4501edo: Difference between revisions

Revision as of 10:59, 19 February 2023

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 It is a very strong 37-limit system, distinctly consistent through the 39-odd-limit, and has the lowest 31-limit and 37-limit relative error of any division until 16808.

Approximation of prime harmonics in 4501edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.022	+0.000	+0.025	+0.026	+0.086	+0.088	+0.021	+0.119	+0.061	+0.043
Error	Relative (%)	+0.0	+8.4	+0.2	+9.5	+9.8	+32.1	+33.0	+7.8	+44.8	+22.8	+16.2
Steps (reduced)		4501 (0)	7134 (2633)	10451 (1449)	12636 (3634)	15571 (2068)	16656 (3153)	18398 (394)	19120 (1116)	20361 (2357)	21866 (3862)	22299 (4295)

4501edo has subset edos 7 and 643.

@@ Line 1: / Line 1: @@
 {{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]].
+{{EDO intro|4501}} It is a very strong 37-limit system, distinctly [[consistent]] through the 39-odd-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|####]] <!-- 4-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|4501}}
+=== Subsets and supersets ===
+edo has subset edos [[7edo|7]] and [[643edo|643]].