHz at -20 dBFS produces a nominal level (-6 dBu) into the Blender. This reduces the distortion by 6 dB, to 0.05%. Second harmonic is now at -72 dBu, which I believe still has an influence on the sound character. Reducing the tube attenuation even further, a mix of -2 SS and -12 tube at nominal level reduces the THD to 0.02% (not shown). At -1 dBFS (nearly full peak level, not shown), tube and solid state mixed each at -6 dB yields 0.4% THD. It doubles to 0.8% with solid state muted and tube at 0 dB (not shown). So we can repeatably produce calibrated amounts of second harmonic distortion. A listener can judge the effect of harmonic structure on sound quality and we can correlate his perception to the amount of second harmonic distortion in the circuit.

SpectraPLUS-SC Sound Card Edition

Fig 6 Blender -6 ss/-6 tube . 1 kHz at -6 dBu, 0.05% THD

II. Now For The Fun Stuff! Listening Tests.
Inquiring minds want to know the answers: Can we mask harsh distortion by adding euphonic harmonic components? Can we change the personality of an amplifier? Without introducing a sonic compromise? How much second harmonic distortion is perceptible and meaningful? I and my assistants auditioned three different solid state headphone amplifiers with the Blender in series. In each case we compared that against the sound of the Mjolnir Pure Bipolar amplifier which did not have the Blender connected. The amplifier analog volume controls were adjusted to yield matched headphone output levels at 1 kHz (loaded by 110 ohms) and the digital attenuator adjusted listening volume.

I used JRiver Media Center on PC to play high resolution audio selections. This fed Acourate Convolver (for dithered volume control), which then went to a Lynx interface which fed the Prism Callia DAC via AES/EBU. The DAC's balanced output was connected to the Mjolnir Pure Bipolar amplifier without any intervening analog circuitry. The passive Y-output of the Mjolnir was connected to the Blender input, whose output was connected to different headphone amplifiers under test. The headphones were Audeze LCD-4. I varied the mix levels in the blender of tube versus solid state to my taste, with the sum being unity gain or close to same, and also compared to hardware bypass, the "naked" sound of the amplifier under examination. I did not use any EQ for this investigation.

AMB versus Mjolnir
A couple of years ago I built an AMB M3 amplifier using the PC board which AMB sells here. (Reviewed in Katz's Corner Episode #7.) This amp has a higher than average voltage power supply (+/- 18 volts), a JFET opamp front end (OPA 637), and Mosfet outputs. A fairly strong amount of overall negative feedback is employed, yielding an output impedance of 0.2 ohms. This amplifier sounds solid and it's kicked a lot of competitors out the door, but it is no longer my listening favorite as I think it sounds a bit "clinical" and "dry" and sometimes a bit harsh. We'll be comparing the AMB fed by the Blender against the Mjolnir Pure Bipolar (reviewed in Katz's Corner Episode 18). For this listening session, my assistant, David Corson, also shared listening duties and he concurred with all of my reactions below.

West Side Story
The first music piece I picked is a bright sounding (but otherwise excellent) recording of West Side Story—a 2496 recording from Blue Coast Records of the San Francisco Symphony conducted by Michael Tilson Thomas. It's a very enthusiastic and exciting performance interpreted by a Bernstein protegé. When I listen to this recording on my loudspeakers, I normally EQ, shelve the high frequencies downward slightly, but I've discovered that the Mjolnir Pure Bipolar headphone amp sweetens transients so that program EQ is not needed when using the LCD-4s with the Mjolnir (see Katz's Corner Episode 24).

Listening to the AMB without Blender my reactions are that the sound has a clinical, bright quality, and is a bit harsh and off-putting. It does not sound real or natural. I definitely do not consider this recording as reproduced on the AMB to be a pleasant or musical listening experience. Imagine the pain in the ear listening to this recording with a pair of bright headphones. But on the Mjolnir, the LCD-4 sound is warm and quite musical, still quite open, yet softer and more natural on the peaks. Since the Mjolnir is a balanced headphone amp and the AMB unbalanced, I can switch the headphones quickly between the two amps by using a balanced headphone cord on the cans, and a special high quality adapter I made from 4-pin XLR female to TRS male.

As soon as I take the Blender out of bypass, the AMB's sound is transformed: it's now warm and sweet, yet clear; the 3 dimensional space has greatly expanded. Its personality has totally altered. In fact, the AMB's tonality now resembles the Mjolnir so much, it's uncanny. I decided that 0 dB tube level sounds pretty but some of the detail is lost, so I settled on reducing the tube level to -6 SS/-6 Tube after some experimentation. This mix setting sounds so seductive I used it for the vast majority of my listening tests. I do not hear any down side to adding the Blender at this setting. This is pure, seductive pleasure with all the detail and clarity that anyone would desire. Now, there's nothing that I prefer about this recording in the Mjolnir, it even seems that the AMB + Blender has more 3-dimensionality than the Mjolnir! My conclusion is that since distortion can only be added, not subtracted in this chain, the psychoacoustic mechanism is distortion masking. I believe that this approach to mask harsh distortion by using euphonic distortion works, very well. As I noted in the measurements section, it's also possible that the tube's broadband noise masks some of the harsh distortion.

