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22ed5/2: Difference between revisions

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Created page with "{{Infobox ET}} {{ED intro}} == Theory == There is a vague similarity to 17edo. It does not approximate harmonics well, but it approximates several half-integer (or /2 in primodality terms) ratios well, in particular it has decent approximations of 7/2, 11/2 and 13/2, and could be analyzed as a 5/2.7/2.11/2.13/2 subgroup temperament. It supports frosthog temperament, equating 11/7 to one step of 2ed5/2. == Intervals == {{Interval table}} == Harm..."
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Standardize layout; reduce decimal places
 
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== Theory ==
== Theory ==
There is a vague similarity to 17edo. It does not approximate harmonics well, but it approximates several half-integer (or /2 in [[primodality]] terms) ratios well, in particular it has decent approximations of [[7/2]], [[11/2]] and [[13/2]], and could be analyzed as a 5/2.7/2.11/2.13/2 subgroup temperament. It supports [[frosthog]] temperament, equating 11/7 to one step of [[2ed5/2]].
22ed5/2 has a vague similarity to [[17edo]] but they cannot be considered truly equivalent due to the severe octave stretch of 25.8 cents. It does not approximate harmonics well, but it approximates several half-integer (or /2 in [[primodality]] terms) ratios well, in particular it has decent approximations of [[7/2]], [[11/2]] and [[13/2]], and could be analyzed as a 5/2.7/2.11/2.13/2 subgroup temperament. It supports [[frosthog]] temperament, equating [[11/7]] to the square root of 5/2.
 
=== Harmonics ===
{{Harmonics in equal|22|5|2|columns=11}}
{{Harmonics in equal|22|5|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 22ed5/2 (continued)}}


== Intervals ==
== Intervals ==
{{Interval table}}
{|class="wikitable center-1 right-2"
 
|-
== Harmonics ==
! #
{{Harmonics in equal
! Cents
| steps = 22
! Approximate ratios*
| num = 5
|-
| denom = 2
| 0
}}
| 0.0
{{Harmonics in equal
| [[1/1]]
| steps = 22
|-
| num = 5
| 1
| denom = 2
| 72.1
| start = 12
| [[26/25]]
| collapsed = 1
|-
}}
| 2
| 144.2
| [[625/572]], [[676/625]]
|-
| 3
| 216.3
| [[25/22]]
|-
| 4
| 288.4
| [[13/11]]
|-
| 5
| 360.5
| [[154/125]]
|-
| 6
| 432.6
| [[125/98]], [[625/484]], [[875/676]]
|-
| 7
| 504.7
| [[35/26]], [[121/91]]
|-
| 8
| 576.8
| [[7/5]]
|-
| 9
| 648.9
| [[182/125]]
|-
| 10
| 721.1
| [[275/182]], [[875/572]]
|-
| 11
| 793.2
| [[11/7]], [[35/22]]
|-
| 12
| 865.3
| [[91/55]]
|-
| 13
| 937.4
| [[625/364]]
|-
| 14
| 1009.5
| [[25/14]]
|-
| 15
| 1081.6
| [[13/7]]
|-
| 16
| 1153.7
| [[49/25]], [[242/125]], [[338/175]]
|-
| 17
| 1225.8
| [[625/308]]
|-
| 18
| 1297.9
| [[55/26]]
|-
| 19
| 1370.0
| [[11/5]]
|-
| 20
| 1442.1
| [[286/125]], [[3125/1352]]
|-
| 21
| 1514.2
| [[125/52]]
|-
| 22
| 1586.3
| [[5/2]]
|}
<nowiki/>* Based on treating 22ed5/2 as a 5/2.7/2.11/2.13/2-subgroup temperament.
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