2814edo: Difference between revisions

In the 7-limit, it is enfactored, with the same commas tempered out as 1407edo. In the 11-limit, it supports rank-3 odin temperament. In the 13-limit it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup double bastille temperament.

Approximation of prime harmonics in 2814edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.036	+0.040	+0.044	+0.068	-0.016	-0.051	+0.142	-0.129	-0.153	-0.046
Error	Relative (%)	+0.0	-8.4	+9.4	+10.3	+15.9	-3.7	-12.0	+33.2	-30.3	-35.9	-10.8
Steps (reduced)		2814 (0)	4460 (1646)	6534 (906)	7900 (2272)	9735 (1293)	10413 (1971)	11502 (246)	11954 (698)	12729 (1473)	13670 (2414)	13941 (2685)

Since 2814 factors into 2 × 3 × 7 × 67, 2814edo has subset edos 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938 and 1407.

Regular temperament properties

Note: 7-limit temperaments represented by 1407edo are not included.

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	593\2814	252.878	53094899/45875200	Double bastille

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

@@ Line 16: / Line 16: @@
 === Rank-2 temperaments ===
 Note: 7-limit temperaments represented by [[1407edo]] are not included.
-{{Rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 23: / Line 30: @@
 | 53094899/45875200
 | [[Double bastille]]
-{{Rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 [[Category:Jacobin]]