Diminished (temperament): Difference between revisions

From Xenharmonic Reference
← Older edit
VisualWikitext
mNo edit summary
mNo edit summary
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
'''Diminished''', [[12edo|12]] & [[16edo|16]], is a 5-limit temperament tempering out 648/625, the difference between four 6/5 minor thirds and the octave. Diminished has period 1\4 and generator 3/2 (or 25/24); it is associated with tetrawood (4L 4s), called the diminished scale in conventional music theory.
'''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, but if you want a better 5/4, you have to flatten the 3/2 generator (as in [[28edo]] or [[40edo]]).
Many tuning optimization algorithms consider Diminished 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 13:06, 28 May 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 consider Diminished 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
Retrieved from "https://xenreference.com/wiki/index.php?title=Diminished_(temperament)&oldid=7360"