1053edo: Difference between revisions

1053edo is consistent in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out [1 -27 18⟩ (ennealimma), [91 -12 -31⟩ (astro comma), and [92 -39 -13⟩ (aluminium comma). It supports and gives a good tuning for the quadraennealimmal temperament, as well as the 27th-octave trinealimmal.

Approximation of prime harmonics in 1053edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.039	+0.011	-0.165	+0.249	+0.498	-0.112	-0.077	-0.354	-0.517	+0.264
Error	Relative (%)	+0.0	+3.4	+1.0	-14.5	+21.9	+43.7	-9.8	-6.8	-31.1	-45.4	+23.1
Steps (reduced)		1053 (0)	1669 (616)	2445 (339)	2956 (850)	3643 (484)	3897 (738)	4304 (92)	4473 (261)	4763 (551)	5115 (903)	5217 (1005)

Since 1053 factors as 3⁴ × 13, 1053edo has subset edos 3, 9, 13, 27, 39, 81, 117, 351.

@@ Line 2: / Line 2: @@
 {{EDO intro|1053}}
-edo is [[consistent]] in the 11-odd-limit. It is a very strong 5-limit tuning where it tempers out the [[astro]] comma, the 13th-octave [[aluminium comma]], and the 9th-octave [[ennealimma]]. As expansions of ennealimmal, it tunes the [[quadraennealimmal]] temperament, as well as the 27th-octave [[trinealimmal]].
+edo is [[consistent]] in the [[11-odd-limit]]. It is a very strong 5-limit tuning where it [[tempering out|tempers out]] {{monzo| 1 -27 18 }} ([[ennealimma]]), {{monzo| 91 -12 -31 }} ([[astro comma]]), and {{monzo| 92 -39 -13 }} ([[aluminium comma]]). It [[support]]s and gives a good tuning for the [[quadraennealimmal]] temperament, as well as the 27th-octave [[trinealimmal]].
 === Prime harmonics ===
@@ Line 8: / Line 8: @@
 === Subsets and supersets ===
-factors as {{Factorization|1053}}, therefore 1053edo has subset edos {{EDOs|1, 3, 9, 13, 27, 39, 81, 117, 351}}.
+Since 1053 factors as {{factorization|1053}}, 1053edo has subset edos {{EDOs| 3, 9, 13, 27, 39, 81, 117, 351 }}.

Revision as of 09:16, 1 January 2024