7ed5/2: Difference between revisions

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 {{Infobox ET}}
-'''7ED5/2''' is the equal division of the [[5/2]] interval into 7 parts of 226.6162 [[cent]]s each, corresponding to 5.2953 [[EDO]]. It is related to the [[Porwell temperaments #Semaja|semaja temperament]]. Its patent val tempers out the same 5-limit commas as [[5edo|5EDO]], but mapping of 7 and higher prime harmonics differs to 5EDO.
+{{ED intro}}
+== Theory ==
+ed5/2 corresponds to 5.2953…[[edo]]. It can function as a generator chain for the [[llywelyn]] temperament. Its [[patent val]] tempers out the same 5-limit commas as [[5edo]], but the mapping of 7 and higher prime harmonics differs.
+=== Harmonics ===
+{{Harmonics in equal|7|5|2|columns=11}}
+{{Harmonics in equal|7|5|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7ed5/2 (continued)}}
 == Intervals ==
-{| class="wikitable mw-collapsible"
+{| class="wikitable center-1 right-2"
 |+
-!Step
+! #
-!Interval (¢)
+! Cents
-!JI approximated
+! Approximated ratio
-!Simplified ratio
 |-
-|1
+| 1
-|226.62
+| 227
-|34/30
+| 8/7, 25/22
-|17/15
 |-
-|2
+| 2
-|453.23
+| 453
-|39/30
+| 13/10
-|13/10
 |-
-|3
+| 3
-|679.85
+| 680
-|34/23
+| 65/44
-|
 |-
-|4
+| 4
-|906.47
+| 906
-|66/39
+| 22/13
-|22/14
 |-
-|5
+| 5
-|1133.08
+| 1133
-|23/12
+| 25/13
-|
 |-
-|6
+| 6
-|1359.70
+| 1360
-|66/30
+| 11/5, 35/16
-|11/5
 |-
-|7
+| 7
-|1586.31
+| 1586
-|5/2
+| 5/2
-|
 |}
-The subgroup interpretation used is 5/2.12.23.34.39.51.58.66. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 12*5/2=30.
-== Harmonics ==
-{{Harmonics in equal
-| steps = 7
-| num = 5
-| denom = 2
-}}
-{{Harmonics in equal
-| steps = 7
-| num = 5
-| denom = 2
-| start = 12
-| collapsed = 1
-}}
-[[Category:Ed5/2]]
-[[Category:Nonoctave]]