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Amplifier harmonics and load stability

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  • #31
    Will it be helpful to first ascertain if we have an idea what introduced harmonics sound like? The electric guitarists (and synthesizer musicians) amongst us, I suspect, might be most familiar with this phenomenon.

    This practical test I believe might answer most, if not all the questions here…If its possible to find an electric guitar and a harmonics stomp box/ effects machine to play with, slowly dial this phenomenon in without altering the volume and making sure its not distorting in the traditional sense. Switch off harmonics and what do we hear?
    We planned to do that from the outset. (Make demo of deliberately increasing harmonic distortion).

    Comment


    • #32
      Separating thoughts from discussions?

      Dear Alan,

      Maybe it's a good idea to open topics which remain closed for comments from other members. As a sort of a 'blog'? You might then open another topic to give people the opportunity to react to the 'blog' topics. This way, thoughts and discussions can better be separated.

      Comment


      • #33
        The sound of THD

        Originally posted by A.S.
        ... What message are you trying to convey? It just sound like a tone to me. If you use a prop to explain a point it's essential that you educate the listener, step by step, with what he is going to hear, how to listen for it and how to interpret it.
        In {previous deleted example} DistortionVH.mp3, a 1% 2kHz wave was introduced to the test tone just after two seconds. In DistortionH, the whole recording consists of 5% of 2kHz along with the test tone. Attached again the same recording but in one 15 seconds file. After the 5th second, a 1% 2Khz added over the original test tone and after the 10 seconds a 5% two kHz added, and you can now hear how the tone changes its sound.



        I will stop here and refrain from continuing so that we can continue to talk about the original topic. ST

        Comment


        • #34
          About harmonics - part 1

          I'd like to take back this discussion now. First, thank you for making the distortion example, but I'm sorry I really can't hear what I think you want me to hear on these cheap PC speakers. Let's step back and do some foundation building as I planned to do.

          First, what are the importance of harmonics to music?


          Musical instruments create a sound by causing vibration of the air pressure around the instrument, and that pressure wave radiates away from the instrument to our ears. We covered that here. For example, the violin has several strings and when these strings are plucked or bowed they are set into vibration. Actually, the close proximity of non excited strings to the excited ones causes them to sing too, but at a low amplitude. The frequency of all notes is precisely defined by maths and we can play all music on a bank of finely tuned laboratory audio oscillators, one per note - this being the concept behind the Moog synthesiser. We can look up the exact frequency of all musical notes here.

          If we set-up the synthesiser and play some classical music just according to the musical note frequencies we will hear something like this Bach tune. The tune is 100% accurate in tempo and notation to Bach's score but it sounds robotic and unnatural. Why? Because the harmonics are unlike what we would expect to hear from real instruments. But if an alien arrived from another planet who had never heard a real acoustic instrument, was given the musical note-to-frequency table above, he could generate the tune with sine wave oscillators and he'd think it quite normal. But we know that what Bach intended was rich in harmonics like here. Or with even more harmonics and hence a brighter tone here.

          Modern musical instruments are tuned to a common base frequency of 440Hz (called musical A). That means, ignoring the harmonics which give each type of instrument their own unique voice, 440Hz will be perfectly in tune with all other instruments playing the same note in their range. But there would be no mistaking A or C on the piano compared with A or C on the flute. Here is what a single sine wave oscillator would generate as a 440Hz pure, harmonic-free tone. And that same note with its rich harmonics being tuned on a concert piano.

          And here, taken to the other extreme is what you hear when there is little or no fundamental tone (because of the tiny, cheap speaker) and all you hear is the harmonics. So this 'rasping' bright high sound is what harmonics alone sound like which is why when there are no harmonics, the sound is so boring like the Bach tune here.

          So can we say that harmonics are necessarily a bad thing? Definitely not; they freshen the sound of music and make it engaging. Can we say that there is an optimum balance between the quantity and loudness of harmonics and the fundamental note? Yes, this is why the same note on the piano and guitar have the same frequency but different richness and brightness. Can we say that amplifiers and other audio equipment should not generate harmonics of the music being played through them? Well, ideally they shouldn't but in the real world they do. Is that necessarily a problem as far as listening to music is concerned? No.

