247edo: Difference between revisions
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[[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]]. | [[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]]. | ||
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{{ | 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{{c}}. 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 {{nowrap|31 & 61e}} temperament known as [[hemivalentino]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||