Antonian

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 = 743.086 ¢
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

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 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 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.

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.