Here's a measurement (Fig. 7) of the AMB amplifier with and without the Blender, headphone output at approximately -6 dBu into a 110 ohm load. Notice that the addition of the tube has raised the noise floor, which is still low enough to be inaudible on the LCD-4s. If I had chosen a high voltage Nuvistor instead of the 8056, the noise would be lower. So, yes, it's possible that the tube noise masks some of the distortion of the AMB amp. I could only disprove that hypothesis by changing to a quieter, higher voltage tube. But we do notice that the 2nd harmonic distortion affects the sound quality, as altering it drastically changes the sound character. In the lower trace, we can barely see some evidence of 2nd, 3rd and higher distortion components in the AMB's native spectrum, which in the upper trace are visibly and possibly audibly masked by the tube noise as well as the dominance of the tube's second harmonic. Notice that the broadband noise of the tube completely covers the 60 Hz component, which is low enough to be inaudible anyway. The 60 Hz hum and its harmonics are due to a floating ground to the analyzer, that I had to use to avoid damage to the AMB's active, driven ground.

SpectraPLUS-SC Sound Card Edition

Fig. 7: AMB M3 amplifier, 1 kHz at -20 dBFS into the Callia DAC. Left channel on top, right channel bottom. The upper traces, in Red (left) or Green (right), with the Blender in series. The lower traces (blue and black) are the AMB amplifier without the Blender.

Genius Loves Company: "Here We Go Again"
This 2496 recording from HD tracks, Ray Charles' anniversary edition, is one of my favorite references, engineered by the great Al Schmidt. Ray and Nora Jones's duet. Billy Preston plays organ with a stereo Leslie supplying grit and depth.

At -6 SS/-6 Tube ratio, the ambience on the side stick is enhanced and more present when the Blender is switched in; ambience is stronger in the AMB amp now than in the Mjolnir, not unpleasant, very pretty. I've known for many years that harmonic distortion can enhance depth and ambience, but this is uncanny—it's like there's a magic reverb chamber in the tube. The ambience is enhanced in a holographic way that's totally pleasant and not at all distracting from the original mix or performance.

Tonally, there are subtle differences but on the whole the AMB with the Blender accurately mimics the Mjolnir's tone. Adding the Blender subjectively brings up the bass, although the frequency response measures ruler flat to well above 100 kHz. So the harmonics add warmth and a sense of "fatter" bottom. This wide bandwidth Nuvistor tube is very transparent and does not audibly soften the sound in any negative way. The sound on this song is 100% preferable with the Blender engaged.

The Audeze Deckard is particularly dry and uses extreme negative feedback. It's quite amazing how ADDING the tube (triode) distortion transforms this amplifier into a sweeter, deeper, warmer and more pleasant-sounding amplifier. My conclusion is that this business of denigrating amplifiers for employing "too much negative feedback" is bunko. It's not the feedback per se that's the problem, it's when the feedback changes the harmonic structure for the worse.

To my ears, the AMB amplifier is perfectly capable of becoming a world-class champ without removing its negative feedback. I conclude that as long as an amplifier is reasonably linear and powerful, it's possible to restore depth, purity of tone and life simply by adding a bit of second harmonic. Any of the issues I had with the AMB seem to vanish when we apply the triode in series, and blend the distortion in at a level that's not too high, not too low.

Marta Gomez, "La Finca" from the album "Cantos De Agua Dulce"
This is a beautiful folk album that I've just discovered, very naturally recorded by Barry Wolifson. Marta's voice is charismatic and pure. Highly recommended. On this material I didn't notice a giant increase in depth, but the sound is not at all deteriorated with the addition of the tube at a -6/-6 ratio.

Matt Davis Joins In The Listening
On another day, I invited my young assistant Matt Davis to give his reactions to the Blender.

Lindsey Webster, Back To Your Heart
Matt: This is Bob's 2496 master. The Blender at -6/-6 on the AMB amp evens out the tonality. The snare gains a more dimensional texture. The vocal pops out in a nice, natural way. The tubes rearrange the ambience in a natural sort of way. The soundstage is deeper. It almost feels like there's a little more reverb on it, but in a very natural and not objectionable sort of way. Really pleasant.

Marta Gomez, "La Finca" from the album "Cantos De Agua Dulce"
Matt: Blender at -6/-6. I hear it on the side stick. The tube makes it sound more involving. The AMB M3 amp is starting to take on a triode personality, but a very clean one. The whole sound is more spacious.

Comparing to the Mjolnir: The Mjolnir's bass is a little punchier and a little less veiled than the tubed-up AMB. But that was with -6/-6 SS/tube mix. Instead, let's try a little less tube on the AMB: -3 SS with -9 tube yields about unity gain. Now the AMB feels a lot more like the Mjolnir. The coloration is roughly equivalent, but the AMB with Blender has more depth than the Mjolnir. Hey Bob, it looks like you just made a Mjolnir killer by accident (by design!). I don't hear any down side after I changed the tube/ss mix. I've got the mix exactly where the Mjolnir is sonically and if anything I hear a depth advantage to the AMB over the Mjolnir. What a discovery!

