Mark K's Speaker Pages

...when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science...Lord Kelvin


Why Distortion(= "displacement") Matters?

The current trend seems to be to dismiss nonlinear distortion, or at least to lessen it's importance. Much of this comes from the studies on harmonic distortion, which generally show it to be not particularly audible. Read Dr. Geddes' comments on multiple DIYaudio posts. Or, consider the quote below from Sean Olive. He's referring to the generally poor harmonic distortions results in some ipod audio docking stations--

Harmonic Distortion Measurements

Harmonic distortion (second and third harmonic only) measurements were made in the anechoic chamber at a SPL of 95 dB. The distortion levels of the harmonics are plotted along with the fundamental for each of the Music Stations in slide 18. Note that the levels of the harmonics have been raised 20 dB for the sake of clarity.


All of the Music Stations exhibited relatively high distortion at low frequencies below 100 Hz, with generally less harmonic distortion at higher frequencies. Music Station B differentiated itself by having higher levels of second and third harmonic distortion between 100 Hz to 1 kHz. Music Station C had the lowest distortion even though it received the lowest preference and distortion ratings from the listeners.


In conclusion, the harmonic distortion measurements of the Music Stations are not particularly good at predicting listeners’ distortion ratings, or overall preference in sound quality. This confirms many previous loudspeaker studies that have reported that harmonic distortion measurements are poor predictors of listeners’ overall impression of the loudspeaker. This can be explained by the fact that the distortions are often below the threshold of audibility, and the measurements themselves do not account for the masking properties of human hearing.

Even the venerable SL has downgraded the importance of nonlinear distortion in his ranking of speaker attributes. Looking at slide 20 of one of his recent presentations--

It's clear that harmonic distortion testing, and by inference, THD, which is dominated by second and third order products for loudspeakers, is not very good at discriminating listener preferences. The situation gets murkier-higher order distortion ("rub and buzz") or gross distortion (>10% second or third) are audible, but generally these levels are low in a well engineered loudspeaker unit. It appears that below a certain threshold, further reductions in distortion do not produce audible benefit.

The question is, where is that threshold? Look at what SL has for #2, volume displacement. And look at the speakers that Dr. Geddes is promoting-the smallest unit is an 8" I asked why Dr. Geddes doesn't use smaller drivers and the response was along the lines of smaller drivers not being able to generate the sound pressure levels necessary. Here's a blunt comment he made in reference to some outlandish marketing claims in a recent DIYaudio thread.

95 dB at 43 Hz! My 15 inch Summa can't do that honestly

Dr. Geddes has commented that he wouldn't generally use a driver near or at it's Xmax. And this would seem to be a good engineering principle.

So distortion has to be set in the right context. The right question needs to be posed. That question is--

What spl level is required for playback?

Now this question has been debated many times before. So, I'll skip that and just say that a full range, dynamic loudspeaker should be able to handle 80-85dB average levels and handle up to 20 dB of headroom for transients. You can debate the actual number and argue whether this should be free space, in room, etc. But the point remains, how does nonlinear distortion play into this? At our recent 2010 DIY some of the two ways struggled a bit with dynamic material in a medium/larger conference sized room.

Contsider that the maximum free space spl generated by a typical, high quality 6.5" driver unit is about 80 dB at Xmax at 30 Hz. For a budget 10", that figure jumps to the low 90's. Even if you factor in ~10-15dB for room gain, a pair of 6.5" drivers will be lucky to achieve 75dB average spls with peaks slightly limited to 90-95dB.

What that means is that, if you are using a pair of 6.5" two ways as your main speakers, and you listen reasonably loud, then you are often listening with your units exceeding Xmax.

I propose that you look at distortion graphs as a measure of maximum output capability. The distortion graphs can give you some indication of which drivers have better spl capability. Consider the following graphs. In it, I've used a 5 tone test and adjusted the fundamentals to be of equal measured amplitude at 20, 38, 44, 64 and 92 Hz.

Below are three graphs. The black curve is the distortion spectra from an SS8554 8" drive unit. In aqua, a very inexpensive 8" Silver Flute. Lastly, a Scan Speak 18w revelator in red. They are all ajusted so the fundamentals are 75 to 73 dB.

It's a bit easier just to look at the envelope of each of these drivers distortion spectra. I did this by hand, so it's a little sloppy, but you get the idea. The lines just follow the peaks of the distortion spectra. In general, the 8554 has a distortion spectra that is 10-15dB lower than the 18W and 5-10dB lower than the Silver Flute.

But, you say, "who cares? You can't hear any of these differences!"

Well, consider the next graph. Here I've increased the gain so the output of the 8554 is 3-4dB higher than the silver flute. I would have done it more, but this represented the maximum gain from the amplifier.

Even with 3dB more output, the 8554 beats the Silver Flute.

So the key is that the distortion testing shows that the 8554 has probably 5dB of extra headroom over the Silver flute. In a two way application, you can see where an extra 5dB of output capability would be beneficial. At low frequencies, 5dB would be perceived as a doubling of loudness.

So the person who looks at my graphs and says "unit A is better than B because the nth order spectra is -80 instead of -75" is probably making an error.

But the person who says, "The SS8554 has 5 more dB of output capability before Xmax is reached" would be correct. Whether or not that 5dB is worth the price, well, that's for you to decide.

If you're astute, you'll also notice that the advanced and expensive revelator design cannot compensate for the extra Sd. This is not an uncommon result. Manufacturers would like you to believe that higher advanced motor and cone/suspension design can overcome the Sd, but the reality is that your very expensive and exotic 6.5 still cannot match a very mundane 8-10" driver.

If you want full range behavior that gives 105dB in room, you cannot get this with even the most expensive 6.5" drivers. However, modestly priced 10" units will. That is, an inexpensive 3 way design will outperform an expensive 2 way.