A warm DAC?

What is your budget $3k-5-$$10k ?

As I stated earlier, I like Audio Note's philosophy; specs don't matter as long as it sounds good and it's faithful to the original recording.

Ideally a DAC is designed to be flat across the frequency range of our hearing, so any deviations from the ideal are considered non-linearities aka distortion. If the DAC adds distortion how can it be faithful to the original recording? In vinyl this is a given there is distortion, but in digital any noise or distorion in well designed DACs have been pushed beyond human hearing. To purposely introduce distortion is not being faithful to the original recording. 

I’ll agree with your last statement. Although the distortion may be a manufacturing flaw and unintentional. Or not audible.
But I still ask, how does it sound?

The Audio Mirror Tubadour III SE is an excellent DAC.  I honestly preferred it over a DirectStream Sr.  I'm using it with a Herron pre amp and Innous Zenith MKII streamer.  

If it's a manufacturer flaw or unintentional that's different than
" specs don't matter". I've never heard the DAC you're talking about. The ones I've had that measure well sound good to me. I could never tell them apart. I've had a couple that measure lousy, I didn't know at the time and they sounded OK. Was never happy with them which I guess is why I went looking for  a new one.  The DAC I use now I have no idea how it measures since I'm using the one in my integrated amp and I've never seen any third party measurements of it. The few specs provided by the manufacturer show it measures well enough for me. At 64 years of age  that's all I can hope for and it sounds wonderful. The DAC it replaced was a Benchmark DAC3 one most consider anaylitical. Since the DAC  in the amp sounds the same to me I guess it would be considered that way as well.