777edo: Difference between revisions

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The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.

~~== Theory ==~~

777edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], and [[17/1|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup.

777edo is ~~a dual fifths system with a consistency~~ limit ~~of only~~ 3.

~~If the harmonic~~ 3 is ~~excluded,~~ it is an excellent 2.5.7.9.11.13 subgroup ~~tuning, with the comma basis~~ {4459/4455, 41503/41472, 496125/495616, 123201/123200~~, 105644/105625~~}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.

=== Odd harmonics ===

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

=== Subsets and supersets ===

Since 777 factors into {{factorization|777}}, 777edo has subset edos {{EDOs| 3, 7, 21, 37, 111, and 333 }}.

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 {{Infobox ET}}
-The '''777 equal divisions of the octave''', or the 777-tone equal temperament (777tet), 777 equal temperament (777et) when viewed from a regular temperament perspective, divides the octave into 777 equal parts of about 1.544 cents each.
+{{ED intro}}
-== Theory ==
+edo is in[[consistent]] to [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], and [[17/1|17]], making it suitable for a 2.9.5.7.11.13.17 [[subgroup]] interpretation. A [[comma basis]] for the 2.9.5.7.11.13 subgroup is {4459/4455, [[41503/41472]], 496125/495616, 105644/105625, [[123201/123200]]}. In addition, it [[tempering out|tempers out]] the [[landscape comma]] in the 2.9.5.7 subgroup.
-edo is a dual fifths system with a consistency limit of only 3.
-If the harmonic 3 is excluded, it is an excellent 2.5.7.9.11.13 subgroup tuning, with the comma basis {4459/4455, 41503/41472, 496125/495616, 123201/123200, 105644/105625}. In addition, it tempers out the [[landscape comma]] in the 2.9.5.7 subgroup.
+=== Odd harmonics ===
 {{Harmonics in equal|777}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 777 factors into {{factorization|777}}, 777edo has subset edos {{EDOs| 3, 7, 21, 37, 111, and 333 }}.