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. | '''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 == | == 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}}. The best approximation of 7/5 is 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, comparable to octave-repeating meantone, | 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}}. The best approximation of 7/5 is 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, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo. | ||
Revision as of 07:34, 22 August 2023
| ← 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]. The best approximation of 7/5 is 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, comparable to octave-repeating meantone, and as such 14ed5 can be considered a no-twos-or-threes analog of 12edo.