Xenharmonic Wiki

836edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,352 edits
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
Line 16: Line 16:


== 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
Line 60: Line 52:
| 0.0337
| 0.0337
| 2.35
| 2.35
|-
|- style="border-top: double;"
| style="border-top: double;" | 2.3.5.7.11.13
| 2.3.5.7.11.13
| style="border-top: double;" | 2200/2197, 3025/3024, 4096/4095, 4375/4374, 31250/31213
| 2200/2197, 3025/3024, 4096/4095, 4375/4374, 31250/31213
| style="border-top: double;" | {{mapping| 836 1325 1941 2347 2892 3094 }} (836)
| {{mapping| 836 1325 1941 2347 2892 3094 }} (836)
| style="border-top: double;" | -0.0085
| &minus;0.0085
| style="border-top: double;" | 0.0785
| 0.0785
| style="border-top: double;" | 5.47
| 5.47
|-
|-
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1275/1274, 2200/2197, 2500/2499, 3025/3024, 4096/4095, 4375/4374
| 1275/1274, 2200/2197, 2500/2499, 3025/3024, 4096/4095, 4375/4374
| {{mapping| 836 1325 1941 2347 2892 3094 3417 }} (836)
| {{mapping| 836 1325 1941 2347 2892 3094 3417 }} (836)
| -0.0014
| &minus;0.0014
| 0.0747
| 0.0747
| 5.21
| 5.21
|-
|- style="border-top: double;"
| style="border-top: double;" | 2.3.5.7.11.13
| 2.3.5.7.11.13
| style="border-top: double;" | 1716/1715, 2080/2079, 3025/3024, 15379/15360, 234375/234256
| 1716/1715, 2080/2079, 3025/3024, 15379/15360, 234375/234256
| style="border-top: double;" | {{mapping| 836 1325 1941 2347 2892 3093 }} (836f)
| {{mapping| 836 1325 1941 2347 2892 3093 }} (836f)
| style="border-top: double;" | +0.0561
| +0.0561
| style="border-top: double;" | 0.0805
| 0.0805
| style="border-top: double;" | 5.60
| 5.60
|-
|-
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
Line 88: Line 80:
| 0.0747
| 0.0747
| 5.20
| 5.20
|}
{{comma basis end}}
* 836et is notable in the 11-limit with a lower absolute error than any previous equal temperaments, past [[612edo|612]] and before [[1084edo|1084]].
* 836et is notable in the 11-limit with a lower absolute error than any previous equal temperaments, past [[612edo|612]] and before [[1084edo|1084]].


=== 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
Line 113: Line 99:
|-
|-
| 2
| 2
| 265\836<br>(56\836)
| 265\836<br />(56\836)
| 380.38<br>(80.38)
| 380.38<br />(80.38)
| 81/65<br>(22/21)
| 81/65<br />(22/21)
| [[Quasithird]] (836)
| [[Quasithird]] (836)
|-
|-
| 19
| 19
| 347\836<br>(5\836)
| 347\836<br />(5\836)
| 498.09<br>(7.18)
| 498.09<br />(7.18)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Enneadecal]]
| [[Enneadecal]]
|-
|-
| 22
| 22
| 347\836<br>(5\836)
| 347\836<br />(5\836)
| 498.09<br>(7.18)
| 498.09<br />(7.18)
| 4/3<br>({{monzo| 16 -13 2 }})
| 4/3<br />({{monzo| 16 -13 2 }})
| [[Major arcana]]
| [[Major arcana]]
|-
|-
| 38
| 38
| 347\836<br>(5\836)
| 347\836<br />(5\836)
| 498.09<br>(7.18)
| 498.09<br />(7.18)
| 4/3<br>(225/224)
| 4/3<br />(225/224)
| [[Hemienneadecal]]
| [[Hemienneadecal]]
|-
|-
| 44
| 44
| 347\836<br>(5\836)
| 347\836<br />(5\836)
| 498.09<br>(7.18)
| 498.09<br />(7.18)
| 4/3<br>(18375/18304)
| 4/3<br />(18375/18304)
| [[Ruthenium]]
| [[Ruthenium]]
|}
{{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}}


[[Category:Quasithird]]
[[Category:Quasithird]]
Retrieved from "https://en.xen.wiki/w/836edo"