Forget the Apple Watch. The real test of Apple’s ecosystem comes Tuesday, when the company finally launches its Apple Music streaming service. For the world’s most valuable company, the offering is unlikely to move the earnings needle, especially with the first three months being offered as a free trial to anyone who signs up. But the consumer reception will say a lot about whether iPhone users still consider themselves to be part of a broader Apple experience, as opposed to just users of a well-designed smartphone.

Twelve...