A Rethink of THD/THD+N (or why both tell us almost nothing)

Discussion in 'Audio Science' started by ChaChaRealSmooth, Jul 6, 2020.

  1. ChaChaRealSmooth

    ChaChaRealSmooth SBAF Poopsmith

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    To be absolutely clear, both THD and THD+N are not completely useless measurements. However, when interpreting these numbers, it is of vital importance to keep in mind what they represent. THD is essentially a summation of all of the harmonics, i.e. 2nd harmonics, 3rd, 4th, etc, and outputted as a single number. The “+N” part, the noise, refers to things like mains noise. This measurement is most useful just as a quick and dirty way to see the harmonic distortion present within a system; however, there are several problems with this singular number approach, some of which I will attempt to identify and explain here. The goal is to be able to explain the dated nature of THD using the examples of some amplifiers, explain how to use the individual harmonic measurements to help extrapolate sonic characteristics from looking at measurements, and introduce @atomicbob’s “crap factor,” which @atomicbob believes to be a much more useful measurement when talking about the bad stuff we don’t like listening to. Keep in mind that I am not downplaying the importance of subjective impressions (after all, we listen to music and not sit there and listen to 1kHz sinusoids), but rather is an attempt to help this community understand the thoroughly detailed measurements that @atomicbob, @purr1n, and others post, how they might correlate to things that you hear, and how to use them to help match the measurements with your personal preferences. After all, Changstar was founded upon the idea of measurements, and measurements should serve as a basis to at least keep us honest.

    First of all, we do need to talk about THD. I highly recommend reading @atomicbob’s thread here for a more thorough explanation than what I’ll go over here. Most THD specifications will be posted as follows:
    • Less than 0.01% THD
    • Less than 0.01% THD @ 1kHz
    • Less than 0.01% THD, 20 Hz to 20 kHz, 0 dBu, 300R load
    To use @atomicbob's own words,
    Definitely read the linked thread to look into this further, but basically, only the third specification actually yields any useful information, and to get an even better understanding, a graph is the way to go.

    At this point, one fact should become clear: knowing the THD/THD+N tells us absolutely nothing about how something actually sounds. The issue is further compounded if one considers two facts: the fact that most gear nowadays actually measures quite well (most spurs nowadays are far below the realm of audibility), and the fact that we recommend things like the SW51+ and Bachelor, with do NOT measure well when put up to the THD tests. So how can we use the measurements of harmonics to really tell us anything?

    There is ample evidence to believe that listeners find some degree of 2nd and 3rd order harmonic distortion to be pleasing. Here, I would like to say that 2nd order harmonic distortion sounds “tubey, wet” and 3rd order sounds “edgy, exciting,” but there is very little evidence to really support these descriptions. Let’s look at @atomicbob’s measurements of SW51+, which subjectively does not sound like a tubey, romantic tube amp:


    SBAF1.png


    There is a LOT of information here, but allow me to explain (or rather, @atomicbob). The THD is about 0.52% - 0.58% (very high by some standards). However, take a real close look at the red highlighted measurements below (not the graphs, the numbers in two columns on the left side of the graphs):


    SBAF2.png
    SBAF3.png


    Take a very close look at the readings. Notice the THD and the THD+N numbers are very close. This means that most of the THD+N is made of the THD. And if we take an even further analysis of the various harmonic distortions, one can easily see that most of the THD is dominated by 2nd order distortion. Everything else, from the other harmonics to the noise, is actually very clean.

    Going by my description of 2nd order distortion, one would expect the SW51+ to sound tonally rich, thick, and warm. However, anyone who has experience with it will tell you that the SW51+ is a tube amp that sounds very much like a clean solid state amp!

    3rd order distortion goes much the same way as 2nd order in terms of trying to describe what it actually sounds like. While not amps, let’s look at the CA Andromeda (the original one, not 2020) and the Raal Requisite SR1a:


    SBAF4.jpg

    SBAF5.png


    While comparisons on different measurements rigs are not directly comparable, note that both the SR1a and the OG Andromeda are dominated by 3rd order distortion. However, the SR1a does not sound like the BA-based Andromeda; in fact the SR1a has probably the best timbre out of any headphone out there on the market. The SR1a out of Jot R does kind of sound unrelenting and can be a bit edgy and forward, but is that the distortion, a characteristic of the chain, a characteristic of the transducer, or some combination of the three? Probably the last option, very unlikely the second, but as of now we can’t really tell why this happens. What we can say is that both SR1a and OG Andromeda have plenty of fans.