Can we make the Audeze Deckard amp improve in the same way by adding the Blender in front? The Deckard uses extreme negative feedback and its output impedance is a few tenths of ohms. So the question is: Can we transform the sound of an amp that uses extreme negative feedback or is extreme negative feedback an irreversible detriment to sound quality?

Comparing the Mjolnir to the altered Deckard: I've got -5 SS/-7 tube. It just doesn't quite get the depth that the Mjolnir does. There's a certain dimensionality to the Mjolnir that we can't get with the Deckard, even with the tubes. The levels feel pretty matched when bypassed or between the two amps. I tried turning the tube level up further, but it starts losing clarity compared to the Mjolnir. So this becomes a matter of diminishing returns.

Bob: Tentative conclusion based on this recording: We have not examined the harmonic distribution and harmonic levels of the Deckard. But this comparison of the Deckard with the AMB implies that sometimes negative feedback can be completely mollified by the addition of a tube stage or harmonic distortion, and sometimes it cannot, but adding the tube stage can certainly improve the situation.

West Side Story
Jet Song [see Bob's notes above]. Mjolnir versus the Deckard modified with tube or AMB modified with tube.

Matt: Beginning with -6/-6 ratio. There do not seem to be any down sides to the modified AMB. Neither the AMB with tubes nor the Mjolnir are more advantageous with this recording. I would call the two presentations comparable. But what about the Deckard? Deckard, beginning at -6/-6 versus the Mjolnir. The high hats and brass have a harsh quality in the source recording. The Mjolnir does a nice job of smoothing them and with the Blender the Deckard performs similarly at -6/-6, I think the character of the high hats is still slightly preferable on the Mjolnir, but it's a tight race tonally. Depth is also very close, so it seems that extreme negative feedback is not necessarily a detriment at least for this recording.

Bob: I conclude sometimes the Deckard can be improved without loss, and sometimes it cannot. I'm sure this is related to the harmonic content and complexity of this recording; the more complex, harsher and brighter the recording, the harder it is to sweeten it up.

FB Pocket Orchestra "I Lost My Girl From Memphis" 2496 master by Bob
Matt: This is a rather bright, brashy recording that could benefit from some sweetening. Another good test of the precept at hand here with the Deckard. I think the tube-modified Deckard and the Mjolnir function pretty well equivalently at the task of softening the objectionable transients on this recording. The depth is also roughly equivalent. However, the mix separation between instruments, which is kind of an asset to this recording, is better in the Mjolnir, the instruments have their own place where they sit more than in the Deckard. It could be level matching or the tube mix, which is at -6/-6. It's very subtle and could just be a level matching issue. This still speaks a lot to the legitimacy of the tube box, because without the tube box in series with the Deckard, there is no comparison, the two amps are not close.

JDS O2 amp
Matt: This is the amp that Bob has given a terrible review. Let's try it with the Blender in comparison with the far more expensive Mjolnir. Can we transform a $129 portable headphone amplifier to the quality of a $2500 boutique amp by the addition of tube distortion?

Donald Fagen, Morph The Cat, 2496 from HD tracks
Matt: Level matching done by ear. The tube really opens up the little O2 amp, it makes a valiant effort. Without the tubes, it's a very flat, undimensional amp. The tubes are transformative, they take a C- amp and make it at least a B+. There's definitely some personality going on in the Mjolnir that I prefer over the modified O2, but the Blender gets it a lot closer than I would have thought at -6/-6 blend.

Now let's try more tubes, turn it up to 0 dB tube. Even with the tubes on all the way, this Nuvistor is a really transparent tube. But this level does soften the details while it mollifies the O2 amp. Do I prefer all tube to no tube? This is a tough call, 0 dB tube veils the mix but I do like that it adds depth to the soundstage. If we were starting with a superior amplifier, we'd need less tube. For example, the AMB needed far less tube to get it in the ball park.

Bob: There could be some other factor going on with the O2 amp, because if the problem with the O2 is harmonic distribution, then adding the Blender in the same proportions as were used for the other amps should be the cure for the problem.

III. Conclusions

Is It Accurate? - Is the Blender accurate? Adding a certain amount of second harmonic can improve the purity of tone and depth of amplifiers without losing any detail, impact or transient response. But as we saw with the West Side Story recording, the Blender is "forgiving" and makes this recording more palatable. In that respect it is not an accurate product because it can mask the sonic differences between recordings. That disqualifies it for use in a mastering studio monitor, where I have to accurately know what my recordings sound like. But my Blender does get studio use as a mastering processor and I do not hesitate to recommend it for audiophile listening. It makes a great audiophile headphone or loudspeaker processor.

