1178edo: Difference between revisions

Approximation of prime harmonics in 1178edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.087	-0.236	-0.065	-0.214	-0.120	-0.032	-0.060	+0.249	+0.304	-0.044
Error	Relative (%)	+0.0	-8.6	-23.1	-6.4	-21.0	-11.8	-3.1	-5.9	+24.4	+29.8	-4.3
Steps (reduced)		1178 (0)	1867 (689)	2735 (379)	3307 (951)	4075 (541)	4359 (825)	4815 (103)	5004 (292)	5329 (617)	5723 (1011)	5836 (1124)

Since 1178 = 2 × 19 × 31, 1178edo is notable for containing both 19 and 31. Its subset edos are 2, 19, 31, 38, 62, and 589.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[-1867 1178⟩	[⟨1178 1867]]	+0.0276	0.0276	2.71
2.3.5	[-14 -19-19⟩, [-99 61 1⟩	[⟨1178 1867 2735]]	+0.0522	0.0415	4.07
2.3.5.7	4375/4374, 703125/702464, [-52 -5 -2 23⟩	[⟨1178 1867 2735 3307]]	+0.0450	0.0380	3.73
2.3.5.7.11	3025/3024, 4375/4374, 234375/234256, [-27 3 -4 10 1⟩	[⟨1178 1867 2735 3307 4075]]	+0.0484	0.0347	3.41
2.3.5.7.11.13	3025/3024, 4225/4224, 4375/4374, 78125/78078, 1664000/1663893	[⟨1178 1867 2735 3307 4075 4359]]	+0.0457	0.0322	3.16
2.3.5.7.11.13.17	2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872	[⟨1178 1867 2735 3307 4075 4359 4815]]	0.0403	0.0327	3.21
2.3.5.7.11.13.17.19	2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913	[⟨1178 1867 2735 3307 4075 4359 4815 5004]]	0.0370	0.0318	3.12

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	337\1178	343.29	8000/6561	Raider
19	489\1178 (7\1178)	498.13 (7.13)	4/3 (225/224)	Enneadecal
31	581\1178 (11\1178)	591.851 (11.205)	936/665 (?)	217 & 1178
38	260\1178 (12\1178)	264.86 (12.22)	500/429 (144/143)	Semihemienneadecal
38	489\1178 (7\1178)	498.13 (7.13)	4/3 (225/224)	Hemienneadecal

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

@@ Line 12: / Line 12: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
@@ Line 62: / Line 71: @@
 | 0.0318
 | 3.12
-{{comma basis end}}
+|}
 === Rank-2 temperaments ===
-{{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 96: / Line 112: @@
 | 4/3<br />(225/224)
 | [[Hemienneadecal]]
-{{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
 == Music ==