193edo: Difference between revisions

+data for the 23-limit
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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 8ve <br>Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 306 -193 }}
| {{monzo| 306 -193 }}
| {{mapping| 193 306 }}
| {{mapping| 193 306 }}
| -0.2005
| &minus;0.2005
| 0.2005
| 0.2005
| 3.23
| 3.23
Line 36: Line 28:
| 15625/15552, {{monzo| 50 -33 1 }}
| 15625/15552, {{monzo| 50 -33 1 }}
| {{mapping| 193 306 448 }}
| {{mapping| 193 306 448 }}
| -0.0158
| &minus;0.0158
| 0.3084
| 0.3084
| 4.96
| 4.96
Line 43: Line 35:
| 5120/5103, 15625/15552, 16875/16807
| 5120/5103, 15625/15552, 16875/16807
| {{mapping| 193 306 448 542 }}
| {{mapping| 193 306 448 542 }}
| -0.1118
| &minus;0.1118
| 0.3146
| 0.3146
| 5.06
| 5.06
Line 50: Line 42:
| 540/539, 1375/1372, 4375/4356, 5120/5103
| 540/539, 1375/1372, 4375/4356, 5120/5103
| {{mapping| 193 306 448 542 668 }}
| {{mapping| 193 306 448 542 668 }}
| -0.2080
| &minus;0.2080
| 0.3408
| 0.3408
| 5.48
| 5.48
Line 57: Line 49:
| 325/324, 364/363, 540/539, 625/624, 4096/4095
| 325/324, 364/363, 540/539, 625/624, 4096/4095
| {{mapping| 193 306 448 542 668 714 }}
| {{mapping| 193 306 448 542 668 714 }}
| -0.1216
| &minus;0.1216
| 0.3662
| 0.3662
| 5.89
| 5.89
Line 64: Line 56:
| 325/324, 364/363, 375/374, 442/441, 595/594, 4096/4095
| 325/324, 364/363, 375/374, 442/441, 595/594, 4096/4095
| {{mapping| 193 306 448 542 668 714 789 }}
| {{mapping| 193 306 448 542 668 714 789 }}
| -0.1302
| &minus;0.1302
| 0.3397
| 0.3397
| 5.46
| 5.46
Line 71: Line 63:
| 325/324, 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
| 325/324, 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
| {{mapping| 193 306 448 542 668 714 789 820 }}
| {{mapping| 193 306 448 542 668 714 789 820 }}
| -0.1414
| &minus;0.1414
| 0.3191
| 0.3191
| 5.13
| 5.13
Line 78: Line 70:
| 325/324, 364/363, 375/374, 400/399, 442/441, 460/459, 507/506, 529/528
| 325/324, 364/363, 375/374, 400/399, 442/441, 460/459, 507/506, 529/528
| {{mapping| 193 306 448 542 668 714 789 820 873 }}
| {{mapping| 193 306 448 542 668 714 789 820 873 }}
| -0.1184
| &minus;0.1184
| 0.3078
| 0.3078
| 4.95
| 4.95
|}
{{comma basis end}}
* 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]].  
* 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]].  
* 193et is also notable in the 19-limit, where it has a lower absolute error than any previous equal temperaments, past 190g and followed by [[212edo|212gh]].  
* 193et is also notable in the 19-limit, where it has a lower absolute error than any previous equal temperaments, past 190g and followed by [[212edo|212gh]].  


=== 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*
! Temperament
|-
|-
| 1
| 1
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| 4/3
| 4/3
| [[Kwai]]
| [[Kwai]]
|}
{{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}}


== Scales ==
== Scales ==