26edo: Difference between revisions
m →Music: Claudi Meneghin, fixed links to music, added a link |
Ordway9001 (talk | contribs) →Rank two temperaments: Modified into Regular Temperament section and move Rank-2 to subsection. |
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== Rank | == Regular temperament properties == | ||
{| class="wikitable" | |||
! rowspan="2" |[[Just intonation subgroup|Subgroup]] | |||
! rowspan="2" |[[Comma basis|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|[-41 26⟩ | |||
|[⟨26 41]] | |||
| +3.043 | |||
|3.05 | |||
|6.61 | |||
|- | |||
|2.3.5 | |||
|81/80, 78125/73728 | |||
|[⟨26 41 60]] | |||
| +4.489 | |||
|3.22 | |||
|6.98 | |||
|- | |||
|2.3.5.7 | |||
|50/49, 81/80, 405/392 | |||
|[⟨26 41 60 73]] | |||
| +3.324 | |||
|3.44 | |||
|7.45 | |||
|- | |||
|2.3.5.7.11 | |||
|45/44, 50/49, 81/80, 99/98 | |||
|[⟨26 41 60 73 90]] | |||
| +2.509 | |||
|3.48 | |||
|7.53 | |||
|- | |||
|2.3.5.7.11.13 | |||
|45/44, 50/49, 65/64, 78/77, 81/80 | |||
|[⟨26 41 60 73 90 96]] | |||
| +2.531 | |||
|3.17 | |||
|6.87 | |||
|- | |||
|2.3.5.7.11.13.17 | |||
|45/44, 50/49, 65/64 78/77, 81/80, 85/84 | |||
|[⟨26 41 60 73 90 96 106]] | |||
| +2.613 | |||
|2.94 | |||
|6.38 | |||
|- | |||
|2.3.5.7.11.13.17.19 | |||
|45/44, 50/49, 57/56, 65/64, 78/77, 81/80, 85/84 | |||
|[⟨26 41 60 73 90 96 106 110]] | |||
| +2.894 | |||
|2.85 | |||
|6.18 | |||
|} | |||
26et is lower in relative error than any previous equal temperaments in the 17-, 19-, 23-, and 29-limit. The next equal temperaments preforming better in those subgroups are 27eg, 27eg, 29g, and 46, respectively. | |||
=== Rank-2 Temperaments === | |||
* [[List of 26et rank two temperaments by badness]] | * [[List of 26et rank two temperaments by badness]] | ||
* [[List of edo-distinct 26et rank two temperaments]] | * [[List of edo-distinct 26et rank two temperaments]] | ||