A Look Toward The Future
I believe that second harmonic distortion is sonic gold for audiophiles: It's very seductive, especially if you want a warm sound quality, three-dimensionality, and beautiful reproduction of ambience and depth. Based on the listening tests, there does not seem to be a sonic negative side if the proportions are done right. Yes, too much second harmonic and detail will be lost or the sound can become flubby, like some inferior tube preamp designs. That's why this listening test was so useful, as we can discover how much harmonic distortion is "just enough".

Also, the process must not cause any artifacts. Since tubes are no longer made, a solid state or a digital solution might work. I question the quality of any DSP solution that I've heard so far. I have plugins which emulate analog distortion which can be used in mixing and mastering. They've reached the point where I can subtly use them to color sound, or produce a special effect, but I have not yet heard a digital emulation that I would call "audiophile-quality", transparent and artifact-free like this Blender. I have friends who are DSP designers who say transparent emulation can be done—so bring it on down, I want to hear it! Remember: A little bit of harsh distortion, especially inharmonic distortion (aliasing), is quite audible. A DSP algorithm without artifacts will require extremely high upsampling and impeccable coding.

I can't predict if this circuit will become popular with audiophiles, but it certainly is going to be popular with me! I think that some designers will be taken aback. The last thing they may want is an amplifier whose personality can be altered by the turn of a dial. The idea seems like a gimmick, no matter how good it sounds to the ear. The process takes away the marketing exclusivity of an amplifier brand and its unique sound, since I've demonstrated that a good, linear amplifier can be literally transformed to a sonic gem. Some relatively inexpensive circuits can take on the personality of high end boxes made from unobtanium. But not all cheap amplifiers can be sufficiently improved, as we learned from this listening experiment.

So I hope some designers will embrace this approach: A smart designer might produce an outboard box with variable second harmonic level like my Blender. Another designer might incorporate this type of circuit inside of an amplifier. Personally I would embrace an amplifier whose personality can be controlled for pleasure listening. Consumers might feel uncomfortable with so much variability under their control, or reject a control knob labeled "distortion". But if you already like to use program EQ, then a knob that affects tonality as well as depth would be a logical extension of your palette. Keep in mind that for over 90% of the program material we auditioned, we agreed on a single blend setting so a box doesn't have to be complicated, the control could be left off the front panel. So designers might incorporate this circuit, even secretly, inside of their amplifiers.

Recommended Settings
The added distortion should subjectively improve sound quality without degrading clarity, depth, or definition. If not, then the device must be adding too much distortion. Based on these listening tests, I recommend a maximum level of second harmonic no higher than 60 dB below the fundamental at nominal level (mezzo forte), typically -20 dBFS. The sound of -60 dB second harmonic is pleasant to the ear and enjoyable to many listeners, but perceived as a bit thick sounding with some loss of detail. Probably -66 dB second harmonic is the ideal setting, as in our listening it produces an attractive, warm, three dimensional quality with no apparent loss of detail or other side effects on any amplifier we tried. With some musical sources and some listeners, we may have to further lower second harmonic. I also suggest that the processor and amplifier be otherwise very linear, with good power supply regulation and extended bandwidth well above 20 kHz. It helps to start with amplifiers that do not have excessive upper harmonics before applying the Blender. Masking works, but it's not a miracle worker.

We did not investigate third harmonic distortion, so we do not know whether third would be a useful addition. But I suspect third harmonic will not be helpful. Analog tape distortion is predominantly third harmonic and it can sound very nice, but my experience is that it's more of a color machine than a cure for bad sound. Third is less invisible than second harmonic, it softens the high frequency peaks and it can strongly compress dynamics. So I recommend that added harmonic distortion should consist solely of the second harmonic; the rest of the harmonic residuals should be at negligible level, very close to the noise floor if at all measurable.

We have to perform further listening tests. We did not investigate IM distortion and since real music consists of multiple mixed tones, the effect of IM will vary with the type of music, depending on how dense it is. Witness that the simple folk music arrangement was less affected by the Blender than the more complex music. But if we stick to just adding second harmonic, it will reduce the complexity and any harmful IM. I enthusiastically invite any reviewer to come down to Florida to check out Bob's Blender. This article changes the way we should think about amplifiers: We are living in very interesting times!

1 I want to thank my two mentors, John Chester and Gordon Rankin, who helped me with aspects of the tube design.

Pokemonn's picture

Great article from Bob Again. Thank you very much Bob!

Pokemonn's picture

dear mighty Bob Katz.
I recently noticed that tubes have 1/f noise spectrum.
Human tend to perceive 1/f noises as very comfortable phenomenon.
I guess this is the one of reason why human tend to prefer tubes noise and not prefer low noise solid state devices.

Bob Katz's picture

I haven't studied 1/f noise enough to be knowledgeable. But I will say that the noise floor of my blender's tube is at the threshold of being perceived, while either a higher voltage tube or a solid state device would be even quieter. So I'm not sure how important the shape of the noise is compared to its level and perceivability. As I mentioned in the article, one way I could isolate whether noise is the contributor to the perception of warmth would be to use a quieter triode with the same distortion spectrum.

A lot more research still has to be done. I think My article is a good pioneer as I actually built a controllable distortion generator that we can quantify.

