Antonian: Difference between revisions

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| 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 & 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]].
== 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]]

Latest revision as of 10:04, 20 October 2026

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
Subgroups 2.3.5, 2.3.5.7
Comma basis 10/9 (5-limit);
10/9, 15/14 (7-limit)
Reduced mapping ⟨1; 1 2 3]
ET join 2cd & 3d
Generators (CWE) ~3/2 = 743 ¢
MOS scales 1L 1s, 2L 1s, 3L 2s
Ploidacot monocot
Pergen (P8, P5)
Minimax error 5-odd-limit: 91.2 ¢;
7-odd-limit: 161.4 ¢
Target scale size 5-odd-limit: 3 notes;
7-odd-limit: 5 notes

Antonian is an exotemperament that tempers out 10/9, the 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.

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.

For technical data, see Very low accuracy temperaments #Antonian.

Interval chain

In the following table, odd harmonics 1–7 are labeled in bold.

# 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

* In 7-limit CWE tuning, octave reduced

Tunings

Tunings spectrum

Edo
generator		 Eigenmonzo
(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
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