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I haven't done any blind testing, but there appears to be a certain harshness in loud and high notes of some female vocalists which goes away when the DAC is set for minimum phase. ...
I would guess that the problem is in the recording, not in the DAC. It's common for recordings to add artificial presence in the upper mids and treble that is most audible with female vocals and sibilants. Large diaphragm condenser mics common used to record vocals can have a rise somewhere in the 8k to 16k range.
A linear phase DAC filter usually has ruler flat response that plays this as it was recorded and it sounds too bright or harsh.
A minimum phase DAC filter usually does not have ruler flat response but starts rolling off in the audible spectrum which can attenuate this presence, making it sound softer or more natural.
If this is the case, blame the recording engineers, not the DAC. I may be stoned by audio purists for admitting this, but when I encounter recordings having this excess treble & sibilance (which is all too often), I raise my eyes to the heavens and silently curse the recording engineers, then use DSP tone controls to make it more listenable.
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My understanding is linear phase filters have pre-ringing. Minimum filters put all the ringing after the pulse. ...
Yes, but a properly implemented linear phase filter rings at the Nyquist frequency, so it should be inaudible, especially since most DACs oversample. Minimum phase filters have all the ringing after the transient, but they ring louder and longer, and have phase distortion in the audible spectrum (in the passband). They also tend to have a more gradual slope, so frequencies in the top audible octave may be attenuated, which can be audible to some people, with some recordings.