Augmented (temperament): Difference between revisions
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'''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. | '''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. | ||
Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth. | Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (AW-jeen), which adds [[Archy]] tempering to the fifth. | ||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Revision as of 00:43, 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.
Because 128/125 = 126/125 * 64/63, Augmented admits a structurally induced 7-limit extension, called Augene (AW-jeen), which adds Archy tempering to the fifth.
| 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 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperaments | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
