209edo: Difference between revisions

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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 209 factors into 11 × 19, 209edo contains [[11edo]] and [[19edo]] as its subsets. [[627edo]], which triples it, gives a good correction to the harmonic 7.
Since 209 factors into {{nowrap|11 × 19}}, 209edo contains [[11edo]] and [[19edo]] as its subsets. [[627edo]], which triples it, gives a good correction to the harmonic 7.


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| -331 209 }}
| {{monzo| -331 209 }}
| {{mapping| 209 331 }}
| {{mapping| 209 331 }}
| 0.4658
| +0.4658
| 0.4660
| 0.4660
| 8.12
| 8.12
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| {{monzo| -13 17 -6 }}, {{monzo| -27 -2 13 }}
| {{monzo| -13 17 -6 }}, {{monzo| -27 -2 13 }}
| {{mapping| 209 331 485 }}
| {{mapping| 209 331 485 }}
| 0.5439
| +0.5439
| 0.3962
| 0.3962
| 6.90
| 6.90
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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| 3/2<br>(225/224)
| 3/2<br>(225/224)
| [[Enneadecal]] (209d)
| [[Enneadecal]] (209d)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


[[Category:Marvo]]
[[Category:Marvo]]