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Hey Becky – this is a great question. I think that while its not required, it will certainly help. It is a multifaceted bonus when you look at things from the perspective of another instrument. Here are the immediate improvements I see on top of just learning how to think like a piano player:
1. Playing multiple notes at the same time lets you hear the intricacies of each chord. Though you can certainly arpeggiate chords on the sax, hearing them at the same time helps your brain to more fully integrate that chord into your mind.
2. Voicings and different configurations of the same chord are very apparent on the piano and something that horn players don’t think about a ton unless pressed to learn piano voicings. Thats not to say it cant be done! The piano really brings this to light though.
3. The Finger Dexterity required for piano will help your saxophone playing, especially in the left hand when you start playing bass figures in that hand. Also, counterpoint becomes much more relevant when you have to play the bass and the chords at the same time.Again, while not required, definitely recommended that you do a couple things with each song your working on. I would:
-Practice playing the melody + bass notes together slowly
-Play LH root and RH 3rd 7th through a progression
-Play root voicings (root 3rd 5th 7th) for each chord in both hands at the same time (for finger strength)
-Learn how to move a piano voicing through a chord progression where the inversion changes for different chords but you remain in the same range of the piano while you are changing chords. This guy has some really great info on this topic:
https://www.youtube.com/watch?v=8eQ9QfqrLQ0I hope this helps!