Nova thats where the graph's on led's manufacturers data sheets come in If you look at them you will usually see a fwd current vs voltage graph and with those it on an upwards slope, ie more current needs a slightly higher forward voltage too which is what you are observing in your real world tests.
Thats why its important to get an understanding of data sheets when you do any electronics work. All the general specs you see with be at some arbitrary point on the graph, usually the point that makes the product sound the best. With leds its usually at the nominal rated values, the average if you will which for most users is fine.
Sabre builders though aren't your average user
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