494edo: Difference between revisions

Cleanup; clarify the title row of the rank-2 temp table; -redundant categories
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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| 783 -494 }}
| {{monzo| 783 -494 }}
| {{mapping| 494 783 }}
| {{mapping| 494 783 }}
| -0.0219
| &minus;0.0219
| 0.0219
| 0.0219
| 0.90
| 0.90
Line 39: Line 31:
| {{monzo| -14 -19 19 }}, {{monzo| 39 -23 3 }}
| {{monzo| -14 -19 19 }}, {{monzo| 39 -23 3 }}
| {{mapping| 494 783 1147 }}
| {{mapping| 494 783 1147 }}
| -0.0032
| &minus;0.0032
| 0.0318
| 0.0318
| 1.31
| 1.31
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| 4375/4374, 703125/702464, {{monzo| 21 3 1 -10 }}
| 4375/4374, 703125/702464, {{monzo| 21 3 1 -10 }}
| {{mapping| 494 783 1147 1387 }}
| {{mapping| 494 783 1147 1387 }}
| -0.0385
| &minus;0.0385
| 0.0670
| 0.0670
| 2.76
| 2.76
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| 3025/3024, 4375/4374, 131072/130977, 234375/234256
| 3025/3024, 4375/4374, 131072/130977, 234375/234256
| {{mapping| 494 783 1147 1387 1709 }}
| {{mapping| 494 783 1147 1387 1709 }}
| -0.0365
| &minus;0.0365
| 0.0600
| 0.0600
| 2.47
| 2.47
Line 60: Line 52:
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213
| {{mapping| 494 783 1147 1387 1709 1828 }}
| {{mapping| 494 783 1147 1387 1709 1828 }}
| -0.0286
| &minus;0.0286
| 0.0576
| 0.0576
| 2.37
| 2.37
Line 67: Line 59:
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095
| {{mapping| 494 783 1147 1387 1709 1828 2019 }}
| {{mapping| 494 783 1147 1387 1709 1828 2019 }}
| -0.0069
| &minus;0.0069
| 0.0752
| 0.0752
| 3.09
| 3.09
|}
{{comma basis end}}
* 494et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 13- and 17-limit. It is the first past [[270edo|270]] with a lower 13-limit relative error, and the first past [[72edo|72]] with a lower 17-limit relative error. It is narrowly beaten by [[684edo|684]] in terms of 13-limit absolute error and by [[581edo|581]] in terms of 17-limit absolute error. Not until [[1506edo|1506]] do we reach an equal temperament with a lower relative error in either subgroup.  
* 494et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 13- and 17-limit. It is the first past [[270edo|270]] with a lower 13-limit relative error, and the first past [[72edo|72]] with a lower 17-limit relative error. It is narrowly beaten by [[684edo|684]] in terms of 13-limit absolute error and by [[581edo|581]] in terms of 17-limit absolute error. Not until [[1506edo|1506]] do we reach an equal temperament with a lower relative error in either subgroup.  


=== 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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|-
|-
| 13
| 13
| 205\494<br>(15\494)
| 205\494<br />(15\494)
| 497.98<br>(36.43)
| 497.98<br />(36.43)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Aluminium]]
| [[Aluminium]]
|-
|-
| 19
| 19
| 205\494<br>(3\494)
| 205\494<br />(3\494)
| 497.98<br>(7.29)
| 497.98<br />(7.29)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Enneadecal]]
| [[Enneadecal]]
|-
|-
| 38
| 38
| 205\494<br>(3\494)
| 205\494<br />(3\494)
| 497.98<br>(7.29)
| 497.98<br />(7.29)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Hemienneadecal]]
| [[Hemienneadecal]]
|-
|-
| 38
| 38
| 109\494<br>(5\494)
| 109\494<br />(5\494)
| 264.78<br>(12.15)
| 264.78<br />(12.15)
| 500/429<br>(144/143)
| 500/429<br />(144/143)
| [[Semihemienneadecal]]
| [[Semihemienneadecal]]
|}
{{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}}


== Music ==
== Music ==
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[[Category:Enneadecal]]
[[Category:Enneadecal]]
[[Category:Kwazy]]
[[Category:Kwazy]]
[[Category:Listen]]
[[Category:Tricot]]
[[Category:Tricot]]
[[Category:Listen]]