614edo: Difference between revisions

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~~==Theory==~~

614edo is [[consistent|inconsistent]] to the [[5-odd-limit]] as [[harmonic]]s [[3/1|3]] and [[5/1|5]] are off in opposite directions. While harmonics 5 and [[7/1|7]] have close to 1/3 relative error, [[11/1|11]] and [[13/1|13]] are more accurate, meaning 614edo can be used as a tuning for the 2.3.15.21.11.13 subgroup in the [[13-limit]]. [[3684edo]], which slices each step in 6, corrects the 3rd and 5th harmonics, however the 11 and 13 are now too inaccurate.

614edo is inconsistent to the 5-odd limit as ~~harmonics~~ 3 and 5 are off in opposite directions. While harmonics 5 and 7 have close to 1/3 relative error, 11 and 13 are more accurate, meaning 614edo can be used as a tuning for the 2.3.15.21.11.13 subgroup in the 13-limit. [[3684edo]], which slices each step in 6, corrects the 3rd and 5th harmonics, however the 11 and 13 are now too inaccurate.

614edo is notable for being the edo with the edostep closest to the [[schisma]] by direct approximation; however it does not consistently represent the schisma, as it actually [[tempering out|tempers out]] the schisma by patent val. 3684edo consistently represents the schisma as 1\614.

=== Prime harmonics ===

614edo is notable for being the edo with the edostep closest to the [[schisma]] by direct approximation, however it does not consistently represent the schisma, as it actually [[tempering out|tempers out]] the schisma by patent val. 3684edo consistently represents the schisma as 1\614.

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 {{ED intro}}
-==Theory==
+edo is [[consistent|inconsistent]] to the [[5-odd-limit]] as [[harmonic]]s [[3/1|3]] and [[5/1|5]] are off in opposite directions. While harmonics 5 and [[7/1|7]] have close to 1/3 relative error, [[11/1|11]] and [[13/1|13]] are more accurate, meaning 614edo can be used as a tuning for the 2.3.15.21.11.13 subgroup in the [[13-limit]]. [[3684edo]], which slices each step in 6, corrects the 3rd and 5th harmonics, however the 11 and 13 are now too inaccurate.
-edo is inconsistent to the 5-odd limit as harmonics 3 and 5 are off in opposite directions. While harmonics 5 and 7 have close to 1/3 relative error, 11 and 13 are more accurate, meaning 614edo can be used as a tuning for the 2.3.15.21.11.13 subgroup in the 13-limit. [[3684edo]], which slices each step in 6, corrects the 3rd and 5th harmonics, however the 11 and 13 are now too inaccurate.
+edo is notable for being the edo with the edostep closest to the [[schisma]] by direct approximation; however it does not consistently represent the schisma, as it actually [[tempering out|tempers out]] the schisma by patent val. 3684edo consistently represents the schisma as 1\614.
+=== Prime harmonics ===
 {{Harmonics in equal|614}}
-edo is notable for being the edo with the edostep closest to the [[schisma]] by direct approximation, however it does not consistently represent the schisma, as it actually [[tempering out|tempers out]] the schisma by patent val. 3684edo consistently represents the schisma as 1\614.