Magic: Difference between revisions

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| Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 13
| Odd limit 2 = 9 | Mistuning 2 = 5.9 | Complexity 2 = 13
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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.


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Revision as of 21:06, 24 February 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.

View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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