241edo: Difference between revisions

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 {{Infobox ET}}
-{{EDO intro|241}}
+{{ED intro}}
 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] in the 5-limit, [[19683/19600]] and [[3136/3125]] in the 7-limit, [[540/539]], 43923/43904, [[65536/65219]], and 151263/151250 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for [[subpental]].
+edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. As an equal temperament, it [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], 43923/43904, [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].
 === Prime harmonics ===
@@ 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| 382 -241 }}
 | {{mapping| 241 382 }}
-| -0.038
+| −0.038
 | 0.038
 | 0.76
@@ Line 24: / Line 33: @@
 | 78732/78125, {{monzo| 56 -28 -5 }}
 | {{mapping| 241 382 560 }}
-| -0.322
+| −0.322
 | 0.403
 | 8.10
@@ Line 31: / Line 40: @@
 | 3136/3125, 19683/19600, 829940/823543
 | {{mapping| 241 382 560 677 }}
-| -0.431
+| −0.431
 | 0.397
 | 7.97
@@ Line 38: / Line 47: @@
 | 540/539, 3136/3125, 8019/8000, 15488/15435
 | {{mapping| 241 382 560 677 834 }}
-| -0.425
+| −0.425
 | 0.355
 | 7.14
@@ Line 45: / Line 54: @@
 | 351/350, 540/539, 676/675, 3136/3125, 10648/10647
 | {{mapping| 241 382 560 677 834 892 }}
-| -0.397
+| −0.397
 | 0.330
 | 6.63
-{{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 82: / Line 98: @@
 | 4/3
 | [[Gary]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Subpental]]