1955edo: Difference between revisions
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1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}. | 1955edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 [[subgroup]] interpretation, with a [[comma basis]] {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}. | ||
In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo| 73 -15 4 -7 }}}. The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 | In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 {{monzo| 80 -8 -13 1 }}, and 2.15.17.21 {{monzo| 73 -15 4 -7 }}}. The {{nowrap|1955 & 6003}} temperament in the 2.15.17.21 subgroup has only 0.000396{{c}} per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 {{monzo| -101 -12 48 -11 }}}. | ||
=== Odd harmonics === | === Odd harmonics === | ||