Diminished (temperament): Difference between revisions
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'''Diminished''', [[12edo|12]] & [[16edo|16]], is a 5-limit temperament | '''Diminished''', [[12edo|12]] & [[16edo|16]], is a 5-limit temperament with period 1\4 (representing 6/5) and generator 3/2 (or 25/24); it is associated with tetrawood (4L 4s), called the diminished scale in conventional music theory. It tempers out 648/625, the difference between four 6/5 minor thirds and the octave. | ||
Many tuning optimization algorithms rate diminished as optimal near 12edo, | Many tuning optimization algorithms rate diminished as optimal near 12edo. However, you might want a better 5/4, and if you do, you have to flatten the 3/2 generator (as in [[28edo]] or [[40edo]]). | ||
== Patent vals == | |||
The following patent vals support Diminished. Vals contorted in 2.3.5 are not included. | |||
{| class="wikitable sortable" | |||
!|Edo!!5/4 tuning | |||
|- | |||
||4||300.000 | |||
|- | |||
||16||375.000 | |||
|- | |||
||28||385.714 | |||
|- | |||
||40||390.000 | |||
|- | |||
||52||392.308 | |||
|- | |||
||64||393.750 | |||
|- | |||
||12||400.000 | |||
|- | |||
||8||450.000 | |||
|} | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Latest revision as of 14:17, 14 April 2026
Diminished, 12 & 16, is a 5-limit temperament with period 1\4 (representing 6/5) and generator 3/2 (or 25/24); it is associated with tetrawood (4L 4s), called the diminished scale in conventional music theory. It tempers out 648/625, the difference between four 6/5 minor thirds and the octave.
Many tuning optimization algorithms rate diminished as optimal near 12edo. However, you might want a better 5/4, and if you do, you have to flatten the 3/2 generator (as in 28edo or 40edo).
Patent vals
The following patent vals support Diminished. Vals contorted in 2.3.5 are not included.
| Edo | 5/4 tuning |
|---|---|
| 4 | 300.000 |
| 16 | 375.000 |
| 28 | 385.714 |
| 40 | 390.000 |
| 52 | 392.308 |
| 64 | 393.750 |
| 12 | 400.000 |
| 8 | 450.000 |
| 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 |
