Xenial - Revision history

Xenllium at 06:00, 9 May 2026

2026-05-09T06:00:54Z

Xenllium at 00:30, 9 May 2026

2026-05-09T00:30:32Z

← Older revision		Revision as of 00:30, 9 May 2026
Line 6:		Line 6:
	\| Mapping = 1; -9 -17 -33 22 -21 26 27 -3		\| Mapping = 1; -9 -17 -33 22 -21 26 27 -3
	\| Generators = 10/9 \| Generators tuning = 188.8 \| Optimization method = CWE		\| Generators = 10/9 \| Generators tuning = 188.8 \| Optimization method = CWE
	\| MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], [[19L 13s]], [[19L 32s]]		\| MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], <br>[[19L 13s]], [[19L 32s]], [[19L 51s]]
	\| Pergen = (P8, P11/9)		\| Pergen = (P8, P11/9)
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.6 \| Complexity 1 = 51		\| Odd limit 1 = 7 \| Mistuning 1 = 4.6 \| Complexity 1 = 51
			\| Odd limit 2 = 9 \| Mistuning 2 = 6.3 \| Complexity 2 = 51
			\| Odd limit 3 = 17 \| Mistuning 3 = 8.9 \| Complexity 3 = 70
			\| Odd limit 4 = 23 \| Mistuning 4 = 9.0 \| Complexity 4 = 70
	}}		}}
	'''Xenial''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a sharpened minor whole tone of [[~]][[10/9]], so that nine generators reach [[4/3]], 17 reach [[8/5]], 21 reach [[16/13]] and 33 reach [[8/7]] with octave reduction. It is also generated by dividing [[11/1\|11th harmonic]] into 22 equal parts, [[17/1\|17th harmonic]] into 26 equal parts, or [[19/1\|19th harmonic]] into 27 equal parts.		'''Xenial''' is a [[rank-2]] [[regular temperament\|temperament]] that is [[generator\|generated]] by a sharpened minor whole tone of [[~]][[10/9]], so that nine generators reach [[4/3]], 17 reach [[8/5]], 21 reach [[16/13]] and 33 reach [[8/7]] with octave reduction. It is also generated by dividing [[11/1\|11th harmonic]] into 22 equal parts, [[17/1\|17th harmonic]] into 26 equal parts, or [[19/1\|19th harmonic]] into 27 equal parts.
Line 288:		Line 291:
	\| 13/11		\| 13/11
	\| 188.623		\| 188.623
	\|		\| 13-odd-limit minimax
	\|-		\|-
	\|		\|
Line 318:		Line 321:
	\| 3/2		\| 3/2
	\| 188.672		\| 188.672
	\|		\| 9, 15 and 17-odd-limit minimax
	\|-		\|-
	\|		\|
	\| 11/9		\| 11/9
	\| 188.685		\| 188.685
	\|		\| 11-odd-limit minimax
	\|-		\|-
	\|		\|
	\| 19/13		\| 19/13
	\| 188.687		\| 188.687
	\|		\| 19, 21 and 23-odd-limit minimax
	\|-		\|-
	\|		\|
Line 443:		Line 446:
	\| 7/6		\| 7/6
	\| 188.880		\| 188.880
	\|		\| 7-odd-limit minimax
	\|-		\|-
	\|		\|
Line 478:		Line 481:
	\| 5/4		\| 5/4
	\| 189.040		\| 189.040
	\|		\| 5-odd-limit minimax
	\|-		\|-
	\|		\|

Xenllium at 13:05, 4 May 2026

2026-05-04T13:05:28Z

← Older revision		Revision as of 13:05, 4 May 2026
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	\| Title = Xenial		\| Title = Xenial
	\| Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.13.23, 2.3.5.7.11.13.17.19.23		\| Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.13.23, 2.3.5.7.11.13.17.19.23
	\| Comma basis = [[126/125]], [[177147/175616]] (7-limit); <br>[[126/125]], [[162/161]], [[169/168]], [[171/170]], [[~~221~~/~~220~~]], [[~~231~~/~~230~~]], [[~~256~~/~~255~~]] (23-limit)		\| Comma basis = [[126/125]], [[177147/175616]] (7-limit); <br>[[126/125]], [[162/161]], [[169/168]], [[171/170]], [[208/207]], [[221/220]], [[231/230]] (23-limit)
	\| Edo join 1 = 19 \| Edo join 2 = 70		\| Edo join 1 = 19 \| Edo join 2 = 70
	\| Mapping = 1; -9 -17 -33 22 -21 26 27 -3		\| Mapping = 1; -9 -17 -33 22 -21 26 27 -3
Line 31:		Line 31:
	\| 2		\| 2
	\| 377.551		\| 377.551
	\|		\| [[56/45]]
	\|-		\|-
	\| 3		\| 3
Line 51:		Line 51:
	\| 7		\| 7
	\| 121.428		\| 121.428
	\|		\| [[15/14]]
	\|-		\|-
	\| 8		\| 8
Line 151:		Line 151:
	\| 32		\| 32
	\| 40.815		\| 40.815
	\|		\| [[36/35]], [[46/45]], [[50/49]]
	\|-		\|-
	\| 33		\| 33

