Arcturus: Difference between revisions

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~~{{URWTC}}~~

'''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 {{sl|2L 5s}} [[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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== Tuning spectrum ==

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

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

{| class="wikitable" style="text-align: center;"

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== Scales ==

* [[9L~~ ~~2s (3/1~~-equivalent)]]~~ (mini chromatic, aka sub-Arcturus)

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

* [[11L~~ ~~2s (3/1~~-equivalent)]]~~ (anti-chromatic, aka anti-Arcturus)

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

* [[15L~~ ~~2s (3/1~~-equivalent)]]~~ (mini enharmonic, aka super-Arcturus 15L~~ ~~2s)

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

* [[17L~~ ~~2s (3/1~~-equivalent)]]~~ (enharmonic, aka super-Arcturus 17L~~ ~~2s)

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

* [[2L~~ ~~17s (3/1~~-equivalent)]]~~ (anti-enharmonic, aka trans-Arcturus 2L~~ ~~7s)

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

[[Category:~~Temperaments~~]]

[[Category:Arcturus| ]]

[[Category:~~Nonoctave~~]]

[[Category:Rank-2 temperaments]]

[[Category:~~Tritave~~-~~equivalent~~ temperaments]]

[[Category:Non-octave temperaments]]

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-{{URWTC}}
+'''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 {{sl|2L 5s}} [[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}}
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 == Tuning spectrum ==
-Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 cents:
+Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0{{c}}:
 {| class="wikitable" style="text-align: center;"
@@ Line 869: / Line 868: @@
 == Scales ==
-* [[9L&nbsp;2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)
+* {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus)
-* [[11L&nbsp;2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)
+* {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus)
-* [[15L&nbsp;2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L&nbsp;2s)
+* {{mos scalesig|15L 2s<3/1>|link=1}} (mini enharmonic, aka super-Arcturus 15L 2s)
-* [[17L&nbsp;2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L&nbsp;2s)
+* {{mos scalesig|17L 2s<3/1>|link=1}} (enharmonic, aka super-Arcturus 17L 2s)
-* [[2L&nbsp;17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L&nbsp;7s)
+* {{mos scalesig|2L 17s<3/1>|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)
-[[Category:Temperaments]]
+[[Category:Arcturus| ]] <!-- main article -->
-[[Category:Nonoctave]]
+[[Category:Rank-2 temperaments]]
-[[Category:Tritave-equivalent temperaments]]
+[[Category:Non-octave temperaments]]