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 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 41: / Line 50: @@
 | 0.3049
 | 5.13
-{{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 81: / Line 97: @@
 | 27/20<br />(21/20)
 | [[Harry]]
-{{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
 == Scales ==