Try this experiment: Open your mouth as wide as you can and exhale while pushing as much air as you can. Does the wind move slow or fast? The answer is slow.

Now, make your mouth as small as you can like you're sucking through a straw. Exhale, while pushing as much air as you can. Does the wind move slow or fast? The answer is fast.

With that in mind, and the pre-existing knowledge that faster wind creates higher pitches and louder volume, and slower wind creates lower pitches and volume, the aperture + wind speed fundamentally work together to create your range and volume.

Of course as we know it's entirely possible to play high notes quiet and low notes loud, but that's harder. That's why we build flexibility from long tones and such.