19edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
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| 2.93 | | 2.93 | ||
| 4.64 | | 4.64 | ||
{{comma basis end}} | |||
* 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 best in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]]. | ||
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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]] | ||
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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]] | ||
|} | |} | ||