494edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
ArrowHead294 (talk | contribs) mNo edit summary |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 783 -494 }} | | {{monzo| 783 -494 }} | ||
| {{mapping| 494 783 }} | | {{mapping| 494 783 }} | ||
| | | −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 | ||
| 0.0318 | | 0.0318 | ||
| 1.31 | | 1.31 | ||
| Line 46: | Line 38: | ||
| 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 | ||
| 0.0670 | | 0.0670 | ||
| 2.76 | | 2.76 | ||
| Line 53: | Line 45: | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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 === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 113: | Line 99: | ||
|- | |- | ||
| 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}} | |||
{{orf}} | |||
== Music == | == Music == | ||
| Line 144: | Line 130: | ||
[[Category:Enneadecal]] | [[Category:Enneadecal]] | ||
[[Category:Kwazy]] | [[Category:Kwazy]] | ||
[[Category:Listen]] | |||
[[Category:Tricot]] | [[Category:Tricot]] | ||