157edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|157}}
+{{ED intro}}
 == Theory ==
-et tempers out 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} (quinticosiennic comma) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit (supporting the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.
+et [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| 37 -16 -5 }} ([[quinticosiennic comma]]) in the 5-limit; [[2401/2400]], [[5120/5103]], and 110592/109375 in the 7-limit ([[support]]ing the [[hemififths]] and the [[catafourth]] temperaments). Using the [[patent val]], it tempers out [[176/175]], 1331/1323, 3773/3750 and [[8019/8000]] in the 11-limit; [[351/350]], [[352/351]], [[847/845]], [[1573/1568]], and [[2197/2187]] in the 13-limit.
-=== Prime harmonics ===
+=== Odd harmonics ===
 {{Harmonics in equal|157}}
 === Subsets and supersets ===
 edo is the 37th [[prime edo]].
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 24: / Line 25: @@
 | 2.3
 | {{monzo| 249 -157 }}
-| [{{val| 157 249 }}]
+| {{mapping| 157 249 }}
-| -0.388
+| −0.388
 | 0.388
 | 5.08
@@ Line 31: / Line 32: @@
 | 2.3.5
 | 78732/78125, {{val| 37 -16 -5 }}
-| [{{val| 157 249 365 }}]
+| {{mapping| 157 249 365 }}
-| -0.760
+| −0.760
 | 0.614
 | 8.04
@@ Line 38: / Line 39: @@
 | 2.3.5.7
 | 2401/2400, 5120/5103, 78732/78125
-| [{{val| 157 249 365 441 }}]
+| {{mapping| 157 249 365 441 }}
-| -0.737
+| −0.737
 | 0.533
 | 6.98
@@ Line 45: / Line 46: @@
 | 2.3.5.7.11
 | 176/175, 1331/1323, 2401/2400, 5120/5103
-| [{{val| 157 249 365 441 543 }}]
+| {{mapping| 157 249 365 441 543 }}
-| -0.532
+| −0.532
 | 0.629
 | 8.24
@@ Line 52: / Line 53: @@
 | 2.3.5.7.11.13
 | 176/175, 351/350, 847/845, 1331/1323, 2197/2187
-| [{{val| 157 249 365 441 543 581 }}]
+| {{mapping| 157 249 365 441 543 581 }}
-| -0.454
+| −0.454
 | 0.600
 | 7.86
@@ Line 59: / Line 60: @@
 | 2.3.5.7.11.13.17
 | 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187
-| [{{val| 157 249 365 441 543 581 642 }}]
+| {{mapping| 157 249 365 441 543 581 642 }}
-| -0.461
+| −0.461
 | 0.556
 | 7.28
@@ Line 66: / Line 67: @@
 | 2.3.5.7.11.13.17.19
 | 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475
-| [{{val| 157 249 365 441 543 581 642 667 }}]
+| {{mapping| 157 249 365 441 543 581 642 667 }}
-| -0.420
+| −0.420
 | 0.531
 | 6.95
@@ Line 73: / Line 74: @@
 === Rank-2 temperaments ===
-{| class="wikitable center-all right-3 left-5"
+{| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
-! Temperament
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 117: / Line 119: @@
 | [[Catafourth]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct