4501edo: Difference between revisions

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The '''4501 division''' divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] of any division until [[16808edo|16808]].

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

4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit|31-]] and [[37-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] of any equal temperament until [[16808edo|16808]]. The 4501m val likewise performs well in the [[41-limit|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo|7361]].

Some of the simpler commas it [[tempering out|tempers out]] include [[10648/10647]] and [[140625/140608]] in the 13-limit; [[14400/14399]], [[31213/31212]], and [[37180/37179]] in the 17-limit; 10830/10829, 14080/14079, and 27456/27455 in the 19-limit; 11662/11661, [[12168/12167]], 16929/16928, and 19551/19550 in the 23-limit; 11340/11339, 13312/13311, and 13456/13455 in the 29-limit; 7936/7935, 11935/11934, 15625/15624, [[19344/19343]], 23716/23715, 24025/24024, and 29792/29791 in the 31-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 4501 factors into 7 × 643, 4501edo has subset edos [[7edo|7]] and [[643edo|643]].

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 {{Infobox ET}}
-The '''4501 division''' divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] of any division until [[16808edo|16808]].
+{{ED intro}}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit|31-]] and [[37-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] of any equal temperament until [[16808edo|16808]]. The 4501m val likewise performs well in the [[41-limit|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo|7361]].
+Some of the simpler commas it [[tempering out|tempers out]] include [[10648/10647]] and [[140625/140608]] in the 13-limit; [[14400/14399]], [[31213/31212]], and [[37180/37179]] in the 17-limit; 10830/10829, 14080/14079, and 27456/27455 in the 19-limit; 11662/11661, [[12168/12167]], 16929/16928, and 19551/19550 in the 23-limit; 11340/11339, 13312/13311, and 13456/13455 in the 29-limit; 7936/7935, 11935/11934, 15625/15624, [[19344/19343]], 23716/23715, 24025/24024, and 29792/29791 in the 31-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|4501|columns=15}}
+=== Subsets and supersets ===
+Since 4501 factors into 7 × 643, 4501edo has subset edos [[7edo|7]] and [[643edo|643]].