    Thus, the conclusion here is that 2nd and 3rd order distortion (and possibly, the ratio between 2nd and 3rd order distortion) play a role in the voicing of the component and might actually be pleasing depending on the user’s preference profile. In that regard, if one were to have a known quantity, it is possible to use the characteristics of that known piece of gear to make a somewhat educated guess on if you’d like something based on measurements. No, it’s not a guarantee, but it’s much better than a shot in the dark.

    Now that we’ve established that 2nd and 3rd order distortion might actually be quite a good thing, allow me to introduce “crap factor,” a phrase @atomicbob coined to describe the actual deleterious aspects of distortion/noise. Kind of like THD+N, it’s a sum; we add up all the distortion from the 4th harmonic onwards and also add in noise (hum, mains noise). The end result is what @atomicbob believes to be a representation of the amount of crap a component has.

    I couldn’t find an example of a bad component that had tons of crap factor from our measurement library, but here’s a thread that has 6 hypothetical amplifiers. Please read that first and then come back here.

    Now that you’ve (hopefully) done that, we can conclude that amps 1, 4, and 5 have large amounts of crap factor and might not necessarily be pleasant to listen to (personal preference/chain notwithstanding).

    Let’s go back to the SW51+ for a second:


    SBAF6.png


    If we accept that 2nd and 3rd harmonic distortion play a large role in the sound which may be pleasing, and thus accept @atomicbob's defined "crap factor," we can see in the red highlighted box on the right side of the picture (on the right side of the graphs) that the SW51+ has very low crap factor (this number roughly translates to -86 dBu, which is well below audibility). While we cannot say that low crap factor automatically means something is awesome (i.e. Magni Heresy is not the greatest thing since sliced bread), we can say that high crap factor is undesirable, as it means very high amounts of the higher level distortions + more noise.

    An interesting "case study" to see on this subject is the Eddie Current 6L6 Ultralinear. That amp appears to measure terribly by almost all measures. However, subjectively it sounds very clean and sounds like a solid state that happens to use tubes! This may not be the case every time we see measurements that would make objectivists faint, but it is something to keep in mind.

    In conclusion, if one puts in a little bit of time and observation, one can use measurements to try to make extrapolations on how something sounds. THD/THD+N needs to be rethought, and personally, I really like @atomicbob’s crap factor. I believe along with him that the crap factor better represents a component’s undesirable traits.

    ***all measurements shown here are the work of @atomicbob and @purr1n. It's their work and they deserve the credit. A thanks to @atomicbob for helping me put this together and proofreading.***
     
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    Last edited: Aug 12, 2020
  2. je2a3

    je2a3 Almost "Made"

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    I don't know if @atomicbob and @purr1n are aware of this page from Radiotron 3rd edition but I'm glad that after 80 years there are people working in this direction.

    Kudos to you guys and @ChaChaRealSmooth for starting this thread!
     
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  3. Senorx12562

    Senorx12562 Case of the mondays

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    I have found the term "crap factor" to be useful in describing things to be avoided irl as well as audio. Measurement in that context is, however, problematic.
     
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  4. Biodegraded

    Biodegraded Friend

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  5. atomicbob

    atomicbob dScope Yoda

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    My awareness came from research at Bell Labs in the early 30s. Also look at the top of that Radiotron page at the percentage harmonic distortion permitted 2nd and 3rd harmonics for a wide range, critical listener. Note 5% and 2.5% respectively. Higher harmonics are considerably lower in permitted values. Sounds familiar.
     
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  6. purr1n

    purr1n Super Friend

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    Little bit on the high side, but this pattern is typical of SET. It's considered a good distortion.

    [​IMG]

    I'll post FFTs of BA drivers. There's a reason why BA drivers, although good in certain ways such as transient response, also drives some people bonkers.
     
