Antonian: Difference between revisions
Created page with "{{Mathematical interest}} {{Infobox regtemp | Title = Antonian | Subgroups = 2.3.5, 2.3.5.7 | Comma basis = 10/9 (5-limit)<br>10/9, 15/14 (7-limit) | Edo join 1 = 2c(d) | Edo join 2 = 3(d) | Mapping = 1; 1 2 3 | Generators = 3/2 | Generators tuning = 743.086 | Optimization method = CWE | MOS scales = 1L 1s, 2L 1s, 3L 2s | Pergen = (P8, P5) | Odd limit 1 = 5 | Mistuning 1 = 91.2 | Complexity 1 = 3 | Odd limit 2 = 7 | Mistuning 2 = 161.4 | Complexity 2..." Tags: Mobile edit Mobile web edit |
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'''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 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]]. | ||
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| ]] <!-- main article --> | [[Category:Antonian| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Exotemperaments]] | [[Category:Exotemperaments]] | ||
Revision as of 11:16, 14 February 2026
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| Antonian |
10/9, 15/14 (7-limit)
7-odd-limit: 161.4 ¢
7-odd-limit: 5 notes
Antonian is an exotemperament that tempers out 10/9, the classic major second, setting the perfect fifth (3/2) equal to the 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.
For technical data see Very low accuracy temperaments #Antonian.
Extensions
There are some extensions of antonian, including septimal antonian (2cd & 3d), antonym (2cd & 3), antony (2c & 3d), and phlegyas (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.