Xenllium at 12:04, 4 May 2026

2026-05-04T12:04:52Z

Show changes

Xenllium at 07:58, 4 May 2026

2026-05-04T07:58:33Z

← Older revision		Revision as of 07:58, 4 May 2026
Line 13:		Line 13:

	See [[Starling temperaments #Xenial]] for more technical data.		See [[Starling temperaments #Xenial]] for more technical data.

			== Interval chain ==
			{\| class="wikitable center-1 right-2"
			\|-
			! #
			! Cents*
			! Approximate ratios
			\|-
			\| 0
			\| 0.000
			\| [[1/1]]
			\|-
			\| 1
			\| 188.775
			\| [[10/9]], [[19/17]], [[28/25]]
			\|-
			\| 2
			\| 377.551
			\|
			\|-
			\| 3
			\| 566.326
			\| [[18/13]], [[32/23]]
			\|-
			\| 4
			\| 755.102
			\| [[17/11]], [[20/13]]
			\|-
			\| 5
			\| 943.877
			\| [[19/11]], [[26/15]]
			\|-
			\| 6
			\| 1132.653
			\| [[23/12]], [[27/14]]
			\|-
			\| 7
			\| 121.428
			\|
			\|-
			\| 8
			\| 310.204
			\| [[6/5]]
			\|-
			\| 9
			\| 498.979
			\| [[4/3]]
			\|-
			\| 10
			\| 687.755
			\| [[40/27]]
			\|-
			\| 11
			\| 876.530
			\|
			\|-
			\| 12
			\| 1065.306
			\| [[13/7]], [[24/13]]
			\|-
			\| 13
			\| 54.081
			\| [[26/25]], [[33/32]]
			\|-
			\| 14
			\| 242.857
			\| [[23/20]]
			\|-
			\| 15
			\| 431.632
			\| [[9/7]], [[23/18]]
			\|-
			\| 16
			\| 620.408
			\| [[10/7]]
			\|-
			\| 17
			\| 809.183
			\| [[8/5]]
			\|-
			\| 18
			\| 997.959
			\| [[16/9]], [[23/13]]
			\|-
			\| 19
			\| 1186.734
			\|
			\|-
			\| 20
			\| 175.510
			\|
			\|-
			\| 21
			\| 364.285
			\| [[16/13]], [[26/21]]
			\|-
			\| 22
			\| 553.061
			\| [[11/8]]
			\|-
			\| 23
			\| 741.836
			\| [[23/15]]
			\|-
			\| 24
			\| 930.612
			\| [[12/7]]
			\|-
			\| 25
			\| 1119.387
			\| [[40/21]], [[44/23]], [[48/25]]
			\|-
			\| 26
			\| 108.163
			\| [[16/15]], [[17/16]]
			\|-
			\| 27
			\| 296.938
			\| [[19/16]]
			\|-
			\| 28
			\| 485.714
			\|
			\|-
			\| 29
			\| 674.439
			\| [[34/23]]
			\|-
			\| 30
			\| 863.265
			\| [[38/23]], [[23/14]]
			\|-
			\| 31
			\| 1052.040
			\| [[11/6]], [[46/25]]
			\|-
			\| 32
			\| 40.815
			\|
			\|-
			\| 33
			\| 229.591
			\| [[8/7]]
			\|-
			\| 34
			\| 418.366
			\| [[32/25]]
			\|}
			<nowiki/>* In 23-limit CWE tuning

	== Tunings ==		== Tunings ==

Xenllium at 11:03, 3 May 2026

2026-05-03T11:03:34Z

@@ Line 7: / Line 7: @@
 | Generators = 10/9 | Generators tuning = 188.8 | Optimization method = CWE
 | MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], [[19L 13s]], [[19L 32s]]
-| Pergen = (P8, P11/3)
+| Pergen = (P8, P11/9)
 | Odd limit 1 = 7 | Mistuning 1 = 4.6 | Complexity 1 = 51
 }}
@@ Line 15: / Line 15: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"

Xenllium: Created page with "{{Infobox regtemp | Title = Xenial | Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.13.23, 2.3.5.7.11.13.17.19.23 | Comma basis = 126/125, 177147/175616 (7-limit);
126/125, 162/161, 169/168, 171/170, 221/220, 231/230, 256/255 (23-limit) | Edo join 1 = 19 | Edo join 2 = 70 | Mapping = 1; -9 -17 -33 22 -21 26 27 -3 | Generators = 10/9 | Generators tuning = 188.8 | Optimization method = CWE | MOS scales = 6L 1s, 6L 7s, 13L 6s, [..."

