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 | ! Cents | ||
!Approximate ratios* | ! Approximate ratios* | ||
|- | |- | ||
|0 | | 0 | ||
|0. | | 0.0 | ||
|[[1/1]] | | [[1/1]] | ||
|- | |- | ||
|1 | | 1 | ||
|72. | | 72.1 | ||
|[[26/25]] | | [[26/25]] | ||
|- | |- | ||
|2 | | 2 | ||
|144. | | 144.2 | ||
|[[625/572]], [[676/625]] | | [[625/572]], [[676/625]] | ||
|- | |- | ||
|3 | | 3 | ||
|216. | | 216.3 | ||
|[[25/22]] | | [[25/22]] | ||
|- | |- | ||
|4 | | 4 | ||
|288. | | 288.4 | ||
|[[13/11]] | | [[13/11]] | ||
|- | |- | ||
|5 | | 5 | ||
|360. | | 360.5 | ||
|[[154/125]] | | [[154/125]] | ||
|- | |- | ||
|6 | | 6 | ||
|432. | | 432.6 | ||
|[[125/98]], [[625/484]], [[875/676]] | | [[125/98]], [[625/484]], [[875/676]] | ||
|- | |- | ||
|7 | | 7 | ||
|504. | | 504.7 | ||
|[[35/26]], [[121/91]] | | [[35/26]], [[121/91]] | ||
|- | |- | ||
|8 | | 8 | ||
|576. | | 576.8 | ||
|[[7/5]] | | [[7/5]] | ||
|- | |- | ||
|9 | | 9 | ||
|648. | | 648.9 | ||
|[[182/125]] | | [[182/125]] | ||
|- | |- | ||
|10 | | 10 | ||
|721. | | 721.1 | ||
|[[275/182]], [[875/572]] | | [[275/182]], [[875/572]] | ||
|- | |- | ||
|11 | | 11 | ||
|793. | | 793.2 | ||
|[[11/7]], [[35/22]] | | [[11/7]], [[35/22]] | ||
|- | |- | ||
|12 | | 12 | ||
|865. | | 865.3 | ||
|[[91/55]] | | [[91/55]] | ||
|- | |- | ||
|13 | | 13 | ||
|937. | | 937.4 | ||
|[[625/364]] | | [[625/364]] | ||
|- | |- | ||
|14 | | 14 | ||
|1009. | | 1009.5 | ||
|[[25/14]] | | [[25/14]] | ||
|- | |- | ||
|15 | | 15 | ||
|1081. | | 1081.6 | ||
|[[13/7]] | | [[13/7]] | ||
|- | |- | ||
|16 | | 16 | ||
|1153. | | 1153.7 | ||
|[[49/25]], [[242/125]], [[338/175]] | | [[49/25]], [[242/125]], [[338/175]] | ||
|- | |- | ||
|17 | | 17 | ||
|1225. | | 1225.8 | ||
|[[625/308]] | | [[625/308]] | ||
|- | |- | ||
|18 | | 18 | ||
|1297. | | 1297.9 | ||
|[[55/26]] | | [[55/26]] | ||
|- | |- | ||
|19 | | 19 | ||
| | | 1370.0 | ||
|[[11/5]] | | [[11/5]] | ||
|- | |- | ||
|20 | | 20 | ||
|1442. | | 1442.1 | ||
|[[286/125]], [[3125/1352]] | | [[286/125]], [[3125/1352]] | ||
|- | |- | ||
|21 | | 21 | ||
|1514. | | 1514.2 | ||
|[[125/52]] | | [[125/52]] | ||
|- | |- | ||
|22 | | 22 | ||
|1586. | | 1586.3 | ||
|[[5/2]] | | [[5/2]] | ||
|} | |} | ||
<nowiki>* | <nowiki/>* Based on treating 22ed5/2 as a 5/2.7/2.11/2.13/2-subgroup temperament. | ||