552edo: Difference between revisions

Notable as a 2.3.5.7.11.13.19 subgroup temp
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 875 -552 }}
| {{monzo| 875 -552 }}
| {{mapping| 552 875 }}
| {{mapping| 552 875 }}
| -0.0691
| &minus;0.0691
| 0.0691
| 0.0691
| 3.18
| 3.18
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| {{monzo| 8 14 -13 }}, {{monzo| 71 -36 -6 }}
| {{monzo| 8 14 -13 }}, {{monzo| 71 -36 -6 }}
| {{mapping| 552 875 1282 }}
| {{mapping| 552 875 1282 }}
| -0.1383
| &minus;0.1383
| 0.1130
| 0.1130
| 5.20
| 5.20
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| 250047/250000, 589824/588245, 33554432/33480783
| 250047/250000, 589824/588245, 33554432/33480783
| {{mapping| 552 875 1282 1550 }}
| {{mapping| 552 875 1282 1550 }}
| -0.1696
| &minus;0.1696
| 0.1118
| 0.1118
| 5.15
| 5.15
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| 5632/5625, 9801/9800, 151263/151250, 161280/161051
| 5632/5625, 9801/9800, 151263/151250, 161280/161051
| {{mapping| 552 875 1282 1550 1910 }}
| {{mapping| 552 875 1282 1550 1910 }}
| -0.1851
| &minus;0.1851
| 0.1048
| 0.1048
| 4.82
| 4.82
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| 1716/1715, 2080/2079, 5632/5625, 10648/10647, 20480/20449
| 1716/1715, 2080/2079, 5632/5625, 10648/10647, 20480/20449
| {{mapping| 552 875 1282 1550 1910 2043 }}
| {{mapping| 552 875 1282 1550 1910 2043 }}
| -0.1892
| &minus;0.1892
| 0.0961
| 0.0961
| 4.42
| 4.42
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| 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625, 15390/15379
| 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625, 15390/15379
| {{mapping| 552 875 1282 1550 1910 2043 2345 }}
| {{mapping| 552 875 1282 1550 1910 2043 2345 }}
| -0.1727
| &minus;0.1727
| 0.0977
| 0.0977
| 4.50
| 4.50
|}
{{comma basis end}}
* 552et is notable for being the first equal temperament to beat [[270edo|270]] in the 2.3.5.7.11.13.19 subgroup in terms of absolute error. The next equal temperament that does better in this subgroup is [[581edo|581]].  
* 552et is notable for being the first equal temperament to beat [[270edo|270]] in the 2.3.5.7.11.13.19 subgroup in terms of absolute error. The next equal temperament that does better in this subgroup is [[581edo|581]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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|-
|-
| 6
| 6
| 229\552<br>(45\552)
| 229\552<br />(45\552)
| 497.83<br>(97.83)
| 497.83<br />(97.83)
| 4/3<br>(128/121)
| 4/3<br />(128/121)
| [[Sextile]]
| [[Sextile]]
|-
|-
| 24
| 24
| 232\552<br>(2\552)
| 232\552<br />(2\552)
| 504.348<br>(4/348)
| 504.348<br />(4/348)
| 7/5<br>(?)
| 7/5<br />(?)
| [[Chromium]]
| [[Chromium]]
|-
|-
| 46
| 46
| 229\552<br>(1\552)
| 229\552<br />(1\552)
| 497.83<br>(97.83)
| 497.83<br />(97.83)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Palladium]] (5-limit)
| [[Palladium]] (5-limit)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}