41st-octave temperaments: Difference between revisions
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{{ | {{Infobox fractional-octave|41}} | ||
[[Countercomp family|Countercomp temperaments]] are a notable subset of 41st-octave temperaments which have a page of their own. | [[Countercomp family|Countercomp temperaments]] are a notable subset of 41st-octave temperaments which have a page of their own. | ||
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== Niobium == | == Niobium == | ||
Niobium can be viewed as the 41st-octave counterpart of atomic. The temperament also maps 2657205/2097152 into 14\41. | Niobium can be viewed as the 41st-octave counterpart of [[atomic]], although their badnesses diverge sharply. Much like [[atomic|Kirnberger's atom]] (12 & 612) is a difference between a stack of 12 fifths flattened by a comma closed against 12edo, niobium (41 & 2460) fulfills a similar function for 41edo. Hence it is also not a countercomp temperament. | ||
It is the difference between a circle of 41 3/2 fifths flattened by {{monzo|215 -121 -10}} and the appropriate octave. The temperament also maps 2657205/2097152 into 14\41 and in higher limits, [[3645/3584]] to 1\41. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Badness]]: 5.57 | [[Badness]]: 5.57 | ||
=== 7-limit === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: {{monzo| -5 -12 -9 16 }}, {{monzo| -55 30 2 1 }} | |||
{{Mapping|legend=1| 41 0 875 259 | 0 1 -12 -6 }} | |||
: mapping generators: ~ 3645/3584, ~3 | |||
[[Optimal tuning]] ([[CTE]]): ~ 3645/3584 = 1\41, ~3/2 = 701.953 | |||
{{Optimal ET sequence|legend=1| 41, ..., 2460 }} | |||
[[Badness]]: 10.676 | |||
=== 11-limit === | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 151263/151250, 6576668672/6576582375, 1722499009/1721868840 | |||
{{Mapping|legend=1| 41 0 875 259 -98 | 0 1 -12 -6 10 }} | |||
: mapping generators: ~ 3645/3584, ~3 | |||
[[Optimal tuning]] ([[CTE]]): ~ 3645/3584 = 1\41, ~3/2 = 701.955 | |||
{{Optimal ET sequence|legend=1| 41, ..., 2460 }} | |||
[[Badness]]: 3.308 | |||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 10648/10647, 196625/196608, 105644/105625, 14350336/14348907 | |||
{{Mapping|legend=1| 41 0 875 259 -98 -256 | 0 1 -12 -6 10 17 }} | |||
: mapping generators: ~ 3645/3584, ~3 | |||
[[Optimal tuning]] ([[CTE]]): ~ 3645/3584 = 1\41, ~3/2 = 701.954 | |||
{{Optimal ET sequence|legend=1| 41, ..., 2460 }} | |||
[[Badness]]: 2.099 | |||
{{Navbox fractional-octave}} | {{Navbox fractional-octave}} | ||
[[Category:41edo]] | [[Category:41edo]] | ||