Augmented (temperament): Difference between revisions

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'''Augmented''', [[12edo|12]] & [[15edo|15]], is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.
'''Augmented''', [[12edo|12]] & [[15edo|15]], is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]).


Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.
Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.

Revision as of 00:49, 9 April 2026

Augmented, 12 & 15, is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator; it has MOS scales triwood (3L 3s) and tcherepnin (3L 6s).

Because 128/125 = 126/125 * 64/63, Augmented admits a structurally induced 7-limit extension, called Augene, which adds Archy tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. 27edo is a notable tuning of Augene.


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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