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cansman said:
In regard to the iTunes digital volume slider, from what you have said and assuming that the volume control is subjectively linear, i.e., a 50% reduction of the slider will result in 1/2 perceived loudness (-10dB), this means that the D/A converter in the DAC1 has a real world S/N ratio of around 126dB, is that right?
How did I come out with that figure? Essentially, a 100% to 50% volume slider reduction will result in -10dB volume reduction; then from 50% to 25% reduction, another -10dB. Finally from 25% to 12.5% reduction - which is around the 10% lower threshold you recommended - another -10dB reduction. This adds up to a total of -30dB reduction. Now, the DAC1 must at least meet the theoretical best S/N ratio of CD reply (when playing 16-bit music), and that is 96dB (is that right?) in order not to compromise sound quality. Consequently, 96dB + 30dB = 126dB!
You had the right idea, but your numbers are off. First of all, a 50% decrease in amplitude corresponds to a 6 dB drop. So, at 12.5% volume, it's actually -18 dB. I'm not sure iTunes volume control is this precise (in other words, I'm not sure that the graphic representation of 50% is equal to an audible 50%), but its pretty close.
In order to add no more then 1 dB of noise, the playback system must have a noise-floor at least 6 dB lower then the music. This is because when you add noises together - one 6 dB lower then the other - the result is 1 dB above the higher noise floor. Likewise, when you add noises together of the same amplitude, you have a 3 dB increase in noise.
For example, if my playback system has a SNR (signal-to-noise ratio) of 102 dB and the music has a SNR of 96 dB (16-bit), the overall SNR will be 95 dB (a 1 dB increase). If my playback system has a SNR of 96 dB and the music's SNR is 96 dB, the result will be a SNR of 93 dB (a 3 dB increase).
So, your complete playback system should have a SNR at least 6 dB below the music to have a minimal noise contribution.
The DAC1 has a SNR of 114 dB (worst case) - measurable both at the built-in HPA2 headphone outputs and the main analog outputs. This means that you can apply 12 dB of digital attenuation before you add more then 1 dB of noise to a 16-bit recording.
If you are using any additional equipment beyond the DAC1 (e.g., a 3rd party headphone amp, a pre-amp, a power amp), you need to add their noises into that equation also.
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Finally, I am relieved to know that I can use a significant portion of the iTunes volume control (without compromising sound quality) because I have been contemplating buying a DAC1 HDR. With some of my cans, the volume level is actually too loud when the DAC1 volume knob is at the 11th indent - around 11 o'clock (as suggested by you and the manual).
Yes, as I mentioned above, if you are using the HPA2 headphone amp that is built into the DAC1, then you can apply up to 12 dB of attenuation in iTunes before adding significant noise to a 16-bit recording.
The higher models of the DAC1 series have selectable gain-ranges that allow you to reduce the headphone output below the standard DAC1 level without diminishing SNR (DAC1 USB has one range 10 dB below the standard DAC1 level, and the DAC1 PRE and DAC1 HDR have two ranges below: 10 dB and 20 dB). This allows you to customize the headphone amp to suit your specific headphones' sensitivities and listening preferences.
Best,
Elias
