Arcturus: Difference between revisions

'''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.

{{tdlink|No-twos subgroup temperaments #Arcturus}}

This temperament is named after the star {{w|Arcturus}}, following a series of non-octave temperaments that are named after stars.

{{todo|add etymology|inline=1|text=Add name (person who coined the term) and year (when it was coined).}}

Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0{{c}}:

* {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus)

* {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus)

* {{mos scalesig|15L 2s<3/1>|link=1}} (mini enharmonic, aka super-Arcturus 15L 2s)

* {{mos scalesig|17L 2s<3/1>|link=1}} (enharmonic, aka super-Arcturus 17L 2s)

* {{mos scalesig|2L 17s<3/1>|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)