          Here is a video of the rich harmonic make-up of the piano. Look at the lower trace on the 'scope which shows vertical spikes at the harmonic frequencies. Compare that with the picture of the distortion generated in an amplifier and you see the same idea of a fundamental (test) tone, plus a series of harmonics of varying level.

          [Typing and researching this post took me 80 mins. on Sunday morning].
          Alan A. Shaw
          Designer, owner
          Harbeth Audio UK

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          • #35
            MUCH appreciated Alan...

            Comment


            • #36
              About harmonics - part 2. Comparing musical note with unwanted amp harmonics

              In the last section of post No. 34 I drew attention to this video, here. The video shows the result of connecting a microphone to a dual channel oscilloscope and displays both the attack and decay of the piano note (top trace) and on the lower trace, the strength and frequency spread of the upper harmonics of the note. The lower 'spectral' trace is really interesting. It is giving us three very useful visual representations of what's happening inside the piano when the note is pressed.

              First, the primary peak, the left most one must be that of the fundamental note, the one we could look up on the note-to-frequency chart; the one all instruments would generate if in-tune. Then the lower trace gives us a spread across the frequency spectrum upwards above the fundamental and we see distinct spikes at evenly spaced intervals along the frequency (left to right) horizontal axis. As the gaps between the spikes are regular, that tells us that the spikes are indeed harmonics of the fundamental tone. And there is a long series of them reaching out to many multiples of the fundamental note's frequency - I can see up to the 8th harmonic on this scale. So if the note played was a C, we know the fundamental frequency is 261.626Hz, what hifi listeners would call the lower midrange, and the 8th harmonic still in evidence on the 'scope screen would suggest some output from the piano at 261.626 x 8 = 2093.008Hz, right at the top end of the midrange driver, just as the tweeter flares-in.

              Finally, the lower graph tells us about the relative loudness of the harmonics both relative to each other and relative to the fundamental. And if you were an expert at interpreting photographs of this oscilloscope screen without actually hearing the sound, you could say with certainty 'ah yes, that is a note being played on a piano' or, 'that's a different harmonic to fundamental balance so that's an organ' or whatever. That fact that wood, brass and string instruments can play in tune yet do sound so unmistakeably different is much to do with the make-up of the fundamental-harmonic structure of their notes. Companies like Yamaha who make excellent electronic pianos that reproduce the sound of a real piano over a built-in loudspeaker have spent years analysing the harmonics of real instruments and electronically synthesise all the vital harmonics in just the right quantity to satisfy the player that he's (almost) playing a real stringed piano.

              We're able now to start drawing some comparisons between the nature of (wanted, desirable) harmonics our piano generates and the graphs we previously looked at of the amplifiers self-generated harmonics. Take a look at the attached picture which presents on the top, Graph A, a screen snap from the video and underneath (Graph B) I've pasted the Stereophile measurement of an amplifier's self-generated distortion. None of those spurious harmonics should be present at all in the amplifier's output. But they are. And that's inevitable because there is no such thing as a perfect amplifier. What the amplifier designer can manipulate during the design is how far up they go in frequency (to the 8th, 9th, 10th harmonic or beyond?) and how loud they are relative to the fundamental and to each other harmonic.

              Is this logical? Can we see the general relationship between (wanted) instrument harmonics and the (unwanted) harmonics generated in an amplifier?

              I'd like to look more closely at the loudness of the harmonic next time - that's really the key to understanding this, but first we needed these basic concepts to be solid.

              >
              Attached Files
              Alan A. Shaw
              Designer, owner
              Harbeth Audio UK

              Comment


              • #37
                Videos for the really curious ....

                Before Alan posts his next interesting contribution to this thread perhaps you may find these educational videos to be of interest.....

