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Quartonic family: Difference between revisions

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Cleanup. Review the optimal ET sequences for 5- and 7-limit quartonic
 
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The '''quartonic family''' of [[regular temperament|temperaments]] [[tempering out|temper out]] the [[quartonic comma]], {{monzo| 3 -18 11 }} = 390625000/387420489.
{{Technical data page}}
The '''quartonic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[quartonic comma]], {{monzo| 3 -18 11 }} = 390625000/387420489.


== Quartonic ==
== Quartonic ==
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=== Overview to extensions ===
=== Overview to extensions ===
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at.
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at.
* [[1728/1715]] or [[4000/3969]] gives septimal quartonic, with interpretation of the generator ~36/35.
* [[1728/1715]] or [[4000/3969]] gives septimal quartonic, with interpretation of the generator ~36/35. It also tempers out [[4375/4374]].  
* [[Hemimage comma|10976/10935]] gives yarman I (80 & 159) and slices the quartonic generator in three.
* [[Hemimage comma|10976/10935]] gives yarman I (80 & 159) and slices the quartonic generator in three.
* 5359375/5308416 gives yarman II (79 & 159) and slices the quartonic generator in three.  
* 5359375/5308416 gives yarman II (79 & 159) and slices the quartonic generator in three.  
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{{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
{{Mapping|legend=1| 1 2 3 3 | 0 -11 -18 -5 }}
{{Multival|legend=1| 11 18 5 3 -23 -39 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~36/35 = 45.2652
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~36/35 = 45.2652
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{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}
{{Mapping|legend=1| 1 2 3 4 | 0 -33 -54 -95 }}
{{Multival|legend=1| 33 54 95 9 58 69 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~126/125 = 15.0714
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~126/125 = 15.0714
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{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}
{{Mapping|legend=1| 1 2 3 2 | 0 -33 -54 64 }}
{{Multival|legend=1| 33 54 -64 9 -194 -300 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~875/864 = 15.0995
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~875/864 = 15.0995
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{{Mapping|legend=1| 1 13 21 15 | 0 -44 -72 -47 }}
{{Mapping|legend=1| 1 13 21 15 | 0 -44 -72 -47 }}
{{Multival|legend=1| 44 72 47 12 -49 -93 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~875/729 = 311.308
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~875/729 = 311.308
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{{Mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}
{{Mapping|legend=1| 3 6 9 10 | 0 -11 -18 -14 }}
{{Multival|legend=1| 33 54 42 9 -26 -54 }}


[[Optimal tuning]] ([[CTE]]): ~63/50 = 1\3, ~250/243 = 45.2083
[[Optimal tuning]] ([[CTE]]): ~63/50 = 1\3, ~250/243 = 45.2083
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{{Mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}
{{Mapping|legend=1| 4 8 12 15 | 0 -11 -18 -25 }}
{{Multival|legend=1| 44 72 100 12 35 30 }}


[[Optimal tuning]] ([[CTE]]): ~25/21 = 1\4, ~250/243 = 45.2411
[[Optimal tuning]] ([[CTE]]): ~25/21 = 1\4, ~250/243 = 45.2411
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{{Mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}
{{Mapping|legend=1| 5 10 15 18 | 0 -11 -18 -21 }}
{{Multival|legend=1| 55 90 105 15 12 -9 }}


[[Optimal tuning]] ([[CTE]]): ~35721/31250 = 1\5, ~250/243 = 45.2563
[[Optimal tuning]] ([[CTE]]): ~35721/31250 = 1\5, ~250/243 = 45.2563
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Quartonic family| ]] <!-- main article -->
[[Category:Quartonic family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Quartonic_family"