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  7. Luckbad

    Luckbad Traded in a unicorn for a Corolla

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    Would be curious what it is about BA drivers that I can't stand.
     
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  8. Hrodulf

    Hrodulf Prohibited from acting as an MOT until year 2050

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    Can we take a Topping A90 amp and predistort it to become an Eddie Current or ECP? In essence create a Kemper for audiophiles. My feeling is that it won't work that way.

    Lately having talked to some of the more fringe thinking local amp designers my feeling is that designing for minimum open loop distortion and lower open loop gain usually gets the "good sound". The current zero chaser school of amp design relies on maximum open loop gain, so negative feedback can be deeper. It seems to do superbly in traditional performance indicators, however subjective impressions often leave a lot to be desired. Especially in longer term. Maybe it is as Brent Butterworth said, we're predisposed to like different things and some of us prefer distorting electronics as long as the distortion isn't too high. Or maybe distortion is the wrong thing to look at...
     
  9. atomicbob

    atomicbob dScope Yoda

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    SET amps that suit my personal preferences typically have a similar harmonic distortion spectrum.

    Achieving the harmonic distortion spectrum @purr1n posted with minimal or no negative feedback, AND having minimal mains noise, non-harmonic noise, residual noise, IMD, tend to correlate with achieving what I prefer in my recreational listening system.
     
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  10. robot zombie

    robot zombie Friend

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    Call me crazy... I never cared about THD. Not for knowing what I now know about it, but because it gets pushed just the same as "high-fidelity range 20hz-20khz" which even a cursory understanding of hearing tells you means nothing. I figure if they can say those numbers and everything is muddy or have fiberglass treble, then maybe a number isnt a guarantee.

    Another way I see it is like a hotel advertising clean rooms, which if you're wise, makes you immediately suspicious... like someone saying "Hey can you turn around for a sec? And dont worry, I won't stab you or anything!"

    Just seems like an odd flex. If youre selling something as high end I already expect a few obvious things.

    Id liken it to taking a cross section cheeseburger and running it through a GCMS just to look at the salt content. Sure, too much salt will ruin the patty but it doesnt tell you how it will really taste. And sometimes it actually needs a little salt. Not to mention how the salt mixes with other things can change everything.
     
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  11. atomicbob

    atomicbob dScope Yoda

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    (sarcasm) Was the cross-section representative of the salt distribution throughout the entire cheeseburger, or was it cherry picked data? Hint, hint, this doesn't occur anywhere on the internet, now does it? (/sarcasm)
     
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  12. robot zombie

    robot zombie Friend

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    I'm gonna need some french fries for all of that salt.

    I'm sorry, I had to. But really... tell me now, who was it that salted your cheeseburger in a way you didn't appreciate? A certain science guy who shant be named? :p

    Okay, really though. It wasn't new to me by the time I was getting into audio more seriously. I learned the tricks from building PC's, before I could even buy my own insurance. It's a bit better now, but still hard to find good benchmarks. A lot of reviewers will do some funny things to paint every product they're given in a good light. Other times it's just kinda arbitrary. A lot of the time it has little to nothing to do with the performance you'll actually see from the component.

    Best example for this is RAM. Every 3-6 months another manufacturer sets a friggin RAM speed record. They're real innovators, those people. Never mind that even doubling from typical speeds will maybe net 1-2% gains in most tasks the people buying them are likely to do. There are ways to bench it that will show it being exponentially faster, but unless you have very specific jobs in mind, dropping the hundreds of dollars more on them won't actually make your computer noticeably faster. And you'll probably have stability issues trying to push those speeds... pulling more power from the IMC, heating up the CPU, decreasing max CPU clocks, fans running louder... point is, the pretty number isn't all it's cracked up to be, because 9 times out of 10 all of that bandwidth serves no purpose and pushing the limits of what RAM can do comes with some annoying compromises that can even make for a slightly worse performing machine.

    The only difference these days is... if you shell out for that ultra-fast RAM and skip on anything else, people will usually laugh at you for building a shittier machine with technically better specs. It's fine to have it if you want it, but silly if it's all you want.

