The following is a script from "The City of Music" which aired on Dec. 7, 2014. Bill Whitaker is the correspondent. Tom Anderson, producer.

If you have ever taken a vacation in Italy, chances are you've been to Florence, Venice or Rome. It's unlikely you have been to a place called Cremona - a small city with a rich heritage. It's home to one of mankind's most glorious and coveted creations: elegant, hand crafted, Stradivarius violins.

Cremona was home to the master himself, Antonio Stradivari, who carved stringed instruments out of raw wood, and set the standard for a vibrant musical tradition that still flourishes today.

Time seems to stand still in the small Northern Italian city of Cremona. It's a quiet place, almost sleepy. It moves to the rhythms of pedals and pedestrians. But to understand the culture of Cremona you have to listen.

It's believed the violin was invented here. To an audience of school children in a Cremona concert hall, Ukrainian musician Anastasiya Petryshak plays a violin made 300 years ago by the most famous violin maker in history, Antonio Stradivari. He plied, many would say perfected, the craft of violin making in Cremona in the 17th and 18th centuries. There are tributes to him all over town. The city's Violin Museum pays homage to Stradivari and his magnificent creations.

Violin Museum CBS News

Paolo Bodini: And they are really our history.

Paolo Bodini, a doctor, the former mayor of Cremona and a director of the museum, took us on a tour of what he calls the Treasure Box.

Bill Whitaker: So Paolo, these four, all by Stradivari?

Paolo Bodini: Yes, we're in the middle of the Stradivari world.

Bill Whitaker: You live with these all the time. Is it possible you have a favorite?

Paolo Bodini: I would say the 1715 that's my favorite as far as the sound.

Many of Stradivari's 1,100 instruments have decayed or disappeared over the years but a number that survived are in remarkable condition - and in great demand by musicians all over the world.

Cremona's creations have been exported worldwide. Here at a Strad-Fest in Los Angeles - an event almost as rare as the instruments: not one but several Stradivarius violins on stage together. These world class violinists played second fiddle to the old master.

Cremona has brought many of Stradivari's violins back home. There are older instruments from Cremona here too, some made by the Guarneri family - and this one, made in 1566 by the man credited with inventing the violin: Andrea Amati.

Bill Whitaker: Now, this could be played today and would still have that ...

Paolo Bodini: Yeah, this is ...

Bill Whitaker:...exquisite sound?

Paolo Bodini: Yeah. It has - this one is sort of a deep sound.

To nurture that sound, these delicate, old instruments must be handled, held, played every month or two.

Bill Whitaker: They're not just museum pieces--

Paolo Bodini: No. If you want to keep them in shape you have to play it-- quite-- I won't say quite often, but once in awhile. You know-- b-- they-- they need to u-- to vibrate-- to be kept alive.

And when these exquisite, valuable instruments are taken from their cases to be played by Anastasiya Petryshak they get armored-car type security. It's a measure of their timeless power and versatility. In Anastasiya's hands the 300-year-old Strad is just as adept playing a serene passage from Paganini as a gypsy melody by a Spanish composer.

Itzhak Perlman: I don't need something better because there isn't something better.

Itzhak Perlman, one of today's most celebrated violinists, plays only a Strad, though he has a more humble name for his - a fiddle.

Itzhak Perlman: This fiddle is so amazing, I don't have to worry about it.

Bill Whitaker: You call it the perfect violin?

Itzhak Perlman: Well, it's the violin of my dreams, you know. If you wanna play a pianissimo that is almost inaudible and yet it carries through a hall that seats 3,000 people, there's your Strad.

Itzhak Perlman CBS News

Bill Whitaker: So describe the sound produced by this Stradivarius.

Itzhak Perlman: I can actually see the sound in my head. I can actually see it. It-- it has silk-- God, it's so difficult to describe. But each sound is different so this one has that sparkle, there is a sparkle to the sound.

Bill Whitaker: Somebody said it's just the Cremona magic.

Itzhak Perlman: Could be. It could be the DNA of the city.

In almost any other Italian city a medieval piazza and cathedral this magnificent would be crawling with foreign tourists, but Cremona is off the beaten path. It doesn't draw many visitors. But don't mistake it for some charming music box time has forgotten. Cremona actually is a very international city, where the past and the present coexist quite harmoniously.

"I can actually see the sound in my head. I can actually see it....But each sound is different so this one has that sparkle, there is a sparkle to the sound."

Thousands of violins still are made here every year. There seem to be more violin shops than espresso shops in Cremona - there are 150 of them. Stefano Conia came here from Hungary more than 40 years ago. Edgar Russ moved from Austria and makes violins, violas and violincellos. Mathijs Heyligers came from Holland. He says he and all the other violin makers were drawn by Cremona's history and tradition.