2026-05-03T02:04:40Z

Created page with "{{Infobox regtemp | Title = Xenial | Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.13.23, 2.3.5.7.11.13.17.19.23 | Comma basis = 126/125, 177147/175616 (7-limit); 126/125, 162/161, 169/168, 171/170, 221/220, 231/230, 256/255 (23-limit) | Edo join 1 = 19 | Edo join 2 = 70 | Mapping = 1; -9 -17 -33 22 -21 26 27 -3 | Generators = 10/9 | Generators tuning = 188.8 | Optimization method = CWE | MOS scales = 6L 1s, 6L 7s, 13L 6s, [..."

New page

{{Infobox regtemp
| Title = Xenial
| Subgroups = 2.3.5.7, 2.3.5.7.13, 2.3.5.7.13.23, 2.3.5.7.11.13.17.19.23
| Comma basis = [[126/125]], [[177147/175616]] (7-limit); [[126/125]], [[162/161]], [[169/168]], [[171/170]], [[221/220]], [[231/230]], [[256/255]] (23-limit)
| Edo join 1 = 19 | Edo join 2 = 70
| Mapping = 1; -9 -17 -33 22 -21 26 27 -3
| Generators = 10/9 | Generators tuning = 188.8 | Optimization method = CWE
| MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], [[19L 13s]], [[19L 32s]]
| Pergen = (P8, P11/3)
| Odd limit 1 = 7 | Mistuning 1 = 4.6 | Complexity 1 = 51
}}
'''Xenial''' is a [[rank-2]] [[regular temperament|temperament]] that is [[generator|generated]] by a sharpened minor whole tone of [[~]][[10/9]], so that nine generators reach [[4/3]], 17 reach [[8/5]], 21 reach [[16/13]] and 33 reach [[8/7]] with octave reduction. It is also generated by dividing [[11/1|11th harmonic]] into 22 equal parts, [[17/1|17th harmonic]] into 26 equal parts, or [[19/1|19th harmonic]] into 27 equal parts.

See [[Starling temperaments #Xenial]] for more technical data.

== Tunings ==
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo generator
! [[Eigenmonzo|Eigenmonzo (unchanged interval)]]
! Generator (¢)
! Comments
|-
|
| 9/5
| 182.404
|
|-
|
| 13/10
| 186.447
|
|-
| 5 ⧵ 32
|
| 187.500
| 32cddefgh val Lower bound of 7-odd-limit diamond monotone
|-
|
| 23/12
| 187.720
|
|-
|
| 13/9
| 187.794
|
|-
|
| 23/13
| 188.208
|
|-
| 8 ⧵ 51
|
| 188.235
| 51cdh val Lower bound of 9-odd-limit diamond monotone
|-
|
| 23/18
| 188.291
|
|-
|
| 13/12
| 188.452
|
|-
|
| 15/14
| 188.492
|
|-
|
| 13/8
| 188.546
|
|-
| 11 ⧵ 70
|
| 188.571
| Lower bound of 11, 13, 15 and 17-odd-limit diamond monotone
|-
|
| 7/5
| 188.593
|
|-
|
| 21/20
| 188.621
|
|-
|
| 23/14
| 188.648
|
|-
|
| 17/16
| 188.652
|
|-
|
| 23/21
| 188.654
|
|-
|
| 3/2
| 188.672
|
|-
|
| 23/15
| 188.6959
|
|-
|
| 11/8
| 188.6963
|
|-
|
| 23/20
| 188.711
|
|-
| 14 ⧵ 89
|
| 188.764
| 19, 21 and 23-odd-limit diamond monotone (singleton)
|-
|
| 21/16
| 188.791
|
|-
|
| 19/16
| 188.797
|
|-
|
| 7/4
| 188.823
|
|-
|
| 7/6
| 188.880
|
|-
|
| 15/8
| 188.913
|
|-
|
| 9/7
| 189.006
|
|-
|
| 21/13
| 189.036
|
|-
|
| 5/4
| 189.040
|
|-
|
| 14/13
| 189.308
|
|-
|
| 5/3
| 189.455
|
|-
| 3 ⧵ 19
|
| 189.473
| Upper bound of 7, 9, 11, 13, 15 and 17-odd-limit diamond monotone
|-
|
| 15/13
| 190.452
|
|-
|
| 23/16
| 190.575
|
|}

[[Category:Xenial| ]] 
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]