    So the chasing zeros thing never caught my attention. I felt like there was no way for me to know what that number sounded like. It was like understanding the distance from the earth to the sun. And also, it kinda smelled funny, like it couldn't be remotely that simple and it can only mean so much. You kinda gotta know that literally everything sounds different. By the time you've used your 3rd audio device (even bad ones,) you kinda start to hear a pattern. And then you're looking at reviews and measurements of the hyped stuff. And they measure the same. And yet, people describe the sound of each one differently from the last, some even explicitly saying one sounds much better. And they have different prices, with different stuff in them.

    So I would get frustrated, kinda thinking, "What does it mean? What does that level of THD sound like in this stuff?" Don't have to be an engineer to question what it's really telling you. I also knew that distortion sounds good from playing guitar - and not just for fuzzy or aggressive sounds. Even the best sounding 'clean' guitar is still distorted, sometimes by a lot. But it still sounds the cleanest and most 'alive'.

    Just kinda looking around, I think more people get it now. THD is kinda like the "it's not TOTAL shit" metric and everything else about the box is up for grabs. I'd hope most people who got ears on enough stuff and cared to learn anything at all naturally drifted towards looking beyond a simple measurement or two.
     
  13. skem

    skem Friend

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    Sorry to Necropost, but I have been musing on distortion in amplifiers this week and it this seemed like the right thread in which to fart out some thoughts.

    In experiments enabled by @dBel84 (thank you again, dB), we explored the effect of positive- and negative- phase H2-dominant distortion at the 1 and 2% levels. Definitely well into the novelty regime, but it was interesting how H2 had a corrective effect for terrible recordings. This comes at the loss of clarity and staging, especially stage depth. Things sound bigger but smeary, like an orchestra playing in the restroom (FYI: this is the origin of the phrase "warmpoo" ;-).

    Over the last week I have been listening to a DAC with an SE I/V stage that I will write about in due course. I knew it had distortion because right out the door I noticed piano sounded like it was made of both strings and bells. There was a lushness to everything. I later measured the output stage and it had huge 0.5% distortion @ -3dBFS across the audio band, though in a nice H2-dominant fashion.

    512hz-warm.png

    Here's the thing: going back and forth between this technically weak DAC and the Metrum Adagio, I found myself enjoying many of my recordings more with the distortion DAC than with Adagio. And even more surprising, while the distortion DAC is unabashedly colored, in certain limited instances it reproduces timbre just as well or maybe even better than Adagio. It has an extremely simple circuit built from oversized components that are able to handle transients with aplomb. It is completely the opposite of these surface-mount monstrosities of modern times.

    It wasn't all guns and roses. There was also music for which the DAC's harmonic structure was a strong negative. Blues, for example, particularly hates even-ordered overtones. Perhaps it's all the V7 chords. In general, classical pieces written in Major scales seem enriched, but more harmonically complex music suffers. And without doubt, this DAC was weaker on stage and vocal clarity—but honestly not in ways that I would've noticed if it weren't for the Adagio as a direct A/B.

    All this got me asking: How much distortion is the right amount for a baseline system? I am finally becoming experienced enough to stop thinking of distortion as a totem of bad design. There is a "If it feels good, do it" philosophy that sets in with age; life is just too short to adhere to Amir's notions of audio purity.

    I recall that Tyll once wrote:

    "[there is] a good few dB margin for deviation from "perfectly neutral" within which a manufacturer can create an aurally pleasurable experience. Things like second harmonic distortion in singe ended tube amps and simple device circuits a-la Nelson Pass. These things are basically unmeasurable in their gestalt producing effect, as I know it. I'll add that I'm not sure we're able to, or know what to, measure relative to that far more complex interior experience of music listening. So, I reckon there's a good margin for slop around technical measures and still remain pleasurable.​

    Exactly. Finding your distortion kink is no bad thing. Perhaps it's not 2% or even 0.5%... but ultra-dry distortion-free sound is THX789 boring.

