(Preface: No relation to a whore whistle.)
Ho hum, surprisingly, is a fairly recent addition to the English language, gaining popularity in the mid 1920s to describe anything mundane, boring, or mediocre. Despite its general negative tone, it's most often used as an acknowledgment of stagnancy i.e., "The band hasn't put out a new album in almost eight years. Ho hum," or, "Whore whistle means exactly what you would think it means. Ho hum." It can also be used as an adjective ("It was a ho hum movie", "I could tell his whore whistle was ho hum from a mile away.") Even more rarely, the phrase can be used sarcastically, as in the following example: "Oh, look, one more soldier has died in the guerilla nightmare that is Iraq. Ho Hum." Or: "The Yankees have once again guaranteed a playoff spot by buying the entire Montreal Expos franchise as a farm team. Ho hum."
The only non-laughable explanation of the word's etymology is that it in some ways mimics a sigh, the universal expression of boredom. Otherwise, its genesis is as mysterious as a whore whistle.
the tiresome chirping of a cricket