                Music teacher Scott Laird from the North Carolina School of Science and Math:

                Where Music Meet Science Part 1: Pitch and Frequency
                http://www.youtube.com/watch?v=npGMh...eature=related

                Where Music Meet Science Part 2: Timbre and Complex Waves
                http://www.youtube.com/watch?v=nlv5bylQDsE&NR=1

                Where Music Meet Science Part 3: Frequency and Harmonics
                http://www.youtube.com/watch?v=sCi-3...eature=related

                Comment


                • #38
                  Harmonics in instruments and amps - thoughts

                  Alan:

                  So far, the information you've posted is extremely clear.

                  (I don't mean to get ahead of you, so please don't post this if I'm out of sequence.)

                  You've shown how the harmonics of an instrument, which occur at multiples of a specific fundamental frequency, determine an instrument's character. You've also shown how an amplifier self-generates harmonics (i.e. harmonic distortion) at specific multiples of a fundamental frequency, i.e. a signal injected from an audio test oscillator. From this I derive the following questions:

                  1. Since I assume the fundamental tone will exceed the harmonics in amplitude, and therefore presumably generate the most harmonic distortion, would not the harmonics of a musical instrument and the harmonic distortion of an amplifier tend to coincide?

                  2. If the answer to question 1 is "yes" (they'd occur at the same frequencies), is it not likely that harmonic distortion would have a subjectively benign character?

                  3. However, even if the harmonics of an instrument and the harmonic distortion of an amplifier coincide in frequency, the relative levels of the different harmonics are not likely to match. I therefore deduce that:

                  (a) above a certain level, harmonic distortion in the amp might begin to change the perceived tonality of an instrument, by preferentially reinforcing certain of its harmonics at the expense of others; and

                  (b) the effect referred to above might vary by instrument depending on how closely (or not) the harmonics of a specific instrument matched the harmonic distortion characteristics of a particular amplifier.

                  Comment


                  • #39
                    What about deleting the harmonics - how does that sound? Part 1

                    Originally posted by EricW View Post
                    ...You've shown how the harmonics of an instrument, which occur at multiples of a specific fundamental frequency, determine an instrument's character. You've also shown how an amplifier self-generates harmonics (i.e. harmonic distortion) at specific multiples of a fundamental frequency, i.e. a signal injected from an audio test oscillator. From this I derive the following questions:

                    1. Since I assume the fundamental tone will exceed the harmonics in amplitude, and therefore presumably generate the most harmonic distortion, would not the harmonics of a musical instrument and the harmonic distortion of an amplifier tend to coincide?

                    2. If the answer to question 1 is "yes" (they'd occur at the same frequencies), is it not likely that harmonic distortion would have a subjectively benign character?

                    3. However, even if the harmonics of an instrument and the harmonic distortion of an amplifier coincide in frequency, the relative levels of the different harmonics are not likely to match. I therefore deduce that:

                    (a) above a certain level, harmonic distortion in the amp might begin to change the perceived tonality of an instrument, by preferentially reinforcing certain of its harmonics at the expense of others; and

                    (b) the effect referred to above might vary by instrument depending on how closely (or not) the harmonics of a specific instrument matched the harmonic distortion characteristics of a particular amplifier.
                    That is precisely and absolutely the point. Your analysis couldn't be better - or at least, it coincides with my own opinions.

                    That leads us a little further into this. You postulate that if, by some happy design fluke, the amplifier generated harmonic distortion with the same characteristic frequency spread (2nd, 3rd, 4th harmonics etc. etc.) as a musical instrument that providing the loudness of those harmonics was sufficiently below that of the instruments harmonics we might not be able to detect the addition of the amp's harmonic distortion. And if we did audibly detect the amps contribution, we might even like what we hear. We might find the extra 'sparkle' in the upper frequencies gives us the impression of 'greater clarity', 'more openness' and the like. The problem is, as we'll see, the characteristic nature of the harmonics is by quantity and frequency extremely unique to the class of instrument. All violins have generally similar violin-like sound so, logically, they must have a generally similar harmonic make-up. Outstandingly beautiful violins have a special blend of harmonics not found in the average violin - but they are still, unmistakably all violin family members. SO if the amp just so happened to generate the right harmonics to spice up the violin, it might be the wrong quantity/frequency of harmonics to give the human voice some sparkle. Or the piano. Or organ. And surely no one would by an amp that's only good on a certain type of solo instrument would they?