    If I could twiddle some knobs for every overtone, where would I set my distortion preferences? Pure H2, and absolutely no higher harmonics? A cascade of harmonics falling off with a certain power spectrum? Negative phase? I sense there is a lot of underexplored territory here—and there are probably some physics-based reasons for why certain patterns of distortion sound more natural than others.

    Anyway, just another 2¢.
     
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    Last edited: Jul 24, 2020
  14. dBel84

    dBel84 Friend

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    Not all reach this epiphany and keep chasing the dragon.

    Alex Cavalli had been working on an article relating the complexity of trying to capture what we hear to what we can measure. iirc it was part of a series of writings that @CEE TEE was working on (still is?) . Simply put, it relates to this discussion and how we might measure those things we perceive and conversely how measurements don’t capture “the full story” of what we hear in music (not pure tone).

    I am not saying that measurements are uninformative, on the contrary, they are the best we have at this point in time but as with all things technological, “better” tools will come and help define our current state of ignorance.

    ..dB
     
  15. atomicbob

    atomicbob dScope Yoda

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    Some additional musings.

    Begin with the following reported measurement:
    At 0 dBu 1 KHz THD+N = 0.35%.

    0 dBu will produce approximately 100 dBSPL in Sennheiser HD800 and HD6x0 headphones, rather loud. Spec chasers would be abhorred with THD+N = 0.35%. However, as noted in posts above, the measurement is an extremely lossy data compression.

    Consider the following graph for SW51+ measured at 0 dBu with Mullard EF184 tubes:
    20200722 SW51+ THD+N 2nd 3rd 4+HD+N vs frequency 0dBu 300R load L ch annotated 3b.png
    Clicking on the graph will enlarge the graphic.

    Reported THD+N number is circled in blue in the graph above. One single data point to represent an amplifier's performance. Rather ridiculous when viewed in context of considerably more data. THD+N vs frequency provides much more information. Additionally, 2nd, 3rd harmonics and 4+HD+N are also plotted. 4+HD+N is THD+N with 2nd and 3rd harmonics removed. Note how the THD+N and D2 lines overlap for much of the graph. THD+N for this amplifier is 2nd harmonic dominant. Also note that 3rd harmonic distortion is considerably lower than D2 and 4+HD+N is substantially lower.

    For context I have overlaid the 80 phon contour of equal loudness. To be precise, the graph should be re-scaled and 100 phon line plotted given the measurements were at 0 dBu, consistent with 100 dBSPL for headphones mentioned. I'm going to ask the reader to imagine the 80 phon line 20 dB higher on the graph, which would be off the chart for this graph. Now consider the respective distortion plots and relate them to the Human Auditory System response at 100 phons. At 100 Hz the 100 phon line would be +12 dBu and 4+HD+N is -65 dBu. Thus 4+HD+N at 100 Hz is 77 dB below the 100 phon line. Similarly at 1000 Hz, 4+HD+N is 85 dB below the 100 phon line.

    If we consider 2nd and 3rd harmonic distortion as voicing of an amplifier and 4+HD+N the undesirable distortion, the single THD+N distortion number at 1 KHz is vastly unrepresentative of the amplifier's performance.

    fine print: the 100 phon line is a little flatter than the 80 phon line. The above discussion is for context, it does lack some precision.
     
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  16. atomicbob

    atomicbob dScope Yoda

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    Further musings on this topic.

    The following graph represents 1 KHz sine distortion measurements for a hypothetical perfect amplifier:
    20200722-00 Perfect Amp  1KHz distortion suite 0 dBu - annotated.png
    Note both THD+N and 4+HD+N measure 0.00000%. There are no other components in the spectrum other than the 1 KHz sine fundamental. No power supply noise, no harmonics, no residual noise, no other crap whatsoever. Perfect performance.

    Now to examine two more hypothetical amps with the following published specifications:
    Amp 1 THD+N: 0.00078%
    Amp 2 THD+N: 0.1%

    To the number chaser Amp 1 is clearly the winner, end of story.

    However, there is more to the story, how each THD+N was achieved and the harmonic spectrum for each amplifier.

