Antonian

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	2c(d) & 3(d)
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

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.

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.