Diminished (temperament): Difference between revisions
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Adopt CWE in the interval chain. Misc. style improvements |
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[[12edo]] is an obvious tuning. Other possible tunings include [[16edo]] and [[28edo]], both of which having the interesting feature of being good in the 2.7.19 subgroup, so that the fifth is approximately [[28/19]]. [[28edo]] is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them. | [[12edo]] is an obvious tuning. Other possible tunings include [[16edo]] and [[28edo]], both of which having the interesting feature of being good in the 2.7.19 subgroup, so that the fifth is approximately [[28/19]]. [[28edo]] is notable as a tuning for the 5-limit temperament, dimipent, as it has very accurate [[5/4]]'s, being a [[strongly consistent circle]] of them. | ||
See [[Dimipent family#Diminished]] for technical data. | See [[Dimipent family #Diminished]] for technical data. | ||
== Interval chain == | == Interval chain == | ||
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{| class="wikitable center-1 right-2 right-4 right-6 right-8" | {| class="wikitable center-1 right-2 right-4 right-6 right-8" | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | # | ||
! colspan="2" | Period 0 | ! colspan="2" | Period 0 | ||
! colspan="2" | Period 1 | ! colspan="2" | Period 1 | ||
| Line 23: | Line 23: | ||
|- | |- | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
! Cents* | ! Cents* | ||
! Approx. | ! Approx. ratios | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 44: | Line 44: | ||
| 92.0 | | 92.0 | ||
| 15/14, 21/20, 25/24, 49/48 | | 15/14, 21/20, 25/24, 49/48 | ||
| | | 396.0 | ||
| '''5/4''', 9/7 | | '''5/4''', 9/7 | ||
| | | 696.0 | ||
| '''3/2''' | | '''3/2''' | ||
| | | 996.0 | ||
| '''7/4''', 9/5 | | '''7/4''', 9/5 | ||
|- | |- | ||
| 2 | | 2 | ||
| | | 191.9 | ||
| '''9/8''' | | '''9/8''' | ||
| | | 491.9 | ||
| 21/16 | | 21/16 | ||
| | | 791.9 | ||
| 45/28, 63/40 | | 45/28, 63/40 | ||
| | | 1091.9 | ||
| 15/8 | | 15/8 | ||
|} | |} | ||
<nowiki />* In 7-limit | <nowiki/>* In 7-limit CWE tuning | ||
== Scales == | == Scales == | ||
* [[Diminished12]] | * [[Diminished12]] – in [[44edo]] tuning | ||
== Tunings == | == Tunings == | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |- | ||
! Edo<br | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 161: | Line 161: | ||
| 8d val, upper bound of 7-odd-limit diamond monotone | | 8d val, upper bound of 7-odd-limit diamond monotone | ||
|} | |} | ||
<nowiki />* Besides the octave | <nowiki/>* Besides the octave | ||
== See also == | == See also == | ||