247edo: Difference between revisions

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The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 247 parts of 4.8583 [[cent]]s each.

~~== Theory ==~~

[[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]].

~~In 247EDO, 144 degree represents~~ [[3/2]] ~~(2.36¢ flat)~~, ~~80 degree represents~~ [[5/4]] ~~(2.35¢ sharp)~~, ~~199 degree represents~~ [[7/4]] ~~(2.02¢ flat)~~, and ~~113 degree represents~~ [[11/8]] ~~(2.33¢ flat). 247EDO~~ lacks consistency to the 5 and higher odd~~-limit~~. It is the largest ~~number EDO~~ that ~~interval representing~~ 3/2 is flatter than that of [[~~12EDO~~]] (700¢, [[Compton family|compton]] ~~fifth~~). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit ~~patent mapping~~, ~~so it~~ [[support]]s the ~~''hemivalentino'' temperament (~~31&61e).

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 ===

[[~~Category:Equal divisions of the octave|###~~]] ~~~~

=== Subsets and supersets ===

Since 247 factors into {{factorization|247}}, 247edo contains [[13edo]] and [[19edo]] as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics.

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 {{Infobox ET}}
-The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 247 parts of 4.8583 [[cent]]s each.
+{{ED intro}}
-== Theory ==
+[[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]].
-In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&amp;61e).
+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 &amp; 61e}} temperament known as [[hemivalentino]].
+=== Odd harmonics ===
 {{Harmonics in equal|247|columns=15}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 247 factors into {{factorization|247}}, 247edo contains [[13edo]] and [[19edo]] as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics.