Arcturus: Difference between revisions

Line 1:

'''Arcturus''' is ~~a no~~-~~twos~~ temperament ~~which~~ tempers out the 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 (2L 5s) 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 [[rank]]-2 [[regular temperament]] on the 3.5.7 [[subgroup]] that [[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]] (2L 5s{{angbr|3/1}}) 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.

== Etymology ==

This temperament is named after the star {{w|Arcturus}}, following a series of [[nonoctave]] temperaments that are named after stars.

== Chords ==

Line 7:

Line 11:

== 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:

~~[[Sub-Arcturus|Mini chromatic]]~~

~~[[Anti-Arcturus|Anti-chromatic]]~~

{| class="wikitable"

Line 1,125:

|}

[[~~Super~~-~~Arcturus_15L_2s|Mini~~ enharmonic]]

== Scales ==

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

[[~~Super~~-~~Arcturus_17L_2s|Enharmonic~~]]

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

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

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

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

~~[[Trans-Arcturus_enneadecatonic|Anti-enharmonic]]~~

[[Category:Temperaments]]

[[Category:Nonoctave]]

[[Category:Tritave-equivalent temperaments]]

@@ Line 1: / Line 1: @@
+{{tdhat|No-twos subgroup temperaments#Arcturus}}
 {{URWTC}}
-'''Arcturus''' is a no-twos temperament which tempers out the 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 (2L 5s) 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 [[rank]]-2 [[regular temperament]] on the 3.5.7 [[subgroup]] that [[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]] (2L 5s{{angbr|3/1}}) 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.
+== Etymology ==
+This temperament is named after the star {{w|Arcturus}}, following a series of [[nonoctave]] temperaments that are named after stars.
 == Chords ==
@@ Line 7: / Line 11: @@
 == 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:
-[[Sub-Arcturus|Mini chromatic]]
-[[Anti-Arcturus|Anti-chromatic]]
 {| class="wikitable"
@@ Line 1,125: / Line 1,125: @@
 |}
-[[Super-Arcturus_15L_2s|Mini enharmonic]]
+== Scales ==
+* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)
-[[Super-Arcturus_17L_2s|Enharmonic]]
+* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)
+* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)
+* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)
+* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)
-[[Trans-Arcturus_enneadecatonic|Anti-enharmonic]]
 [[Category:Temperaments]]
 [[Category:Nonoctave]]
 [[Category:Tritave-equivalent temperaments]]