                    It's rather difficult to add harmonics to a pre-existing recording. I don't have the technology to do that, although I assume that it can be done. But what I can do is to let you hear the inverse - stripping harmonics from an existing recording so that you can get an idea of just how vital these harmonics are to truly high fidelity sound. Then perhaps you can imagine how should an amplifier (or any other component in the chain, including the speakers) tinker with the harmonics we can expect the overall sound to change a lot.

                    What I'm going to do, to kill the harmonics (this should work, but I need time to play with it) is to take a great recording - for example tonight's Radio 3 concert of Stravinsky delivered to me at 320kb AAC, saved as WAV at 48k, and then passed through an MP3 encoder at a moderate bit rate once, then passed through the encoder again, and again and again, recoding each time. We know that MP3 achieves file size reduction because it uses some psychoacoustic maths to decide what is really important to the human ear, and what can be dumped. And since the tune must remain recognisable, and the melody is all in the lower registers, MP3 achieves dramatic data reduction by discarding the fine detail - and those are our precious harmonics. My guess is that the harmonics will be severely diminished with progressive decode/re-encode, and by the 10th pass through, much detail will have been lost. After twenty cycles the tune is unchanged and perfectly recognisable, but the detail locked in the harmonics has been severely attenuated. Let's see ...

                    OK so here are the clips. Perhaps this isn't the best way to illustrate this sonic effect of good, clean harmonics in just the right quantity but I hope it will suffice.

                    1. First, the original source file (3.69MB):

                    Loading the player ...


                    2. Then after ten MP3 encode-decode cycles (175kB)

                    Loading the player ...


                    3. After twenty encode-decode cycles (137kB)

                    Loading the player ...



                    The file size tells its own story ... something has definitely been junked from the audio. The first generation as a WAV file was 3.69MB, and after twenty encode cycles down to 0.13MB. I calculate that, compared with the original WAV file, by the time we have reached example 3, the twentieth pass, 97% of the audio data has been erased.

                    Note: I picked this excerpt because of the dominance of the trumpet. We know that the shock wave, explosive nature of the brass generates strong harmonics, and whilst the MP3 coder would normally surreptitiously ignore harmonics if it can, the brass section is so loud that it can't be conveniently ignored - hence the coder's struggle and the smeared 'wooshing' quality after it reduces the fine harmonic detail. We are losing fidelity and that's very obvious. In fact, if you listen to the brass on 3 compared with 1, I think it sounds 'brighter'. And that is odd. I suspect that the codec has either deleted than tried to guess what the harmonic structure was, and then unconvincingly fake-it, or that the harmonics closer to the brass' fundamental have been processed differently (suppressed) and hence subjectively those further away from the fundamental sound disembodied. Hence the old term 'disembodied top'. Or it could be that the encode-decode process has generated additional spurious harmonics which we don't recognise as being part of the natural brass sound. Or all three hypothesis.
                    Alan A. Shaw
                    Designer, owner
                    Harbeth Audio UK

                    Comment


                    • #40
                      What about adding harmonics - how does that sound? Part 3

                      OK, next step. What would it sound like if we deliberately add some harmonics to subjectively brighten the tone of an instrument? To give it more 'air', or 'sheen', more 'resolution' or 'detail'? We could add them in at the recording, the amplifier or speaker ... at any (or every) stage of the audio chain.

                      Let's imagine that this clip is our norm, our reference, exactly what the piano sound like in real life:

                      7. Our 'reference' piano here ....

                      Loading the player ...


                      8. And now we spice-up the hifi system, by adding some harmonics to bring out the detail ...

                      Loading the player ...


