202edo: Difference between revisions

202et tempers out 2401/2400, 19683/19600 and 65625/65536 in the 7-limit, and 243/242, 441/440, 4000/3993 in the 11-limit. It also notably tempers out the quartisma. It is the optimal patent val for the 11-limit rank-2 temperaments harry and tertiaseptal, the rank-3 temperament jove tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.

Approximation of prime harmonics in 202edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.96	-0.18	-0.51	+1.16	-2.90	+1.98	-0.48	+1.43	-1.85	+1.50
Error	Relative (%)	+0.0	-16.2	-2.9	-8.6	+19.5	-48.9	+33.3	-8.1	+24.0	-31.2	+25.2
Steps (reduced)		202 (0)	320 (118)	469 (65)	567 (163)	699 (93)	747 (141)	826 (18)	858 (50)	914 (106)	981 (173)	1001 (193)

Since 202 factors into 2 × 101, 202edo contains 2edo and 101edo as its subsets.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[-160 101⟩	[⟨202 320]]	+0.3044	0.3045	5.13
2.3.5	[-13 17 -6⟩, [23 6 -14⟩	[⟨202 320 469]]	+0.2280	0.2710	4.56
2.3.5.7	2401/2400, 19683/19600, 65625/65536	[⟨202 320 469 567]]	+0.2164	0.2356	3.97
2.3.5.7.11	243/242, 441/440, 4000/3993, 65625/65536	[⟨202 320 469 567 699]]	+0.1061	0.3049	5.13

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	13\202	77.23	256/245	Tertiaseptal
1	51\202	302.97	25/21	Quinmite
1	85\202	504.95	104976/78125	Countermeantone
1	87\202	516.83	27/20	Larry
2	12\202	71.29	25/24	Narayana
2	87\202 (14\202)	516.83 (83.17)	27/20 (21/20)	Harry

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|202}}
+{{EDO intro}}
 == Theory ==
@@ Line 26: / Line 26: @@
 | {{monzo| -160 101 }}
 | {{mapping| 202 320 }}
-| 0.3044
+| +0.3044
 | 0.3045
 | 5.13
@@ Line 33: / Line 33: @@
 | {{monzo| -13 17 -6 }}, {{monzo| 23 6 -14 }}
 | {{mapping| 202 320 469 }}
-| 0.2280
+| +0.2280
 | 0.2710
 | 4.56
@@ Line 40: / Line 40: @@
 | 2401/2400, 19683/19600, 65625/65536
 | {{mapping| 202 320 469 567 }}
-| 0.2164
+| +0.2164
 | 0.2356
 | 3.97
@@ Line 47: / Line 47: @@
 | 243/242, 441/440, 4000/3993, 65625/65536
 | {{mapping| 202 320 469 567 699 }}
-| 0.1061
+| +0.1061
 | 0.3049
 | 5.13
@@ Line 98: / Line 98: @@
 | [[Harry]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Scales ==
@@ Line 107: / Line 107: @@
 == Music ==
 ; [[Mundoworld]]
-* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] &ndash; in Oktone scale
+* [https://www.youtube.com/watch?v=_bNbb2o5K80 ''Home Planet Nostalgia''] – in Oktone scale
 [[Category:Harry]]