Years back, having borrowed a trumpet for the weekend, after subjecting my neighbors to hell and learning the gross way what that valve on the bottom is for, I'm now an expert on this topic.
That soft sound from Davis has to be a mix of what he's playing, how he's playing it and the fact it was recorded live on 1958 vintage gear, remastered to DVD recently by at least two different people and then ripped and uploaded to the YouTubes for some whack form of compression, then I heard it.
How much do you have to spend?

My initial impressions would be to tell you he was on a RCA 77 DX? But he in fact may have been on a Neumann U47? But it is a Kinescope film recording of a live video event. So in all likelihood, we are in all probability listening to the optical film sound whose high frequency response is certainly not stellar. With all that loss in the high frequencies, it has that nice warm RCA ribbon sound but like I said, I saw what appeared to be a U47 body/grill at one point. Either way he was within 1 to 1 1/2 feet from the microphone which also increased the proximity effect to make even warmer sounding. Like he didn't need to sound warm to begin with?

That and some nice real tube preamp/mixer sound.

I love 77 DX or Beyer M160/130's on trumpet. However I did have the pleasure of sitting in on a Maynard Ferguson overdub session, way back in 1978 at Media Sound. He was making that bloody trumpet scream its ass off, while sticking the Bell right into the front of a U87. It sounded simply phenomenal! Fat and forward. NO OVERLOAD! So now you know how I like my trumpets.

Blatty Broad
Ms. Remy Ann David

I recently bought a pair of Cascade Fat head ribbon mics. [[url=http://[/URL]="http://www.recordin…"]Here[/]="http://www.recordin…"]Here[/] are some tests. So far, I've used them on Marimba and alto and soprano sax. They are darker and lack the high end articulation of better/more expensive ribbons, but I am really looking forward to using them on more pop and jazz projects. I'd definitely like to try them on jazz trumpet. I would nave gone with the Beyer if I had the money, but I'm glad I tried the Cascades given my current finances.

Obviously Bob is a lot smarter than myself, but he already knew that (after all, he's a math professor/engineer & sometimes I feel like a nut, sometimes I don't). He purchased some affordable ribbon microphones that don't cost much more than a Shure Beta 58. So if it gets destroyed during a gig, you don't freak out because it didn't cost you 900 to $1500, or more. You still get that classic ribbon sound, albeit with a little boxiness around 250 hertz (my observations when I checked those out). Those probably sound a lot better with the optional Lundahl transformer but that jacks up the price of those affordable ribbon microphones considerably to replace the Chinese transformers. Of course that may actually correct for that 250 hertz bump I heard?

In the end, I rarely take out my ribbon microphones for any kind of popular music gigs since they're both fragile & expensive top shelf models. Now if it was one of those newer fangled HEAVY DUTY ribbon microphones designed for rock-and-roll like David Royer's or Wes Dooley's, provided you have the financial wherewithal for those, it would be cool.

Certainly not an English major either, I think the period goes here?
Ms. Remy Ann David

If you are short on $$$ and need to purchase gear specifically for this purpose, I would definitely go with cheap ribbons over cheap condensers.

Only Miles can sound like Miles, live or recorded.

Soldering skills (DIY) can help reduce the Lundahl transformer upgrade costs significantly.

You might also think about getting the broadcast mics, that way they can handle the intense volume from the trumpet with no worries on destroying the mic. SM7 and the RE20