247edo: Difference between revisions

Line 2:

[[Prime harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family|compton fifth]]). ~~Using~~ the [[~~patent val~~]], ~~it tempers out [[126/125]], [[243/242]] and [[1029/1024]] in~~ the ~~11-limit , so it~~ [[~~support~~]]~~s the ''hemivalentino'' temperament (31 & 61e)~~.

[[Prime harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].

~~As every other step~~ of the ~~monstrous~~ [[~~494edo~~]], 247edo ~~can be used~~ in the ~~2.9.15.21~~ [[~~subgroup~~]].

The [[wart_notation|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{cent}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the [[hemivalentino]] temperament (31 & 61e).

=== Odd harmonics ===

@@ Line 2: / Line 2: @@
 {{EDO intro}}
-[[Prime harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family|compton fifth]]). Using the [[patent val]], it tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit , so it [[support]]s the ''hemivalentino'' temperament (31 &amp; 61e).
+[[Prime harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family|compton fifth]]). 247edo tunes the 2.9.13.15.21 [[subgroup]] very well, as every other step of the monstrous [[494edo]].
-As every other step of the monstrous [[494edo]], 247edo can be used in the 2.9.15.21 [[subgroup]].
+The [[wart_notation|247cg val]] has lower errors: this edo has a [[stretched_and_compressed_tuning|flat tendency]], so its tuning accuracy may be improved by an octave stretch of approximately +0.8{{cent}}. 247cg is a good tuning for [[miracle]], tempering out [[225/224]] and [[1029/1024]] in the [[7-limit]], [[243/242]], [[385/384]], [[441/440]], and [[540/539]] in the [[11-limit]], [[847/845]] in the [[13-limit]], and [[375/374]] and [[561/560]] in the [[17-limit]]. Alternatively, using the [[patent val]], 247edo tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit, [[support]]ing the [[hemivalentino]] temperament (31 &amp; 61e).
 === Odd harmonics ===