Magic: Difference between revisions

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'''Magic''' is a 2.3.5 temperament that equates a stack of five 5/4 major thirds to one 3/1. It also equates 25/24 to 128/125, shrinking the difference between 5/4 and 6/5.
'''Magic''' is a 2.3.5 temperament that equates a stack of five 5/4 major thirds to one 3/1. It also equates 25/24 to 128/125, shrinking the difference between 5/4 and 6/5.


== Extensions ==
Magic divides ~16/15 in half (the 25/24~128/125), so it easily extends to prime 31 (at +3 generators). Since in 7-limit Magic, the 16/15 is also a 15/14, we can also extend 7-limit Magic to add prime 29 (at +9 generators) by equating 16/15 to 31/29.
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Revision as of 03:10, 1 March 2026

Magic
Subgroups 2.3.5, 2.3.5.7
Reduced mapping ⟨1; 5 1 12]
ET join 19 & 22
Generators (CWE) ~5/4 = 380.5¢
MOS scales 3L 4s, 3L 7s, …, 3L 16s, 19L 3s
Ploidacot alpha-pentacot
Comma basis 3125/3072 (5-limit);
225/224, 245/243 (7-limit)
Minimax error 5-odd-limit: 5.9¢;
9-odd-limit: 5.9¢
Target scale size 5-odd-limit: 7 notes;
9-odd-limit: 13 notes

Magic is a 2.3.5 temperament that equates a stack of five 5/4 major thirds to one 3/1. It also equates 25/24 to 128/125, shrinking the difference between 5/4 and 6/5.

Extensions

Magic divides ~16/15 in half (the 25/24~128/125), so it easily extends to prime 31 (at +3 generators). Since in 7-limit Magic, the 16/15 is also a 15/14, we can also extend 7-limit Magic to add prime 29 (at +9 generators) by equating 16/15 to 31/29.