How to describe a "noise" which is intentional and not annoying?

The word "noise" inherently has a negative meaning: an uncertainty in measurements, or an assortment of annoying background sounds.

What word or term can be used when a "noise" is intentionally produced, for example, the running of an engine, the sounds of a marketplace, or the sound of the wind and birds, etc. to provide a specific mood.

It is sometimes called background, ambient, or bioacoustic noise:

Examples of background noises are environmental noises such as waves, traffic noise, alarms, people talking, bioacoustic noise from animals or birds and mechanical noise from devices such as refrigerators or air conditioning, power supplies or motors.

Environmental noise

Noise at low levels is not necessarily harmful; environmental noise can also convey a sense of liveliness in an area, and is not then always considered 'unwanted'.

^{Source: Wikipedia}

I can't think of any common word describing just that. You could use other, more specific words like murmur or rustle, depending on which sound you're trying to describe.

Consider phrasing your sentence in a way that frames the noise with a positive connotation. E.g.,

• A whispered hush of autumn leaves in wind
• The vibrant chirping of spring robins
• The gently breathing susurrus of the tide upon the shore

You could also use an an adjective, describing the sound as "musical" or "euphonic."

"Music" is what it is if you like the sound. A broker hears "the music of the marketplace", a naturalist hears "the music of the wind and the birds". Even an auto mechanic might hear "the music of the lifters, clattering harmony with the soft whistle of the fan belt."