# 14ed5

← 13ed5 | 14ed5 | 15ed5 → |

**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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