Unidec: Difference between revisions

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-'''Unidec''' is the [[regular temperament]] defined in the 7-limit by [[tempering out]] [[1029/1024]], the gamelisma, and [[4375/4374]], the ragisma, with the 11-limit extension adding [[385/384]] or [[441/440]] to the comma list, featuring a period of a semioctave and a generator of a classic whole tone.
+{{Infobox regtemp
+| Title = Unidec
+| Subgroups = 2.3.5.7, 2.3.5.7.11
+| Comma basis = [[1029/1024]], [[4375/4374]] (7-limit); <br>[[385/384]], [[441/440]], [[4375/4374]] (11-limit)
+| Edo join 1 = 26 | Edo join 2 = 46
+| Mapping = 2; 6 11 -2 -3
+| Generators = 14/11 | Generators tuning = 416.9 | Optimization method = CWE
+| MOS scales = [[6L 2s]], [[6L 8s]], [[6L 14s]], [[20L 6s]]
+| Odd limit 1 = 9 | Mistuning 1 = 2.41 | Complexity 1 = 46
+| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.95 | Complexity 2 = 46
+}}
+'''Unidec''' is a [[regular temperament|temperament]] [[generator|generated]] by a wide major third representing [[80/63]] which can be taken as [[14/11]] from the [[11-limit]] onwards. Two generators minus a [[semi-octave]] [[period]] make a [[~]][[8/7]], and three ~8/7's make a perfect fifth of [[3/2]], [[tempering out]] [[1029/1024]], the gamelisma, and [[4375/4374]], the ragisma, with the 11-limit [[extension]] adding [[385/384]] or [[441/440]] to the comma list.
-Unidec has two viable 13-limit extensions: '''hendec''' and '''ekadash'''.
+Unidec has two viable 13-limit extensions: hendec and ekadash, discussed in [[Unidec extensions]].
 See [[Gamelismic clan #Unidec]] for technical data.
+== Interval chain ==
+In the following table, odd harmonics 1–21 and their inverses are in '''bold'''.
+{| class="wikitable center-1 right-2 right-4"
+|-
+! rowspan="2" | #
+! colspan="2" | Period 0
+! colspan="2" | Period 1
+|-
+! Cents*
+! Approximate ratios
+! Cents*
+! Approximate ratios
+|-
+| 0
+| 0.00
+| '''1/1'''
+| 600.00
+| 99/70, 140/99
+|-
+| 1
+| 416.85
+| 14/11
+| 1016.80
+| 9/5
+|-
+| 2
+| 833.71
+| 81/50, 160/99
+| 233.71
+| '''8/7'''
+|-
+| 3
+| 50.56
+| 33/32, 36/35
+| 650.56
+| '''16/11'''
+|-
+| 4
+| 467.42
+| '''21/16'''
+| 1067.42
+| 50/27
+|-
+| 5
+| 884.27
+| 5/3
+| 284.27
+| 33/28
+|-
+| 6
+| 101.13
+| 35/33
+| 701.13
+| '''3/2'''
+|-
+| 7
+| 517.98
+| 27/20
+| 1117.98
+| 21/11, 40/21
+|-
+| 8
+| 934.83
+| 12/7
+| 334.83
+| 40/33
+|-
+| 9
+| 151.69
+| 12/11
+| 751.69
+| 54/35
+|-
+| 10
+| 568.54
+| 25/18
+| 1168.54
+| 55/28, 63/32, 96/49, 108/55
+|-
+| 11
+| 985.40
+| 99/56
+| 385.40
+| '''5/4'''
+|-
+| 12
+| 202.25
+| '''9/8'''
+| 802.25
+| 35/22
+|-
+| 13
+| 619.11
+| 10/7
+| 19.11
+| 81/80, 99/98, 100/99
+|}
+<nowiki/>* In 11-limit CWE tuning, octave reduced
 == Chords and harmony ==
@@ Line 12: / Line 123: @@
 == Tunings ==
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~80/63 = 416.9403{{c}}
+| CWE: ~80/63 = 416.8688{{c}}
+| POTE: ~80/63 = 416.8385{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~14/11 = 416.9262{{c}}
+| CWE: ~14/11 = 416.8543{{c}}
+| POTE: ~14/11 = 416.8350{{c}}
+|}
 === Tuning spectrum ===
 {| class="wikitable center-all left-3"