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14edo: Difference between revisions

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| Fifth = 8\14 (685.714¢) (→[[7edo|4\7]])
| Fifth = 8\14 (685.714¢) (→[[7edo|4\7]])
| Major 2nd = 2\14 (171¢)
| Major 2nd = 2\14 (171¢)
| Semitones = 0:2 (0¢:171¢)
| Semitones = 0:2 (0¢ : 171¢)
| Consistency = 3
| Consistency = 3
| Monotonicity = 13
| Monotonicity = 13
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{| class="wikitable"
{| class="wikitable"
|+
|+
!N
! N
! L-Nedo
! L-Nedo
!s-Nedo
! s-Nedo
|-
|-
|3
| 3
|28.429¢
| 28.429¢
| -57.143¢
| -57.143¢
|-
|-
|4
| 4
|42.857¢
| 42.857¢
| -42.857¢
| -42.857¢
|-
|-
|5
| 5
|17.143¢
| 17.143¢
| -68.571¢
| -68.571¢
|-
|-
|6
|6
|57.143¢
| 57.143¢
| -28.571¢
| -28.571¢
|-
|-
|8
| 8
|21.429¢
| 21.429¢
| -68.571¢
| -68.571¢
|-
|-
|9
| 9
|38.095¢
| 38.095¢
| -95.238¢
| -95.238¢
|-
|-
|10
| 10
|51.429¢
| 51.429¢
| -34.286¢
| -34.286¢
|-
|-
|11
| 11
|62.338¢
| 62.338¢
| -23.376¢
| -23.376¢
|-
|-
|12
| 12
|71.429¢
| 71.429¢
| -14.286¢
| -14.286¢
|-
|-
|13
| 13
|79.121¢
| 79.121¢
| -6.593¢
| -6.593¢
|}
|}
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! Steps
! Steps
! Cents
! Cents
! Nearest<br>[[Harmonic]]
! Approximate<br>[[Harmonic]]s
! Approximate<br>Ratios 1 <ref>based on treating 14edo as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.</ref>
! Approximate<br>Ratios 1 <ref>based on treating 14edo as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.</ref>
! Approximate<br>Ratios 2 <ref>based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c)</ref>
! Approximate<br>Ratios 2 <ref>based on treating 14edo as an 11-limit temperament of {{val| 14 22 32 39 48}} (14c)</ref>
Line 269: Line 269:


== Regular temperament properties ==
== Regular temperament properties ==
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 14et.
{| class="wikitable center-4 center-5 center-6"
 
! rowspan="2" | Subgroup
Note: the 14c [[val]] is used for full 7- and 11-limit for lower overall error.
! rowspan="2" | [[Comma list]]
{| class="wikitable center-all"
! rowspan="2" | [[Mapping]]
! colspan="2" |
! rowspan="2" | Optimal<br>8ve stretch (¢)
! 3-limit
! colspan="2" | Tuning error
! 7-limit no-5
|-
! 11-limit no-5
! [[TE error|Absolute]] (¢)
! 5-limit
! [[TE simple badness|Relative]] (%)
! 7-limit
! 11-limit
|-
|-
! colspan="2" |Octave stretch (¢)
| 2.3.7
| +5.12
| 49/48, 2187/2048
| [{{val| 14 22 39 }}]
| +6.52
| +6.52
| 4.64
| 5.38
|-
| 2.3.7.11
| 33/32, 49/48, 243/242
| [{{val| 14 22 39 48 }}]
| +7.58
| +7.58
| +9.68
| +9.59
| +9.83
|-
! rowspan="2" |Error
! [[TE error|absolute]] (¢)
| 5.15
| 4.64
| 4.42
| 4.42
| 7.71
| 5.12
| 6.68
| 6.00
|-
![[TE simple badness|relative]] (%)
|5.98
|5.38
|5.12
|8.93
|7.73
|6.94
|}
|}


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