398edo: Difference between revisions

Revision as of 13:00, 16 November 2024

398edo is only consistent to the 5-odd-limit, though it has a reasonable approximation to the full 13-limit using the patent val, which tempers out 10976/10935, 65625/65536, 1500625/1492992, 102760448/102515625, 102942875/102036672, and 200120949/200000000 in the 7-limit; 3025/3024, 4000/3993, 6250/6237, 59290/59049, 117649/117128, and 131072/130977 in the 11-limit; and 625/624, 1575/1573, 2080/2079, 2200/2197, 4096/4095, and 4225/4224 in the 13-limit. It supports yarman I, bisupermajor and semiquindromeda.

Approximation of prime harmonics in 398edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.56	-0.38	-0.99	+0.44	+0.68	+0.57	+0.98	-1.14	-1.44	+0.69
Error	Relative (%)	+0.0	+18.5	-12.7	-32.7	+14.6	+22.5	+19.0	+32.5	-37.8	-47.6	+23.0
Steps (reduced)		398 (0)	631 (233)	924 (128)	1117 (321)	1377 (183)	1473 (279)	1627 (35)	1691 (99)	1800 (208)	1933 (341)	1972 (380)

Since 398 factors into 2 × 199, 398edo has 2edo and 199edo as its subsets.

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Absolute (¢)	Relative (%)
2.3	[631 -398⟩	[⟨398 631]]	−0.1759	0.1759	5.83
2.3.5	390625000/387420489, [-53 10 16⟩	[⟨398 631 924]]	−0.0622	0.2157	7.15
2.3.5.7	10976/10935, 65625/65536, 200120949/200000000	[⟨398 631 924 1117]]	+0.0412	0.2588	8.58
2.3.5.7.11	3025/3024, 4000/3993, 10976/10935, 65625/65536	[⟨398 631 924 1117 1377]]	+0.0075	0.2411	8.00
2.3.5.7.11.13	625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935	[⟨398 631 924 1117 1377 1473]]	−0.0243	0.2313	7.67

Table of rank-2 temperaments by generator
Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	5\398	15.08	126/125	Yarman I
1	183\398	551.76	11/8	Emkay
2	54\398	162.81	11/10	Bisupermajor

* 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
 | {{monzo| 631 -398 }}
 | {{mapping| 398 631 }}
-| -0.1759
+| &minus;0.1759
 | 0.1759
 | 5.83
@@ Line 24: / Line 33: @@
 | 390625000/387420489, {{monzo| -53 10 16 }}
 | {{mapping| 398 631 924 }}
-| -0.0622
+| &minus;0.0622
 | 0.2157
 | 7.15
@@ Line 45: / Line 54: @@
 | 625/624, 1575/1573, 2080/2079, 2200/2197, 10976/10935
 | {{mapping| 398 631 924 1117 1377 1473 }}
-| -0.0243
+| &minus;0.0243
 | 0.2313
 | 7.67
-{{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 70: / Line 86: @@
 | 11/10
 | [[Bisupermajor]]
-{{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