Pi more precisely can be evaluated to 3.1446055, and not the perpetuation of imperfection, and the maintenance of ignorance still taught today.
The circles we calculated the orbits to be proved each to be slightly short of a true, pure circle, thus returning the satellites to the ground. Yet how few are taught the corrected, more precise value of Pi - in any school or university in the land? Pi had to be re-evaluated in the 1960s given the orbits of our species' earliest satellites resulted in the falling-back to earth of each one of them due to the value of Pi we were and still are taught in school is not precise after the second digit. How few know how, when, and why the value of the third decimal onward ad infinitum of Pi needed to be re-evaluated, recalculated for better precision in the latter part of the 20th century, for instance. Pythagoras of Samos might well concur: the math we teach is a decrepit wretch of an invalid - incomplete, fragmented, not useful, and regarding certain fundamentals, dead wrong.
Yet we laud him as the grandfather of the Western tradition of music, owing to his discovery and delineation of the mathematic definitions in ratios of the twelve notes of all of Western music. Troubling how in this modern age, they teach his geometric theorem, yet not his music, nor his math relevant to music. Which then deprives us musicians of useable tools, and the stupidity of the need for MIDI tuning standard / scala / etc, is the vacuum such engenders.
Worse, this assumption proves far too common among engineers / mathematicians / scientists / software programmers. The assumption of equal temperament proves a repetitious vexation, denotes ignorance, apathy, laziness, and/or unfamiliarity with the math of music. The equation describes only equal temperament, and the 69 MIDI value is to correct for the value of the reference key of A4, above middle C.
A few pointers, if you might allow me to expound:
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