|Ben's Old & Slightly Worn Mouthpiece|
Ligature placement on the mouthpiece might not significantly affect what is heard in front of the horn, but it can significantly affect the sound from behind the horn as well as the feeling of playing the horn. There are several main experiments I'd like to suggest.
|Ligature toward the front|
|Ligature toward the back|
First, is how far back or forward the ligature is placed. You might like it at one extreme or the other or possibly someplace in between. I'd suggest experimenting with the extremes (pictured on my mouthpiece above) first so that you have a better chance at detecting any contrasts. Of course, try the middle too and figure out what works for you.
Though these two variations are simple enough you might find yourself going back and forth for at a couple of hours trying different combinations. I'd suggest having a couple of different ligatures and reeds to confirm your findings. Also, make sure to try the different placements out in different rooms with varying levels of of natural reverberation. The more consistent your conclusions on ligature placement are when changing up the room, reed, and ligature, the more confident you can be that you've figured out the best placement.
Like I mentioned before, when trying different ligature placements myself I can hear significant differences in the sound and the feeling of playing the saxophone, however they don't carry so significantly to listeners in front of the saxophone. Following are some recording I did with the different ligature placements. For the record this reed is a little more buzzy than my normal fare.
Ligature on the Right.mp3
The above is an mp3 clip with my ligature toward the back and rotated so its putting pressure on the right side of the reed. This is my preferred ligature placement. On my particular mouthpiece this is what feels and sounds the best from the my (the player's) perspective.
Ligature in the Middle.mp3
This is an mp3 clip with the ligature centered. It sounds a little brighter, but it's also a little distorted, feels slightly more difficult to play, and is less expressive.
Finally, here is an mp3 clip of my ligature towards the front of the mouthpiece, which for me doesn't sound as full from behind the horn.