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7L 3s (8/3-equivalent): Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Name =
{{MOS intro}} The [[bright]] [[generator]] of these scales is close to an octave.
| Periods = 1
| nLargeSteps = 7
| nSmallSteps = 3
| Equalized = 10
| Collapsed = 7
| Pattern = LLLsLLsLLs
|Equave=8/3|Neutral=4L 6s}}
{{MOS intro}} A [[pathological]] trait these scales exhibit is that normalization to [[edo]] collapses the range for the [[bright]] [[generator]] to the octave.


== Scale properties ==
== Scale properties ==
{{TAMNAMS use}}
{{TAMNAMS use}}
{{MOS data}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


== Scale tree ==
== Scale tree ==
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== Rank-2 temperaments ==
== Rank-2 temperaments ==
The '''Bolivar''' [[rank-2]] temperament spells its major [[tetrad]] 4:5:6:8 or 14:18:21:28<code>root-3(2g-p)-(2g-p)-(1g)</code> (p = 8/3, g = 2/1) and its minor tetrad 6:7:9:12 or 10:12:15:20 <code>root-2(p-2g)-(2g-p)-(1g)</code> (p = 8/3, g = 2/1). Basic ~17ed8/3 fits both interpretations.
The '''Bolivar''' [[rank-2]] temperament spells its major [[tetrad]] 4:5:6:8 or 14:18:21:28<code>root-3(2g-p)-(2g-p)-(1g)</code> ({{nowrap|p {{=}} 8/3|g {{=}} 2/1}}) and its minor tetrad 6:7:9:12 or 10:12:15:20 <code>root-2(p-2g)-(2g-p)-(1g)</code> ({{nowrap|p {{=}} 8/3|g {{=}} 2/1}}). Basic ~17ed8/3 fits both interpretations.


=== Bolivar-Meantone ===
=== Bolivar–Meantone ===
[[Subgroup]]: 8/3.2.5/4
[[Subgroup]]: 8/3.2.5/4


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[[Optimal ET sequence]]: ~([[17ed8/3]], [[27ed8/3]], [[44ed8/3]])
[[Optimal ET sequence]]: ~([[17ed8/3]], [[27ed8/3]], [[44ed8/3]])


=== Bolivar-Archy ===
=== Bolivar–Archy ===
[[Subgroup]]: 8/3.2.7/6
[[Subgroup]]: 8/3.2.7/6


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