                      Which do you prefer? The reference recording (7) or the 'more detailed' recording (8)? Maybe (although this is really a side issue) Example 7 could perhaps be considered a 'valve' sound and Example 8 a 'transistor' sound? Not that they are, but I wonder if they have some characteristics associated with those two amplifiers?
                      Alan A. Shaw
                      Designer, owner
                      Harbeth Audio UK

                      Comment


                      • #41
                        What about adding harmonics - how does that sound? Part 4, 2nd harmonics

                        Next let's look at the characteristic 'sonic signature' of certain harmonics which we'll deliberately add to a pure tone. That may help us attribute a character to what I've described as '2nd harmonic', '3rd harmonic' or whatever. Within the limit of my test equipment I can generate any whole harmonic of the fundamental, or even any in between frequencies such as the '3.7th harmonic' which, believe it or not could conceivably be generated by an instrument or hifi system, including the speakers. But let's keep it to the basic exact-multiples-of-fundamental for now.

                        9. First we should acclimatise ourself with 440Hz (Concert A), pure tone for ten seconds. This should sound sweet and completely free of any edginess. If you are listening on cheap PC speaker, they almost certainly will have some distortion but hopefully not so much.

                        Loading the player ...
                        This is the reference sound.

                        10. Now we will add 10% 2nd harmonic distortion to that 440Hz. The second harmonic of 440Hz is 880Hz, so I've mixed in 10% of 880Hz on top of the 440Hz. Is the 10% second harmonic distortion audible?

                        Loading the player ...


                        11. We increase the 2nd harmonic distortion of Example 10 from 10% to 50%. Is the 50% second harmonic distortion audible?

                        Loading the player ...


                        9a. And back to the reference pure tone again (as Ex.9)

                        Loading the player ...


                        12. Finally, can we hear 3% 2nd harmonic distortion?

                        Loading the player ...


                        I would anticipate that now you've trained yourself to recognise second harmonic distortion, you may just about hear it* at the 3% level (assuming your speakers are not themselves generating even more than 3%) - that is, 3% relative to 100% of the pure 440Hz tone. But if we used music rather than a pure tone, it would be virtually or actually impossible to identify harmonic distortion at such a low level; the musical instrument themselves would be generating so many harmonics that a few percent added from the recording or reproducing equipment would merge with the instrument's own sound and be undetectable except under very carefully controlled conditions. Second harmonic distortion at around 3% would be typical for a pickup cartridge tracking a loud disk, analogue magnetic tape recording and even quality loudspeakers working hard in the low frequencies.

                        So that's second harmonic distortion. What about third harmonic? That means, taking our 440Hz pure tone we need to add-in some 1320Hz tone at varying levels.

                        *Don't worry if you can't identify 3% 2nd harmonic distortion especially on cheap PC speakers. You should be able to distinguish 10% 2nd harmonic more easily.
                        Alan A. Shaw
                        Designer, owner
                        Harbeth Audio UK

                        Comment


                        • #42
                          What about adding harmonics - how does that sound? Part 5, 3rd harmonics

                          In post No. 41 we listened to the addition of varying amounts of second harmonic distortion to our pure 440Hz tone. We compared 10%, 50% and finally 3%. But what if we introduce some third (3rd) harmonic distortion - will that have the same corrupting character as the 2nd harmonic distortion or not. Let's put it to the test.

                          9b. Here again is our nice pure 440Hz reference tone. There is no added distortion to this tone - it will replay as perfectly as your equipment will allow.

                          Loading the player ...


                          10a. And just to refresh our memory, here is what 10% second harmonic distortion sounded like (Ex. 10 from post #41)

                          Loading the player ...


                          13. And now, here is what 10% third harmonic distortion sounds like:

                          Loading the player ...


                          Hopefully you can hear 10% of either 2nd or 3rd harmonic distortion. But would you agree that the sonic character of these two rather subtle distortions is very different?

                          Now what happens if we combine the 2nd and 3rd harmonic distortion with the original pure tone into one example:

                          14. Pure tone with 10% 2nd harmonic and 10% 3rd harmonics:

                          Loading the player ...