Pokemonn's picture

RIAA curve, dynamic drivers distortions, some headphone/loudspeaker target curves are trying to mimic 1/f curve? maybe or may not.

Bob Katz's picture

Thanks for your kind words about my article.

mnaganov's picture

So, Fielding DSP state that their Reviver plugin which adds 2nd and 3rd harmonics is "free of aliasing in audible frequencies." How does it compare to Blender?

jjk's picture

I have been looking for a plug-in for JRiver for harmonics and tube. Have you used Reviver and do you recommend it?
Thanks, jjk

mnaganov's picture

Yes, I started using Reviver for listening on headphones via solid state amplifier. I agree 2nd harmonics add some "dimension" into the sound.

You may try it yourself, it's free for some period, and it costs just $30. Although it's not per user but per computer, but still not much.

jjk's picture

Thanks mnag,
Can you suggest some beginning settings for me; particularly the input and output gains?
Thanks for your help.

mnaganov's picture

jjk, the gains only need to be adjusted if you add too much energy with harmonics (which you shouldn't be doing :) and get clippings. In my setup, I didn't have to change gains at all. I'm adding modest amount of 2nd harmonics (25-30) and a bit of 3rd (10-15) in "Serial" mode. This works good for 80-s rock and jazz. In fact, Reviver shows input and output levels so you can always check that. I also double check with Bitter meter from Stillwell Audio.

jjk's picture

Thanks very much. Good stuff!
Is Reviver available on Android? (Onkyo DAP)

fabian@fielding's picture

Hi Fabian from Fielding DSP here. Thank you all for the kind words on Reviver :-)

Just to clarify: Reviver is not per computer - but per user. You can install Reviver on as many computers as you like as long as you don't use two copies at the exact same time.

mnaganov's picture

Indeed, I have just activated it on my second laptop. I must have misread the license. Thank you very much for correcting me. And thanks for the great product and especially for accessible price :)

Bob Katz's picture

I have no experience with Reviver, so I cannot say. I would view their claim with skepticism. It is possible to be alias free and transparent, but I haven't heard that yet from any plugins I've tried so far.

risotto's picture

What headphones were used? THD of a headphone is ~ 0.1-0.5 %. Won't headphone's THD mask the effects of the THD of this device?

detlev24's picture

That would only be valid for the very best [not the most expensive] headphones on the market and starting from the midrange FR upwards + at moderate listening SPL. Otherwise, THD of headphones is higher.

@Bob Katz: If I understood correctly, your Blender goes up to a max. of 1% THD (2nd harmonic). 1% is much less than the most refined tube amplifiers provide and 1%, most of the listeners would not even be able to hear for different reasons: lack of training, masking by other gear, room acoustics for speakers...

Furthermore, tube amplifiers do not only provide 2nd harmonic distortion, but also relatively high levels of k3/k5 etc. - unpleasant IM. I agree the option to add a controlled amount of 2nd harmonics to impeccable (solid-state) amplifiers, by software or hardware DSP, could improve the listening experience on some music, though. Thanks for the article!

Bob Katz's picture

THD masking is a complex subject in itself. I do not believe that transducer distortion typically can mask electronic distortion. I'm basing this totally on experience, not by any kind of measurement. When I mentioned my article to a psychoacoustic expert friend of mine, he was not so sure that distortion masking is what's going on, and advanced a theory about the cochlear response. But even he could not state absolutely that masking is not the cause of what I and my assistants heard in the listening tests.

Jazz Casual's picture

Release the trolls! ;)

SonicSavourIF's picture

regarding the influence of noise spectra on phychoacoustic sound impression when they are very low. Likewise regarding the difference in sound of amplifiers that differ by inaudible amounts of noise of varying spectra. These claims are most likely result of the sighted listening method applied here (together with the scientifically unsound belief of the author(s) that double blind tests cannot reveal subtle differences in audio equipment).
But of course such a device could be the basis of a scientifically more thorough investigation, if someone finds the time and is willing do do it. In this sense it is helpful.

And of course it is nice to have an effect box to play around with coloration of the sound. It is pretty much an implementation of the „niceness nob“ that Douglas Self describes in the introduction to his poweramp design handbook.

Regarding DSP: It seems to me, that with the help of convolution filters and profiling very convincing imitation of distortion effects of analog circuitry can be achieved. See the Axe Effets II, the Kemper profiling amp, or the BluGuitar Speaker simulation.
In principle, there is no reason to not implement a similar box in the digital domain. But of course this takes a lot of time and effort (and no, not due to minuscule aliasing effects, but due to taking the time to find and implement good frequency responses).

Bob Katz's picture

I think the science is against you.... you cannot simulate non-linear distortion in the PCM domain without requiring upsampling, because the harmonics which are produced beat against the sample rate. It's part of the laws of physics. So I don't think distortion generation in the digital domain can be done well without extreme upsampling.

SonicSavourIF's picture

thanks for your reply.

I don't quite understand what you mean technically by „harmonics which are produced beat against the sample rate“. If you have time to elaborate or have a reference, I'll be glad to read about it.

