552edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[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 | ||
| 0.0691 | | 0.0691 | ||
| 3.18 | | 3.18 | ||
| Line 26: | Line 35: | ||
| {{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 | ||
| 0.1130 | | 0.1130 | ||
| 5.20 | | 5.20 | ||
| Line 33: | Line 42: | ||
| 250047/250000, 589824/588245, 33554432/33480783 | | 250047/250000, 589824/588245, 33554432/33480783 | ||
| {{mapping| 552 875 1282 1550 }} | | {{mapping| 552 875 1282 1550 }} | ||
| | | −0.1696 | ||
| 0.1118 | | 0.1118 | ||
| 5.15 | | 5.15 | ||
| Line 40: | Line 49: | ||
| 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 | ||
| 0.1048 | | 0.1048 | ||
| 4.82 | | 4.82 | ||
| Line 47: | Line 56: | ||
| 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 | ||
| 0.0961 | | 0.0961 | ||
| 4.42 | | 4.42 | ||
| Line 54: | Line 63: | ||
| 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 | ||
| 0.0977 | | 0.0977 | ||
| 4.50 | | 4.50 | ||
|} | |||
* 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" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 92: | Line 108: | ||
| 4/3<br />(?) | | 4/3<br />(?) | ||
| [[Palladium]] (5-limit) | | [[Palladium]] (5-limit) | ||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||