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19edo: Difference between revisions

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{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|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
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| 2.3
| 2.3
| {{monzo| -30 19 }}
| {{monzo| -30 19 }}
| [{{val| 19 30 }}]
| {{mapping| 19 30 }}
| +2.28
| +2.28
| 2.28
| 2.28
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| 2.3.5
| 2.3.5
| 81/80, 3125/3072
| 81/80, 3125/3072
| [{{val| 19 30 44 }}]
| {{mapping| 19 30 44 }}
| +2.58
| +2.58
| 1.91
| 1.91
Line 554: Line 554:
| 2.3.5.7
| 2.3.5.7
| 49/48, 81/80, 126/125
| 49/48, 81/80, 126/125
| [{{val| 19 30 44 53 }}]
| {{mapping| 19 30 44 53 }}
| +3.85
| +3.85
| 2.76
| 2.76
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| 2.3.5.7.13
| 2.3.5.7.13
| 49/48, 65/64, 81/80, 91/90
| 49/48, 65/64, 81/80, 91/90
| [{{val| 19 30 44 53 70 }}]
| {{mapping| 19 30 44 53 70 }}
| +4.14
| +4.14
| 2.53
| 2.53
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| 2.3.5.7.13.23
| 2.3.5.7.13.23
| 49/48, 65/64, 70/69, 81/80, 91/90
| 49/48, 65/64, 70/69, 81/80, 91/90
| [{{val| 19 30 44 53 70 86 }}]
| {{mapping| 19 30 44 53 70 86 }}
| +3.32
| +3.32
| 2.93
| 2.93
| 4.64
| 4.64
|}
|}
 
* 19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit – ''both'' 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are [[34edo|34]], [[31edo|31]], [[27edo|27e]], [[22edo|22]], and [[26edo|26]], respectively.  
19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit – ''both'' 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are [[34edo|34]], [[31edo|31]], [[27edo|27e]], [[22edo|22]], and [[26edo|26]], respectively.  
* 19et is best in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].
 
19et is prominent in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].


=== Uniform maps ===
=== Uniform maps ===
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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 group="note">{{rd|10}}</ref>
! [[Ratio]]<ref group="note">{{rd|10}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
! [[Color notation/Temperament Names|Color Name]]
! [[Color notation/Temperament names|Color name]]
! Name
! Name
|-
|-
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| 35.70
| 35.70
| Zozo
| Zozo
| Slendro diesis
| Semaphoresma, slendro diesis
|-
|-
| 7
| 7
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| 1.63
| 1.63
| Latriru-asepyo
| Latriru-asepyo
| [[Meter comma]]
| [[Metric comma]]
|-
|-
| 7
| 7
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| 25.42
| 25.42
| Thuthutrizo
| Thuthutrizo
|
|  
|-
|-
| 13
| 13
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! Cents
! Cents
! Interval
! Interval
! MOSes
! Mos scales
! Temperaments
! Temperaments
|-
|-
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| M2
| M2
| [[1L 5s]], [[6L 1s]], [[6L 7s]]
| [[1L 5s]], [[6L 1s]], [[6L 7s]]
| [[Deutone]]<br />[[Spell]]
| [[Deutone]]<br>[[Spell]]
|-
|-
| 4
| 4
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| A4
| A4
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br />[[2L 9s]], [[2L 11s]], [[2L 13s]], <br />[[2L 15s]]
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br />[[2L 9s]], [[2L 11s]], [[2L 13s]], <br />[[2L 15s]]
| [[Liese]] / [[pycnic]]<br />[[Triton]]
| [[Liese]] / [[pycnic]]<br>[[Triton]]
|}
|}


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