14ed5: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 2: | Line 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. | '''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}}. 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, | 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. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo. | ||
{{Stub}} | {{Stub}} | ||
Revision as of 07:35, 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]. 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. As such 14ed5 can be considered a no-twos-or-threes analog of 12edo.
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |