The exhibition “Ain’t Nothing Like the Real Thing,” which opens on Tuesday at the Museum of the City of New York, really ain’t anything like the real thing, but that is not really its fault. The “real thing” in this case is almost beyond the reach of a museum show. It is to be found not in Louis Armstrong’s trumpet or Miles Davis’s flugelhorn, or James Brown’s black jumpsuit studded with rhinestones spelling “Sex,” or Ella Fitzgerald’s orange dress or Michael Jackson’s fedora (all of which are on display here), but in the music those performers made while wearing these clothes and playing these instruments.