09 AUG 2014 by ideonexus

 12X Spiral

The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 eggs in a carton, 12 inches in a foot, 12 months in a year, 24 hours in a day, 360 degrees in a circle, 60 seconds in minute? Because highly composite numbers can be divided evenly in many ways. For...
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Building a spiral around a clock, with 12-segments in the rotation, puts multiples of 3 at {3,6,9,12}, multiples of at {4,8,12}, multiples of 2 at {2,4,6,8,10,12}, and primes at {1,5,7,11}.

01 APR 2013 by ideonexus

 The 12-Note Octave is Too Good to be True

[Playing notes on a piano] One... Two... Three... Four... Five... Six... Seven... Eight... Nine... Ten... Eleven... Twelve... 12 different pitches, and then back to where we began. Incredible! Fantastic! The mystical number 12. There are 12 hours in the A.M. and 12 hours in the P.M. The new day begins at 12 midnight. There are 12 months in a year. Both the Western and Chinese Zodiac have 12 signs. Further, the Chinese use a 12-year cycle for reckoning time. There are 12 eggs in a dozen. 12 d...
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The number 12 seems so perfect, but a 12-note scale made of 3/2 ratios brings the circle around to a point a little sharper than the the next octave.