14ed5

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← 13ed514ed515ed5 →
Prime factorization 2 × 7
Step size 199.022¢ 
Octave 6\14ed5 (1194.13¢) (→3\7ed5)
Twelfth 10\14ed5 (1990.22¢) (→5\7ed5)
Consistency limit 3
Distinct consistency limit 2

The 14 equal divisions of 5/1 system divides the 5th harmoinc or pentave into 14 equal steps of 199.022 cents each. It is essentially a compressed 6edo whole tone scale with a tempered octave of 1194.13 cents.

Theory

14ed5 is the first ED5 which can reasonably be described as a 5.7.11 subgroup temperament, excluding harmonics 2 and 3 as implied by pentaves, with the mapping 14 17 21]. 7/5 is mapped to near 2edo's tritone at 597 cents, while 11/5 mapped to the square root of five, a major ninth of 1393 cents. The mapping of 11/5 to the square root of five means 14ed5 supports juggernaut temperament, one of the lowest-badness 5.7.11 temperaments, much lower than even 5-limit meantone, where the period is the square root of five (~11/5) and the generator is ~7/5. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo and 13edt.

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