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| Line 180: |
Line 180: |
| === Interval mappings === | | === Interval mappings === |
| {{Q-odd-limit intervals|19}} | | {{Q-odd-limit intervals|19}} |
| | | (pretend I put a hidden badness table here) |
| === Zeta peak index ===
| |
| {{ZPI
| |
| | zpi = 65
| |
| | steps = 18.9480867166984
| |
| | step size = 63.3309324546460
| |
| | tempered height = 5.980169
| |
| | pure height = 5.214351
| |
| | integral = 1.313799
| |
| | gap = 16.699651
| |
| | octave = 1203.28771663827
| |
| | consistent = 10
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| | distinct = 7
| |
| }}
| |
| | |
| == Regular temperament properties ==
| |
| {| class="wikitable center-4 center-5 center-6"
| |
| |-
| |
| ! rowspan="2" | [[Subgroup]]
| |
| ! rowspan="2" | [[Comma list]]
| |
| ! rowspan="2" | [[Mapping]]
| |
| ! rowspan="2" | Optimal<br>8ve stretch (¢)
| |
| ! colspan="2" | Tuning error
| |
| |-
| |
| ! [[TE error|Absolute]] (¢)
| |
| ! [[TE simple badness|Relative]] (%)
| |
| |-
| |
| | 2.3
| |
| | {{monzo| -30 19 }}
| |
| | {{mapping| 19 30 }}
| |
| | +2.28
| |
| | 2.28
| |
| | 3.61
| |
| |-
| |
| | 2.3.5
| |
| | 81/80, 3125/3072
| |
| | {{mapping| 19 30 44 }}
| |
| | +2.58
| |
| | 1.91
| |
| | 3.02
| |
| |-
| |
| | 2.3.5.7
| |
| | 49/48, 81/80, 126/125
| |
| | {{mapping| 19 30 44 53 }}
| |
| | +3.85
| |
| | 2.76
| |
| | 4.35
| |
| |-
| |
| | 2.3.5.7.13
| |
| | 49/48, 65/64, 81/80, 91/90
| |
| | {{mapping| 19 30 44 53 70 }}
| |
| | +4.14
| |
| | 2.53
| |
| | 3.99
| |
| |-
| |
| | 2.3.5.7.13.23
| |
| | 49/48, 65/64, 70/69, 81/80, 91/90
| |
| | {{mapping| 19 30 44 53 70 86 }}
| |
| | +3.32
| |
| | 2.93
| |
| | 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 best in the 2.3.5.7.13 subgroup, and the next equal temperament that does better in this is [[53edo|53]].
| |
|
| |
|
| === Linear temperaments === | | === Linear temperaments === |