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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|718}}
{{ED intro}}


== Theory ==
== Theory ==
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== Regular temperament properties ==
== Regular temperament properties ==
{{comma basis begin}}
{| 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]] (%)
|-
|-
| 2.3.5
| 2.3.5
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| 4375/4374, 40500000/40353607, {{monzo| 31 -6 -2 -6 }}
| 4375/4374, 40500000/40353607, {{monzo| 31 -6 -2 -6 }}
| {{mapping| 718 1138 1667 2016 }}
| {{mapping| 718 1138 1667 2016 }}
| &minus;0.0207
| −0.0207
| 0.1063
| 0.1063
| 6.36
| 6.36
Line 33: Line 42:
| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607
| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607
| {{mapping| 718 1138 1667 2016 2484 }}
| {{mapping| 718 1138 1667 2016 2484 }}
| &minus;0.0290
| −0.0290
| 0.0965
| 0.0965
| 5.77
| 5.77
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| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007
| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007
| {{mapping| 718 1138 1667 2016 2484 2657 }}
| {{mapping| 718 1138 1667 2016 2484 2657 }}
| &minus;0.0305
| −0.0305
| 0.0881
| 0.0881
| 5.27
| 5.27
Line 47: Line 56:
| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095
| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095
| {{mapping| 718 1138 1667 2016 2484 2657 2935 }}
| {{mapping| 718 1138 1667 2016 2484 2657 2935 }}
| &minus;0.0379
| −0.0379
| 0.0836
| 0.0836
| 5.00
| 5.00
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| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249
| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249
| {{mapping| 718 1138 1667 2016 2484 2657 2935 3050 }}
| {{mapping| 718 1138 1667 2016 2484 2657 2935 3050 }}
| &minus;0.0326
| −0.0326
| 0.0795
| 0.0795
| 4.76
| 4.76
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| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024
| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024
| {{mapping| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}
| {{mapping| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}
| &minus;0.0323
| −0.0323
| 0.0749
| 0.0749
| 4.48
| 4.48
{{comma basis end}}
|}
* 718et has a lower [[Tenney-Euclidean temperament measures #TE error|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo|581]] and followed by [[742edo|742i]].  
* 718et has a lower [[Tenney-Euclidean temperament measures #TE error|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo|581]] and followed by [[742edo|742i]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{{rank-2 begin}}
{| 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
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| 44/39
| 44/39
| [[Abigail]]
| [[Abigail]]
{{rank-2 end}}
|}
{{orf}}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
Retrieved from "https://en.xen.wiki/w/718edo"