Orwell: Difference between revisions

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~~[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]~~

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| Odd limit 2 = (L11) 21 | Mistuning 2 = ??? | Complexity 2 = 22

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[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]

'''Orwell''' – so named because 19 steps of [[84edo]], i.e. 19\84, is a possible generator – is an excellent [[7-limit]] [[regular temperament|temperament]] and an amazing [[11-limit]] temperament because of the simplicity of [[harmonic]] [[11/1|11]].

In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]] (alternatively, the [[5/1|5th harmonic (5/1)]] is divided into 3 equal steps that represent [[~]][[12/7]]), so that [[1728/1715]] = {{S|6/S7}} is tempered out. After two 8/5s (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.

In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]] (alternatively, the [[5/1|5th harmonic (5/1)]] is divided into 3 equal steps that represent [[~]][[12/7]]), so that [[1728/1715]] ({{S|6/S7}}) is tempered out. After two 8/5's (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.

In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. (A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament.)

In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament.

Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit.

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 {{interwiki
+| en = Orwell
 | de = Orwell
-| en = Orwell
 | es =
 | ja =
 }}
-[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]
 {{Infobox regtemp
 | Title = Orwell
@@ Line 19: / Line 17: @@
 | Odd limit 2 = (L11) 21 | Mistuning 2 = ??? | Complexity 2 = 22
 }}
+[[File:Orwell generator in 31.jpg|thumb|Martin Aurell's diagram showing Orwell[9] generated in 31 tone equal temperament.]]
 '''Orwell''' – so named because 19 steps of [[84edo]], i.e. 19\84, is a possible generator – is an excellent [[7-limit]] [[regular temperament|temperament]] and an amazing [[11-limit]] temperament because of the simplicity of [[harmonic]] [[11/1|11]].
-In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]] (alternatively, the [[5/1|5th harmonic (5/1)]] is divided into 3 equal steps that represent [[~]][[12/7]]), so that [[1728/1715]] = {{S|6/S7}} is tempered out. After two 8/5s (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.
+In orwell, [[8/5]] is divided into three equal steps, each of which represent [[7/6]] (alternatively, the [[5/1|5th harmonic (5/1)]] is divided into 3 equal steps that represent [[~]][[12/7]]), so that [[1728/1715]] ({{S|6/S7}}) is tempered out. After two 8/5's (six generators), [[9/7]] is found by [[tempering out]] the marvel comma, [[225/224]], and thus the [[3/1|just perfect twelfth (3/1)]] is divided into 7 equal steps.
-In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. (A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament.)
+In the 11-limit, two generators are equated to [[15/11]] and [[11/8]] (meaning [[99/98]] and [[121/120]] are tempered out). This means that three stacked generators makes the [[orwell tetrad]] 1–7/6–11/8–8/5, a chord in which every interval is a (tempered) 11-odd-limit consonance. Other such chords in undecimal orwell are the [[keenanismic chords]] and the [[swetismic chords]]. A far more complicated mapping of 11 at 33 generators, tempering out [[441/440]] instead, is also possible and is known as [[newspeak]] temperament.
 Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit.