The quick answer is where the “taper” starts on the bass string.
The first thing we all need to know is what scale length your bass is.
You can usually find scale length information online on the manufacturer of your bass’ website, but if you don’t know for sure, you only need to grab a tape measure and measure your bass from the saddle to the nut on the smallest string to find out what the scale length is on your bass.
It is also a good idea to measure the distance from where the ball-end goes to the nut. Basses that have strings-thru-body bridges will usually need an additional 1.75 inches of full string gauge diameter length.
Short-scale basses are usually around 32 inches. Long-scale basses are 34 inches and extra-long-scale basses are 35 inches. What determines the difference in the strings is where the taper starts on the larger, multiple-wrapped .095 to .145 gauge strings.
The “taper” is the place on the string toward the end of the winding where the string begins to reduce in size from its full diameter down to a size that can fit into the eye of the tuning post and wrap around the tuning post so that the core wire doesn’t have excessive pressure that might cause the core wire to break.
Where the “taper” begins on string gauges .095-.145 that are used for a low “E,” low “B,” and low “F” strings is the most critical. The full diameter of the string must reach just past the nut but then must reduce quickly after the nut to a size that will fit into the eye of the tuning post and also allow no part of the full diameter of the string will wrap around the tuning post.
Since the tuning posts for gauges .020-.090 are usually further from the nut on the headstock and gauges .020 to .080 can also easily fit in most eyes and are then able to wrap around the post, we start the taper on our string sizes .060 to .090 at 38.75 inches. These string gauges with this taper fit virtually all short-scale, long-scale, and extra-long-scale basses. Gauges 020 to .055 are single wrap strings and will fit all scale lengths.
Our bass strings have an overall length including the exposed core wire of 52.5 inches. The winding stops and 47-48 inches. As long as the exposed core wire, like a plain string, reaches the tuning post, the string will perform properly.
On our .095 to .145 gauged strings, taper for short-scale starts at 34.75 inches with long-scale string taper starting at 36.75 inches and extra-long-scale starting at 38.75 inches.
Our long-scale bass strings will fit 34-inch scale basses with either plate/top mount or strings-thru-body bridges as well as 35-inch scale basses with plate/top mount bridges. 35-inch scale basses with strings-thru-body bridges require our extra-long-scale bass strings.