Arcturus: Difference between revisions
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'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{mos scalesig|2L 5s<3/1>|link=1}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament. | '''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out|tempers out]] the arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{mos scalesig|2L 5s<3/1>|link=1}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament. | ||
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== Scales == | == Scales == | ||
* {{mos scalesig|9L 2s<3/1>|link | * {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus) | ||
* {{mos scalesig|11L 2s<3/1>|link | * {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus) | ||
* {{mos scalesig|15L 2s<3/1>|link | * {{mos scalesig|15L 2s<3/1>|link=1}} (mini enharmonic, aka super-Arcturus 15L 2s) | ||
* {{mos scalesig|17L 2s<3/1>|link | * {{mos scalesig|17L 2s<3/1>|link=1}} (enharmonic, aka super-Arcturus 17L 2s) | ||
* {{mos scalesig|2L 17s<3/1>|link | * {{mos scalesig|2L 17s<3/1>|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s) | ||
[[Category: | [[Category:Arcturus| ]] <!-- main article --> | ||
[[Category: | [[Category:Rank-2 temperaments]] | ||
[[Category: | [[Category:Non-octave temperaments]] | ||