Most attempts at designing the perfect saxophone ligature have centred around using a small metal harness wrapped around the mouthpiece that can be loosened and tightened by the turn of one or two screws. Other designs incorporate cloth, plastic or hardwood. One of the most efficient ways to attach the reed to the mouthpiece, however, is also one least expensive: use small rubber o-rings of the kind normally used as a seal in various types of engines and machines.
Use a tape measure to measure the circumference of your mouthpiece at the point where the ligature will hold the reed.
Determine the diameter of your mouthpiece by dividing the circumference by the value of Pi, or 3.14.
Find o-rings a size slightly smaller than the diameter of your mouthpiece. O-rings are sized using the diameter on the inside of the ring and the thickness of the rubber. You can purchase a dozen or more online or at any home-improvement mega-store for just a couple of dollars. They're often packaged in an assortment of sizes.
Hold the reed securely to the mouthpiece and roll the o-ring over the end, taking care to shield the tip of the reed as the o-ring passes over it.
Play the horn and gauge how secure the reed is on the mouthpiece. If it moves excessively, use a smaller o-ring and add more, if necessary. Experiment with size, numbers and placement. The horn's sound can be brighter or duller, and the horn can blow more freely or stuffier, according to where on the mouthpiece the ligature is placed.
If you find that the o-ring does not hold the reed securely enough for your taste but you like the way it makes the horn sound, some companies manufacture ligatures out of wood and plastic based on the o-ring concept. These are much more expensive but accomplish similar results. Even if you don't use this as an everyday ligature, keep a few appropriately-sized o-rings as an inexpensive backup.