Xenharmonic Wiki

422edo: Difference between revisions

← Older editNewer edit →

FloraC (talk | contribs)

4 user groups
27,346 edits
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,991 edits
→Prime harmonics: Added higher primes as many are approximated well
m Cleanup
Line 11: Line 11:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 422 factors into 2 × 211, 422edo has subset edos [[2edo]] and [[211edo]].
Since 422 factors into primes as {{nowrap| 2 × 211 }}, 422edo has subset edos [[2edo]] and [[211edo]].


== Regular temperament properties ==
== Regular temperament properties ==
Line 19: Line 19:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
Line 26: Line 26:
|-
|-
| 2.3
| 2.3
| {{monzo| 669 -422 }}
| {{Monzo| 669 -422 }}
| {{mapping| 422 669 }}
| {{Mapping| 422 669 }}
| −0.1308
| −0.1308
| 0.1308
| 0.1308
Line 33: Line 33:
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| 23 6 -14 }}, {{monzo| 33 -34 9 }}
| {{Monzo| 23 6 -14 }}, {{monzo| 33 -34 9 }}
| {{mapping| 422 669 980 }}
| {{Mapping| 422 669 980 }}
| −0.1469
| −0.1469
| 0.1092
| 0.1092
Line 41: Line 41:
| 2.3.5.7
| 2.3.5.7
| 4375/4374, 589824/588245, 29360128/29296875
| 4375/4374, 589824/588245, 29360128/29296875
| {{mapping| 422 669 980 1185 }}
| {{Mapping| 422 669 980 1185 }}
| −0.1852
| −0.1852
| 0.1155
| 0.1155
Line 48: Line 48:
| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 4375/4374, 5632/5625, 589824/588245
| 3025/3024, 4375/4374, 5632/5625, 589824/588245
| {{mapping| 422 669 980 1185 1460 }}
| {{Mapping| 422 669 980 1185 1460 }}
| −0.1679
| −0.1679
| 0.1090
| 0.1090
Line 55: Line 55:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 1716/1715, 2080/2079, 2200/2197, 3025/3024, 5632/5625
| 1716/1715, 2080/2079, 2200/2197, 3025/3024, 5632/5625
| {{mapping| 422 669 980 1185 1460 1562 }}
| {{Mapping| 422 669 980 1185 1460 1562 }}
| −0.1930
| −0.1930
| 0.1142
| 0.1142
Line 62: Line 62:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2200/2197, 2431/2430
| 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2200/2197, 2431/2430
| {{mapping| 422 669 980 1185 1460 1562 1725 }}
| {{Mapping| 422 669 980 1185 1460 1562 1725 }}
| −0.1744
| −0.1744
| 0.1151
| 0.1151
Line 69: Line 69:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1716/1715, 2200/2197
| 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1716/1715, 2200/2197
| {{mapping| 422 669 980 1185 1460 1562 1725 1793 }}
| {{Mapping| 422 669 980 1185 1460 1562 1725 1793 }}
| −0.1839
| −0.1839
| 0.1106
| 0.1106
Line 76: Line 76:
| 2.3.5.7.11.13.17.19.23
| 2.3.5.7.11.13.17.19.23
| 736/735, 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1496/1495, 1716/1715
| 736/735, 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1496/1495, 1716/1715
| {{mapping| 422 669 980 1185 1460 1562 1725 1793 1909 }}
| {{Mapping| 422 669 980 1185 1460 1562 1725 1793 1909 }}
| −0.1675
| −0.1675
| 0.1142
| 0.1142
Line 87: Line 87:
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
Line 109: Line 109:
| 435.07
| 435.07
| 9/7
| 9/7
| [[Supermajor]]
| [[Supermajor (temperament)|Supermajor]]
|-
|-
| 1
| 1
Line 130: Line 130:
|-
|-
| 2
| 2
| 153\422<br />(58\422)
| 153\422<br>(58\422)
| 435.07<br />(164.93)
| 435.07<br>(164.93)
| 9/7<br />(11/10)
| 9/7<br>(11/10)
| [[Semisupermajor]]
| [[Semisupermajor]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct


[[Category:Countritonic]]
[[Category:Countritonic]]
[[Category:Gamera]]
[[Category:Gamera]]
[[Category:Vishnu]]
[[Category:Vishnu]]
Retrieved from "https://en.xen.wiki/w/422edo"