# Skeptico Saloon: An Objectivist Joint

Discussion in 'Sound Science' started by gnarlsagan, Jun 27, 2013.

1. The application of dynamics is a creative decision and should be up to the performers and engineers.

2. Wow, that's quite an interesting mapping you have! I wonder what r value you would get if you drew a linear line through that data.
How long did it take you to go through all of your music?

I only recently got thinking about a track's dynamic range measurement because I'm interested in calculating how much power an amplifier would need to provide from the track's RMS value to the track's peak, which happen to relate to the crest factor.

Furthermore, I'm interested in calculating how much power an amplifier would need to provide to get a quiet track A to sound as loud as loud track B. These calculations might be useful for determining what kind of power your amp would need in a practical situation.

e.g. I'm listening to a loud track with an average loudness of around -18.7 dBFS (0 dBFS peaks) and I switch to a track in my playlist that's fairly quiet at -32.65 average dBFS (-9.6 dBFS average peaks, which is a 23.05 dB difference). How much more power would my amp need to get the quiet track to sound as loud as the louder one?

For volume differences:
-18.7 dBFS - -32.65 dBFS= 13.96 dB difference in volume (RMS)
10^(13.96/10) = 24.89

For volume and peak differences
13.96 dB volume + 23.05 dB peaks = 37.01 dB total
10^(37.01/10) = 5023.43

So the amplifier would need to output 24.89 times the power output to get the quieter track to sound as loud as the louder one if I understand this correctly, or 5023.43 times the power output to cover both the volume difference and the peaks of the track.

Let's say I'm listening to the HE-560 (43 ohm, 0.330 Vrms to reach 90 dB SPL) with an OPPO HA-2 DAC/amp (300 mW max, 3 Vrms max, 136.931 mA max). If I listen to the louder track above and an SPL device says the headphones are outputting 69 dB SPL, the HE-560 would need 0.020 mW of power (0.029 Vrms, 0.684 mA). If I then switch to the quieter track, I have to turn the volume knob, obviously, to get it to sound as loud as the louder track. From the calculations above, that's 24.89 times the power output, or 0.722 mW, which the HA-2 can provide. Covering peaks, I would need 5023.43 times the power output or 145.68 mW (2.5 Vrms, 39.39 mA), which the HA-2 can provide still but it's reaching its maximum potential.

Subjectively, I have done a similar listening session but without an SPL meter so it's not totally accurate. I'm assuming 69 dB SPL is around my average listening level because I listened to a calibrated system at a local meet and I was averaging 75-80 dB SPL with an open-back headphone in a somewhat quiet-ish room with some chatter in the background. Anyway, with the HE-560 on the HA-2, I was on high gain and about volume level 2.5/5 on the volume knob. I could actually listen to the quiet track at maximum volume, but the average volume level was too loud for my preferences; I wasn't able to detect any clipping in the brief time that I listened to it though.

......okay then. That turned out to be a longer ramble than I thought. I was just thinking out loud there. Are these calculations even valid in the first place? XD

3.
Actually, you would need to subtract 3.01 from the dB value, rather than divide it by sqrt(2), so it is 6.9 - 3.01 = 3.89 dB. However, the overall RMS level of this track seems to be in fact -6.9 dBFS referenced to a full scale sine wave, and the peak is obviously 0 dBFS as it is clipped, so the adjustment is not needed.

For music, it really depends on what you intend to use the measured value for. The purpose of the DR rating is primarily to show the amount of peak limiting or "brickwalling" applied to the track. It is not a reliable measure of the overall loudness, nor the the required DAC/amplifier/etc. dynamic range for transparent reproduction.

Measuring the frequency response of headphones as if they were loudspeakers does not give an accurate frequency response, because the effect of actually wearing them is different from just the HRTF in free air. For example, without a seal, headphones are not capable of an extended bass response. That is only one of the issues, but it already shows that setup #1 is not accurate, and the acoustic properties of the head and ears need to be simulated somehow, i.e. using a HATS like Inner Fidelity.

