22ed5/2: Difference between revisions
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== Theory == | == Theory == | ||
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. | 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 == | ||
{|class="wikitable" | {|class="wikitable center-1 right-2" | ||
|- | |||
! # | |||
! Cents | |||
! Approximate ratios* | |||
|- | |||
| 0 | |||
| 0.0 | |||
| [[1/1]] | |||
|- | |||
| 1 | |||
| 72.1 | |||
| [[26/25]] | |||
|- | |||
| 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>* | <nowiki/>* Based on treating 22ed5/2 as a 5/2.7/2.11/2.13/2-subgroup temperament. | ||