4501edo: Difference between revisions

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{{EDO intro|4501}}
{{EDO intro|4501}}


4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 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- and 43-limit, with the lowest relative error of any equal temperament until [[7361edo|7361]].  
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 ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
4501edo has subset edos [[7edo|7]] and [[643edo|643]].
Since 4501 factors into 7 × 643, 4501edo has subset edos [[7edo|7]] and [[643edo|643]].

Revision as of 09:55, 12 January 2025

← 4500edo 4501edo 4502edo →
Prime factorization 7 × 643
Step size 0.266607 ¢ 
Fifth 2633\4501 (701.977 ¢)
Semitones (A1:m2) 427:338 (113.8 ¢ : 90.11 ¢)
Consistency limit 39
Distinct consistency limit 39

Template:EDO intro

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

Some of the simpler commas it 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

Approximation of prime harmonics in 4501edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error Absolute (¢) +0.000 +0.022 +0.000 +0.025 +0.026 +0.086 +0.088 +0.021 +0.119 +0.061 +0.043 +0.067 -0.091 +0.102 -0.055
Relative (%) +0.0 +8.4 +0.2 +9.5 +9.8 +32.1 +33.0 +7.8 +44.8 +22.8 +16.2 +25.0 -34.2 +38.2 -20.4
Steps
(reduced)
4501
(0)
7134
(2633)
10451
(1449)
12636
(3634)
15571
(2068)
16656
(3153)
18398
(394)
19120
(1116)
20361
(2357)
21866
(3862)
22299
(4295)
23448
(943)
24114
(1609)
24424
(1919)
25001
(2496)

Subsets and supersets

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