Xenharmonic Wiki

Antonian: Difference between revisions

← Older edit
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,991 edits
better language (don't exaggerate as much as in bixby)
Update & expand
 
(2 intermediate revisions by 2 users not shown)
Line 3: Line 3:
| Title = Antonian
| Title = Antonian
| Subgroups = 2.3.5, 2.3.5.7
| 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 = 2cd | Edo join 2 = 3d
| Edo join 1 = 2cd | Edo join 2 = 3d
| Mapping = 1; 1 2 3
| Mapping = 1; 1 2 3
| Generators = 3/2 | Generators tuning = 743.086 | Optimization method = CWE
| Generators = 3/2 | Generators tuning = 743 | Optimization method = CWE
| MOS scales = [[1L 1s]], [[2L 1s]], [[3L 2s]]
| MOS scales = [[1L 1s]], [[2L 1s]], [[3L 2s]]
| Pergen = (P8, P5)
| Pergen = (P8, P5)
Line 12: Line 12:
| Odd limit 2 = 7 | Mistuning 2 = 161.4 | Complexity 2 = 5
| 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 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]].
'''Antonian''' is an [[exotemperament]] that [[tempering out|tempers out]] 10/9, the [[10/9|classic major second]]. This 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]].


For technical data see [[Very low accuracy temperaments #Antonian]].
In septimal antonian, [[7/6]] is equated to 5/4 and 9/8, by tempering out [[15/14]] and [[28/27]]. An alternative extension is [[phlegyas]], which tempers out [[35/32]] and [[64/63]], so [[8/7]] is equated with 5/4 and 9/8 instead.


== Extensions ==
For technical data, see [[Very low accuracy temperaments #Antonian]].
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]].
== Interval chain ==
In the following table, odd harmonics 1–7 are labeled in '''bold'''.
 
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0
| '''1/1'''
|-
| 1
| 743
| '''3/2''', 5/3, 7/5
|-
| 2
| 286
| '''5/4''', 7/6
|-
| 3
| 1029
| '''7/4'''
|}
<nowiki/>* In 7-limit CWE tuning, octave reduced
 
== Tunings ==
=== Tunings spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator !! Eigenmonzo<br>(unchanged-interval) !! Generator (¢) !! Comments
|-
|  || 7/5 || 583 ||
|-
| 1\2 ||  || 600 ||
|-
| || 3/2 || 702 ||
|-
| || 7/4 || 723 ||
|-
| || 7/6 || 733 ||
|-
| || 5/4 || 793 ||
|-
| 2\3 ||  || 800 ||
|-
| || 5/3 || 884 ||
|}


[[Category:Antonian| ]] <!-- main article -->
[[Category:Antonian| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Exotemperaments]]
[[Category:Trienstonic clan]]
[[Category:Greenwoodmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Antonian"