Even before I saw Australia I knew you from the UK. When I went to 5th grade in Oxford they called it "Maths." The other kids thought I was funny because I said "Math."
They've had a rapacious Feudal system and lying pols longer is all.
Wait 'til we elect a Sandalista as Prez, and we'll have a dozen flavours of "maths", plural, to empty one pocket or pay envelope into another "hole" as well. "Free"
anything means free of ass and related ass-ettes, no more "money worries" 'coz you won't HAVE any. Money, nor ass, either one. Just worries. Humankind is meant to keep doing this shit until they get it all, right?
Tapers: Oscar "jarno" Beale was B&S head guru when he invented jarno. Note from MT, B&S, Jacobs that it only NEEDS a very slight change in angle to get easy-release MT - good for drills - walk-out resistant B&S - good for mills - or damned-near WELDED-on Jacobs tapers.
Also note they all have CHANGES within their size ranges off the back of pragmatic experience and minor optimizations.
Beale tried to eliminate those with a mathematically regular plan. ANY size of jarno - even in-between or imaginary ones - has the same angle and has its size specs embedded right in its nomenclature.
As with the Metric system vs "US" fasteners, it looked right sweet as a "standard" ...on paper. But...didn't work as well in practice as all those irregular ones, each OPTIMIZED to do the job best in their size.
Run into any GENUINE oddball taper? Don't bitch. Just prepare to duplicate it, and be glad that isn't all that difficult to do that.
Probability is VERY high it was the result of testing to get best results for the mating alloys, hardness, wall thicknesses, balance of working stresses, hold & release, etc. - to serve its given application as well as it could BE served.
I did say "optimize"?