Loki, you need to get the audio signal to your 2160 as a digital signal and let the 2160s DAC decode and produce the music. Streaming from your phone or your computer is likely using the DAC in your phone/computer to decode the signal. High quality digital streaming is made garbage if not decoded by a quality DAC which you paid big $$$ for in your 2160. As Stach said above the streaming quality control is just not consistently consistent.
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Music system
Model 990/7500/Magnepan 1.6 QRs/Technics SL1200 MK2/Aperion S-12 Subwoofer/OWA3/Sony NS75H DVD
APC H15 Power Conditioner
TV System
Large Advent Loudspeakers/ Polk center/Monoprice surrounds/Panasonic Viera 42 inch/Onkyo HT-RC260/Sony BDP S590/Directv
Home Theater System
Onkyo PR-SC886/Outlaw 7125 Klipsch RF-82 L/R,RC-62 center, RB-35 SR/SL, BENQ HT1075, Outlaw LFM1-EX/OPPO BDP-83/Directv
Harmony ONE
Blue Jeans and Monoprice interconnects
APC H15 Power Conditioner