Diminished (temperament): Difference between revisions
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'''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. | '''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 | 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 == | == Patent vals == | ||
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 |