                          And there is something rather interesting about Ex.14 (so much so that I double checked I'd made it correctly). Compare 10a and 13 with 14 and what do you conclude about the audibility of the distortion in Ex. 14?
                          Alan A. Shaw
                          Designer, owner
                          Harbeth Audio UK

                          Comment


                          • #43
                            What about adding harmonics - Part 6, multiple even and odd harmonics

                            In post #42 we sonically compared 2nd harmonics with 3rd harmonics. Hopefully you could hear a difference in the characteristic sonic nature of even order harmonics (2nd) and odd-order harmonics (3rd).

                            We can add a whole series of even order harmonics or odd order harmonics and see what they sound like. I'm going to add them in the same quantity, to emphasise the point.

                            [I have run-out of available MP3 in-thread players (temporarily) so am reverting to the Flash audio player for now and will re-encode for MP3 later]

                            15: Our 440Hz pure reference tone again:



                            16: 440Hz tone plus 10% 2nd, 4th, 6th (even order) harmonics:



                            17. 440Hz tone plus 10% 3rd, 5th, 7th (odd order) harmonics:



                            What I hope we can hear now is that Ex.16 with the even-order harmonics sound like a cheap electronic organ. You could play simple chords on this and it would sound 'robotic' but nevertheless passable as a child's toy. But in the case of Ex. 17, do you think that the presence of such strong odd-order harmonics could ever sound tuneful, no matter what notes were actually being played? The point is, just as the text books warn us, even order harmonics at moderate levels (say, a percent or two) blend very nicely with the music and are masked by it. But odd-order harmonics have a nasty, rasping edge which never sounds musical and are much more audible and irritating.

                            And guess what type of harmonics are typical of amplifiers? As a rule of thumb, tube amps will generate significant even order harmonics and poorly designed transistor amps mainly generate odd order harmonics. And hence there is some objective fact behind the 'warm' tube sound and the (sometimes) 'hard' solid state sound. But whilst the even order harmonics just can't be removed from the tube amp because that are the very nature of the valves themselves, a well designed transistor amplifier can have (as we observed in post #24) effectively zero harmonic distortion of either even-order or odd-order harmonics. But would you prefer zero harmonic distortion when a little second order distortion could nicely warm-up the sound?

                            Subject now open for debate.
                            Alan A. Shaw
                            Designer, owner
                            Harbeth Audio UK

                            Comment


                            • #44
                              Ex. 14 - comment

                              Originally posted by A.S. View Post
                              And there is something rather interesting about Ex.14 (so much so that I double checked I'd made it correctly). Compare 10a and 13 with 14 and what do you conclude about the audibility of the distortion in Ex. 14?
                              On first listen I thought 14. less distorted than either of the other two.

                              Comment


                              • #45
                                Distortion in the real world of the loudspeaker

                                Originally posted by weaver View Post
                                On first listen I thought 14. less distorted than either of the other two.
                                Ummm. That's not what I expected you'd say although I can image a reason why you deduced that.

                                What I was hoping you'd say was that in Ex. 14 (Pure tone with 10% 2nd harmonic and 10% 3rd harmonics) that the dominant distortion appeared to be the 3rd harmonic one, and that the 2nd harmonic was buried 'under' the third harmonic. Agree?

                                And how about in the real world? How much distortion does a typical loudspeaker generate in normal use? We can look as an example (although distortion is a little on the high side) at a sealed box, very highly regarded, well reviewed and innovative speaker system popular in the late 1980s (I just have this review to hand - there may be other better examples). What we can see is that at 100Hz @ 86dB - what we here consider to be a normal, safe-on-the-ears domestic listening level - this highly respected speaker generates about 9% second harmonic distortion and under 1% third harmonic. At 96dB, quite loud domestically, the second harmonic distortion is about 15% and the third at about 2.5%. This is not atypical for a good speaker system. And is far, far more distortion than all but the very worst audio amplifier you could find at a junk store.

                                One wonders how "rhythm and pace" may relate to an abundance (or not) of distortion.

                                >
                                Attached Files
                                Alan A. Shaw
                                Designer, owner
                                Harbeth Audio UK

                                Comment

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