9edf: Difference between revisions

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 == Theory ==
-edf corresponds to 15.391524edo. It is closely related to [[Carlos Alpha]], and can be used as a temperament of the 3/2.5/4.7/8.11/8 subgroup. Carlos Alpha can be seen as 9edf with an independent dimension for 2.
+edf corresponds to 15.385602edo. It is closely related to [[Carlos Alpha]] (though the Carlos Alpha generator is 0.03{{C}} narrower at 77.965{{C}}), and can be used as a temperament of the 3/2.5/4.8/7.11/8 subgroup. [[Valentine]] can be seen as 9edf with an independent dimension for 2.
 === Harmonics ===
@@ Line 63: / Line 63: @@
 |-
 | 9
-| 701.9
+| 702.0
 | [[3/2]]
 | C
@@ Line 69: / Line 69: @@
 == Scales ==
-Three [[period]]s shown per scale, with first period in '''bold'''.
+{{Idiosyncratic terms}}
-* Livewire^: '''1 8 1 8 1 8 1 8 1 8 1''' 1 8 1 8 1 8 1 8 1 8 1 1 8 1 8 1 8 1 8 1 8 1
+{| class="wikitable sortable"
-* Corrugated^: '''2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2''' 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2
+|+
-* Snowcone^: '''3 6''' 3 6 3 6...
+! rowspan="2" | Name
-* Swan^: '''4 5 4 5 4 5 4''' 4 5 4 5 4 5 4 4 5 4 5 4 5 4...
+! rowspan="2" | Step pattern within 1 period
-* Cloudscape^: '''5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5''' 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 55 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
+! colspan="3" | Interval of repetition
-* Pylon^: '''6 3''' 6 3 6 3...
+! rowspan="2" | First described by
-* Quest^: '''7 2''' 7 2 7 2...
+|-
-* Purgatory^: '''8 1 8 1 8 1 8 1 8 1 8 1 8''' 8 1 8 1 8 1 8 1 8 1 8 1 8 8 1 8 1 8 1 8 1 8 1 8 1 8...
+! (In 9edf steps)
-* Molten [[pelog]]^: '''2 2 5 2 5''' 2 2 5 2 5 2 2 5 2 5...
+! (In cents)
-* Molten [[slendro]]^: '''3''' 3 3...
+! (Nearby JI)
+|-
-(^ ''this is the original/default tuning'')
+| Molten [[slendro]]
+| 3
-For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]].
+| 3
+| 234.0
+| [[8/7]]
+| ''[[Budjarn Lambeth]] (2023)''
+|-
+| Pylon
+| 6 3
+| 9
+| 702.0
+| [[3/2]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Quest
+| 7 2
+| 9
+| 702.0
+| [[3/2]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Snowcone
+| 3 6
+| 9
+| 702.0
+| [[3/2]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Molten [[pelog]]
+| 2 2 5 2 5
+| 16
+| 1247.9
+| [[33/16]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Swan
+| 4 5 4 5 4 5 4
+| 31
+| 2417.8
+| [[4/1]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Livewire
+| 1 8 1 8 1 8 1 8 1 8 1
+| 46
+| 3587.8
+| [[8/1]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Purgatory
+| 8 1 8 1 8 1 8 1 8 1 8 1 8
+| 62
+| 4835.7
+| [[16/1]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Cloudscape
+| 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
+| 72
+| 5615.6
+| [[128/5]]
+| ''Budjarn Lambeth (2023)''
+|-
+| Corrugated
+| 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2
+| 135
+| 10529.3
+| [[437/1]]
+| ''Budjarn Lambeth (2023)''
+|}
+None of these scales are approximated from another tuning unless specified otherwise. For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]].
 == Music ==
 See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf.
+== See also ==
+* [[Alpha, beta, and gamma family of equal divisions]]
 [[Category:Listen]]