Anyone who hasn’t tried one of the popular build-it-yourself online radio stations will have a difficult time appreciating the opportunity these services represent for the future of the entertainment industry — or the trepidation these big music “webcasters” also cause among those who make, market and sell the soundtracks of our lives.

One place to build a free music station is Pandora.com, a seven-year-old Web site that’s taking a leading role in challenging the way the recording industry wants to do business online. As soon as a consumer picks a single song — “A Day in the Life” by The Beatles, for example — the site uses that one snippet of information to assemble a customized stream of similarly psychedelic hits. Click on one of those tunes as it’s playing and, if it’s for sale, it may be purchased and downloaded.

This is how webcasters such as Pandora, AOL and Yahoo! Music, and retailers such as Amazon and Apple’s iTunes, have brought back “the single” — the stand-alone hits that once were the stock and trade of pop music. They’ve also created new revenue streams for music companies and artists, who collect royalties from a portion of each service’s advertising revenue, sales and subscription fees.

All of which makes one wonder why the recording industry would pick a protracted legal fight with the very companies that are some of the best financial backup singers the major labels have had in years.

Part of the explanation begins with The Beatles, whose iconic eighth album, “Sgt. Pepper’s Lonely Hearts Club Band,” transformed the music business 40 years ago this summer by securing the status of pop albums as an art form, instead of merely a collection of songs. “Sgt. Pepper” marked the beginning of the demise of “the hit single,” a slow process that climaxed in the 1980s and 1990s as first cassette and then compact disc sales grew and the sales of individual songs became less important.

Two generations later, technology is transforming the business model again: Why buy the whole CD when you can just make a digital copy of the individual song or songs you want?

The recording industry has worried about this kind of piracy and copyright infringement since before the original Napster.com helped popularize digital music copying and online file sharing in the late 1990s. Years of court cases, many targeting individual digital music swappers, have better defined what constitutes copyright infringement in an interactive, online age. Those fights alienated some potential customers, but they also helped give rise to legitimate, royalty-paying online music retailers and webcasters.

The latest skirmish involves a plan approved by the Copyright Royalty Board of the Library of Congress to dramatically raise the amount Web services pay to stream music online. Webcasters say the hike is excessive when compared with what other media pay to use copyrighted music, and might put some of them out of business. That would hurt royalty recipients as much as those who pay them — as well as customers.

A federal appeals court refused block the new royalty system this month, but industry talks on a possible compromise have limped along. Obstacles have included how to track what music is being streamed and requirements for digital rights management systems to prevent users from creating illegitimate copies of legitimate music streams, a practice known as “streamripping.”

While recording companies have legitimate concerns about protecting their copyrights, the fight only seems to underscore the industry’s overall failure for the past decade to give online customers what they want — and that rarely is a good business strategy. A system that would address many customers’ wants would replace today’s proprietary hodgepodge of digital rights systems, which make it hard for users to play the music they have paid for with different software and devices — in Windows Media Player as well as with iTunes, for instance. A new system would define “fair use” in a way that would allow paying customers to readily make personal copies of their music files without the current, typically stringent limits on non-commercial reproductions. And it would provide an inexpensive and unobtrusive way to pay for the right to share files with friends, perhaps with an additional royalty fee added to the cost of software or services customers use for legal file swapping.

Most of all, many customers want a system that works not only with music but with other forms of electronic entertainment, including video from Web sites, digital video recorders and DVDs.

The biggest barrier to achieving any of this has been the entertainment industry’s focus on finding foolproof legal and technological systems to stamp out copyright infringement, rather than making up for today’s losses by creating new revenue streams for the future.

It’s reminiscent of a track on side one of my crackly vinyl copy of “Sgt. Pepper,” in which Paul McCartney sings about “fixing a hole.”

Mark Stencel is deputy publisher and a technology columnist for Governing magazine, published by Congressional Quarterly Inc.