I don't know any of the technical details of how Fractal Audio or Kemper (or distortion plugin manufacturers for that matter) achieve their modelling/profiling, so I don't know if they upsample or not, but it seems that their products imitate so convincingly tube amp distortion, that professional musicians like Metallica, Animals as Leaders, Plini, Intervals, basically most of the prog scene, uses this either for their live setups (reliability, transportability) or even for recording. Apparently, digital is getting there in being convincing enough for artistic purposes.

Since your device is a „sound enhancing“ device, moving away from fidelity for artistic reasons, I don't see a principal problem in achieving the same in the digital domain, even if it would not be exactly the same. May this require upsampling, or not.

Bob Katz's picture

When you create harmonic distortion, you create harmonics at higher frequencies than the original. If you do this in a sampled system (DSP in PCM) the harmonics which you create can be HIGHER than the highest permissible frequency in PCM. For example, no frequencies above 22.05 kHz are permitted in 44.1 kHz sampled PCM. So, there's aliasing potential when you generate harmonics. I don't want to either minimize or exagerrate the mathematical reasons because I'm not a DSP technician, I'll just tell you that my ears tell me that I hear a harshness due to the inharmonic aliasing products (which can be at a very low level, understandably) in the plugins that I have auditioned. And each time I've tested the plugin for aliasing by generating a high frequency test tone, it's failed and produced aliases in the critical mid-frequency range.

There is hope.... it can be done in the digital domain... as you said, "you don't see a principal problem".... But I'm a skeptic having heard a lot of these in my profession as a mastering engineer. The all-analog blender is not subject to the same issues, no matter what sample rate you are working at. The A to D converter filters out all frequencies that would alias. That kind of filtering is not a process that can be emulated in the digital domain without causing artifacts, unless you upsample. If you ask me any more technical questions than that, I can't answer because it would be over my head. I know just enough about this subject to be dangerous, but not completely knowledgeable.

joelha's picture


What a fantastic article.

There was one point you made which surprises me.

Did I misread you or did you say that you don't find reel to reel (done well of course) as a superior playback medium?

Reel to reel has been the best medium I've ever heard. Maybe that's a matter of personal preference, but if I could find a way to replicate that sound in the digital domain, I'd be a very happy (let's say even "happier") guy.

Thanks for your excellent work. You obviously put a great deal of time and energy into this fascinating effort.


Bob Katz's picture

No, at this point I do not consider reel to reel to be a superior recording or playback medium. 30 IPS 1/2" two track is very good, however, and I wouldn't kick it out of bed, but it's very expensive. I think that digital recording has finally matured to the point where it does not sound harsh and has excellent resolution. I think if you like tape at this point you like its euphonics.

joelha's picture

Thanks a lot for your reply, Bob.

I agree with you about reel to reel if we're talking about accuracy. But I'm increasingly inclined to believe there are elements to what we (or at least many of us) find pleasing which defy what we currently define as "accurate". This is of course only theory on my part. But just as you've explained how adding distortion can create a more "accurate" or at least more pleasing sound, I can't help but wonder if there's something about reel to reel tape which also provides a more pleasing sound.

Putting aside which medium is superior, purely from the standpoint of enjoyment, you would prefer to listen to well recorded digital vs. well recorded reel to reel?

All the best.


GimmeCans's picture

To quote audio designer Frank van Austin, "Any difference between input and output has a name... It's called distortion." This article points up the counterintuitive truth that not all distortion sounds"bad". Even-order distortion can sound pleasant, and you may 'like' it, and have very right to,but since it is not part of the music I'm attempting to reproduce, I don't want it there. My goal is high fidelity, which to me means nothing added or subtracted by my playback gear. The 'concert hall sound' of Bose speakers sometimes sounds pleasant, but... it's not an accurate reproduction of the input, and neither is this. So if I want that kind of sound, I'll buy some old tube gear (even-order harmonics galore), the nostalgia for which may be explained by some of the factors discussed in the article.

Bob Katz's picture

So you prefer the harshness of some of the amplifiers that I auditioned to the alternative? The article presents an argument that adding 2nd harmonic of a particular amplitude can not only eliminate the harshness, but sound every bit as resolved as a competing amplifier. So basically you disagree with the conclusions of my article.

SoundScape's picture

Great article Bob, nice and easy to read too.
It seems to be going a long way towards explaining what, why and why we enjoy certain brands and types of equipment; something I've been pondering for a very long time. I was very surprised, when I read that adding distortion could improve depth of sound; it was a real eye opener. Let's hope all the audio engineers out there get to read this.
Keep up the good work.

castleofargh's picture

if we discuss speakers, and assume we have fairly good gears in a ok room, I'd put preference for distortions as a purely personal concept. or if everybody was to find the result to be better than the original master, then IMO the conclusion wouldn't be about 2nd order harmonic, but about how the mastering job could have been made to please more people(maybe by adding 2nd harmonics, maybe not). it falls back to the creative side of making sound instead of playback gear.

on headphones, things are very different. between the cues we're missing from HRTF and the exaggerated panning, the very concept of fidelity is blurred. so it doesn't seem all that extraordinary when lower fidelity ends up feeling like superior fidelity on occasion. or at least be preferred to a different model of wrong.

crenca's picture

While I get your point, to expand it stereo recording itself (from the mike, to the mix, etc.) does not equal "fidelity" as such, though it is an attempt to get there. How do you mike a full orchestra and mix it to reach fidelity?

