14ed5: Difference between revisions

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'''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 {{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 mapping of 11/5 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]].

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 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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 '''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 ==
-ed5 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 mapping of 11/5 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]].
+ed5 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 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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