hey folks, given that there is a lot of discussion about the suitability of various woofers to pair up with econowave and this inevitably leads to looking at distortion measurements, i thought that i would conduct a little experiment in order to see how much distortion would actually be audible.
design
fundamental is sine wave at 261.626hz, which is the frequency of middle c on piano. i chose this frequency because it has harmonics that run right through the midrange, which is where our ears tend to be most sensitive to distortion.
second harmonic is 523.252hz
third harmonic is 784.878hz
fifth harmonic is 1308.130hz
the program i used was audacity
tones were played over sony headphones
my best guess for fundamental level spl is about 80db or so
i claim not to be a golden ear and i surely have some hearing damage. i can hear from about 18hz to 17khz on the test headphones (i'm not sure if the bounds are determined by my ears or the headphones).
test of audibility of second harmonic
subjective analysis:
-0db 100% distortion; clearly audible, distortion sound overwhelms the fundamental
-10db, 30% distortion; still clearly audible, distortion sounds about even with fundamental
-20db, 10% distortion; low enough that if i wasn't listening for it, i could miss it, however a/b switching reveals it easily
-30db, 3% distortion; i can only hear a difference when focusing very, very hard in an a/b switching.
-36db (as low as audacity can decrease spl), 1.6% distortion; i 'think' i might here something, but i'd probably fail a blind a-b test, so i'm calling this level inaudible.
test of audibility of third harmonic
subjective analysis:
-0db 100% distortion; clearly audible, distortion sound overwhelms the fundamental
-10db, 30% distortion; still clearly audible, distortion sounds about even with fundamental
-20db, 10% distortion; unlike the second harmonic, third harmonic still audible at this level. tone sounds "wrong" like an annoying buzz.
-30db, 3% distortion; this is sort of like the experience with 10% distortion on the second fundamental, if i was not listening for it, i could miss it. however, it is there in a/b switching, but i have to be focusing to hear it.
-36db (as low as audacity can decrease spl), 1.6% distortion; i can hear this only when focusing very closely in a-b switching. if blinded, i think that i would fail to hear the tone as it is removed, but i suspect that i could pick it up when it is added.
test of audibility of fifth harmonic
subjective analysis:
-0db 100% distortion; clearly audible, distortion sound overwhelms the fundamental
-10db, 30% distortion; still clearly audible, distortion sounds about even with fundamental
-20db, 10% distortion; as with third harmonic, fifth harmonic still audible at this level. tone sounds "wrong" like an annoying buzz. subjectively, it is worse then the third and *much* worse than the second; when played by itself, the tone sound smooth, just at a higher frequency, but in combination with the fundamental, the sound turns very harsh.
-30db, 3% distortion; still audible even without a-b switching.
-36db (as low as audacity can decrease spl), 1.6% distortion; at this level it is audible even without a-b switching.
back in business...
i created a second fifth harmonic distortion, but at 10% of power, this has the effect of reducing the level by 20db, so i can test further down than -36db. as a check i played the third harmonic which was created at 100% power at -20db, and it is the same subjective spl as the 10% power tone, played at 0db.
-40db, 1% distortion, if you know what you are listening for, it can be heard without a-b, also a-b reveals it pretty easily
-50db, 0.3% distortion, i can barely hear it, but it's there in a-b comparison.
-56db, 0.16% distortion, i can just barely hear it in a-b comparison. however, at -56db, i can just barely heat it even without playing the fundamental tone.
my conclusion is that similar to other reports, second harmonic distortion is not as bad as the third and certainly no where near as bad as fifth. i wouldn't be surprised if music masks distortion by 10db or more, so that should be considered. in other words, 3% second harmonic distortion is barely audible in this experiment, so a woofer with 10% second harmonic distortion would probably be okay, even though that seems like a lot of distortion. for third harmonic distortion, i would look for about 10db lower distortion than the second fundamental as the maximum. so, for test tones, i would want to keep 3rd harmonic distortion to about 2% or so, and with a 10db masking effect in music, 5% is probably about where third harmonic distortion starts to become audible.
it's too bad that most companies don't report fifth harmonic distortion. in this experiment, it was by far the greatest offender, being audible down to below -50db. i would like to see a driver with less than 0.3% fifth harmonic distortion for test tones and with 10db of masking, i think 1% would be the level where it would become audible.