This is a brief excerpt of a conversation on this subject that can be found here:
Well, the sax is a lovely beast. If you're playing an instrument, it gives you a personal knowledge of the way it takes time and repetition to gain mastery.
With the saxophone, it's difficult to play if the ambient air temperature gets too cold, because it's metal and the instrument gets cold, stiffening your fingers up. This is vastly important, because there is no volume control on a saxophone. That means you can't do repetitive practice indoors if other people are around - such as condo and apartment buildings - without bugging your neighbors. I tend to practice outside a lot, at parks and such.
All these facts make it very difficult to get in practice time during the winter. I go weeks sometimes in the cold months without being able to play, so that first day it goes above 60 degrees F, it is a treasure.
Playing the sax also requires fine control of the reed. How much pressure you put on it. When to let your tongue touch it. You can bend or stop notes and shift octaves higher or lower by the way you control the reed. You can also get a raspy vibrato effect by rattling your tongue against the roof of your mouth just behind the reed, like when rolling your R's in speaking Spanish.
Of course, fingering the keys is just as critical. How abrupt you are moving from key to key, how fast you raise and lower the keys, all of it matters.
Once you learn to blend the mastery of the reed with the mastery of the keys, you can finally make the instrument your second voice - and then seriously consider being able to play music in proper time. Then comes expanding your range by practicing endless varieties of transitions and timing from note to note to note.
It's a growth-by-inches process and both daunting and wonderful.
I've also started learning guitar for times when I feel like I'm stuck in a rut with the sax. It also gives me another option in winter. I have a really nice Fender Stratocaster that's got a red body, white pick guard, and rosewood neck. It plays beautifully. Coincidentally, it requires blending two skills to play as well. The left and right hands must be doing two very, very different tasks that must be perfectly blended together to create the finished work. Being electric, you can also modify the sound in many, many ways.
Finally, I've learned that no matter the instrument, finesse is every bit as important as strength - and you can only gain the finesse through practice after you first build up the strength.
The key is to put in time daily. Even 15-20 minutes a day will help.