Bill Whitaker: Do you feel the old master when you're walking through these streets?

Mathijs Heyligers: Well, yes. It's a matter of realizing that the man who made all those incredible instruments that we are admiring every day and we're listening at in the concert halls were made by a man that actually walked on the street here, because these streets haven't changed. The houses have-- isn't changed.

Neither has the way Mathijs Heyligers and the other craftsmen make their violins. About the only thing that has changed in the past 500 years - workshops today have electric lights. The violin makers use compasses, hand saws, glue, no nails. The tools are simple, the craftsmanship precise.

Bill Whitaker: This is the way Stradivari did it?

Mathijs Heyligers: Yeah, 300 years ago, he was sitting in the same town, doing the same job.

Bill Whitaker: The same way.

Mathijs Heyligers: The same way, absolutely. I mean, no power tools, no-- no big-- technology, you know?

Bill Whitaker: How do you decide what piece of wood to use?

Mathijs Heyligers: Well, that is very much a matter of sound. You know, if you listen to this one, for instance, you can hear it.

Bill Whitaker: What are you listening for?

Mathijs Heyligers: That's the note this blade has, OK? Now it has a kind of clear resonance note. This violin is going to have a clear sound.

Bill Whitaker: Can I hear?

Mathijs Heyligers: It's kind of high, but it's-- it's clear in color, not so dark.

The violin makers of Cremona have used wood from the very same forests for hundreds of years - maple from Bosnia and red spruce from this one valley in the Italian Dolomites. It's said Stradivari first discovered the acoustic qualities of these woods. Now visitors show up every year to honor the trees, and Italy being Italy, there's a violinist to play a concert -- not for the spectators, for the trees.

Mathijs Heyligers: The material needs to be cut in the right place, but also the right way. We need to have the right moon and the right air humidity and the right wind when we cut the tree in the right season to make sure.

Bill Whitaker: Really.

Mathijs Heyligers: Absolutely.

Italian Dolomites CBS News

Bill Whitaker: Is anyone today making violins as good as the old masters in Cremona?

Itzhak Perlman: I don't think so, but you know, I hope somebody proves me wrong, that will be great.

Bill Whitaker: Three hundred years we're talking about and people still want to have a Stradivarius. What is it?

Itzhak Perlman: What is it? There is nothing like a fine Italian sound.

Bill Whitaker: That's the magic?

Itzhak Perlman: Yeah.

There are only about 650 of Stradivari's creations still in existence. The old instruments from Cremona are so rare and beautiful they've ignited a kind of feeding frenzy.

Sotheby's has this very rare Stradivari viola up for sale and says it's worth $45 million. No takers yet...

But Stradivari violins have fetched as much as $16 million, snapped up by collectors and investors.

Bill Whitaker: Could you afford your--

Itzhak Perlman: No, no, no--

Bill Whitaker: --violin today?

Itzhak Perlman: --no, no, absolutely not.

Bill Whitaker: Would you ever sell your violin?

Itzhak Perlman: Right now--

Bill Whitaker: Your Strad?

Itzhak Perlman: --the way-- the way-- the way it feels?

Bill Whitaker: No?

Itzhak Perlman: I don't think so, no.

Musicians lucky enough to have an old Cremonese instrument, like to play them as often as possible. But being played decade after decade for centuries can be rough on old bodies and joints.

Bruce Carlson: I wish it could talk...

Bruce Carlson, born in Michigan, has been restoring violins in Cremona for 40 years. He has to take them apart to fix them.

Bruce Carlson: Once we're all the way around then we can slip the table off.

He did this to a Stradivarius that literally had fallen apart in a violinist's hands.

Bill Whitaker: What is that like to pry open a violin made by Stradivari? I'd be scared to death to try to open that thing?

Bruce Carlson: It may be something like a surgeon, you know, when he-- when he's operating. Can't think about-- too much about the human side of things as-- as to just getting on with the business and doing it.

Bruce Carlson learned his craft at this school in Cremona. Students from all over the world come here to learn to make violins in the way of the old masters. Chris Kurz dropped out of Penn State to study here. It took him a year to make his first instrument.

Bill Whitaker: What can you get in Cremona that you couldn't get say, if you studied at Penn State, or went to New York?

Chris Kurz: I mean, like, I can walk down the street and walk by three or four shops on my way to-- get a coffee. And the fact that I can bring my instrument along to any one of those people, and walk in and say, "Hey maestro, do you have a minute or two to look at what I'm doing?" And then they give me their input.

Bill Whitaker: It's the city of violins?

Chris Kurz: Yeah, yeah, it's like living, breathing right here in Cremona.

Living...breathing here on the stage of the city's grand old hall -- a 21st century chamber orchestra featuring a 300-year-old Stradivarius. It's a tradition, a sound, a gift from Cremona.