198edo: Difference between revisions

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The 198b val [[support]]s a [[septimal meantone]] close to the [[CTE tuning]], although [[229edo]] is even closer, and besides, the 198be val supports an undecimal meantone almost identical to the [[POTE tuning]].

~~198 factors into 2 × 32 × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.~~

=== Prime harmonics ===

=== Miscellany ===

198 factors into 2 × 32 × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.

== Intervals ==

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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| 4.50

|}

* 198et has a lower absolute error in the 13-limit than any previous equal temperaments, past [[190edo|190]] and followed by [[224edo|224]].

=== Rank-2 temperaments ===

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{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

@@ Line 12: / Line 12: @@
 The 198b val [[support]]s a [[septimal meantone]] close to the [[CTE tuning]], although [[229edo]] is even closer, and besides, the 198be val supports an undecimal meantone almost identical to the [[POTE tuning]].
-factors into 2 × 3<sup>2</sup> × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.
 === Prime harmonics ===
 {{Harmonics in equal|198|columns=11}}
+=== Miscellany ===
+factors into 2 × 3<sup>2</sup> × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.
 == Intervals ==
@@ Line 23: / Line 24: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! 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]] (¢)
@@ Line 46: / Line 47: @@
 | 4.50
 |}
+* 198et has a lower absolute error in the 13-limit than any previous equal temperaments, past [[190edo|190]] and followed by [[224edo|224]].
 === Rank-2 temperaments ===
@@ Line 52: / Line 54: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-