What I am saying is that in the context of Bob's experiment, your point is moot I believe...

Bob Katz's picture

Valid points. Although I have found a great deal of correlation between my perception of certain recordings on speakers as on headphones. For example, the West Side Story sounds bright and harsh on both speakers and phones, Phones on the AMB and speakers on the Hypex. So the cure (euphonic distortion) applies across both platforms.

But in many other ways, you are correct, headphone listening is VERY different from speaker listening.

The Federalist's picture
The Federalist's picture

In case anyone wants to read further on the subject. Nelson Pass wrote a paper about harmonic distortion and feedback a few years back. It delves a little deeper into what harmonic and other types of distortion actually are and how they effect audio.


mnaganov's picture

Read with great interest.

trcose's picture

Fantastic article. This is an experiment I've wanted to try as well. I'm happy to see someone playing with mixing devices.

Any hints as to how you are mixing the signals? I'd love a schematic but understand if you are not sharing. wtfamps at gmail dot com

Bob Katz's picture

Write me at bobkatz[at sign]digido.com and I'll send you a schematic.

crenca's picture

Perhaps having your assistant switch the device in and out?

sciencemajor's picture

This is all misinformation and delusion.

Pokemonn's picture

do you really understand that this is just a "hobby" things...
we are not inspecting something like goverment's enviroment regulations etc. lol

tony's picture

Tyll is gone,

are you staying?

Tony still in Michigan

Bob Katz's picture

Tony. I'm still in shock. I miss my friend Tyll very much. He told me we are friends and I can reach out to h im whenever I want, but I want to give him space. Tyll wants to explore the highways and byways and we need to give him space. The new editor of this site has not yet reached out to me.... I expect to be staying, but things are in flux until Tyll's replacement reaches out to me and we discuss where do we go from here....

chip_mk's picture

Great experiment. I’m curious, why tube as H2 generator? Isn’t it easier to use FET since they have quadratic transfer function, which means they produce 2nd harmonic only?

Bob Katz's picture

I don't know enough about FETs to answer your question. I'm an amateur designer, not a day-to-day professional so there is much that I do not know. Several of my friends, current commercial designers, have designed solid state 2nd harmonic generators. But I'm all tuckered out after having build my Blender. I need some rest. I'd love to see someone build a solid state blender and I'll be the first to test it!

zobel's picture

Good work Bob.

You did a semi-scientific experiment that has value, especially if you can eliminate some of those nasty variables, such as;

1)...What else, besides 2nd order Harmonic distortion, does this box add to the signal, and at what output levels?
2)...What influence are expectations and bias playing in your findings?
3)...What are the sources of, and nature of the distortions you are covering up with more distortion? Distortion starts with the microphone, and adds with each process, from mic pre-amps to recording methods and electronics, to recorded media, to playback device, to transducers. Is it possible to distinguish 'electronic' distortion from mechanically induced electronic distortion, for example in microphones? https://www.dpamicrophones.com/mic-university/the-basics-about-distortio...
4)...What distortion does the solid state half of the box produce, and how does it interact with the tube distortion?
5)...What role does IM distortion play here?
6)...Does the S/N ratio change in this process?
7)...If people prefer a low distortion solid state amp of good design over the examples you use, when and why?
8)...With all the tube hybrid headphone amps on the market, which have similar measured distortion figures to this box when set to ideal balance? Alternatively, which tube hybrid HP amp that is deemed to sound best by many, measures similarly in what you are measuring at the preffered settings of the box?..for example the Massdrop CTH by Cavalli.

it goes on and on Bob...but doesn't negate your efforts here, which though is a sledgehammer approach to eliminating audible distortion, seems to be valid in some cases. It is definitely a psychoacoustic trick, that has tons of easy practicality and an apparent benefit on certain musical signals before the final stage of the recording / playback process. It needs more exploring, me thinks.

Thank you Bob....verrrrrry interestink!

Bob Katz's picture

Thanks. All good points. If you would like to fund a unversity-level investigation of all your points I'll be happy to participate. I've only scratched the surface, but I believe I picked the essence of a set of controls that make audible changes and can be quantified (blind, too, if you want).

1) I can answer that question, with measurements I've made of noise and harmonic distortion and IM distortion at different levels. An even fuller answer would require correlating those answers to the sensitivity of the power amplifier and the sensitivity of the headphones under test to guess at audibility. But guess what.... in the end we listen, and there is one thing that we know unequivocably: Altering the 2nd harmonic level 1 dB at a time makes tremendous changes in the sonic character of the music recording. I'm very satisfied with the results and I won't need to spend years of academic isolation and blind tests to put this box to use to my satisfaction.

