estimating loudness when using the fiio X1 and an IEM/headphone.
it looks scary and way too long because I try to follow a complete reasoning, but it's really one measurement and 2 or 3 simple calculi. at best it's something you will want to do for one or 2 IEMs once, to get an idea of how loud you're going, and that will be it.
I used a multimeter into a few loads(and confirmed the smallest values with an ADC and a RTA), there are some small variations but mostly the voltage is pretty stable on that DAP whatever load I plug into it. so I end up giving only one list of measured voltages that I consider precise enough(all things considered) for this particular purpose of guessing if we're ruining our own ears.
here we go, for that example I used a close to 20ohm resistor instead of an IEM, sent a full scale sine wave at different volume settings and measured the voltages:
X1 value voltage rms loudness
100 1.345 v + 5 db
90 0.75 v + 5 db
80 0.43 v + 5 db
70 0.24 v + 5 db
60 0.14 v + 5 db
50 0.08 v + 6 db
40 0.04 v +10 db
30 0.012 v +10 db
20 0.004 v +16 db
10 0.0006 v 0 db
the loudness column is useless for this exercise, but I added it just in case somebody cares(they're rounded values). if I was at volume 20 and rise it to volume 40 the loudness will go from 20 to 30(+10db) and from 30 to 40(+10db) so 10+10=20db louder than the previous loudness at volume 20. if I push to volume 50 it will go another +6db louder. etc
now what to do with all that that crap?
let's take an example, I use my shure se215 on the X1, and while walking down the street full of speeding cars, I end up going as high as 18 sometimes. so let's round this to 20 and read the voltage value I measured on the X1. for the value of 20, that's 0.004v. I keep that somewhere for later.
on shure's website you can read:
Sensitivity (1 kHz): 107 dB SPL/mW
Impedance 17 Ω
the sensitivity here is saying that for a 1mw tone of 1khz, you get 107db loud.
let's simply use P=U²/R to get a simple estimated voltage value
1mW that's 0.001W= U² / 17ohm
or U= 0.13V so for 0.13 volt we could get 107db loud on the se215 at 1khz and I'm using 0.004v from my X1
go there http://www.sengpielaudio.com/calculator-gainloss.htm enter 0.13 as "reference voltage V0" and use 0.004(because I listened at volume 20 on the X1) for "measured voltage". it calculates -30.2db
so 107-30.2=76.8db max at 1khz when using the X1 at volume 20 with the se215.
to get more accurate, we now need to have a look at the entire frequency response of the IEM, because what we've calculated so far is the loudest possible at 1khz. on my RAW measurement of the SE215(done with Room Eq Wizard and a microphone) I get the loudest around 4.77khz where the signature is 10.8db louder than 1khz.
Tyll seems to measure something close enough, with a peak also concentrated a little below 5khz http://www.innerfidelity.com/images/ShureSE215.pdf . on his graph the difference between 1khz and the 5khz peak(grey raw line) seems to come close to 13db I'd say. we can use whatever graph we can find for this, but keep in mind that it's the RAW graph that has meaning for the measured loudness, not the compensated one. here I'll stick to my own measurements as so far all was done based on my own gears and measurements so it just feels more consistent, but Tyll measurements are clearly a great help and I steal them all the time^_^.
so for me,the graph shows that the IEM goes 10.8db louder than the 1khz value, that I add to my previous estimate of 76.8db at 1khz when listening at volume 20 on the X1 with the SE215.
10.8+76.8=
87.6db.
this should be a pretty accurate estimate of the
loudest peak signal I can ever get in a song while using my SE215 at volume 20 on my X1. here we can say that while it's still ok, it's also clearly high enough to maybe avoid spending too many hours that way.
so now you can do the same using the volume level you're using with your IEM, and the specs you can find for that particular IEM (sensitivity, impedance and if possible, a nice raw frequency response graph).
I won't redo it all a second time, but while typing this, I'm using that very combo in my quiet room in still calm morning, I'm a little below 10 on the X1 with a final estimate of 70db using the previous method. and an actual measured loudness mostly closer to 58db because of replay gain. if I turn it off and play pop music, I indeed come close to 70db peaks sometimes. but around 58db, I could spend the entire day like that and not really fear for my ears. it doesn't mean I won't get any fatigue over time, but temporary fatigue is different from permanent damage. a good night sleep will deal with temporary fatigue.
to end this, I want to repeat that it's an estimate of the maximum possible peak levels. not perceived loudness and not the actual loudness of a song at all times. aside from boosting the loudest frequency with an EQ, everything else from the gears to the way I estimate things, will tend to actually lower the real loudness compared to what I've calculated. it's a kind of worst case scenario. for example, a song is not all the time at max loudness. it's obvious but that does matter in the long run, and how many calm passages a song will have is also a significant factor over time.
PS: if somebody notices a mistake or has a proper(AKA expensive) multimeter for audio signals and finds different voltages into 20ohm, please tell me.
I hope this can help one or 2 courageous people who will read and try it. ^_^
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