Diminished (temperament): Difference between revisions
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'''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 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. | ||
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]]). | ||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Revision as of 00:58, 9 April 2026
Diminished, 12 & 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.
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).