    Hypothetical Amp 1 distortion suite at 1 KHz:
    20200722-01 Perfect Amp - High NFB -  1KHz distortion suite - annotated.png
    The 0.00078% THD+N comprises numerous harmonics which are partially the product of a high amount of negative feedback employed to lower the amplifier overall distortion. Note 4+HD+N is 0.00064%.

    Hypothetical Amp 2 distortion suite at 1 KHz:
    20200722-02 Preferred Amp - No NFB - 1KHz distortion suite - annotated.png
    True, Amp 2 has 0.1% THD+N, but this amp has zero negative feedback with only two harmonics present, 2nd and 3rd in a descending pattern. Compare 4+HD+N of 0.00002% to that of the previous amp with 0.00064%.

    Empirical evidence gathered over the years suggest that listeners would prefer to hear music rendered from amplifiers exhibiting behavior similar to Amp 2 than Amp 1 above.
     
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    Last edited: Aug 12, 2020
  17. Royaume

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    THD IS NOT A FIGURE OF MERIT (THD is worthless as a "goodness number" as it is commonly (incorrectly) used)

    Total Harmonic distortion is calculated by measuring the harmonics produced and adding them all up (for a number of test tones spread throughout the audio band).
    The ear does not work like this!!! Higher order harmonics are more psychoacoustiacally destructive than lower order harmonics. This means that higher order harmonics make an amplifier/DAC sound worse than lower order harmonics.
    In fact, order n harmonics must be weighted (n^4)/4 !!!!
    Since THD does not weigh harmonics appropriately to the human ear, it is completely useless as a figure of merit.
    In his paper titled "A New Methodology for Audio Frequency Power Amplifier Testing", Daniel Cheever explains all this, and describes a new method of testing which he calls Total Aural Disconsonance (TAD). TAD works similarly to THD, but weighs the harmonics appropriately

    This simple fact ends the objectivist-subjectivist debate. The industry was measuring the wrong thing. TAD does correlate with subjective audio quality as one might expect.

    Because the industry began targeting and advertising THD figures, vacuum tubes/thermionic valves fell out of favour and solid-state devices using negative feedback became popular. Negative feeback decreases lower order harmonic distortion, but introduces higher order distortion products. This cheats a good THD figure but introduces higher order distortion products.

    @Biodegraded in post #58 quoted research from 1978 indicating that it had already been known for a long time that there was no correlatinon between THD and subjective audio quality, but the quote doesn't explain why.
    Statements like "measurements dont matter beyond 0.1%", "Measurements confirm what you hear, not the other way round", "Measurements only tell you if it's broken" etc. abound here on sbaf and elsewhere. Yet nowhere can any complete explanation be found. For years I bounced back and forth between the two sides of the argument until I finally stumbled across a link to Cheever's paper somewhere on this site. WHY ISN'T THIS FACT BEING CIRCULATED?

    After reading the first part of the paper, everything suddenly made sense. "THD is not a figure of merit, use TAD instead" is the only message we need to spread. Share it everywhere. Go and preach the word of God!

    Edited for spelling
     
    Last edited: Oct 21, 2020
  18. Degru

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    That still doesn't give you the full picture since by your description it only measures harmonics, just weights them differently for the final distortion figure. It still doesn't include non harmonic, multitone, and transient information that you will encounter in real music.

    Rtings does a similar thing for headphones they call WHD, and honestly I would rather they just show a graph of all the harmonics since their methodology for the weighting is unclear.
     
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  19. Royaume

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    That may well be!
    What do you mean by "non-harmonic"? As far as I understand, anything unrelated to the input signal is just noise, hence THD+N figures. Also what extra information do multitone tests reveal that testing individual tones does not? (genuine question, seeking to understand) What do you mean by "transient information"? Again, if I understand correctly, while testing impulse response does give us a useful representation of the information, mathematically, all the information is already present in distortion plots.
    I agree with you that compressing a graph down to just one number is a large loss of information. But do you not agree that correctly weighing the harmonics is a very significant improvement? n^4 is massive! I'm quite convinced TAD would fix the industry's bias against tubes, and bring the numbers in line with subjective experience.
     
  20. Elnrik

    Elnrik Super Friendly

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    Oh fuck off. This is a hobby, not a religion.
     
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