616edo: Difference between revisions

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616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. ~~Finally~~, as every third step of [[1848edo]], it provides an excellent tuning for the [[K*N subgroups|3*616]] 2.5/3.7/3.11 [[subgroup]]~~, approximating~~ [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057{{c}}.

616edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It supports [[22nd-octave temperaments#Titanium|titanium]], a 22nd-octave temperament. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering.

616ee val additionally is close to the [[POTE]] tuning for the [[alphaxenic]] temperament, tempering out 131769/131072.

However, a much better usage of this temperament would be as every third step of [[1848edo]], it provides an excellent tuning for the [[K*N subgroups|3*616]] 2.5/3.7/3.11 [[subgroup]] where it tempers out exactly the same commas and approximates [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057{{c}}.

=== Odd harmonics ===

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 {{ED intro}}
-edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering. Finally, as every third step of [[1848edo]], it provides an excellent tuning for the [[K*N subgroups|3*616]] 2.5/3.7/3.11 [[subgroup]], approximating [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057{{c}}.
+edo is [[consistent]] to the [[7-odd-limit]], but it tends heavily flat in the first few [[harmonic]]s. The equal temperament [[tempering out|tempers out]] [[2401/2400]], 48828125/48771072, and 129140163/128450560 in the 7-limit; [[9801/9800]], 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. It supports [[22nd-octave temperaments#Titanium|titanium]], a 22nd-octave temperament. Alternatively, the 2.9.15.21.11 [[subgroup]] may be worth considering.
+ee val additionally is close to the [[POTE]] tuning for the [[alphaxenic]] temperament, tempering out 131769/131072.
+However, a much better usage of this temperament would be as every third step of [[1848edo]], it provides an excellent tuning for the [[K*N subgroups|3*616]] 2.5/3.7/3.11 [[subgroup]] where it tempers out exactly the same commas and approximates [[6/5]], [[7/6]], [[7/5]], and [[11/8]] within 0.057{{c}}.
 === Odd harmonics ===