The British music magazine The Word has this account from music producer Stuart Price discussing the Madonna song "I Love New York":

Stuart Price On I LOVE NEW YORK by Madonna (2005)

An electronic musician and a member of Madonna's touring band since 2001, Price attracted acclaim for his remixes of No Doubt's It's My Life and The Killers' Mr Brightside before co-writing and co-producing Madonna's Confessions On A Dance Floor in 2005. He recently produced Seal's System and is currently working on the new Keane album.

We were at Madison Square Garden in the middle of the 2004 Re-Invention tour, and it had got to that point where everyone was just completely bored. Touring with Madonna is like taking everything you've learned from the age of 14 about playing small pubs and clubs in bands and chucking it all out of the window. It's more like Cirque Du Soleil than the Pheasant & Firkin, put it that way. Essentially, the show has so many moving parts that if you go out on a limb you might end up losing a limb.

Madonna can be quite spontaneous, but she's not spontaneous when it comes to doing a show in front of 20,000 people! Similarly, the soundcheck is often quite a choreographed affair, but this time she just started messing around. She started playing this very basic, two-chord riff on the guitar and making up these lyrics about how she loved New York. It was just a real fun, mess-around song. Later I went into her dressing room with a guitar and a portable multi-track and said, "We're just going to stick something down for a reference", so we had a rough sketch of the song.

Later on in the tour we were playing Slane Castle with Iggy Pop, and while we were watching him Madonna said, "Let's make the song a bit like The Stooges." She was making a documentary on that tour, I'm Going To Tell You A Secret, and there was a scene in it that featured New York, and she decided she wanted a kind of Stooges version of I Love New York to play over it.

So I took the riff and the guide vocal away to a friend's house in Reading. We went into his bedroom and propped the bed up against the wall to make room for the drum-kit. His brother played guitar, I played bass and we tracked this Madonna song in the bedroom of a house on the Wokingham Road! And that's the version that appears on the documentary.

Right after that, we started making Confessions On A Dance Floor. Madonna said, "We're doing a dance record. I really like this song, but it doesn't fit in. Let's work on it." That week I was going to Australia to DJ and I promised to try and figure something out while I was away. As a travelling producer, working by yourself, you don't want to book into a two grand-a-day studio. It's overkill. You're looking for smaller places. I was in Sydney and I found this guy who said he had a small studio – I got there and it was literally a shed in his back garden! Right, OK! Let's see what we can do! So I effectively started remixing it in a shed in Australia.

I did what I normally do when I remix. I pull it all back to just the vocal, stick in a kick drum and try and work around it. I had this old Yamaha ZX100 keyboard which had a nice Detroit-y sound. That's where one of the main keyboard lines in the album version of the song came from. I remixed it and reworked it, and it went from Detroit rock to Detroit techno. I was sending it backwards and forwards to Madonna from Australia. Obviously the time difference couldn't have been worse, but that was how the final version of the song began to emerge. While I was away patching together the track, she was forming the lyrics. When I came back to London I took a version of the track to a club where I was DJing and it really worked on the dancefloor.

Then we came back to Olympic Studios in London and reunited to finish it for the album. As a collaborator she knows exactly what she wants, but on the other hand she wants you to do it! She'll say, "You need to be the visionary now; I'll be the visionary later." It's a complex chemistry but it plays out really well. What's brilliant about Madonna is that she's blissfully unaware of how a computer really works, so she's not there saying, "Can we try this effect?" or (pointing at a screen), "Can we move that bit over there." There's none of that. She sits on the couch and says, "I don't like it", or, "I like it." You're left to do your own thing without someone leaning over your shoulder.

Madonna works on instinct a lot more than people realise. I Love New York travelled all round the world, but everything – the riff, the vocal melodies, the lyric ideas – really came pouring out at that initial soundcheck.

Source: The Word (found on Drowned Madonna)