Antonian: Difference between revisions

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| Title = Antonian

| Subgroups = 2.3.5, 2.3.5.7

| Comma basis = [[10/9]] (5-limit)<br>10/9, [[15/14]] (7-limit)

| Comma basis = [[10/9]] (5-limit)<br>[[10/9]], [[15/14]] (7-limit)

| Edo join 1 = ~~2c(d)~~ | Edo join 2 = ~~3(d)~~

| Edo join 1 = 2cd | Edo join 2 = 3d

| Mapping = 1; 1 2 3

| Generators = 3/2 | Generators tuning = 743.086 | Optimization method = CWE

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| Odd limit 2 = 7 | Mistuning 2 = 161.4 | Complexity 2 = 5

}}

'''Antonian''' is an [[exotemperament]] that [[tempering out|tempers out]] 10/9, the classic major second, setting the [[3/2|perfect fifth (3/2)]] equal to the [[5/3|classic major sixth (5/3)]]. This temperament ~~is less accurate than more common archetypal exotemperaments like [[father]] or [[dicot]], doing something with such high damage as to make~~ 3/2 ~~and~~ 5/3, [[4/3]] ~~and~~ [[6/5]], or [[5/4]] ~~and~~ [[9/8]] ~~the same interval~~. It can be represented by only [[3edo]] in its [[patent val]].

'''Antonian''' is an [[exotemperament]] that [[tempering out|tempers out]] 10/9, the classic major second, setting the [[3/2|perfect fifth (3/2)]] equal to the [[5/3|classic major sixth (5/3)]]. This temperament equates 3/2 with 5/3, [[4/3]] with [[6/5]], and [[5/4]] with [[9/8]], being even less accurate than more common archetypal exotemperaments like [[father]] or [[dicot]]. It can be represented by only [[3edo]] in its [[patent val]].

~~The canonical extension for the 7-limit is tempering out~~ [[~~15/14~~]] ~~and [[28/27]], identifying [[7/6]] with 5/4 and 9/8~~.

For technical data see [[Very low accuracy temperaments #Antonian]].

~~For technical data see~~ [[~~Very low accuracy temperaments #Antonian~~]].

== Extensions ==

There are some extensions of antonian, including septimal antonian ({{nowrap|2cd & 3d}}), antonym ({{nowrap|2cd & 3}}), antony ({{nowrap|2c & 3d}}), and phlegyas ({{nowrap|2c & 3}}).

In the septimal antonian, [[7/6]] is equated to 5/4 and 9/8, by tempering out [[15/14]] and [[28/27]]. Antonym tempers out [[7/6]] and [[21/20]]. Antony tempers out [[8/7]] and [[36/35]]. Phlegyas tempers out [[35/32]] and [[64/63]].

[[Category:Antonian| ]]

[[Category:Rank-2 temperaments]]

[[Category:Exotemperaments]]

@@ Line 3: / Line 3: @@
 | Title = Antonian
 | Subgroups = 2.3.5, 2.3.5.7
-| Comma basis = [[10/9]] (5-limit)<br>10/9, [[15/14]] (7-limit)
+| Comma basis = [[10/9]] (5-limit)<br>[[10/9]], [[15/14]] (7-limit)
-| Edo join 1 = 2c(d) | Edo join 2 = 3(d)
+| Edo join 1 = 2cd | Edo join 2 = 3d
 | Mapping = 1; 1 2 3
 | Generators = 3/2 | Generators tuning = 743.086 | Optimization method = CWE
@@ Line 12: / Line 12: @@
 | Odd limit 2 = 7 | Mistuning 2 = 161.4 | Complexity 2 = 5
 }}
-'''Antonian''' is an [[exotemperament]] that [[tempering out|tempers out]] 10/9, the classic major second, setting the [[3/2|perfect fifth (3/2)]] equal to the [[5/3|classic major sixth (5/3)]]. This temperament is less accurate than more common archetypal exotemperaments like [[father]] or [[dicot]], doing something with such high damage as to make 3/2 and 5/3, [[4/3]] and [[6/5]], or [[5/4]] and [[9/8]] the same interval. It can be represented by only [[3edo]] in its [[patent val]].
+'''Antonian''' is an [[exotemperament]] that [[tempering out|tempers out]] 10/9, the classic major second, setting the [[3/2|perfect fifth (3/2)]] equal to the [[5/3|classic major sixth (5/3)]]. This temperament equates 3/2 with 5/3, [[4/3]] with [[6/5]], and [[5/4]] with [[9/8]], being even less accurate than more common archetypal exotemperaments like [[father]] or [[dicot]]. It can be represented by only [[3edo]] in its [[patent val]].
-The canonical extension for the 7-limit is tempering out [[15/14]] and [[28/27]], identifying [[7/6]] with 5/4 and 9/8.
+For technical data see [[Very low accuracy temperaments #Antonian]].
-For technical data see [[Very low accuracy temperaments #Antonian]].
+== Extensions ==
+There are some extensions of antonian, including septimal antonian ({{nowrap|2cd &amp; 3d}}), antonym ({{nowrap|2cd &amp; 3}}), antony ({{nowrap|2c &amp; 3d}}), and phlegyas ({{nowrap|2c &amp; 3}}).
+In the septimal antonian, [[7/6]] is equated to 5/4 and 9/8, by tempering out [[15/14]] and [[28/27]]. Antonym tempers out [[7/6]] and [[21/20]]. Antony tempers out [[8/7]] and [[36/35]]. Phlegyas tempers out [[35/32]] and [[64/63]].
 [[Category:Antonian| ]] <!-- main article -->
 [[Category:Rank-2 temperaments]]
 [[Category:Exotemperaments]]