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The Chromecast Audio instructions make High Dynamic Range sound like something very different from what's described in your link. They say:
High Dynamic Range
Chromecast Audio supports high dynamic range output. This provides premium and professional audio equipment such as HiFi audio systems, AV receivers, and monitor style speakers with the highest quality sound output.
When connecting your Chromecast Audio to such sound systems using 3.5mm or RCA analog cable (see here for compatible cables), you can enable Chromecast Audio’s High Dynamic option:
-From your Android or iOS device, open the Chromecast app .
-Touch the DEVICES tab.
-Scroll to find the device card for your Chromecast Audio.
-In the top right corner of the device card, touch the settings gear .
-Look for High Dynamic Range, and toggle the setting On.
Note: Many common speaker systems such as desktop computer speakers, docking speakers, portable and Bluetooth speakers are not built to support such a high dynamic range, causing the volume level to be very loud and sound to be somewhat distorted. Please avoid turning this setting on in those cases.
When Chromecast Audio is connected through an optical interface (see here for compatible cables), it will always use High Dynamic Range. Setting the High Dynamic Range to OFF won't have an effect.
Google says the goal is the highest quality sound output, not more loudness.
I have been using the digital output of the Chromecast (meaning the HDR is active) and the resulting sound is indistinguishable from the digital output of my Squeezebox Touch, which I believe performs bit-perfectly. And I'm using some very high dynamic range recordings.
Being curious, I reconnected the Chromecast using analog cable and switched the HDR ON and OFF. There is a very definite difference with the ON being open sounding and dynamic and the OFF being veiled and compressed in comparison. This is true even when compensating with the amp volume control. The ON position sounds nearly as good the digital output.