181edo: Difference between revisions

Revision as of 12:47, 16 November 2024

181et tempers out 2109375/2097152 (semicomma) and [14 -22 9⟩ in the 5-limit; 2401/2400, 5120/5103, and 390625/387072 in the 7-limit (supporting the hemififths and the cotritone). Using the patent val, it tempers out 385/384, 1375/1372, 2200/2187, and 4000/3993 in the 11-limit; 325/324, 352/351, 847/845, and 1575/1573 in the 13-limit.

Approximation of prime harmonics in 181edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.81	-1.78	-0.87	-1.04	+1.46	+1.12	+0.83	+1.56	-1.95	+1.93
Error	Relative (%)	+0.0	+12.2	-26.9	-13.1	-15.7	+22.0	+16.9	+12.5	+23.5	-29.5	+29.0
Steps (reduced)		181 (0)	287 (106)	420 (58)	508 (146)	626 (83)	670 (127)	740 (16)	769 (45)	819 (95)	879 (155)	897 (173)

181edo is the 42nd prime edo.

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[287 -181⟩	[⟨181 287]]	−0.255	0.255	3.84
2.3.5	2109375/2097152, [14 -22 9⟩	[⟨181 287 420]]	+0.086	0.525	7.92
2.3.5.7	2401/2400, 5120/5103, 390625/387072	[⟨181 287 420 508]]	+0.142	0.465	7.01
2.3.5.7.11	385/384, 1375/1372, 2200/2187, 4000/3993	[⟨181 287 420 508 626]]	+0.174	0.421	6.35
2.3.5.7.11.13	325/324, 352/351, 385/384, 1375/1372, 1575/1573	[⟨181 287 420 508 626 670]]	+0.079	0.439	6.62
2.3.5.7.11.13.17	325/324, 352/351, 375/374, 385/384, 595/594, 1275/1274	[⟨181 287 420 508 626 670 740]]	+0.028	0.425	6.40
2.3.5.7.11.13.17.19	325/324, 352/351, 375/374, 385/384, 400/399, 595/594, 1275/1274	[⟨181 287 420 508 626 670 740 769]]	+0.000	0.404	6.09

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	18\181	119.34	15/14	Septidiasemi
1	35\181	232.04	8/7	Quadrawell
1	39\181	258.56	[-32 13 5⟩	Lafa
1	41\181	271.82	75/64	Orson
1	53\181	351.38	49/40	Hemififths (7-limit)
1	88\181	583.43	7/5	Cotritone (181f)

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

"Today Or Tomorrow?" from Questions (2024) – Spotify | Bandcamp | YouTube – slurpee in 181edo tuning

@@ 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: @@
 | 0.404
 | 6.09
-{{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 102: / Line 118: @@
 | 7/5
 | [[Cotritone]] (181f)
-{{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 ==