Bob Katz's picture

2) Expectation bias.... present. How much of it? I leave it up to you to decide. As soon as we go blind, the apparent differences will reduce by a considerable amount. How much of it is due to placebo at that point? I reply: Placebo can work both ways. in the case of ambient judgment, placebo can make you think that there's more ambience when there is less, and vice versa, if you tell your mind that A is X, the mind is powerful enough to color the ambience for you. So as a result, a definitive blind test would require hours and hours and hours and trials and trials and trials to be statistically valid. If you do 20 trials on this blender and they come up null (as is quite possible, given my experience with subtle phenomenon like this) does it mean that there's no audible difference? Or does it mean that the very act of blind testing is extremely difficult in itself? This is not a question with a definitive answer. I only raise the alternative question so that we can make progress in audio design without getting too bogged down in medical-grade questions for what is ultimately a very subjective subject that you either can agree with me on or disagree. That simple.

3) I can't begin to answer that...

4) We don't know the full answer, but it's highly likely that the 0.000x% THD is so low it's inaudible. Non-blind subjective listening tests to the THAT chips by myself and many other pros whose ears I trust indicate the THAT chips are very transparent. So a sighted concensus indicates that the solid state portion of my circuit is effectively neutral. I mentioned in the article that researchers are welcome to try even more neutral solid state circuits if they would like.

5) IM distortion. I hinted that the more complex the music, the more likely IM will take place. HOWEVER, given that the mechanism of the triode is extremely simple and it produces pure 2nd with nothing else but noise, and its IM is very low (not shown but I did measure it), I doubt that IM is the dominant or even contributory mechanism going on here. A full scientific test of the precept isolating variables is beyond the scope of my pay grade :-)

5) I mentioned that SNR could change the process, but irrespective of that, as close to single variable as I could make it, the dominant mechanism appears to be 2nd harmonic: varying the 2nd harmonic changes the sound. I would need to build a quieter circuit that does not mask the AMB's distortion in order to be sure that SNR is not the least influence.

7) Solid state amp and preferences. If I write any further investigations on this blender I'll be sure to do some more testing to try to investigate your excellent question. One thing I do know is that Nelson Pass uses the tiniest smallest bit of 2nd harmonic sugar in his amps, so I should emulate that by using a much smaller amount of 2nd and see if it still appears to improve the sound of the AMB. I'm pretty sure that the settings we used were of the "very euphonic and pleasant" variety. A setting that does not appear to increase the depth but sweetened the sound would be very interesting to try. No question that the Pass HPA-1 does NOT enhance the depth, but that it is a warm-sounding amp, so there are levels of 2nd harmonic that are worth trying, lower than I have tried. And it's available to me, at the turn of a knob!

8) Other amps on the market.... worthy of some tests. I predict that as I listen to other models of amplifiers here at Innerfidelity in the future, I should pay attention to their harmonic distribution more and see if there is correlation to their sound character. What a can of worms we have opened here! I hope you enjoyed it and it doesn't taste too bad :-).



KeithHoward's picture

Why do I get the sense that nobody has read http://stereophile.com/reference/406howard or tried AddDistortion? You can experiment with any harmonic pattern you like - and it costs nothing but your time.

mnaganov's picture

Keith, thanks a lot for pointing out your article! I didn't realize until reading it that the non-linear process used to create harmonic distortions also generates intermodular distortion components.

I've experimented with Fielding Reviver, and it seems that level of IMD as measured according to SMTPE grows much faster than THD (IMD CCIF does not). E.g. when I'm adding 2nd harmonic at 0.3%, IMD SMTPE is 0.5%, and when 2nd is 1%, IMD SMTPE is 4%. Same thing, if not worse, for the 3rd harmonic alone.

So it's actually possible that IMDs contribute a significant amount of what is heard during these distortion experiments.

@BobKatz: Bob, could you please measure what levels of IMD does Blender generate?

mnaganov's picture

Found this article by Dr. Uli Brüggemann, the author of Acourate: http://www.acourate.com/freedownload/k2/TheHarmonicDistortionMyth.pdf

He explains why it's not possible to add only 2nd or 3rd harmonic for real music without also adding non-harmonic frequencies.

Pharmaboy's picture

This is one of the best & most fascinating audio articles I've read in a long time. Besides the intriguing results of the listening tests, what I appreciate most is that you join the empiricism with music appreciation. So often these are weaponized, at pitched odd with each other--but not here. Thanks for advancing our understanding of distortion's multivariate effects on sound.

pietjepuk's picture

Bob,did you try grounding the input of the nuvistor so that it does not deliver anything but noise ?

random's picture

All that time to construct some top notch equipment but a really poorly implemented listening evaluation, sorry to be blunt.

If you conducted a blind test you may have found people couldn't reliably tell the difference until quite significant levels are reached, my memory may not serve me correctly but I believe AES investigated the audibility of harmonic distortion and found you needed 1% before people could reliably tell. It would be interesting to do a blind A/B to determine the threshold of 2nd harmonic at which a difference is audible, then you would have a real conclusion.