14th-octave temperaments: Difference between revisions
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{{Infobox fractional-octave|14}} | |||
While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list. | While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list. | ||
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[[Badness]]: 0.196 | [[Badness]]: 0.196 | ||
===11-limit=== | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.0450 | Badness: 0.0450 | ||
===13-limit=== | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.0269 | Badness: 0.0269 | ||
{{Navbox fractional-octave}} | |||
[[Category:14edo]] | [[Category:14edo]] | ||
Latest revision as of 13:42, 13 April 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
While 14edo is poor in simple harmonics, some of its multiples (such as 224edo and 742edo) are members of zeta edo list.
Silicon
The name of silicon temperament comes from the 14th element. Defined upwards to the 13-limit. When tuned in 742edo, it is generated by a 53edo fifth intermingled with 14edo periods.
Subgroup: 2.3.5.7
Comma list: 14348907/14336000, 56358560858112/56296884765625
Mapping: [⟨14 0 -145 239], ⟨0 1 8 -9]]
Mapping generators: ~6125/5832, ~3
Optimal tuning (CTE): ~3/2 = 701.870
Optimal ET sequence: 224, 518, 742, 966, 1708, 2674
Badness: 0.196
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 1240029/1239040, 2359296/2358125
Mapping: [⟨14 0 -145 239 115], ⟨0 1 8 -9 -3]]
Optimal tuning (CTE): ~3/2 = 701.872
Optimal ET sequence: 224, 518, 742, 966, 1708, 4382e
Badness: 0.0450
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 6656/6655, 9801/9800, 24192/24167
Mapping: [⟨14 0 -145 239 115 74], ⟨0 1 8 -9 -3 -1]]
Optimal tuning (CTE): ~3/2 = 701.8733
Optimal ET sequence: 224, 518, 742, 966, 1708f
Badness: 0.0269