AFAIK... best results for Jazz bass pots are linear volumes and audio taper (log) tone pot, this is supoused to give a nice volume sweep when playing clean uncompressed sounds and a usefull tone range. Last night I re-did the wiring on a jazz bass, I tried a 500k pot in volume position, it was supoused to be an audio taper pot as described by the ebay seller as I later checked, to find out that most of the volume was in the final 8-10 turn instead of evenly distributed. "OK, dumb me, this is an audio/log volume pot" so it's uneven in volume, let's use it for the tone pot. But to my surprise, when wired as a tone pot most of the highs reduction happens in the first 0-2 range!! What's going on? A suppoused audio/log pot gives uneven volume (volume jump from 8 to 10) AND uneven tone (Brightness jump, from 0-2 it works, but from 2 to 10 it does little or nothing for the tone sweep)
What brand pot is it? A lot of audio or log taper pots are not really log taper, but a composite of linear tapers. Some brands are better than others. Also look at the pot and see if it says A500K or B500K (A=Audio, B=Linear).
It's a chinese pot from ebay no marking other than 500k... But what I find confusing is that it behaves as an audio pot when used as volume and like a linear when used as tone pot
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