Splendid!
I have no critique on the music itself. Your rhythms are very nice and interesting! Harmony is nice too.
As a saxophonist, I love that you have considered to write for saxophone quartet.
Sometimes the music of the Prelude reminds me of some Mario Kart songs.
The melodies are simple, but still blend well with the complex rhythms.
Make sure that the baritone saxophone for which you write has a low A key. Some have it and some don't. Check it!
You prove in this Prelude that you master the saxophone writing skill.
The tongue slaps will add an extra dimension when the music is performed by real musicians.
The Fugue reminds me of Bach, I don't know which piece, but it's also in 9/8. I think it's one of the 15 inventions in G (major or minor).
This movement is my favourite, because all voices are independent, yet they form a very dense atmosphere.
The saxophone has an octave key, which makes it possible to play an octave higher without having to press many other fingerings for playing the same note, but then an octave higher:
If you want to play a low G (written) and then a high G, you will first have the fingering of the low G and when playing the high G you only have to add the octave key. When playing legato and ascending from a G to a high G the transition is very smooth, but when playing legato and descending from high G to low G there can be a 'sob.' Especially the transitions from middle D, E and F (with octave key) to any other note without the octave key can be hard to not let it sob. The problem is that your main theme contains many of these intervals: m. 84 D* - G; m.85 E* - F#; etc.
Saxophonist can train to prevent this sob effect, but it depends on the level of the players. You shouldn't worry that much about this problem, because it occurs in almost every piece. However, I think it's useful for you to know this information.
The third movement is very nice. It stimilates me to dance!
M.179. Tenor. The D - Eb trill is very awkward and almost impossible, you have to change that.
Mm. 211 - 214 + mm. 247 - 249. Baritone. Don't 8va in any saxophone part. We hate to read it, because we can't, honestly. All notes should be written normal, i.e. without octave clefs or 8va lines, except when writing in the altissimo register. However, even then the notes are mostly written without any 'reading supports.'
By the way, I would delete all the saxophone names, except the names on the first line of each movement. There are namely no other instruments than these four saxophones, so you don't have to indicate these at every line in the score.
Can you tell me why you change the key signatures in the music? I tend to make more accidental mistakes when the music is full of key changes than when there is no key signature (or one) and all accidentals are written in front of the notes. Why don't you stop with one key signature?
Overall I love it! Note that the feedback I give to you are mostly details and finishing touches. This is because I see that you already know basics about the saxophone family.
The music is wonderful and I look forward to hear the recording of the music performed by actual players.
Kind regards,
Maarten
*Thank you for tagging me! @Monarcheon