Augmented (temperament)
From Xenharmonic Reference
Augmented, 12 & 15, is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood (3L 3s) and tcherepnin (3L 6s). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.
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. 15edo and 27edo are notable tunings of Augene.
List of patent vals
The following patent vals support Augmented. Vals contorted in the 5-limit are not included.
| Edo | 7 extension | 3/2 tuning | 7/4 tuning |
|---|---|---|---|
| 9 | 12 & 21 | 666.667 | 933.333 |
| 21 | 12 & 21 | 685.714 | 971.429 |
| 33 | 12 & 21 | 690.909 | 981.818 |
| 12 | 12 & 15, 12 & 21 | 700.000 | 1000.000 |
| 39 | 707.692 | 953.846 | |
| 27 | 12 & 15 | 711.111 | 977.778 |
| 42 | 12 & 15 | 714.286 | 971.429 |
| 15 | 12 & 15 | 720.000 | 960.000 |
| 30 | 12 & 15 | 720.000 | 960.000 |
| 18 | 733.333 | 1000.000 | |
| 3 | 12 & 15 | 800.000 | 800.000 |
| 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 |
