Image source: Apple.

There are now more than 60 million people subscribing to the big three on-demand streaming music platforms. Spotify announced this month that it has 40 million subscribers, just after Apple (AAPL -0.35%) announced that Apple Music has 17 million subscribers. Earlier this year, Tidal said it had 3 million subscribers. Other high-profile streaming services such as YouTube Red haven't released any official subscriber numbers.

But the fastest growing of all the popular on-demand streaming platforms is also the largest and oldest. Spotify added 10 million new subscribers in the period from March to September. Apple, by comparison, added somewhere between 4 million and 6 million in that same period.

The growth of on-demand music subscriptions is eating away at Apple's iTunes revenue, and Apple plans to make up that lost revenue and more with Apple Music. Spotify's popularity represents a much bigger loss to Apple than a bit of music revenue, though.

Apple the services company

On Apple's second-quarter earnings call, CEO Tim Cook pointed out that services revenue growth accelerated to 27% from 24% in the first quarter. That growth slowed to 19% in the third quarter, however, as Apple came up against the initial release of Apple Music from the prior year.

The healthy clip of service revenue growth is supported by Apple's large and ever-growing install base, which topped 1 billion at the beginning of the year. Even with declining iPhone sales, it's a safe assumption that the install base continues to climb.

But even that huge install base isn't enough to convert a lot of users into loyal paid streaming subscribers. Even if every Apple user had two devices from the company, Apple Music's take rate is just 3.4%. It's probably much lower.

Spotify, by comparison, historically converts about 25% of its total listeners into paid subscribers. More recently, that number has been climbing higher.

Spotify's subscriber rate may be growing faster than its total audience because the idea of subscribing to a service has finally gone mainstream. Apple may be in part to thank for that, but Spotify is seeing more of the benefits. Its increased conversion rate has allowed Spotify to add double the number of new subscribers over the past six months as Apple.

The real value of Apple services

The rapid growth of Spotify's paid subscriber base isn't a threat to Apple investors because it's representative of the opportunity Apple is missing in services revenue. It's a threat because the real value of Apple's services such as Apple Music comes when users decide to upgrade their hardware. An Apple Music subscriber is much more likely to choose an Apple product since its functionality is built right into the device.

Put simply, Apple Music increases the value of the iPhone, iPad, and all of Apple's devices for those who subscribe.

That's true for all Apple services, including iCloud, Apple Pay, iMessage, iTunes, or the App Store, among others. The more Apple services an iPhone, iPad, or Mac user uses, the higher the switching costs.

Despite Apple's efforts to outmaneuver the competition with Apple Music's executive team of music insiders -- Jimmy Iovine, Dr. Dre, and Trent Reznor -- it's been unable to overcome Spotify. Apple is even throwing its considerable pile of cash around, signing deals for exclusives and producing original videos for artists. Spotify refuses to engage in those tactics. Clearly, that's not the determining factor for many subscribers.

That said, Apple Music hasn't been a failure by any means. Being able to claim 17 million subscribers in a little over one year is nothing to sneeze at. It took Spotify more than six years to reach that point. Those 17 million are some of Apple's most valuable users -- producing service revenue, and probably buying new Apple hardware year after year.

Apple Music's slower growth over the past six months compared with Spotify suggests that Apple's services strategy will need more than the streaming service to have the desired impact of increasing the value of Apple's hardware.