Oolong: Difference between revisions

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


== Interval chain ==
== Interval chain ==
{| class="wikitable center-all right-2"
In the following table, prime harmonics are in '''bold'''.
 
{| class="wikitable center-1 right-2"
! #
! #
! Cents*
! Cents*
Line 8: Line 10:
|-
|-
| 0
| 0
| 0.000
| 0.0
| 1/1
| 1/1
|-
|-
| 1
| 1
| 311.669
| 311.7
| 6/5
| 6/5
|-
|-
| 2
| 2
| 623.338
| 623.3
| 10/7
| 10/7
|-
|-
| 3
| 3
| 935.007
| 935.0
| 12/7
| 12/7
|-
|-
| 4
| 4
| 46.676
| 46.7
| 36/35~40/39
| 36/35, 40/39
|-
|-
| 5
| 5
| 358.345
| 358.3
| 16/13
| '''16/13'''
|-
|-
| 6
| 6
| 670.014
| 670.0
|
| 96/65
|-
|-
| 7
| 7
| 981.683
| 981.7
|
| 160/91
|-
|-
| 8
| 8
| 93.352
| 93.4
|
| 96/91
|-
|-
| 9
| 9
| 405.021
| 405.0
|
| 91/72
|-
|-
| 10
| 10
| 716.689
| 716.7
|
| 91/60
|-
|-
| 11
| 11
| 1028.358
| 1028.4
|
| 49/27, 65/36
|-
|-
| 12
| 12
| 140.027
| 140.0
| 13/12
| 13/12
|-
|-
| 13
| 13
| 451.696
| 451.7
| 13/10
| 13/10
|-
|-
| 14
| 14
| 763.365
| 763.4
| 14/9
| 14/9
|-
|-
| 15
| 15
| 1075.034
| 1075.0
| 50/27~28/15~13/7
| 13/7, 28/15, 50/27
|-
|-
| 16
| 16
| 186.703
| 186.7
| 10/9~28/25
| 10/9, 28/25
|-
|-
| 17
| 17
| 498.372
| 498.4
| 4/3
| '''4/3'''
|-
|-
| 18
| 18
| 810.041
| 810.0
| 8/5
| '''8/5'''
|-
|-
| 19
| 19
| 1121.710
| 1121.7
| 48/25~40/21
| 40/21, 48/25
|-
|-
| 20
| 20
| 233.379
| 233.4
| 8/7
| '''8/7'''
|}
|}
<nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning
<nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning


== Spectrum of oolong tunings ==
== Tuning spectrum ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! Eigenmonzo
! ET<br>generator
! Generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! generator<br>(¢)
|-
|-
|
| 7/5
| 7/5
| 308.744
| 308.744
|-
|-
|
| 7/6
| 7/6
| 311.043
| 311.043
|-
|-
| (7\27)
| 7\27
|
| 311.111
| 311.111
|-
|-
|
| 10/9
| 10/9
| 311.400
| 311.400
|-
|-
|
| 14/13
| 14/13
| 311.447
| 311.447
|-
|-
|
| 49/48
| 49/48
| 311.491
| 311.491
|-
|-
| (27\104)
| 27\104
|
| 311.538
| 311.538
|-
|-
|
| 13/12
| 13/12
| 311.548
| 311.548
|-
|-
|
| 8/7
| 8/7
| 311.559
| 311.559
|-
|-
| (47\181)
| 47\181
|
| 311.602
| 311.602
|-
|-
|
| 13/9
| 13/9
| 311.608
| 311.608
|-
|-
|
| 4/3
| 4/3
| 311.650
| 311.650
|-
|-
| (20\77)
| 20\77
|
| 311.688
| 311.688
|-
|-
|
| 28/27
| 28/27
| 311.708
| 311.708
|-
|-
|
| 15/13
| 15/13
| 311.742
| 311.742
|-
|-
|
| 16/15
| 16/15
| 311.764
| 311.764
|-
|-
|
| 9/7
| 9/7
| 311.780
| 311.780
|-
|-
|
| 13/10
| 13/10
| 311.863
| 311.863
|-
|-
|
| 5/4
| 5/4
| 311.871
| 311.871
|-
|-
|
| 16/13
| 16/13
| 311.894
| 311.894
|-
|-
| (13\50)
| 13\50
|
| 312.000
| 312.000
|-
|-
|
| 15/14
| 15/14
| 312.037
| 312.037
|-
|-
|
| 25/24
| 25/24
| 312.070
| 312.070
|-
|-
| (6\23)
| 6\23
|
| 313.043
| 313.043
|-
|-
|
| 6/5
| 6/5
| 315.641
| 315.641
|}
|}


[[Category:Oolong]]
[[Category:Oolong| ]] <!-- main article -->
[[Category:Soft redirect]]
[[Category:Rank-2 temperaments]]
[[Category:Starling temperaments]]

Latest revision as of 14:29, 28 April 2025

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=194472"