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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" | [[Just intonation subgroup|Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma basis|Comma List]]
! rowspan="2" | [[Comma basis]]
! 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
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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|-
|-
| 2.3
| 2.3
| [-41 26⟩
| {{monzo| -41 26 }}
| [⟨26 41]]
| {{mapping| 26 41 }}
| +3.043
| +3.043
| 3.05
| 3.05
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| 2.3.5
| 2.3.5
| 81/80, 78125/73728
| 81/80, 78125/73728
| [⟨26 41 60]]
| {{mapping| 26 41 60 }}
| +4.489
| +4.489
| 3.22
| 3.22
Line 462: Line 462:
| 2.3.5.7
| 2.3.5.7
| 50/49, 81/80, 405/392
| 50/49, 81/80, 405/392
| [⟨26 41 60 73]]
| {{mapping| 26 41 60 73 }}
| +3.324
| +3.324
| 3.44
| 3.44
Line 469: Line 469:
| 2.3.5.7.11
| 2.3.5.7.11
| 45/44, 50/49, 81/80, 99/98
| 45/44, 50/49, 81/80, 99/98
| [⟨26 41 60 73 90]]
| {{mapping| 26 41 60 73 90 }}
| +2.509
| +2.509
| 3.48
| 3.48
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 45/44, 50/49, 65/64, 78/77, 81/80
| 45/44, 50/49, 65/64, 78/77, 81/80
| [⟨26 41 60 73 90 96]]
| {{mapping| 26 41 60 73 90 96 }}
| +2.531
| +2.531
| 3.17
| 3.17
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| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 45/44, 50/49, 65/64 78/77, 81/80, 85/84
| 45/44, 50/49, 65/64 78/77, 81/80, 85/84
| [⟨26 41 60 73 90 96 106]]
| {{mapping| 26 41 60 73 90 96 106 }}
| +2.613
| +2.613
| 2.94
| 2.94
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| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 45/44, 50/49, 57/56, 65/64, 78/77, 81/80, 85/84
| 45/44, 50/49, 57/56, 65/64, 78/77, 81/80, 85/84
| [⟨26 41 60 73 90 96 106 110]]
| {{mapping| 26 41 60 73 90 96 106 110 }}
| +2.894
| +2.894
| 2.85
| 2.85
| 6.18
| 6.18
|}
|}
26et is lower in relative error than any previous equal temperaments in the [[17-limit|17-]], [[19-limit|19-]], [[23-limit|23-]], and [[29-limit]] (using the 26i val for the 23- and 29-limit). The next equal temperaments performing better in those subgroups are [[27edo|27eg]], 27eg, [[29edo|29g]], and [[46edo|46]], respectively.  
* 26et is lower in relative error than any previous equal temperaments in the [[17-limit|17-]], [[19-limit|19-]], [[23-limit|23-]], and [[29-limit]] (using the 26i val for the 23- and 29-limit). The next equal temperaments performing better in those subgroups are [[27edo|27eg]], 27eg, [[29edo|29g]], and [[46edo|46]], respectively.  


=== Rank-2 Temperaments ===
=== Rank-2 Temperaments ===
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{| class="wikitable center-all left-3"
{| class="wikitable center-all left-3"
|-
|-
! Periods<br>per octave
! Periods<br>per 8ve
! Generator
! Generator
! Temperaments
! Temperaments
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| 1
| 1
| 1\26
| 1\26
| [[Quartonic]]/[[Quarto]]
| [[Quartonic]] / [[quarto]]
|-
|-
| 1
| 1
| 3\26
| 3\26
| [[Jerome]]/[[Chromatic_pairs|Bleu]]/[[Secund]]/[[Glacier]]
| [[Glacier]] / [[bleu]] / [[jerome]] / [[secund]]
|-
|-
| 1
| 1
| 5\26
| 5\26
| [[Cynder]]/[[Mothra]]
| [[Cynder]] / [[mothra]]
|-
|-
| 1
| 1
| 7\26
| 7\26
| [[Superkleismic]]/[[Orgone]]/[[Shibboleth]]
| [[Orgone]] / [[superkleismic]]
|-
|-
| 1
| 1
| 9\26
| 9\26
| [[Roman]]/[[Wesley]]
| [[Wesley]] / [[roman]]
|-
|-
| 1
| 1
| 11\26
| 11\26
| [[Meantone]]/[[Flattone]]
| [[Flattone]] / [[flattertone]]
|-
|-
| 2
| 2
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| 2
| 2
| 3\26
| 3\26
| [[Fifive]]/[[Crepuscular]]
| [[Fifive]] / [[crepuscular]]
|-
|-
| 2
| 2
| 4\26
| 4\26
| [[Unidec]]/[[Gamelismic_clan#Unidec-Hendec|Hendec]]/[[Dubbla]]
| [[Dubbla]]<br>[[Unidec]] / [[hendec]]
|-
|-
| 2
| 2
| 5\26
| 5\26
| | [[Lemba]]
| [[Lemba]]
|-
|-
| 2
| 2
| 6\26
| 6\26
| [[Doublewide]]/[[Cavalier]]
| [[Doublewide]] / [[cavalier]]
|-
|-
| 13
| 13
Line 572: Line 572:


=== Hendec in 26et ===
=== Hendec in 26et ===
[[Gamelismic_clan#Unidec-Hendec|Hendec]], the 13-limit 26&amp;46 temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy.
[[Hendec]], the 13-limit 26&amp;46 temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy.


=== Commas ===
=== Commas ===
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{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
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| 0.23
| 0.23
| Quadla-sepquingu
| Quadla-sepquingu
| [[Senior]]
| [[Senior comma]]
|-
|-
| 7
| 7
Line 626: Line 626:
| 13.47
| 13.47
| Sarurutriyo
| Sarurutriyo
| Octagar
| Octagar comma
|-
|-
| 7
| 7
Line 633: Line 633:
| 13.07
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma, Orwell comma
| Orwellisma
|-
|-
| 7
| 7
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| 16.57
| 16.57
| Thuzoyo
| Thuzoyo
| Animist
| Animist comma
|}
|}
<references/>
<references/>
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