4.
For matching the loudness of tracks, it is best to use ReplayGain, as it was designed specifically for this purpose. The relative increase in power needed to play the quiet track as loud as the loud one without clipping can then be calculated from the ratio of the peak levels after ReplayGain has been applied (as the loudness-matched quiet track will now have the higher peak level). Of course, the amplifier also needs to have enough gain if the peaks are well under 0 dBFS.

5.
That is why the DR rating is based on the loudest (in terms of RMS level) 20% of blocks. If at least 20% of a track is brickwalled, then it will basically ignore the rest, and report only the dynamic range of the compressed parts.

6. Power levels are in watts, but the actual output power in W (which depends on a number of other factors) does not matter here, as we ultimately only need the ratio of the peak and the RMS level.

In any case, when you convert between dB and W (power, or squared sample values), the multiplier is 10, and for dB and voltage/current (i.e. the actual sample levels in digital audio) it is 20. So, for a sine wave it is either 10 * log10(2) (half power relative to a square wave of the same peak level), or 20 * log10(1.4142), and in both cases the result is 3.01 dB.

7.
I let it run overnight. The R² is 0.73.

8. Why are you saying that the volume would be 13.96dB different? If you want them to sound as loud as each other, the volume difference is 0, since they're the same volume. You'll need more power for the higher peaks, and you'll need more gain to get the same output level from a lower input level, but the power required for the RMS volume won't change.

9. Say I have a cylindrical tube that has a top/bottom surface area that's the same circumference of a typical headphone, and I have flat-measuring microphones on said surfaces. If I get a good seal around the tube, maybe use some weatherstrip foam to help with that, wouldn't the measurements be fairly accurate? Flat-tuned speakers produce a flat frequency response from a flat-frequency response microphone. If headphones produce a flat frequency response from a flat-frequency microphone, why would that be inaccurate? As you mentioned, the setup would have to account for the properties of the head and ears, but that could be applied to the flat response could it not? The HRTF is produced as a direct result of those properties when an otherwise flat-measuring speaker is played; can't the HRTF also be produced by those same properties when an otherwise flat-measuring headphone is played? In one instance the head is absent, in the other it isn't; both setups would be using the same speakers (or headphones in this case).

True, but in OS X, the Audirvana Plus media player doesn't support ReplayGain, nor does my iPhone.

But what if I listen to a loud track and then I switch to a quiet track? The difference in volume is obviously there so the volume in terms of SPL per se isn't the same. I'm trying to calculate how much more power output an amp would need to provide to get that quieter track to sound as loud as the louder track in terms of SPL. Gain has nothing to do with it I think since I can use a 1.0x gain amp for both cases and for the quieter track I would simply just need to turn the volume knob, and hence power output no? That's always been the case for me with the Objective 2 at least. I have never found the need to use 2.5x gain or higher.

10. The volume knob adjusts gain - power is determined by the signal amplitude and the load being driven. When you switch to the quieter track, the power output by the amp will decrease, and by increasing the gain by turning up the volume, you are bringing the power back up to the same level it was before. For a given pair of headphones, the same power will produce about the same SPL, so if something sounds quieter, the amp is delivering less power. Now, if your quiet track has peaks that approach 0dBFS, your amp will need more power because the peaks are farther above the average level than they would be on a "loud" track, so if you set the average to be the same, the peaks will be more demanding. However, simply taking a track and dropping its level by 20dB (and then turning your amp up 20dB to compensate) won't demand any more power from the amp than before (but your amp will need to be higher gain).

11. Pardon me while pick this nit.

Typically, gain is fixed. The volume knob just attenuates the incoming signal, and the amplifier's fixed gain is applied to that.

Ok, proceed.

se

12. Depends on how you define gain, really. I'm defining it as Vout/Vin, and not really caring what happens in the intermediate steps. You're correct about how it is frequently implemented though.

13. Like I said, I was just picking a nit, that's all.

se

14. If I have enough vin I got plenty of vout-o-roonie!

15. HA!

se