Oolong: Difference between revisions

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See [[Starling temperaments #Oolong]].  
{{Infobox regtemp
| Title = Oolong
| Subgroups = 2.3.5.7, 2.3.5.7.13
| Comma basis = [[126/125]], [[117649/116640]] (2.3.5.7); <br>[[126/125]], [[196/195]], [[15379/15360]] (2.3.5.7.13)
| Edo join 1 = 27 | Edo join 2 = 50
| Mapping = 1; -17 -18 -20 -5
| Generators = 6/5
| Generators tuning = 311.7
| Optimization method = CWE
| MOS scales = [[4L&nbsp;3s]], [[4L&nbsp;7s]], [[4L&nbsp;11s]], [[4L&nbsp;15s]], [[4L&nbsp;19s]], [[23L&nbsp;4s]]
| Pergen = (P8, c<sup>4</sup>P4/17)
| Odd limit 1 = 7 | Mistuning 1 = 5.6 | Complexity 1 = 23
}}


[[Category:Soft redirect]]
See [[Starling temperaments #Oolong]] for more technical data.
 
== Interval chain ==
In the following table, prime harmonics are in '''bold'''.
 
{| class="wikitable center-1 right-2"
! #
! Cents*
! Approximate Ratios
|-
| 0
| 0.0
| 1/1
|-
| 1
| 311.7
| 6/5
|-
| 2
| 623.3
| 10/7
|-
| 3
| 935.0
| 12/7
|-
| 4
| 46.7
| 36/35, 40/39
|-
| 5
| 358.3
| '''16/13'''
|-
| 6
| 670.0
| 96/65
|-
| 7
| 981.7
| 160/91
|-
| 8
| 93.4
| 96/91
|-
| 9
| 405.0
| 91/72
|-
| 10
| 716.7
| 91/60
|-
| 11
| 1028.4
| 49/27, 65/36
|-
| 12
| 140.0
| 13/12
|-
| 13
| 451.7
| 13/10
|-
| 14
| 763.4
| 14/9
|-
| 15
| 1075.0
| 13/7, 28/15, 50/27
|-
| 16
| 186.7
| 10/9, 28/25
|-
| 17
| 498.4
| '''4/3'''
|-
| 18
| 810.0
| '''8/5'''
|-
| 19
| 1121.7
| 40/21, 48/25
|-
| 20
| 233.4
| '''8/7'''
|}
<nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning
 
== Tuning spectrum ==
{| class="wikitable center-all"
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! generator<br>(¢)
|-
|
| 7/5
| 308.744
|-
|
| 7/6
| 311.043
|-
| 7\27
|
| 311.111
|-
|
| 10/9
| 311.400
|-
|
| 14/13
| 311.447
|-
|
| 49/48
| 311.491
|-
| 27\104
|
| 311.538
|-
|
| 13/12
| 311.548
|-
|
| 8/7
| 311.559
|-
| 47\181
|
| 311.602
|-
|
| 13/9
| 311.608
|-
|
| 4/3
| 311.650
|-
| 20\77
|
| 311.688
|-
|
| 28/27
| 311.708
|-
|
| 15/13
| 311.742
|-
|
| 16/15
| 311.764
|-
|
| 9/7
| 311.780
|-
|
| 13/10
| 311.863
|-
|
| 5/4
| 311.871
|-
|
| 16/13
| 311.894
|-
| 13\50
|
| 312.000
|-
|
| 15/14
| 312.037
|-
|
| 25/24
| 312.070
|-
| 6\23
|
| 313.043
|-
|
| 6/5
| 315.641
|}
 
[[Category:Oolong| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]

Latest revision as of 00:34, 3 May 2026

Oolong
Subgroups 2.3.5.7, 2.3.5.7.13
Comma basis 126/125, 117649/116640 (2.3.5.7);
126/125, 196/195, 15379/15360 (2.3.5.7.13)
Reduced mapping ⟨1; -17 -18 -20 -5]
ET join 27 & 50
Generators (CWE) ~6/5 = 311.7 ¢
MOS scales 4L 3s, 4L 7s, 4L 11s, 4L 15s, 4L 19s, 23L 4s
Ploidacot iota-beta-17-cot
Pergen (P8, c4P4/17)
Minimax error 7-odd-limit: 5.6 ¢
Target scale size 7-odd-limit: 23 notes

See Starling temperaments #Oolong for more technical data.

Interval chain

In the following table, prime harmonics are in bold.

# Cents* Approximate Ratios
0 0.0 1/1
1 311.7 6/5
2 623.3 10/7
3 935.0 12/7
4 46.7 36/35, 40/39
5 358.3 16/13
6 670.0 96/65
7 981.7 160/91
8 93.4 96/91
9 405.0 91/72
10 716.7 91/60
11 1028.4 49/27, 65/36
12 140.0 13/12
13 451.7 13/10
14 763.4 14/9
15 1075.0 13/7, 28/15, 50/27
16 186.7 10/9, 28/25
17 498.4 4/3
18 810.0 8/5
19 1121.7 40/21, 48/25
20 233.4 8/7

* In 2.3.5.7.13 POTE tuning

Tuning spectrum

ET
generator 		eigenmonzo
(unchanged-interval) 		generator
(¢)
7/5 308.744
7/6 311.043
7\27 311.111
10/9 311.400
14/13 311.447
49/48 311.491
27\104 311.538
13/12 311.548
8/7 311.559
47\181 311.602
13/9 311.608
4/3 311.650
20\77 311.688
28/27 311.708
15/13 311.742
16/15 311.764
9/7 311.780
13/10 311.863
5/4 311.871
16/13 311.894
13\50 312.000
15/14 312.037
25/24 312.070
6\23 313.043
6/5 315.641
Retrieved from "https://en.xen.wiki/index.php?title=Oolong&oldid=229456"