14ed5: Difference between revisions
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== Theory == | == 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 {{val|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. | 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 {{val|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 approximation of the 11/5 is off by 28 cents, so it is a very basic system for this subgroup, but nonetheless the 14-form is very important to the 5.7.11 subgroup in much the same way the 7-form is to the [[5-limit]]. The [[pentadacus]] temperament is based on the 14-form and is basically a compressed 14ed5 generator chain. 14ed5 represents the intersection of the [[juggernaut]] and [[pentadacus]] temperaments. | ||
== Intervals == | == Intervals == | ||